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In situ measurements of aggregate structures' fractal dimensions inside index matched granular media

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In situ measurements of aggregate structures' fractal dimensions inside index matched granular media
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Cannon, Orion Taiyo
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x, 86 leaves : ; 28 cm

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Granular materials ( lcsh )
Sewage -- Purification -- Filtration ( lcsh )
Fractals ( lcsh )
Fractals ( fast )
Granular materials ( fast )
Sewage -- Purification -- Filtration ( fast )
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bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

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Includes bibliographical references (leaves 85-86).
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Orion Taiyo Cannon.

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University of Florida
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Full Text
IN SITU MEASUREMENTS OF AGGREGATE STRUCTURES FRACTAL
DIMENSIONS INSIDE INDEX MATCHED GRANULAR MEDIA
by
Orion Taiyo Cannon B.S., Colorado School of Mines, 2005
A thesis submitted to the University of Colorado Denver in partial fulfillment of the requirements for the degree of Master of Science Civil Engineering
2009


This thesis for the Master of Engineering Degree by Orion Taiyo Cannon Has been approved by

Dr. David Mays, Assistant Professor
Dr. Nien-Yin Chang, Dean and Professor
Dr. Arunprakash Karunanithi, Assistant Research Professor
Date


Cannon, Orion Taiyo (M.S. Civil Engineering-Water Resources Specialty)
In Situ Measurements of Aggregate Structures Fractal Dimensions inside Index Matched Granular Media
Thesis directed by Assistant Professor Dr. David C. Mays
ABSTRACT
Clean water is a valuable resource that is crucial to a healthy society. Water treatment, therefore, is an important civil engineering task that has great social significance. One of the most simple, yet effective, components within a water treatment process is a granular media filter.
A nearly perfectly optically transparent granular filter was prepared using a polymer material called Nafion inside a solution of deionized water and isopropyl alcohol per procedures developed by Adam Kanold, a former graduate student at UC Denver. Test tube samples were prepared to which 0.1 and 1.0 (Jm polystyrene micro spheres of varying concentrations were added. The concentration of polystyrene micro spheres ranged from 0 to 200 ppm. To half of the samples Nafion was added to effectively simulate conditions similar to a granular sand bed. The other half of the samples were left as simple in-suspension samples. To each of these two sets of samples calcium nitrate was added to half to induce aggregation/flocculation of the polystyrene micro spheres in suspension. Measurements of fractal dimensions of aggregated/flocculated polystyrene micro spheres inside the samples were made using a static light scattering apparatus.
The fractal dimensions of aggregated/flocculated polystyrene micro spheres inside the optically transparent granular filter media (Nafion) were found to be similar to those aggregated/flocculated micro spheres in suspension. The similarity of fractal dimensions of aggregated/flocculated micro spheres, both inside granular filter media and in simple suspension, were observed for nearly all samples.


These results suggest it is possible to accurately measure the fractal dimensions of aggregated structures in situ, inside an optically transparent granular filter. Using optically transparent granular media together with a light scattering apparatus will make it possible to learn how the fractal dimension of aggregated/flocculated structures made of suspended solids affects the clogging of granular media filters over time.
This abstract accurately represents the contents of the candidates thesis.
Signed
- ____________________________
Dr. David C. Mays


ACKNOWLEDGEMENT
Thank you to everyone who assisted in so many ways to keep this research project going forward. A partial list showing those who gave a significant amount of their time is shown below. This project would not have taken form without their help. Thank you for your time and energy you put into this project!
Helen Frey Benjamin Gilbert Rick Glesner Tim Lei David Mays Randy Ray Larry Scherrer Randy Tagg Sam Wheeler
UC Denver
Lawrence Berkley National Laboratory Community College of Denver, Program Chair, CAD UC Denver, Department of Electrical Engineering UC Denver, Department of Civil Engineering UC Denver, Machine Shop
Colorado Advanced Photonics Technology Laboratory UC Denver, Department of Physics UC Denver


TABLE OF CONTENTS
Figures....................................................................xiii
Tables.....................................................................x
Chapter
1. Introduction........................................................1
1.1 Background..........................................................1
1.2 Motivation and Purpose ofStudy.......................................2
2. Granular Media and Other Types of Filters............................5
2.1 Common Applications of Granular Media Filters........................5
2.2 Service Cycles of Granular Filter Media Filters......................6
2.3 Other Types of Filters and Their Applications........................7
3. Fractal Dimension and Static Light Scattering........................9
3.1 Background of Light Scattering.......................................9
3.2 Fractal Dimension...................................................10
3.3 Using Light Scattering to Measuring the Fractal Dimensions of Fractal
Aggregate Structures................................................14
3.4 Light Scattering Procedures.........................................16
3.4.1 Sample Preparation..................................................16
3.4.2 Measurements........................................................16
3.4.3 Interpretation of Data..............................................17
4. Optical Refractive Index Matching...................................22
4.1 Index of Refraction.................................................22
4.2 Optical Index Matching..............................................24
4.3 Refraction..........................................................25
4.4 Snells Law.........................................................31
4.5 Works by Adam Kanold................................................33
5. Experimental Methods................................................34
VI


5.1 Experiments with Compositions of DI Water and IPA..................34
5.2 Preparation of Index Matched Granular Filter Media.................34
5.3 Preparation of Colloid Suspension Using Micro spheres..............35
5.3 Preparation of Colloid Suspension Using Micro Sphres...............35
5.3.1 Sizes and Concentrations...........................................35
5.3.2 Stable and Aggregated Micro Spheres................................36
5.4 Static Light Scattering............................................39
5.4.1 Static Light Scattering Apparatus..................................39
5.4.2 Scanning Samples Using the SLS Apparatus...........................41
5.5 Data Reduction.....................................................42
5.6 Interpretation of Data.............................................45
5.6.1 Scaling Method.....................................................45
5.6.2 Model Fitting Method...............................................47
6. Experimental Results...............................................48
6.1 Qualitative Observations...........................................48
6.2 Quantitative Results...............................................49
6.2.1 Scaling Approach...................................................50
6.2.2 Form Fitting Approach..............................................55
7. Conclusion.........................................................61
7.1 Application of Light Scattering in Civil Engineering...............61
7.2 Problems Encounered................................................61
7.3 Future Work........................................................62
Appendix
A Detailed Static Light Scattering Data..............................65
B AutoCAD Drawings of SLS Column.....................................78
Bibliography.............................................................85
VII


LIST OF FIGURES
FIGURE
2.1 Schematic Diagram of How Granular Media Filters Work..................6
2.2 Picture of a Hand Operated Backpacking Pump...........................8
3.1 Illustration of a Colloidal Fractal Aggregate.......................11
3.2 Illustration of Various Colloidal Fractal Aggregates with Varying Fractal
Dimensions...........................................................13
3.3 Scatter Plot of Scattered Light Intensity vs. q-vector...............15
3.4 Scatter Plot of I vs. q-vector (Stable & Aggregated Micro Spheres)..19
4.1 Illustration of Light Refraction.....................................25
4.2 Conceptual Illustration of Light Bending.............................27
4.3 Relationship of Wavelength and Refractive Index......................29
4.4 Outward Movement of Concentric Waves.................................30
4.5 Illustration of Snells Law..........................................32
4.6 Nafion inside Different Fluids.......................................34
5.1 Schematic Diagram Showing the Path of Laser Beam.....................40
5.2 Photograph of a Sample Test Tube and the SLS Light Detector..........42
5.3 Intensity vs. q-vector Scatter Plot Made using a 2 ppm Sample........44
5.4 Ideal Scatter Plot...................................................44
6.1 Theoretical Scatter Plot of Stable Micro Spheres in Suspension.......49
6.2 Light Intensity vs. q-vector Plot, 1 pm, Aggregated Micro Spheres...51
6.3 Zoom-In of I vs. q, 1 pm, Aggregated Micro Spheres...................52
6.4 Intensity vs. q-vector Plot, 1 pm, Stable Micro Spheres..............53
6.5 Zoom-In of I vs. q, 1 pm, Stable Micro Spheres.......................54
6.6 Non-Linear Least Squares Fit Plot, 1 ppm, Stable Micro Spheres.......56
6.7 Non-Linear Least Squares Fit Plot, 2 ppm, Stable Micro Spheres.......57
VIII


6.8 Non-Linear Least Squares Fit Plot, 1 ppm,
Aggregated Micro Spheres.....................................58
6.9 Non-Linear Least Squares Fit Plot, 2 ppm,
Aggregated Micro Spheres.....................................59
IX


LIST OF TABLES
TABLE
4.1 Common Transparent Materials and Their Refractive Indices...........23
4.2 List of Common Solvents, Their Densities, and Refractive Indices.24
5.1 Compositions Samples................................................38
5.2 List of Concentrations Prepared.....................................39
6.1 Summary of Fractal Dimensions Measured Using the Form Fitting
Approach.......................................................55
6.2 Summary of Fractal Dimensions and Primary Particle Radii Calculated
Using the Non-Liner Least Squares Fit Approach.................60
X


1. Introduction
1.1 Background
Granular media filters, such as sand filters, are used to remove suspended solids for the purpose of water treatment. Granular media filters are used in water treatment plants and in facilities with swimming pools. Clogging of granular media filters is affected by the amount of suspended solids it removes from water as well as the morphology of these suspended solids. Small, suspended particles come together to form larger aggregated structures when chemically induced with alum or salts. Fractal aggregate structures are formed when uniformly sized particles come together to form larger structures.
Static light scattering is an analytical method that is used in the areas of polymer science and physics to study small-scale particles in suspension, such as proteins and polymers. Sorensen (2001), Bushell et al. (2002), and Teixeira (1988) have shown that light scattering can be used to quantify the fractal dimension, a geometric scaling factor of aggregated fractal structures, using static light scattering. By making an optically transparent granular filter by following procedures developed by Kanold (2008), the fractal dimension of aggregated structures were measured inside the granular filter media via light scattering. Measurements of fractal dimensions were made on aggregated structures in suspension for comparison purposes, as well. The measured values of fractal dimensions of aggregated structures in suspension were found to be very close to those inside granular filter media.
The text has been written in a way that first introduces the reader to several concepts that were important in the research project. These concepts


include: (1) granular filter media, (2) light scattering, and (3) optical index matching. Experimental procedures and experimental results follow those sections.
1.2 Motivation and Purpose of Study
Granular media filters are a vital component in water treatment systems. They are designed to filter out suspended solids and other objects from water.
The clogging of granular media filters depends not only on the quantity of suspended solids it removes, but the morphology of those structures as well. It has been shown that clay, which is composed of particles which have a sheet-like configuration, has much lower permeability than does silt. The shape of the particles has an effect on how water is able to travel through the pore spaces between individual particles and hence affect the permeability (Mays and Hunt 2007). In a similar way, it will be beneficial to study how the fractal dimension of aggregated structures affect clogging of granular media filters. This research project is a pilot project to accomplishing that goal, and it focuses on in situ measurement of fractal aggregates inside a transparent granular filter. The motivation of the project is to learn if it is possible to measure the fractal dimension of aggregated structures inside granular filter media.
Past projects have measured the fractal dimensions of aggregate structures in suspension, and have found values to be between 1.8 and 2.2 (Bushell et al. 2002). Jt is of interest to find out how the values of fractal dimensions of aggregate structures inside a granular filter media compare to values measured previously using classical methods.
A previous study researched the correlation between aggregate structure morphology and clogging of granular filter media. In this study deposits that
2


caused clogging and were trapped inside granular filter media were collected and used it to prepare suspended solid samples with. The samples were analyzed and the results showed that the fractal dimension of aggregate structures had no correlation with clogging (Veerapaneni and Wiesner 1997). However, there are good reasons to believe that the aggregate structure deposits were significantly disturbed during sample preparation, and the fractal dimension of the deposits may not have been preserved. If so, the fractal dimensions of the prepared samples that were measured will not have been representative of what existed in-situ. That is another reason for the motivation of measuring the fractal dimension of aggregate structure deposits in situ.
3


2. Granular Media and Other Types of Filters
2.1 Common Applications of Granular Media Filters
Granular media filters are used in both drinking water and waste water treatment. Granular media filters are essentially containers with an inlet and an outlet that is filled with various grain sizes of aggregates. The sand and gravel aggregates are held in place inside a container usually by a screen that allows for water to pass through but not the sand and gravel. Raw water from wells, streams, and lakes is treated in several steps before being distributed for the purpose of municipal use. Some of these treatment steps include hardness treatment, removal of iron and manganese, and disinfection. One of the final steps in water treatment is a filtration process which removes suspended solids in water by passing it through a porous granular filter media. Suspended solids that naturally exist in water, such as small debris and vegetation, become trapped between grains of sand and gravel as water passes through a porous granular media filter. Water that goes through these treatment processes is clean and safe for consumption.
Granular media filers are also used in places such as recreational centers where there are swimming pools. Water in pools is continually cycled through porous granular media filters to remove solids.
4


2.2 Service Cycles of Granular Filter Media Filters
There are two stages that granular media filters cycle through. The first stage is the actual removal of suspended solids from water, or the production stage.
Water is actively being treated when porous granular media filters are in this stage. The amount of suspended solids that accumulate within a granular media filter is nearly proportional to the duration in which this granular media filter remains in operation the more water that is processed, the more solids accumulate. Unless the driving head is continually increased, the rate at which water can pass through a granular media filter decreases as suspended solids accumulate and pore spaces become clogged. As pore spaces within granular media filters become clogged the paths which water travels through become increasingly restricted. To address this problem granular media filters need to be backwashed periodically to remove suspended solids, clear out the pore spaces, and increase the rate of flow.
The process of backwashing is the second stage in a regular cycle of filter operation. Clean, treated water is pumped through the filter body in a direction that is opposite to regular flow. Clean, treated water is pumped vigorously to fluidize the granular media and solids trapped inside the filter body.
5


Figure 2.1 Illustration of how granular media filters works
Solids and other material trapped inside a filter body become mobilized and carried away with the clean water vigorously flowing in the backwards direction during backwashing. This water used for backwashing which contains fluidized solids is either routed to directly to a waste water treatment plant or recycled and reused for conservation purposes. Backwashing effectively removes most trapped solids from within the filter body, and restores the filter to a nearoriginal operational state of working. The frequencies at which filters used in water treatments plants are backwashed vary with many factors. Some of these include the type of filter used, age of the filer, extent of clogging, grain size of sand used inside the filter, and the morphology of solids deposited inside the filter (Weisner 1999), (Mays 2009).
6


Clogging of granular media filters is affected not only by the quantity of suspended solids trapped inside the filter body, but also by their morphology as well. The fractal dimension of aggregate structures has been shown to affects how granular media filters become clogged (Weisner 1999), (Mays 2009).
2.3 Other Types of Filters and Their Applications
In addition to porous granular media filters, there exists a wide variety of filters for many applications. One of these filters currently under intense research is membrane filters which are used for many purposes including separating salts dissolved in sea water from pure water. This process of separating salts from sea water using membrane filters is called desalination by reverse osmosis.
Relatively inexpensive backpacking filers, such as one shown in Figure
2.2 are designed to treat water from lakes, ponds, streams, and creeks. These filters filter out both pathogens, such as bacteria, viruses, and protozoa, as well as suspended solids at once. These filters clog after certain use, and will stop working at that time. Once these filters clog, the inner filter cartridges must be replaced.
7


Figure 2.2 A hand operated backpacking and camping water filter. (Backcountrygear.com)
8


3. Fractal Dimensions and Static Light Scattering
3.1 Background of Light Scattering
Light interacts with matter in several ways there is reflection, refraction, and absorption. Beams of light can reflect off of a surface of an object, go through an object such as glass, or simply become absorbed and change to heat. There are two broad categories of light scattering static and dynamic light scattering both utilize the ways in which light interacts with matter. Both methods measure the scattered light from small suspended particles within a sample cell to determine certain physical characteristics of those particles. Light scattering is used in the fields of physical chemistry and polymer science. In static light scattering a single light detector, which can take measurements about a sample at different angles, is used to make these measurements. In comparison, dynamic light scattering machines have multiple light detectors that can detect very rapid changes in scattered light at different angles simultaneously. Static light scattering machines are used to obtain the root mean square radius (or radius of gyration) and the average molecular weight. In addition to the above mentioned physical parameters, Sorensen (2001) and Bushell et al. (2002) have successfully used static light scattering to measure the fractal dimension, a geometric scaling factor used to characterize the relative mass-length scaling of aggregate structures.
9


3.2 Fractal Dimension
Fractal aggregates are intricate structures composed of individual suspended solid particles that have come into contact with one another through one of two processes. These two processes are called diffusion limited aggregation (DLA) and rate limited aggregation (RLA) respectively, and discussed later. One process by which drinking water is treated prior to distribution is flocculation and filtration. Small suspended solids in water are made to stick to one another by inducing a flocculating agent, such as alum. The purpose of using alum is to make suspended solids more chemically attractive toward one another, and ultimately causing them to form larger structures. These larger structures are either settled or filtered and separated from clean water. Aggregate structures, such as one shown in Figure 3.1, form through continued collision of suspended particles with one another and sticking together. An aggregate structure will continue to grow as long as the collision processes of suspended solids continue.
Fractal aggregates have what is called a fractal dimension, a relative measurement of a structures radius of gyration in proportion to the number of particles comprising the structure. The fractal dimension of an aggregate structure can vary anywhere from a one dimensional string (fractal dimension = 1) to a solidly compacted structure without gaps inside (fractal dimension = 3). The fractal dimension of an aggregate structure can never be less than one or greater than 3. Most aggregate structures composed of suspended solid particles will have fractal dimensions between 1.8 and 2.2. According to Bushell et al. (2002) equation 3.1 describes the relationship between the radius of gyration of aggregate structures, the number of particles, and the fractal dimension.
10


N = kg(RJr0)D (Eq. 3.1)
N = Number of colloidal particles in an aggregate structure kg =Structure prefactor, a constant
7?^=Radius of gyration, the root-means-square distance of the colloidal
particles from the center of mass r0=Colioidal particle radius DHFractal dimension
Figure 3.1 An illustration of an aggregate structure composed of uniformly sized spherical colloids. (Astronomy and Astrophysics website)
11


The first process whereby particles come into contact is when all collisions lead to aggregation, which is called diffusion limited aggregation (DLA). When aggregates, or clusters, join together this process of aggregation is called Diffusion Limited Cluster Aggregation (DLCA). The second process in which individual suspended solid particles stick together and form aggregate structures is when collisions may or may not lead to aggregation, which is called rate limited aggregation (RLA). Clusters can also join together through a process called Rate Limited Cluster Aggregation (RLCA). What makes the RLCA process different from the previous aggregation is the charge and affinity which individual particles carry that controls the probability with which they stick to one another.
As discussed earlier, fractal dimensions can only be between 1 and 3. In general, the more intricate and strung out a structure is, the lower its fractal dimension will be. Conversely, a densely packed structure with little voids will have a greater fractal dimension. Some examples of fractal aggregates with various fractal dimensions are shown on Figure 3.2.
12


D{ = 2.8
Df = 2.4
D( = 1.8
D, = 1.2
5
S
" II
i z
s
3.
o
w Z
£ z
E
in
o r~ o n II n
y = 1.57
y = 1.56
y = 2.13
y = 3.84
Figure 3.2 Aggregate structures with 1,16, 125, 1000, and 3375 particles (sorted by rows from top to bottom), and fractal dimensions of 1.2, 1.8, 2.4, and 2.8 (sorted by columns from right to left). (Astronomy & Astrophysics website)
13


3.3 Using Light Scattering to Measuring the Fractal Dimensions of Fractal Aggregate Structures
Unlike in the process of imaging, which disturbs fractal aggregates during sample preparation, light scattering can be used to take measurements on fractal aggregates that are in suspension without disturbing samples. The theory behind light scattering is that multiple light waves in phase with one another will experience constructive interference and vice versa. Depending on how light passes through fractal objects and the size of the primary particles that make up the fractal structures, light waves will either (1) add constructively, (2) add destructively, or (3) experience a mixture of both, which cancels out to approximately zero net interference effect. Sorensen (2001) derived three theoretical scenarios in which how scattered light will behave. The scenarios are broken up into three by the primary particle size and the radius of gyration as they relate to the scattering wave vector, q. The three theoretical scenarios of light scattering and their intensities are as follows:
1. I(q) cc N2 I(q) = constant
2. l(q)KkNs(qar1D-'D I(q)~qD
3. l(q)r-kriNs I(q)~qJ
I(q) = Intensity of scattered light from a sample
(q) = Scattering wave vector, which is a function of scattering angle 0, and wavelength of incident light, X. The relationship between those parameters is characterized by the formula: q = 4nnXx sin(#/2)
A =Wavelength of incident light used for light scattering
for q < R1 for R'1 < q < a'1 for q > a'1
14


n =Refractive index of fluid used in sample R=Radius of gyration a=radius of primary particle Dm= Mass fractal dimension
Above equations are graphically represented in a log of light intensity vs. log of q-vector plot as shown in Figure 3.3.
I
q
Figure 3.3 Intensity vs. q-vector plot showing three zones and their theoretical scattering patterns on a log-log scale. Dm=mass fractal dimension, R=average radius of gyration of aggregate structures, a=primary suspended particles size
15


3.4 Light Scattering Procedures
3.4.1 Sample Preparation
Samples containing suspended solid particles are prepared by either dissolving or placing in suspension within a solute. It is extremely important to keep all samples clean because any foreign particles, such as dust, will interact with light and give false readings. Test tubes used to hold samples are cleaned with care using soap and water, followed by rinsing using a solvent, such as acetone. It is also important to keep the solute used for sample preparation as clean as possible. Usually a solvent will be filtered multiple times through a filter paper or similar with openings equal to or less than 0.2 pm in size. This ensures there are no particles in suspension that will affect the light scattering measurements. Samples prepared for this research project were given a minimum of 24 hours prior to being placed for measurement. This ensured particles in suspension had time to come in contact with one another and form aggregate structures.
3.4.2 Measurements
There are various types of static light scattering devices, and each has slightly different measurement procedures. The fundamental concept of sample measurements is the same however scattered light from samples are measured as accurately as possible at either one or multiple angles.
First, samples are placed in a sample holder. If necessary, samples are aligned within the sample holder.
16


A carefully aligned beam of light is passed through a test tube containing the sample solution/mixture. It is common to use a laser beam because of its high quality of focus.
The intensity of the scattered light from the sample is measured at various angles. For our project, a measurement was taken every 1/10 of a degree from approximately 0 to 155 degrees. A computer with data acquisition software is typically used to record and store collected light intensity data. Stored data is easily converted to spreadsheet or other desired format for analysis.
3.4.3 Interpretation of Data
Collected data consists of intensity of scattered light in pW as a function of angle, 0. In other words, the brightness of scattered light has been recorded from some starting angle, Gstart, to the ending angle, 0end- There are several steps that are required in order to calculate and obtain meaningful results from collected data.
Fractal Dimension (Scaling Approach):
(1) Samples with multiple dilutions of suspended solids were prepared. A blank solution with no suspended solids was also prepared. The purpose of preparing multiple dilutions was to measure each sample and see how the concentration of suspended solids affected measurements. The possibility of multiple scattering was a source of concern, and it was of interest to find out if multiple scattering became a factor at a certain concentration of suspended solids. It could be concluded that multiple scattering was a factor if in fact there was multiple scattering observed for samples with a certain concentration or greater suspended solids but not for other samples. What are
17


called Mie humps as shown in Figure X.x can be observed when multiple scattering is not a significant factor. Mie humps are characteristic signs that are observable on a scattering plot and are caused by light refracting off of uniformly sized spherical particles in suspension.
(2) The intensity of scattered light at angles from start to end are measured using a static light scattering apparatus.
(3) The measured intensity from the blank sample is subtracted from the measured intensity of the dilute sample at each angle at which measurements were made.
(4) The adjusted data is normalized to account for the differences in scattering volume at each angle by dividing the adjusted intensity by the sine of the scattering angle.
(5) Convert values of 0 to q-vector values for each data point using the equation: q = 4 tt/T1 sin(# / 2)
(6) Plot a log-log plot of q vs. adjusted, normalized intensity of scattered light.
(7) The slope of the linear region as shown on Figure 3.4 is the calculated fractal dimension of aggregate structures in suspension.
18


1
q
Figure 3.4 Theoretical intensity vs. q-veetor plots. Stable colloids in suspension (top), and aggregated structures in suspension (bottom). From Sorensen (2001)
Fractal Dimension (Form Fitting Approach):
(1) Collect data of scattered light intensity vs. angle, 0, in the same way as described in steps (l)-(5) above.
(2) Simultaneously fit the collected data points to a series of equations using a non-linear least squares fit. The equations to which the data points are fit are:
a. q - sin(6>/2) (Sorensen 2001)
q =Scattering vector [nnf1]
19


9 =Scattering angle [degrees]
X =Wavelength of incident beam [nm]
b. I(q) = P(q)S(q) (Teixeira 1988)
l(q) intensity of scattered light [mW, or |JW]
N =Number of scattering particles [unit less]
V0 ^Scattering volume of the sample [cm3]
P(q) =Form Factor of primary particle [cm ]
5(^)=Structure factor of fractal aggregates [unit less]
c. = (Teixeira 1988)
(qro)
V =Volume of uniform spheres/primary particles [cm ] p =Density of primary particles
d. S(q) = \ +--------------~7TT~ ------------------- (Teixeira
(?>'o)P[l + -^-r] 2 sin[(D-l)tan (^)]
q Z
1988)
D=Fractal dimension [unit less]
r(D -1) =Gamma function of the argument, D-l
£=Upper limit of fractal correlations [nm]

(Teixeira 1988)
Rx =Radius of gyration of aggregate structure [nm]
20


(3) This method yields the primary particle radius, the radius of gyration of the fractal aggregate structure, and the fractal dimension simultaneously. Through a process of iteration, a relatively simple computer program will simultaneously and repeatedly fit three variables into the above shown equations until the sum of difference in calculated values compared to empirical values are minimized. The three values found through this process of trial and error are the primary particle radius, the radius of gyration of the aggregate structure, and the fractal dimension of the aggregate structure.
The average molecular weight and the radius of gyration can also be calculated using static light scattering. The procedures include preparation and scanning of multiple samples with various concentrations followed by a process of linear interpolation. Details on these procedures can be found in several texts, including Huglin (1972).
21


4. Optical Refractive Index Matching
4.1 Index of Refraction
The index of refraction is a measure used to characterize the optical property of transparent materials. It quantitatively describes how fast light travels through a given material compared to the velocity at which light travels through a vacuum. Materials, such as air, water, and glass each have different indices of refraction, indicating light travels at different velocities through each.
The index of refraction, n, of a given material is the ratio of two velocities the velocity at which light travels through a vacuum is compared to the velocity at which light travels through a given material, and is shown in Equation X.l.
, = mcuum (Eq.4.1)
Q
mater ial,a
nmaterial,a =Index of refraction of material, a cvacuum =Speed of light in a vacuum cmaterials =Speed of light through material, a
For example, the index of refraction of glass is the velocity at which light travels through a vacuum divided by the velocity at which light travels through common glass. Given that light travels through a vacuum at approximately 3.00x108 m/s or 300 million meters per second and the index of refraction of crown glass is known to be 1.52 (Huglin 1972), the velocity at which light travels
22


through glass is calculated to be approximately 1.97x108 m/s, or roughly 2/3 of the velocity in a vacuum.
Table 4.1 shows an abbreviated list of common transparent materials and their indices of refraction.
Table 4.1 Common transparent materials and their indices of refraction (www.en.wikipedia.org/wiki/List_of_refractive_indices)
Name Index of Refraction, n
Diamond 2.42
Eye, Cornea 1.38
Eye, Lens 1.41
Fused Silica 1.57
Glass, Crown 1.52
Glass, Pyrex 1.47
Lucite 1.50
Nylon 1.53
Obsidian 1.50
Plastic 1.46-1.55
Polystyrene 1.49
Table 4.2 shows an abbreviated list of solvents and their indices of refraction (Johnson and Smith 1972). As shown in the list, wavelength of light has a small effect on the effective indices of refraction.
23


Table 4.2 A brief list of solvents, their densities, and indices of refraction.
Name of solvent Density, p (g/ml) @ 25C Index of Refraction, n @ >.=546.1 nm Index of Refraction, n @ /.=435.8nm
Acetic Acid 1.0437 1.3713 1.3789
Acetone 0.7846 1.3581 1.3647
Benzene 0.8737 1.5020 1.5196
Carbon Tetrachloride 1.5844 1.4596 1.4691
Cyclohexane 0.7738 1.4253 1.4328
Ethyl Alcohol 0.7852 1.3612 1.3677
Methyl Alcohol 0.7866 1.3284 1.3337
Isopropyl Alcohol 0.7809 1.3772 1.3835
Toluene 0.8623 1.4980 1.5151
Water 0.9970 1.3340 1.3390
4.2 Optical Index Matching
Optical index matching is a process where a pair of transparent materials -a solid and a liquid are selected and matched according to their indices of refraction, n. A transparent solid material with a given index of refraction, when submersed in a liquid with the same index of refraction, will effectively appear to disappear. Optic index matching, in another sense, is a way of carefully choosing a solid and a liquid according to their indices of refraction such that light travels through both materials without changing its velocity. Light travels linearly through a homogenous material, given the temperature and density of the material
24


is constant. Similarly, given a pair of index matched materials, such as glass and toluene, light travels linearly through both without refraction, or bending.
4.3 Refraction
The reason why light experiences refraction at the interface of two different transparent materials is because light experiences a change in speed at the interface. Figure 4.1 illustrates how the trajectory of light changes between air and water.
(a) Angle of incidence
(b) Angle of refraction (n) Normal line
n
Figure 4.1 A simple illustration that demonstrated refraction of light
25


The velocity at which light travels through a given material is dependent on the index of refraction of that material. The velocity of light will decrease as it leaves a material with a relatively low index of refraction and enters a material with a relatively large index of refraction. As an example, as light travels from air, a material with an index of refraction of approximately 1.0003, into common glass, a material with an index of refraction of approximately 1.52, the velocity of light will decrease from approximately 2.98x10 m/s to 1.97x10 m/s.
In a similar way as illustrated in Figure 4.1, light experiences diffraction or bending in order to keep its continuity at the interface of two transparent materials. Just as it is impossible for only a portion of a barrel to roll and travel at a different rate than the remainder of the barrel, so also light must adjust its course of travel at the interface of two transparent materials. This is illustrated in Figure 1.2.
26


Figure 4.2 A conceptual illustration showing how the direction of travel of a barrel changes as it travels from one surface to another. (Serway & Beichner 2000)
Since light has a wave nature, it must have both amplitude and a frequency. The amplitude of light waves is associated with the intensity, or brightness of light, and the frequency describes its color. Equation X.2 describes the relationship between frequency and time.
# of cycles unit time, t
f=Frequency
(Equation 4.2)
27
whnIHS


A wavelength is the distance a wave will travel in the time it takes to complete one wave cycle. Wavelengths will change as it leaves one medium and enters another. The wave frequency, however, remains the same in both media (Figure 4.3).
28


H
Amsmim
$Smsm
V'y&V^T^-rJ&S** .-A *? Ik, . , !* < 5*t
1-tVi §3 0^01^ '£&&*
i^:*V-r.:
£&Jllll
~ 2
f$S$&r-.
im.
Figure 4.3 An illustration of how wavelength of a given incident light differs in
two different media. (Serway & Beichner 2000)
f
Light traveling from a source will undergo some amount of refraction at all angles, except when traveling at a normal angle to a given material which it enters. This is qualitatively illustrated in Figure 4.4.
29


Figure 4.4 Concentric rings represent waves traveling in an outward direction from a given source. As shown, the directions in which waves travel undergo refraction at all angles except when normal to the material which it enters (en.wikipedia.org/wiki/List_of_refractive_indices)
30


The distances between concentric rings shown in Figure 4.4, which represent single wavelengths of light, changes at the interface of two media with differing indices of refraction. The velocity and wavelength at which light travels through each material is different the frequency, however, remains unchanged. Energy is conserved because the frequency of light, which is associated with the energy of light, is unchanged. If the distances between concentric circles did not change at the interface of two transparent materials with differing indices of refraction, then the frequency of light must change. This would violate the principle of conservation of energy. If this were hypothetically possible, the color of the incident beam would change as it left one transparent material and entered another.
4.4 Snells Law
Some portion of light will reflect at the interface of two transparent materials. The angle of reflection will be the same as the angle of incidence. The remaining portion of light will experience refraction at the same interface of two transparent materials. Figure 4.5 illustrates the paths of incident, reflected, and refracted light at the interface of two transparent materials.
31


I
I
I
B
Refracted
ray
Figure 4.5 The relationship between incident angle, reflection angle, and refraction angle are illustrated (Serway & Beichner 2000).
Snells Law relates the angle of refraction to the angle of incidence and indices of refraction of the two transparent materials as shows in Equation X.3.
, sin 0, = n2 sin 02
(Equation 4.3)
32


Snells Law shows that the path of light will remain unchanged and will not experience refraction at the interface of two transparent materials when ni and nj, the indices of refraction of those materials are the same. It also shows that at an angle of 0 degrees, light traveling normal to the interface of the two transparent materials will not experience refraction.
4.5 Works by Adam Kanold
Adam Kanold, a previous University of Colorado Denver graduate student under Dr. David Mays guidance, experimented with several combinations of transparent solids and liquids in search of an index matched pair. The purpose of the search was to make an optically transparent granular media filter. Some of the solids that were tested include fused silica, polished glass, and a polymer material called Nafion. After experimentations with several solid-liquid combinations, Kanold found Nafion to be nearly invisible when it was boiled in isopropyl alcohol for a couple of hours, then placed in a mixture of 40% isopropyl alcohol and 60% deionized water (Kanold 2008).
Figure 4.6 Photograph shows four glass containers from left to right with (1) water, (2) index matched granular filter media, (3) non index matched granular filter media, and (4) dry Nafion in bottle.
33


5. Experimental Methods
5.1 Experiments with Compositions of DI Water and IPA
Following the procedures developed by Kanold (2008) for making index matched Nafion submersed in a mixture of deionized water (Dl) and isopropyl alcohol (IPA), several batches of index matched Nafion were prepared. To verily that the mixture developed by Kanold was the best possible, 6 additional Nafion samples were prepared with slightly varied proportions of Dl water and IPA. The six different percent DI water to percent IPA compositions (by volume) were: 60:40, 58:42, 56:44, 54:46, 52:48, and 50:50. The samples were given approximately 3 days time to reach an equilibrium state after preparation. After waiting for 3 days after preparation of these 6 samples, the Nafion sample made using 58% DI and 42% IPA appeared to be best index matched based on visual inspection. Through this experimentation, it was observed that Nafions refractive index varied by with the fluid is has absorbed. Additionally, it was observed that the fluid which Nafion has absorbed required some time to reach a state of equilibrium with the surrounding fluid. Thus samples of Nafion were given a minimum of 3 days to reach an equilibrium state before final observations were made.
5.2 Preparation of Index Matched Granular Filter Media
Approximately 500 mL of filtered deionized water was prepared by running deionized water through a vacuum filter apparatus using 0.2 pm filter
34


paper. The use of improperly purified fluids has lead to calculated values of average molecular weight using light scattering that are lower than actual values (Huglin 1972). To minimize the chance of this, the filtration process was repeated at least twice to ensure removal of particulates that could distract from getting accurate light scattering results. Approximately 500 cc of filtered isopropyl alcohol was prepared in the same way by using a vacuum filter and 0.2 pm filter paper. After filtered deionized water and isopropyl alcohol were prepared, Nafion of desired grain sizes were allowed to soak in a solution of 58% deionized water and 42% isopropyl alcohol for at least one day. After soaking the Nafion for at least a day, the mixture of isopropyl alcohol and water was decanted and replaced with a fresh, clean batch of the same solution of 58% deionized water and 42% isopropyl alcohol for at least an additional day. The Nafion was observed to swell slightly during the soaking process. During the same time, the Nafion reached an equilibrium state where its index of refraction was approximately the same as that of the mixture of 58% deionized water and 42% isopropyl alcohol.
5.3 Preparation of Colloid Suspension Using Micro spheres
Quality controlled uniformly-sized polystyrene micro spheres were used to simulate suspended solids in suspension. Two different sizes of polystyrene micro spheres were chosen 1.0 pm and 0.1 pm diameter micro spheres were used to prepare samples with. The two sizes were never mixed; samples were kept monodisperse, meaning all the suspended solid micro spheres were the same size. This simplified the analysis of data simpler. In addition to samples with various concentrations of suspended solids, blank samples containing no suspended solids were prepared. These were used as controls.
35


Index matched Nafion was decanted and placed into eight 10 mL glass test tubes until the test tubes were approximately half filled. A solution of filtered 58% DI and 42% IPA containing various concentrations of 1.0 pm polystyrene micro spheres were prepared using the method of multiple dilutions. Using the method of multiple dilutions made it possible to accurately prepare samples with very small concentrations. The concentrations of micro spheres used for each set of measurements were as follows: 0, 1,2, 5, 10, 20, 40, and 80 ppm. Samples with various concentrations were prepared to find out if multiple scattering occurred within test tubes, and if so at what concentration it became a significant factor that affected the measurements. Another purpose for preparing a set of eight samples for each composition was to find out at what concentration multiple scattering became a factor.
5.3.3 Stable and Aggregated Micro Spheres
Similarly to above mentioned 16 samples of varying concentrations and sizes of micro spheres an additional 16 samples were prepared with 0.1 M Ca(N02)3 added to induce chemical aggregation of micro spheres. Calcium Nitrate was chosen as the aggregation inducing agent following work by other researchers who used it to induce aggregation of colloidal micro spheres (Veerapaneni and Wiesner 1997). The 0.1M solution of Calcium Nitrate was prepared by adding approximately 0.05 moles of calcium nitrate to 500mL of DI water/IPA solution. The volume of Nafion in test tubes were not counted as part of the total makeup volume of the 0.1M Ca(NC>3)2. Using the equation shown below (Snoeylink and Jenkins 1980)), the ionic strength of these samples were calculated to be equal to 0.25 M:
36


(Eq. 5.1)
L i
Where p = calculated ionic strength, in M
C = concentration of ionic species, i, in M Z = charge of ionic species, i
Samples prepared, including those with and without calcium nitrate, with and without micro spheres, and with and without nafion are summarized in Table 5.1.
37


Table 5.1 Compositions of samples used for each concentration of suspended colloids prepared.
Sample No. Micro Spheres Size of Micro Spheres (pm) Nafion Ca(N02)3
1 No No No
2 Yes 1.0 No No
3 No No Yes
4 Yes 1.0 No Yes
5 No Yes No
6 Yes 1.0 Yes No
7 No Yes Yes
8 Yes 1.0 Yes Yes
9 No No No
10 Yes 0.1 No No
11 No No Yes
12 Yes 0.1 No Yes
13 No Yes No
14 Yes 0.1 Yes No
15 No Yes Yes
16 Yes 0.1 Yes Yes
38


A total of seven sub-samples each with varying concentrations were prepared for samples containing micro spheres. In other words samples 2, 4, 6, 8, 10, 12, 14, and 16 were prepared with differing concentrations to measure the effects of multiple scattering. An example of this is summarized in Table 5.2.
Table 5.2 Concentration series from 1 to 80 ppm
Sample Concentration of
No. Micro Spheres (ppm)
2-1 1
2-2 2
2-3 5
2-4 10
2-5 20
2-6 40
2-7 80
5.4 Static Light Scattering
5.4.1 Static Light Scattering Apparatus
A static light scattering apparatus was constructed by Dr. Lei, a professor of electrical engineering at the University of Colorado Denver. A schematic-diagram of how the apparatus works is shown in Figure 5.1.
39


The apparatus is essentially composed of Helium-Neon laser (source of incident light beam), a sample holder with adjustments in the x and y-axis, and a light sensor that is aimed at the center of the sample test tube. The light sensor is mounted on a rotating arm which is able to rotate the sensor about the sample test tube from 0 to 155 degrees. The angle of the rotating arm is controlled by a motor, and is controlled using a computer software program, LabView.
In addition to the components mentioned above, several additional components added by Dr Lei has improved the functionality of the instrument significantly. These components include:
(1) Polarizer
(2) Signal noise filter
(3) A second He-Ne laser used for aligning the sample test tube
(4) A photo detector to measure the power of the incident beam
(5) Mirrors to adjust and fine-tune the path of the laser beam
(6) Lenses to account and correct for the curvature of the sample test tube
40


(7) A protective, movable mirror to protect the light sensor from direct exposure
5.4.2 Scanning Samples Using the SLS Apparatus
Samples were brought to the Colorado Advanced Photonics Laboratory (CAPT Lab) to be scanned using the static light scattering apparatus.
All the instruments that are part of the static light scattering apparatus were turned on. The laser was warmed up for approximately 15 minutes in order to stabilize its power output. The alignment of the laser beam was checked prior to starting the measurement process each day. If necessary, the alignment of the beam was fine tuned using the 4 mirrors, which are placed in line with the path of the laser beam following exact procedures outlined by Dr. Mays. Test tube sample were gently inverted back and forth 25 times to mix the contents well without stirring air bubbles into the solution. A single sample was placed into the sample holder at a time in a position that is straight and vertical as possible by visual inspection. Once the sample was placed in the sample holder, its x and y-axis were adjusted, if necessary, by slowly turning the adjustment knobs until both the incident beam and the secondary beam entered the sample test tube squarely in the center of the test tube.
The power/intensity of light passing through the sample was recorded both prior to starting a scan and after completion of the scan. A light curtain used to block outside light from coming in was closed. The scattering intensity of light in gW was measured from 0 to 155 degrees, initially with constant angular spacing in increments of 0.1 degrees. The LabView program used to control the angular position of the light sensor and record data was later modified such that it could take measurements in q-vector units. Data of scattering angle, 0, in degrees vs. scattered light intensity in pW were recorded using data acquisition
41


instrumentation and computer software, LabView. The light transmission intensity through the sample was measured again after completion of the scan. The process was repeated for each sample.
Figure 5.2 Test tube sample (center), and light detector (rear) are shown in photograph.
5.5 Data Reduction
Data points collected using LabView was analyzed using a spreadsheet program, and using a MatLab script written by Dr. David Mays. The first step
42


with the analysis of data was to convert the angles in degrees to a q-vector value by using equation 5.2 show below. After this conversion step, data points were plotted with q-vector values on the x-axis and the log of intensity of scattered light in on the y-axis. Next, a data points collected from a blank sample with no micro spheres were plotted in the same way. Thirdly, the light intensity values of the blank sample were subtracted from the light intensity value of the colloidal sample of interest. This was done to subtract out the amount of scattering that are caused by the glass test tube, internal reflections, and other factors other than scattering caused by the actual micro spheres which are of interest. This is similar to pushing the tare button on an electronic scale that is used to subtract out the mass of a container that is used in order to get only the mass of the material of interest. The adjusted values of the log of light intensity vs. angle were plotted on a graph for visual inspection. The raw, unadjusted intensity, the blank intensity, and adjusted intensity vs. q-vector values are illustrated on Figure 5.3.
43


Intensity [pW]
Raw and Adjusted Intensity vs. q-Vector (Aggregated Samples in Granular Filter Media, 1pm Colloids)
q[1/A]
2 ppm
Blank
* raw 2ppm
Figure 5.3 Intensity vs. q-vector plot showing scattered light intensity from blank, and adjusted/unadjusted scattered light intensity from 2 ppm sample.
44


5.6 Interpretation of Data
5.6.1 Scaling Method
The units of the x-axis were converted from angle in degrees to the magnitude of the scattering wave vector, q, using the following equation from Sorenson (2001):
q = Annk 1 sin()
Where X = wavelength of the light source, in nm 0 = angle in degrees
(Eq. 5.2)
The fractal dimension, primary particle size, and average aggregate size were estimated by visual inspection of the plots showing light intensity vs. q-vector. According to Sorensen (2001), log-log plots of light intensity vs. scattering vector, q for samples containing aggregated micro spheres look like one shown in Figure 5.4.
45


1
2
3
I
mmm www hrp
q
Figure 5.4 An ideal scatter plot with three regions labeled 1,2, and 3.
As seen in the figure, there are three linear regions which are of importance, which are labeled 1,2, and 3. The first region is the linear region where the measured light intensity stays constant with q, followed by a region with a negative slope. According to Sorensen (2001) the slope of this region is equal to the fractal dimension of the aggregate structures formed by micro spheres in the sample. The value of q at which the transition in slope occurs is the inverse of the radius of gyration of the fractal structure. Lastly, there is a region with a slope of -4. The value of q at which the slope transitions from -D to -4, labeled as a'1 is the inverse of the primary particle radius.
46


This method is the simpler of the two methods. The fractal dimension and the average radius of gyration of aggregate structures in suspension can both be found by visual inspection. This approach, however, can be problematic because of its simplicity. Scatter plots created, such as one shown in Figure 5.3 are rarely as distinct as one shown above. The exact location where the slope transitions from one region is not clear, therefore room for interpretation exists. With the method of non-linear least squares fit, or the model fitting approach described in the following section, there is not room for interpretation.
5.6.2 Model Fitting Method
The second, and possibly more accurate method, is one of fitting the data points to a series of model equations simultaneously using a non-linear least squares fit method. Sorensen (2001), Bushell et al. (2002), and Teixeira (1988) use similar equations to model the structure factor, particle factor, fractal dimension, and primary particle radius. A non-liner least squares fit program will go through a process of iteration to minimize the difference between the models and collected data until optimum values are calculated. The primary particle radius, the radius of gyration of the fractal aggregate, and the fractal dimension are calculated simultaneously at once. This method requires some time for the computers to run through the process of iterations in order to optimize the fit.
47


6. Experimental Results
6.1 Qualitative Observations
This research project relied heavily on instrumentation and quantitative outputs for the results. It was unlike testing soils in a laboratory where senses, such as touching, seeing, smelling, and even listening to how soils behave, are in tune with the testing procedures and help technicians characterize soils. There were very little signs that colloidal samples exhibited which helped characterize fractal aggregate structures of samples. For this reason it was important to make careful observations on each colloidal sample and run the experimental procedures as identically and methodically as possible from one sample to another.
Aggregation was observed inside the test tubes of those samples which contained calcium nitrate. These aggregated structures were usually observed to stick to one side of the test tubes instead of settling. The aggregated structures were big enough that they were visible to the naked eye.
Samples without calcium nitrate remained cloudy in appearance for several days, possibly even a couple of weeks. Eventually, however, particles were observed to settle to the bottom of the test tube. It was unclear exactly when the particles settled and the appearance of the mixture was noticed being clear. These same samples (stable colloids) at high concentrations yielded a gentle glow when incident beam passed through it. The scattered light appeared nearly uniform at all angles. This may be a sign that multiple scattering of light was taking place within the sample test tube. Incident light may have scattered off multiple colloids before exiting the test tube. These samples showed no sign of
48


Mie humps on a scatter plot. Mi humps are sharp humps that are generally characteristics of uniformly sized spherical suspended colloids (Bushell 2002) and are illustrated on a scatter plot in Figure 6.1.
1 io T0
qR
Figure 6.1 A theoretical plot of stable spherical particles in suspension. The sharp humps, called Mei humps, are characteristics of scattering caused by spherical colloids. Illustration taken from Bushell (2002)
6.2 Quantitative Results
Fractal dimensions were measured and calculated for each concentration series of samples. Results obtained using both the scaling and the form fitting approaches are summarized below.
49


6.2.1 Scaling Approach
Samples of aggregated 1 pm diameter colloids in suspension had a range of calculated fractal dimensions from 1.8 to 2.1. Aggregated structures with the same concentrations and sizes of colloids inside granular filter media had calculated fractal dimensions between 1.5 and 2.2. Plots in Figures 6.2 through
6.5 show adjusted intensity vs. q for samples with various concentrations of micro sphere colloids. High concentration samples scattered more light than those with low concentrations as shown in the figures below. The calculated fractal dimensions, however, were not affected greatly by the sample concentrations.
50


Adjusted Intensity [pW]
Adjusted Intensity vs. q-Vector
(Aggregated In-Suspension Samples, 1pm Colloids)
1.E-08
1.E-09
1.E-10
1.E-11
1.E-05
1.E-04
1.E-03
1.E-02
q [1/A]
1 ppm -----2 ppm 5 ppm -------10ppm ------20 ppm
40ppm -----60 ppm ------80 ppm-------Blank ------100ppm
Figure 6.2 I vs. q-vector plot for aggregated samples in suspension with various concentrations of micro sphere colloids.
51


1.E-07
Closeup of Adjusted Intensity vs. q-Vector
(Aggregated In-Suspension Samples, 1pm Colloids)
1.E-03
q [1/A]
1 ppm 2 ppm 5 ppm ----10ppm
----20 ppm ----40 ppm ---60 ppm ----80 ppm
----100ppm Power (5 ppm) ----Power (1 ppm) -----Power (2 ppm)
Power (10ppm) ----Power (20 ppm) Power (40 ppm) Power (60 ppm)
Power (80 ppm) ---Power (100ppm)
Figure 6.3 A zoom-in plot showing linear sections of I vs. q plot above. Best fit equations for each concentration are shown to the left. The exponents of those equations show the calculated -D values.
52


Adjusted Intensity [pW]
Adjusted Intensity vs. q-Vector
(Aggregated Samples in Granular Filter Media, 1pm Colloids)
q [1/A]
-----1 ppm --------2 ppm 5 ppm -------10ppm --------20 ppm
-----40ppm --------60 ppm ------80 ppm-------Blank 100ppm
Figure 6.4 I vs. q plot for aggregated samples with various concentrations of micro sphere colloids in granular filter media.
53


Closeup of Adjusted Intensity vs. q-Vector
(Aggregated Samples in Granular Filter Media, 1pm Colloids)
q [1/A]
1 ppm 20 ppm 100ppm Power (10ppm) Power (80 ppm)
2 ppm -40 ppm Power (5 ppm)
- Power (20 ppm) Power (1 OOppm)
5 ppm 60 ppm Power (1 ppm) Power (40 ppm)
10ppm -80 ppm Power (2 ppm) Power (60 ppm)
Figure 6.5 A zoom-in plot showing only linear sections of I vs. q plot above. Exponents of the best-fit equations to the left are the negative of the calculated fractal dimensions, -D.
54


Calculated results from the plots above are summarized in Table 6.1.
Table 6.1 Summary of measured fractal dimensions for each concentration series using 1pm diameter suspended colloids
Sample Aggregated Aggregated
Concentration Colloids in Colloids in
(ppm) suspension granular media
1 2.14 2.17
2 2.08 2.21
5 1.92 2.21
10 1.98 1.92
20 1.96 1.95
40 1.90 1.49
60 1.81 N/A
80 1.88 1.75
100 1.77 N/A
6.2.2 Form Fitting Approach
Several sets of data were analyzed by Dr. David Mays using a non-linear least squares fit script with software, MatLab. The equations used for running the non-linear least squares fit are summarized in Section 3.4.3. The fractal dimension, D, and the primary particle radius, r, were fitted simultaneously. Resulting primary particle radii had a range of 531 nm to 535nm. Given the fact that lOOOnm diameter colloids with a coefficient of variation of 3.2% were used to prepare the samples with, the calculated results were very close to actual
55


values. Code used for the analysis is attached in Appendix X. Figures 6.6 through 6.9 show the resulting plots from the analysis.
Figure 6.6 Non-linear least squares fit plot of aggregated, lppm sample in suspension. Fitted results are D=1.8, and r=531nm. From Mays et al. (2009)
56


10
-8

10
-9

%h
*N

\
fy-
%

\

10
-10

10
.-11
10
Fn
-3
4T
1/r.
FIT

10
-2
Figure 6.7 Non-linear least squares fit plot of aggregated, 2ppm sample in suspension. Fitted results are D=2.3, and r=535nm. From Mays et al. (2009)
57


Figure 6.8 Non-linear least squares fit plot of lppm, aggregated sample inside a granular filter media. Fitted results are D=2.3, and r=535nm. From Mays et al.
(2009)
58


Figure 6.9 Non-linear least squares fit plot of 2ppm, aggregated sample inside a granular filter media. Fitted results are D=2.3, and r=535nm. From Mays et al. (2009)
59


Results that were calculated using the form fitting approach are summarized in Table 6.2.
Table 6.2 Summary of calculated fractal dimensions and primary particle radii.
In-Suspension Sample, Ippm In-Suspension Sample, 2ppm Granular Media Sample, lppm Granular Media Sample, 2ppm
Fitted Fractal Dimension, D 1.8 2.1 2.3 2.7
Fitted Particle Radius, r |nm| 531 535 535 535
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7. CONCLUSION
7.1 Application of Light Scattering in Civil Engineering
Light scattering has been shown to be effective in measuring fractal dimensions of aggregate structures in suspension as well as inside index matched granular media. Experimentation with the light scattering has shown that it can be a practical tool in water treatment research.
In addition, there is some possibility that light scattering can be used to study small-particle soils, such as silts and clays, in the field of soil science. ASTM D 422 method utilizes a hydrometer to measure the specific gravity of soil-water mixture at given time intervals to estimate the relative gradation of soils passing the #200 sieve. The test assumes there is a direct relationship between particle size and time it takes for the particles to settle. Light scattering can potentially be used to supplement existing tests used to better and more quickly characterize small particles in soils.
7.2 Problems Encountered
Many problems having to do with minor details were encountered throughout the duration of the research project. A few examples include (1) sample preparation and multiple scattering, (2) calibration of the static light scattering apparatus, and (3) difficulty interpreting collected data. Sample preparation and multiple scattering was a source of uncertainty in terms of if the samples were yielding good data or not. Because there was nothing to compare
61


the collected data to, it was very hard to tell if the samples were of good quality or not. Samples of various concentrations, as described in chapter section 5.3 were prepared and data were collected for each sample using the SLS apparatus. By so doing, it was found that samples with concentrations in the range of 1-10 ppm lead to collection of clear data. The best sets of data were usually obtained using the 2 ppm sample. Similarly, it was hard to found out if the light scattering apparatus was calibrated correctly or not because there was nothing to compare sets of data that were obtained. Dr. Tagg in the physics department provided some reassurance regarding the functionality of the static light scattering apparatus. His experience in the field of light scattering allowed to project to continue forward after experiencing some difficulty.
7.3 Future Work
It is of interest to learn how the fractal dimensions of aggregate structures affect clogging of granular filters. Basic, foundational laboratory procedures were established during the approximately 17 months of preliminary research. It was found that in-site measurements fractal dimensions of aggregate structures inside index matched granular media was possible dureing. This was a very important step to establish before proceeding to more specific phases of the project.
Proposed future work involves measuring the fractal dimension of aggregate structures inside an index matched filter body as water containing suspended solids is passed through. Figure 7.1 shows an apparatus that was built by Randy Ray at the University of Colorado Denvers machine shop.
62


Figure 7.1 A glass flow-through column with transducer ports held in place by an apparatus built by Randy Ray at the University of Colorado-Denver.
63


The above shown apparatus is designed in a way such that raw water entering the top and exiting at the bottom is filtered while the hydraulic head at various points along the filter body is measured in real-time. The glass body allows for visual inspection of the filter body as it clogs, as well as the use of static light scattering method to measure the fractal dimension of aggregated structures inside the filter body. This apparatus will make it possible to measure the fractal dimension of aggregate structures inside the filter body, and find how that affects clogging over time.
64


APPENDIX A Detailed Static Light Scattering Data (Samples with Nafion and Calcium Nitrate)
65


* Notes:
(1) Fluid is 0.1 M Calcium Nitrate in 58% Dl water & 42% Isopropyl alcohol
(2) The concentration of lpm microspheres varies from lppm to 80ppm
(3) Adjusted sample intensities are shown on plots (intensity of blank sample subtracted)
(4) Samples contain Nation
Angles Raw Data (Light Intensity in Micro Watts)
Angle, 0 n Angle, 0 [radiants] q-vector Blank 1 ppm 2 ppm 5 ppm 10 ppm 20 ppm 40 ppm 80 ppm
0.43401 0.0075749 1.01505E-05 0.00E+00 0.00E+00 0.00E+00 O.OOE+OO O.OOE+OO O.OOE+OO 0 0
0.44931 0.0078419 1.05083E-05 0.00E+00 0.00E+00 0.00E+00 0.00E+00 O.OOE+OO O.OOE+OO O.OOE+OO O.OOE+OO
0.46516 0.0081186 1.0879E-05 7.28E-12 0.00E+00 0.00E+00 0.00E+00 O.OOE+OO O.OOE+OO O.OOE+OO O.OOE+OO
0.48156 0.0084048 1.12625E-05 2.18E-11 0.00E+00 0.00E+00 0.00E+00 O.OOE+OO O.OOE+OO O.OOE+OO O.OOE+OO
0.49854 0.0087012 1.16597E-05 4.37E-11 0.00E+00 0.00E+00 0.00E+00 O.OOE+OO O.OOE+OO O.OOE+OO O.OOE+OO
0.51612 0.009008 1.20708E-05 8.73E-11 0.00E+00 0.00E+00 O.OOE+OO O.OOE+OO O.OOE+OO O.OOE+OO O.OOE+OO
0.53432 0.0093256 1.24965E-05 1.60E-10 0.00E+00 0.00E+00 0.00E+00 O.OOE+OO O.OOE+OO O.OOE+OO O.OOE+OO
0.55317 0.0096546 1.29373E-05 2.55E-10 0.00E+00 0.00E+00 O.OOE+OO O.OOE+OO O.OOE+OO O.OOE+OO O.OOE+OO
0.57268 0.0099952 1.33936E-05 3.78E-10 000E+00 0.00E+00 O.OOE+OO O.OOE+OO O.OOE+OO O.OOE+OO O.OOE+OO
0.59287 0.0103475 1.38658E-05 6.77E-10 0.00E+00 0.00E+00 O.OOE+OO O.OOE+OO O.OOE+OO O.OOE+OO O.OOE+OO
0.61378 0.0107125 1.43548E-05 1.28E-09 0.00E+00 0.00E+00 O.OOE+OO O.OOE+OO O.OOE+OO O.OOE+OO O.OOE+OO
0.63542 0.0110902 1.48609E-05 2.02E-09 0.00E+00 0.00E+00 O.OOE+OO O.OOE+OO O.OOE+OO O.OOE+OO O.OOE+OO
0.65783 0.0114813 1.5385E-05 3.08E-09 0.00E+00 0.00E+00 0 00E+00 O.OOE+OO O.OOE+OO O.OOE+OO O.OOE+OO
0.68103 0.0118862 1.59276E-05 4.85E-09 0.00E+00 0.00E+00 O.OOE+OO 7.28E-12 O.OOE+OO O.OOE+OO O.OOE+OO
0.70505 0.0123054 1.64894E-05 7.64E-09 0.00E+00 0.00E+00 O.OOE+OO 2.18E-11 O.OOE+OO O.OOE+OO O.OOE+OO
0.72991 0.0127393 1.70708E-05 1.05E-08 0.00E+00 0.00E+00 O.OOE+OO 6.55E-11 O.OOE+OO O.OOE+OO O.OOE+OO
0.75565 0.0131886 1.76728E-05 1.29E-08 0.00E+00 0.00E+00 O.OOE+OO 1.75E-10 O.OOE+OO O.OOE+OO O.OOE+OO
0.7823 0.0136537 1.8296E-05 1.40E-08 0.00E+00 0.00E+00 O.OOE+OO 3.35E-10 O.OOE+OO 7.28E-12 O.OOE+OO
0.80989 0.0141352 1.89413E-05 1.43E-08 0.00E+00 0.00E+00 O.OOE+OO 5.89E-10 O.OOE+OO 2.91E-11 O.OOE+OO
0.83845 0.0146337 1.96092E-05 1.41E-08 0.00E+00 0.00E+00 O.OOE+OO 7.71E-10 O.OOE+OO 5.82E-11 O.OOE+OO
0.86802 0.0151498 2.03008E-05 1.38E-08 0.00E+00 0.00E+00 7.28E-12 1.03E-09 O.OOE+OO 1.16E-10 O.OOE+OO
0.89863 0.0156841 2.10167E-05 1.34E-08 0.00E+00 0.00E+00 1.46E-11 1.82E-09 7.28E-12 2.26E-10 O.OOE+OO
0.93032 0.0162371 2.175/8E-05 1.32E-08 0.00E+00 0.00E+00 4.37E-11 3.52E-09 2.18E-11 4.66E-10 O.OOE+OO
0.96313 0.0168098 2.25251E-05 1.38E-08 0.00E+00 0.00E+00 8.00E-11 6.13E-09 2.18E-11 1.13E-09 O.OOE+OO
0.99709 0.0174025 2.33193E-05 1.54E-08 7.28E-12 0.00E+00 1.67E-10 1.23E-08 2.91E-11 2.76E-09 O.OOE+OO
1.03226 0.0180163 2.41418E-05 1.65E-08 3.64E-11 0.00E+00 3.86E-10 2.61E-08 5.09E-]1 6.50E-09 O.OOE+OO


Angles Raw Data (Light Intensity in Micro Watts)
Angle, n Angle, 0 [radiants] q-vector Blank 1 ppm 2 ppm 5 ppm 10 ppm 20 ppm 40 ppm 80 ppm
1.06866 0.0186516 2.49931E-05 1.62E-08 8.00E-11 0.00E+00 8.51E-10 4.50E-08 1.16E-10 1.05E-08 0.00E+00
1.10635 0.0193095 2.58746E-05 1.48E-08 1.67E-10 0.00E+00 2.23E-09 6.89E-08 2.62E-10 1.51E-08 0.00E+00
1.14537 0.0199905 2.67871E-05 1.45E-08 4.00E-10 2.18E-11 4.92E-09 8.98E-08 5.82E-10 2.81E-08 0.00E+00
1.18576 0.0206954 2.77317E-05 1.54E-08 1.03E-09 7.28E-11 9.12E-09 9.92E-08 2.21E-09 4.59E-08 0.00E+00
1.22758 0.0214253 2.87097E-05 1.52E-08 2.86E-09 1.60E-10 1.28E-08 1.01E-07 1.07E-08 6.34E-08 0.00E+00
1.27087 0.0221809 2.97221E-05 1.38E-08 5.07E-09 3.93E-10 1.57E-08 1.01E-07 2.65E-08 8.00E-08 0.00E+00
1.31569 0.0229631 3.07703E-05 1.32E-08 7.50E-09 1.04E-09 2.04E-08 1.01E-07 3.66E-08 1.07E-07 2.91E-11
1.36209 0.023773 3.18554E-05 1.33E-08 8.51E-09 1.96E-09 2.72E-08 9.87E-08 4.75E-08 1.27E-07 1.02E-10
1.41012 0.0246112 3.29786E-05 1.33E-08 9.19E-09 4.05E-09 3.44E-08 9.31E-08 5.96E-08 1.28E-07 3.06E-10
1.45985 0.0254792 3.41416E-05 1.37E-08 1.04E-08 9.63E-09 4.07E-08 8.54E-08 7.10E-08 1.25E-07 9.46E-10
1.51134 0.0263779 3.53457E-05 1.36E-08 1.21E-08 1.65E-08 4.46E-08 7.77E-08 7.86E-08 1.28E-07 3.71E-09
1.56464 0.0273081 3.65922E-05 1.31E-08 1.30E-08 2.15E-08 4.67E-08 7.91E-08 8.36E-08 1.30E-07 1.08E-08
1.61982 0.0282712 3.78826E-05 1.22E-08 1.36E-08 2.40E-08 4.82E-08 8.39E-08 9.30E-08 1.24E-07 2.36E-08
1.67695 0.0292683 3.92186E-05 1.16E-08 1.49E-08 2.38E-08 4.97E-08 8.37E-08 1.04E-07 1.19E-07 4.59E-08
1.73609 0.0303005 4.06016E-05 1.14E-08 1.67E-08 2.44E-08 5.20E-08 8.15E-08 1.10E-07 1.17E-07 8.80E-08
1.79731 0.031369 4.20332E-05 1.11E-08 1.72E-08 2.69E-08 4.77E-08 7.92E-08 1.05E-07 1.18E-07 1.34E-07
1.8607 0.0324753 4.35156E-05 1.06E-08 1.68E-08 2.98E-08 4.11E-08 7.44E-08 1.06E-07 1.24E-07 1.55E-07
1.92633 0.0336208 4.50503E-05 1.04E-08 1.65E-08 3.04E-08 3.28E-08 7.15E-08 9.31E-08 1.27E-07 1.60E-07
1.99426 0.0348064 4.66388E-05 9.33E-09 1.56E-08 2.80E-08 2.85E-08 6.95E-08 8.48E-08 1.10E-07 1.56E-07
2.0646 0.0360341 4.82836E-05 8.99E-09 1.39E-08 2.42E-08 3.00E-08 6.63E-08 8.06E-08 8.92E-08 1.50E-07
2.13742 0.037305 4.99864E-05 8.96E-09 1.42E-08 2.20E-08 3.05E-08 6.14E-08 7.90E-08 8.22E-08 1.52E-07
2.2128 0.0386206 5.17491E-05 8.78E-09 1.63E-08 2.10E-08 2.89E-08 5.26E-08 8.05E-08 7.80E-08 1.41E-07
2.29085 0.0399829 5.35741E-05 9.60E-09 1.84E-08 1.97E-08 2.62E-08 4.13E-08 8.16E-08 7.52E-08 1.32E-07
2.37164 0.0413929 5.54632E-05 1.01E-08 2.02E-08 1.87E-08 2.30E-08 3.58E-08 8.48E-08 6.70E-08 1.26E-07
2.45529 0.0428529 5.74192E-05 1.00E-08 2.25E-08 1.90E-08 2.20E-08 3.47E-08 8.46E-08 6.01E-08 1.18E-07
2.54189 0.0443643 5.94441E-05 9.98E-09 2.28E-08 2.00E-08 2.12E-08 3.32E-08 7.90E-08 6.24E-08 1.11E-07
2.63155 0.0459292 6.15405E-05 1.11E-08 2.02E-08 2.17E-08 2.02E-08 3.17E-08 7.61E-08 6.56E-08 1.07E-07
2.72436 0.0475491 6.37105E-05 1.21E-08 1.73E-08 2.09E-08 1.84E-08 2.94E-08 8.18E-08 6.35E-08 1.15E-07
2.82046 0.0492263 6.59574E-05 1.09E-08 1.60E-08 1.79E-08 1.61E-08 2.88E-08 8.61E-08 5.48E-08 1.21E-07
2.91994 0.0509626 6.82833E-05 9.74E-09 1.45E-08 1.59E-08 1.52E-08 3.08E-08 8.14E-08 5.00E-08 1.09E-07
3.02294 0.0527603 7.06914E-05 8.47E-09 1.34E-08 1.57E-08 1.56E-08 3.49E-08 6.96E-08 5.75E-08 9.49E-08
3.12957 0.0546213 7.31843E-05 7.33E-09 1.24E-08 1.51E-08 1.64E-08 3.63E-08 5.75E-08 6.22E-08 9.05E-08


Angles Raw Data (Light Intensity in Micro Watts)
Angle, n Angle, 0 [radiants] q-vector Blank 1 ppm 2 ppm 5 ppm 10 ppm 20 ppm 40 ppm 80 ppm
3.23996 0.056548 7.57651E-05 6.35E-09 1.26E-08 1.35E-08 1.69E-08 3.51E-08 5.49E-08 5.68E-08 8.84E-08
3.35425 0.0585427 7.8437E-05 5.09E-09 1.40E-08 1.14E-08 1.64E-08 3.02E-08 5.85E-08 5.10E-08 7.84E-08
3.47257 0.0606078 8.1203E-05 3.97E-09 1.46E-08 1.09E-08 1.50E-08 2.72E-08 5.49E-08 5.38E-08 7.54E-08
3.59507 0.0627458 8.40666E-05 3.28E-09 1.44E-08 1.00E-08 1.37E-08 2.18E-08 5.25E-08 6.18E-08 6.95E-08
3.7219 0.0649594 8.70313E-05 3.73E-09 1.40E-08 9.90E-09 1.24E-08 1.90E-08 5.29E-08 7.26E-08 5.98E-08
3.8532 0.067251 9.01005E-05 3.81E-09 1.21E-08 1.01E-08 1.19E-08 2.11E-08 5.19E-08 7.44E-08 5.30E-08
3.98913 0.0696235 9.32777E-05 3.46E-09 9.35E-09 1.12E-08 1.28E-08 2.63E-08 4.76E-08 5.99E-08 5.07E-08
4.12987 0.0720798 9.65672E-05 3.11E-09 7.65E-09 1.08E-08 1.33E-08 2.54E-08 4.15E-08 4.95E-08 6.32E-08
4.27558 0.0746229 9.99727E-05 2.84E-09 6.80E-09 9.44E-09 1.30E-08 2.16E-08 3.81E-08 4.95E-08 7.13E-08
4.42643 0.0772558 0.000103498 2.44E-09 5.73E-09 9.36E-09 1.42E-08 2.03E-08 3.50E-08 5.25E-08 7.89E-08
4.58261 0.0799816 0.000107148 2.11E-09 5.13E-09 9.67E-09 1.27E-08 1.91E-08 3.53E-08 5.08E-08 8.82E-08
4.7443 0.0828037 0.000110927 2.06E-09 5.94E-09 8.91E-09 1.16E-08 1.76E-08 3.29E-08 4.57E-08 8.54E-08
4.91171 0.0857255 0.000114838 2.10E-09 6.13E-09 9.73E-09 1.08E-08 1.67E-08 3.04E-08 3.99E-08 7.54E-08
5.08503 0.0887505 0.000118888 1.87E-09 5.54E-09 8.95E-09 9.50E-09 1.70E-08 3.36E-08 4.01E-08 6.87E-08
5.25448 0.0918825 0.000123081 1.47E-09 4.69E-09 6.86E-09 8.58E-09 1.48E-08 3.27E-08 4.02E-08 6.15E-08
5.45027 0.0951252 0.000127421 1.33E-09 4.88E-09 5.37E-09 6.92E-09 1.23E-08 3.21E-08 3.63E-08 5.59E-08
5.64263 0.0984825 0.000131915 1.35E-09 4.63E-09 4.50E-09 7.51E-09 1.17E-08 3.23E-08 3.78E-08 5.06E-08
5.84178 0.1019583 0.000136567 1.35E-09 4.73E-09 4.58E-09 8.57E-09 1.25E-08 3.07E-08 4.29E-08 4.65E-08
6.04798 0.1055572 0.000141383 1.24E-09 4.86E-09 4.63E-09 8.03E-09 1.26E-08 2.63E-08 3.39E-08 4.36E-08
6.26147 0.1092833 0.000146368 1.10E-09 4.21E-09 4.48E-09 7.88E-09 1.32E-08 2.49E-08 2.90E-08 4.S0E-08
6.48251 0.1131411 0.00015153 1.14E-09 3.89E-09 4.37E-09 7.04E-09 1.19E-08 2.42E-08 3.07E-08 4.63E-08
6.71138 0.1171357 0.000156874 1.07E-09 3.63E-09 4.73E-09 5.66E-09 1.06E-08 2.71E-08 2.86E-08 4.29E-08
6.S4834 0.1212714 0.000162406 1.06E-09 3.34E-09 4.99E-09 5.28E-09 9.53E-09 2.68E-08 2.88E-08 3.96E-08
7.19369 0.1255536 0.000168133 1.11E-09 2.95E-09 4.20E-09 6.09E-09 8.84E-09 2.37E-08 2.75E-08 3.61E-08
7.44772 0.1299872 0.000174062 9.60E-10 2.68E-09 3.75E-09 5.30E-09 8.88E-09 2.08E-08 2.29E-08 3.64E-08
7.71076 0.1345781 0.000180201 8.00E-10 2.41E-09 4.15E-09 4.80E-09 9.39E-09 2.09E-08 2.24E-08 3.17E-08
7.98311 0.1393316 0.000186555 7.42E-10 2.35E-09 4.18E-09 4.83E-09 1.01E-08 1.96E-08 1.76E-08 2.67E-08
8.26512 0.1442536 0.000193134 8.00E-10 2.01E-09 3.39E-09 5.01E-09 9.46E-09 1.90E-08 1.52E-08 2.65E-08
8.55712 0.1493499 0.000199945 7.35E-10 1.99E-09 3.10E-09 4.90E-09 8.28E-09 1.75E-08 1.73E-08 2.53E-08
8.85948 0.1546271 0.000206996 7.13E-10 1.86E-09 2.74E-09 4.77E-09 7.35E-09 1.64E-08 1.69E-08 2.45E-08
9.17256 0.1600914 0.000214296 7.13E-10 1.83E-09 2.79E-09 4.55E-09 5.93E-09 1.69E-08 1.58E-08 2.53E-08
9.49676 0.1657497 0.000221853 6.18E-10 1.67E-09 2.58E-09 4.50E-09 5.98E-09 1.51E-08 1.26E-08 2.73E-08


Angles Raw Data (Light Intensity in Micro Watts)
Angle, 0 n Angle, [radiants] q-vector Blank 1 ppm 2 ppm 5 ppm 10 ppm 20 ppm 40 ppm 80 ppm
9.83248 0.1716091 0.000229677 5.82E-10 1.68E-09 2.30E-09 4.02E-09 5.84E-09 1.42E-08 1.28E-08 2.22E-08
10.18012 0.1776766 0.000237776 5.09E-10 1.75E-09 1.91E-09 4.02E-09 6.56E-09 1.32E-08 1.23E-08 1.84E-08
10.54012 0.1839598 0.000246162 5.09E-10 1.62E-09 1.91E-09 3.49E-09 6.16E-09 1.25E-08 1.07E-08 1.70E-08
10.91292 0.1904664 0.000254842 4.51E-10 1.54E-09 1.76E-09 3.01E-09 4.78E-09 1.13E-08 9.47E-09 1.43E-08
11.29899 0.1972046 0.000263829 3.93E-10 1.41E-09 1.59E-09 2.92E-09 4.38E-09 1.09E-08 1.06E-08 1.34E-08
11.69882 0.2041829 0.000273133 4.07E-10 1.40E-09 1.60E-09 3.24E-09 3.94E-09 1.01E-08 1.07E-08 1.41E-08
12.11289 0.2114098 0.000282765 3.42E-10 1.27E-09 1.51E-09 2.75E-09 4.05E-09 8.78E-09 9.04E-09 1.23E-08
12.54174 0.2188947 0.000292737 2.91E-10 1.21E-09 1.41E-09 2.47E-09 3.79E-09 8.03E-09 7.28E-09 1.06E-08
12.98589 0.2266465 0.00030306 2.55E-10 1.16E-09 1.30E-09 2.02E-09 3.41E-09 6.65E-09 6.61E-09 9.51E-09
13.44591 0.2346754 0.000313748 2.62E-10 1.01E-09 1.14E-09 1.94E-09 3.04E-09 6.37E-09 6.29E-09 9.38E-09
13.92239 0.2429915 0.000324812 2.26E-10 7.93E-10 1.03E-09 1.78E-09 2.84E-09 6.43E-09 6.66E-09 8.81E-09
14.41592 0.2516053 0.000336266 1.96E-10 7.57E-10 8.88E-10 1.54E-09 2.62E-09 5.78E-09 5.94E-09 7.49E-09
14.92714 0.2605277 0.000348125 2.04E-10 7.35E-10 8.66E-10 1.39E-09 2.55E-09 4.96E-09 4.56E-09 8.23E-09
15.45671 0.2697705 0.000360402 1.60E-10 6.91E-10 7.13E-10 1.27E-09 2.29E-09 4.85E-09 5.31E-09 6.90E-09
16.0053 0.2793452 0.000373111 1.53E-10 6.HE-10 6.48E-10 1.03E-09 1.71E-09 4.42E-09 4.63E-09 6.21E-09
16.57362 0.2892642 0.000386269 1.31E-10 4.87E-10 6.18E-10 9.90E-10 1.40E-09 3.61E-09 3.75E-09 5.77E-09
17.16242 0.2995407 0.00039989 1.09E-10 4.51E-10 4.95E-10 9.17E-10 1.27E-09 3.22E-09 3.38E-09 4.55E-09
17.77247 0.3101881 0.000413993 1.09E-10 4.15E-10 4.29E-10 8.66E-10 1.22E-09 3.54E-09 3.46E-09 3.90E-09
18.40457 0.3212203 0.000428592 1.02E-10 3.64E-10 4.00E-10 7.20E-10 1.23E-09 2.95E-09 2.80E-09 4.61E-09
19.05955 0.3326519 0.000443706 1.09E-10 3.13E-10 3.93E-10 6.33E-10 1.11E-09 2.42E-09 2.48E-09 4.15E-09
19.73829 0.3444981 0.000459354 8.73E-11 2.76E-10 3.49E-10 5.68E-10 9.68E-10 2.07E-09 2.47E-09 3.42E-09
20.44171 0.3567751 0.000475553 8.00E-11 2.55E-10 3.20E-10 4.87E-10 8.44E-10 2.00E-09 2.42E-09 2.97E-09
21.17075 0.3694993 0.000492323 7.28E-11 2.18E-10 2.91E-10 4.73E-10 8.44E-10 1.59E-09 2.36E-09 2.63E-09
21.92642 0.3826882 0.000509685 7.28E-11 1.75E-10 2.26E-10 3.57E-10 6.62E-10 1.43E-09 1.73E-09 2.36E-09
22.70975 0.3963599 0.000527659 5.82E-11 1.53E-10 1.75E-10 3.49E-10 5.97E-10 1.36E-09 1.64E-09 2.25E-09
23.52185 0.4105337 0.000546267 5.82E-11 1.53E-10 1.60E-10 2.84E-10 5.89E-10 1.15E-09 1.56E-09 2.03E-09
24.36384 0.4252292 0.000565531 5.82E-11 1.31E-10 1.31E-10 2.47E-10 4.73E-10 1.03E-09 1.47E-09 1.67E-09
25.23694 0.4404677 0.000585474 5.82E-11 1.02E-10 1.24E-10 2.11E-10 4.29E-10 9.02E-10 1.29E-09 1.64E-09
26.14241 0.4562711 0.000606121 4.37E-11 1.02E-10 1.02E-10 1.67E-10 3.42E-10 7.49E-10 1.25E-09 1.70E-09
27.08155 0.4726622 0.000627495 3.64E-11 7.28E-11 8.00E-11 1.53E-10 3.13E-10 6.11E-10 9.53E-10 1.39E-09
28.05578 0.4896657 0.000649624 4.37E-11 6.55E-11 7.28E-11 1.24E-10 2.40E-10 5.68E-10 7.42E-10 1.16E-09
29.06655 0.507307 0.000672533 3.64E-11 5.82E-11 5.82E-11 1.02E-10 1.89E-10 4.66E-10 7.71E-10 9.53E-10


Angles Raw Data (Light Intensity in Micro Watts)
Angle, 0 n Angle, 0 [radiants] q-vector Blank 1 ppm 2 ppm 5 ppm 10 ppm 20 ppm 40 ppm 80 ppm
30.1154 0.5256129 0.00069625 2.91E-11 5.09E-11 3.64E-11 8.00E-11 1.60E-10 4.00E-10 6.69E-10 8.37E-10
31.20397 0.544612 0.000720803 2.18E-11 3.64E-11 2.91E-11 6.55E-11 1.53E-10 3.20E-10 5.60E-10 6.84E-10
32.33398 0.5643344 0.000746222 2.18E-11 2.91E-11 2.91E-11 5.82E-11 1.24E-10 2.69E-10 5.46E-10 6.26E-10
33.50725 0.5848118 0.000772537 1.46E-11 2.18E-11 2.18E-11 4.37E-11 9.46E-11 1.89E-10 3.93E-10 5.31E-10
34.72573 0.6060783 0.000799781 1.46E-11 2.18E-11 1.46E-11 3.64E-11 7.28E-11 1.53E-10 3.71E-10 4.22E-10
35.99145 0.6281693 0.000827985 1.46E-11 1.46E-11 1.46E-11 2.91E-11 6.55E-11 1.31E-10 3.13E-10 3.86E-10
37.30662 0.6511234 0.000857184 7.28E-12 1.46E-11 7.28E-12 2.18E-11 5.82E-11 1.16E-10 2.69E-10 3.35E-10
38.67356 0.674981 0.000887413 7.28E-12 1.46E-11 7.28E-12 2.18E-11 4.37E-11 1.09E-10 2.26E-10 2.98E-10
40.09476 0.6997856 0.000918707 7.28E-12 1.46E-11 7.28E-12 2.18E-11 3.64E-11 8.00E-11 2.18E-10 2.33E-10
41.5729 0.725584 0.000951105 0 7.28E-12 7.28E-12 1.46E-11 3.64E-11 7.28E-11 1.82E-10 1.89E-10
43.11082 0.7524258 0.000984646 0 7.28E-12 7.28E-12 1.46E-11 2.91E-11 6.55E-11 1.67E-10 1.67E-10
44.71162 0.780365 0.001019369 0 7.28E-12 7.28E-12 1.46E-11 2.91E-11 5.82E-11 1.46E-10 1.53E-10
46.37863 0.8094598 0.001055317 0 7.28E-12 0.00E+00 7.28E-12 2.18E-11 5.82E-11 1.24E-10 1.31E-10
48.11544 0.8397728 0.001092533 0 0.00E+00 0.00E+00 7.28E-12 2.18E-11 5.82E-11 1.16E-10 1.09E-10
49.92598 0.8713727 0.001131061 0 0.00E+00 0.00E+00 7.28E-12 1.46E-11 3.64E-11 1.09E-10 9.46E-11
51.81451 0.9043338 0.001170948 0 0.00E+00 0.00E+00 O.OOE+OO 1.46E-11 2.91E-11 8.73E-11 8.73E-11
53.78571 0.9387377 0.001212241 0 0.00E+00 0.00E+00 O.OOE+OO 7.28E-12 2.91E-11 6.55E-11 6.55E-11
55.84472 0.9746742 0.001254991 0 0.00E+00 0.00E+00 O.OOE+OO 7.28E-12 2.18E-11 5.82E-11 5.82E-11
57.99721 1.0122423 0.001299248 0 0.00E+00 0.00E+00 O.OOE+OO 7.28E-12 1.46E-11 5.09E-11 3.64E-11
60.2495 1.0515521 0.001345066 0 0.00E+00 0.00E+00 O.OOE+OO O.OOE+OO 7.28E-12 3.64E-11 3.64E-11
62.60861 1.0927264 0.0013925 0 0.00E+00 0.00E+00 O.OOE+OO O.OOE+OO 7.28E-12 2.18E-11 2.91E-11
65.08246 1.1359032 0.001441606 0 0.00E+00 O.OOExOO O.OOE+OO O.OOE+OO O.OOE+OO 1.46E-11 2.18E-11
67.67999 1.1812387 0.001492444 0 0.00E+00 O.OOE+OO O.OOE+OO O.OOE+OO O.OOE+OO 1.46E-11 2.18E-11
70.41142 1.2289111 0.001545075 0 0.00E+00 O.OOE+OO O.OOE+OO O.OOE+OO O.OOE+OO 1.46E-11 2.18E-11
73.28846 1.2791249 0.001599562 0 0.00E+00 O.OOE+OO O.OOE+OO O.OOE+OO O.OOE+OO 1.46E-11 1.46E-11
76.32474 1.332118 0.00165597 0 0.00E+00 O.OOE+OO O.OOE+OO O.OOE+OO O.OOE+OO 1.46E-11 1.46E-11
79.53623 1.3881691 0.001714368 0 0.00E+00 O.OOE+OO O.OOE+OO O.OOE+OO O.OOE+OO 7.28E-12 1.46E-11
82.94193 1.4476098 0.001774825 0 0.00E+00 O.OOE+OO O.OOE+OO O.OOE+OO O.OOE+OO 7.28E-12 1.46E-11
86.56472 1.5108394 0.001837414 0 0.00E+00 O.OOE+OO O.OOE+OO O.OOE+OO O.OOE+OO O.OOE+OO 7.28E-12
90.43268 1.578348 0.001902211 0 0.00E+00 O.OOE+OO O.OOE+OO O.OOE+OO O.OOE+OO O.OOE+OO 7.28E-12
94.58093 1.6507486 0.001969292 0 0.00E+00 O.OOE+OO O.OOE+OO O.OOE+OO O.OOE+OO O.OOE+OO 7.28E-12
99.05445 1.7288263 0.002038739 0 0.00E+00 O.OOE+OO O.OOE+OO O.OOE+OO O.OOE+OO O.OOE+OO O.OOE+OO


Angles Raw Data (Light Intensity in Micro Watts)
Angle, 0 n Angle, [radiants] q-vector Blank 1 ppm 2 ppm 5 ppm 10 ppm 20 ppm 40 ppm 80 ppm
103.9126 1.8136172 0.002110635 0 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 7.28E-12
109.2368 1.9065411 0.002185066 0 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00
115.1439 2.0096403 0.002262122 0 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 7.28E-12
121.814 2.1260547 0.002341896 0 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00
129.5516 2.2611016 0.002424483 0 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00
138.9598 2.4253066 0.002509982 0 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 7.28E-12 7.28E-12
151.6614 2.6469911 0.002598496 0 0.00E+00 0.00E+00 0.00E+00 7.28E-12 2.18E-11 2.91E-11 4.37E-11


*Notes:
(1) Fluid is 0.1 M Calcium Nitrate in 58% C
(2) The concentration of l|jm microspher
(3) Adjusted sample intensities are shown
(4) Samples contain Nafion
Angles Adjusted Data (Light Intensity in Micros Watts)
Angle, n Angle, 0 [radiants] q-vector Blank lppm 2ppm 5ppm lOppm 20ppm 40ppm 80ppm
0.43401 0.0075749 1.01505E-05 7.57E-102 7.5748E-102 7.57E-102 7.5748E-102 7.5748E-102 7.5748E-102 7.575E-102 7.5748E-102
0.44931 0.0078419 1.05083E-05 7.84E-102 7.8419E-102 7.84E-102 7.8419E-102 7.8419E-102 7.8419E-102 7.842E-102 7.8419E-102
0.45516 0.0081186 1.0879E-05 5.91E-14 8.1185E-102 8.12E-102 8.1185E-102 8.1185E-102 8.1185E-102 8.118E-102 8.1185E-102
0.48156 0.0084048 1.12625E-05 1.83E-13 8.4047E-102 8.40E-102 8.4047E-102 8.4047E-102 8.4047E-102 8.405E-102 8.4047E-102
0.49854 0.0087012 1.16597E-05 3.80E-13 8.7011E-102 8.70E-102 8.7011E-102 8.7011E-102 8.7011E-102 8.701E-102 8.7011E-102
0.51612 0.009008 1.20708E-05 7.86E-13 9.0079E-102 9.01E-102 9.0079E-102 9.0079E-102 9.0079E-102 9.008E-102 9.0079E-102
0.53432 0.0093256 1.24965E-05 1.49E-12 9.3255E-102 9.33E-102 9.3255E-102 9.3255E-102 9.3255E-102 9.326E-102 9.3255E-102
0.55317 0.0096546 1.29373E-05 2.46E-12 9.6545E-102 9.65E-102 9.6545E-102 9.6545E-102 9.6545E-102 9.654E-102 9.6545E-102
0.57268 0.0099952 1.33936E-05 3.78E-12 9.995E-102 9.99E-102 9.995E-102 9.995E-102 9.995E-102 9.995E-102 9.995E-102
0.59287 0.0103475 1.38658E-05 7.00E-12 1.0347E-101 1.03E-101 1.0347E-101 1.0347E-101 1.0347E-101 1.035E-101 1.0347E-101
0.61378 0.0107125 1.43548E-05 1.37E-11 1.0712E-101 1.07E-101 1.0712E-101 1.0712E-101 1.0712E-101 1.071E-101 1.0712E-101
0.63542 0.0110902 1.48609E-05 2.2.4E-11 1.109E-101 1.11E-101 1.109E-101 1.109E-101 1.109E-101 1.109E-101 1.109E-101
0.65783 0.0114813 1.5385E-05 3.53E-11 1.1481E-101 1.15E-101 1.1481E-101 1.1481E-101 1.1481E-101 1.148E-101 1.1481E-101
0.68103 0.0118862 1.59276E-05 5.77E-11 1.1886E-101 1.19E-101 1.1886E-101 1.1886E-101 1.1886E-101 1.189E-101 1.1886E-101
0.70505 0.0123054 1.64894E-05 9.40E-11 1.2305E-101 1.23E-101 1.2.305E-101 1.2305E-101 1.2305E-101 1.231E-101 1.2305E-101
0.72991 0.0127393 1.70708E-05 1.34E-10 1.2739E-101 1.27E-101 1.2739E-101 1.2739E-101 1.2739E-101 1.274E-101 1.2739E-101
0.75565 0.0131886 1.76728E-05 1.70E-10 1.3188E-101 1.32E-101 1.3188E-101 5.67058E-14 1.3188E-101 1.319E-101 1.3188E-101
0.7823 0.0136537 1.8296E-05 1.92E-10 1.3653E-101 1.37E-101 1.3653E-101 1.95063E-12 1.3653E-101 1.365E-101 1.3653E-101
0.80989 0.0141352 1.89413E-05 2.02E-10 1.4135E-101 1.41E-101 1.4135E-101 5.47393E-12 1.4135E-101 1.413E-101 1.4135E-101
0.83845 0.0146337 1.96092E-05 2.06E-10 1.4633E-101 1.46E-101 1.4633E-101 8.26806E-12 1.4633E-101 1.463E-101 1.4633E-101
0.86802 0.0151498 2.03008E-05 2.09E-10 1.5149E-101 1.51E-101 1.5149E-101 1.23776E-11 1.5149E-101 1.515E-101 1.5149E-101
0.89863 0.0156841 2.10167E-05 2.10E-10 1.5683E-101 1.57E-101 1.5683E-101 2.52333E-11 1.5683E-101 2.427E-13 1.5683E-101
0.93032 0.0162371 2.17578E-05 2.15E-10 1.6236E-101 1.62E-101 1.6236E-101 5.3685E-11 1.6236E-101 4.0679E-12 1.6236E-101
0.96313 0.0168098 2.25251E-05 2.32E-10 1.6809E-101 1.68E-101 1.6809E-101 9.90826E-11 1.6809E-101 1.5061E-11 1.6809E-101
0.99709 0.0174025 2.33193E-05 2.67E-10 1.7402E-101 1.74E-101 1.7402E-101 2.09076E-10 1.7402E-101 4.3464E-11 1.7402E-101
1.03226 0.0180163 2.41418E-05 2.99E-10 1.8015E-101 1.80E-101 1.55841E-12 4.6545E-10 1.8015E-101 1.118E-10 1.8015E-101


Angles Adjusted Data (Light Intensity in Micros Watts)
Angle, n Angle, [radiants] q-vector Blank lppm 2ppm 5ppm lOppm 20ppm 40ppm 80ppm
1.06866 0.0186516 2.49931E-05 3.01E-10 1.8651E-101 1.87E-101 1.02559E-11 8.32878E-10 1.8651E-101 1.8965E-10 1.8651E-101
1.10635 0.0193095 2.58746E-05 2.86E-10 1.9308E-101 1.93E-101 3.7469E-11 1.32545E-09 1.9308E-101 2.8515E-10 1.9308E-101
1.14537 0.0199905 2.67871E-05 2.91E-10 2.18767E-12 2.00E-101 9.25066E-11 1.78849E-09 5.82372E-12 5.5675E-10 1.9989E-101
1.18576 0.0206954 2.77317E-05 3.18E-10 1.48063E-11 2.07E-101 1.82239E-10 2.04689E-09 3.91986E-11 9.4367E-10 2.0694E-101
1.22758 0.0214253 2.87097E-05 3.26E-10 5.42674E-11 2.14E-101 2.66262E-10 2.15676E-09 2.21992E-10 1.3506E-09 2.1424E-101
1.27087 0.0221809 2.97221E-05 3.07E-10 1.05667E-10 1.90E-12 3.41597E-10 2.24274E-09 5.80916E-10 1.7681E-09 2.2179E-101
1.31569 0.0229631 3.07703E-05 3.04E-10 1.65271E-10 1.69E-11 4.62145E-10 2.31522E-09 8.33531E-10 2.4472E-09 2.2961E-101
1.36209 0.023773 3.18554E-05 3.16E-10 1.94682E-10 3.90E-11 6.3935E-10 2.33829E-09 1.12051E-09 3.007E-09 2.3771E-101
1.41012 0.0246112 3.29786E-05 3.27E-10 2.18098E-10 9.17E-11 8.37981E-10 2.28365E-09 1.45804E-09 3.149E-09 2.4609E-101
1.45985 0.0254792 3.41416E-05 3.49E-10 2.55634E-10 2.36E-10 1.0275E-09 2.16713E-09 1.80104E 09 3.1865E-09 1.52148E-11
1.51134 0.0263779 3.53457E-05 3.58E-10 3.09701E-10 4.27E-10 1.16655E-09 2.03952E-09 2.06254E-09 3.3698E-09 8.84359E-11
1.56464 0.0273081 3.65922E-05 3.58E-10 3.45241E-10 5.77E-10 1.26568E-09 2.15095E-09 2.27412E-09 3.5283E-09 2.8584E-10
1.61982 0.0282712 3.78826E-05 3.45E-10 3.74848E-10 6.69E-10 1.35365E-09 2.36083E-09 2.61978E-09 3.5093E-09 6.56004E-10
1.67695 0.0292683 3.92186E-05 3.40E-10 4.25701E-10 6.86E-10 1.44561E-09 2.43913E-09 3.0351E-09 3.4644E-09 1.33276E-09
1.73609 0.0303005 4.06016E-05 3.44E-10 4.95022E-10 7.29E-10 1.5639E-09 2.45819E-09 3.32229E-09 3.5328E-09 2.65592E-09
1.79731 0.031369 4.20332E-05 3.49E-10 5.29898E-10 8.34E-10 1.4847E-09 2.47236E-09 3.28866E-09 3.698E-09 4.18776E-09
1.8607 0.0324753 4.35156E-05 3.44E-10 5.35497E-10 9.55E-10 1.32197E-09 2.40588E-09 3.4241E-09 4.0275E-09 5.0195E-09
1.92633 0.0336208 4.50503E-05 3.48E-10 5.42516E-10 1.01E-09 1.09013E-09 2.39031E-09 3.11793 E-09 4.2462E-09 5.35704E-09
1.99426 0.0348064 4.66388E-05 3.25E-10 5.31567E-10 9.64E-10 9.79728E-10 2.40829E-09 2.94076E-09 3.8047E-09 5.4267E-09
2.0646 0.0360341 4.82836E-05 3.24E-10 4.88213E-10 8.61E-10 1.0683E-09 2.37711E-09 2.89323E-09 3.2012E-09 5.38161E-09
2.13742 0.037305 4.99864E-05 3.34E-10 5.17512E-10 8.07E-10 1.12565E-09 2.27707E-09 2.93459E-09 3.054E-09 5.65046E-09
2.2128 0.0386206 5.17491E-05 3.39E-10 6.1592E-10 7.96E-10 1.10334E-09 2.01693E-09 3.096E-09 2.9971E-09 5.41454E-09
2.29085 0.0399829 5.35741E-05 3.84E-10 7.19892E-10 7.73E-10 1.03254E-09 1.63603E-09 3.24611E-09 2.9893E-09 5.26802E-09
2.37164 0.0413929 5.54632E-05 4.18E-10 8.17339E-10 7.56E-10 9.35064E-10 1.46619E-09 3.4901E-09 2.7554E-09 5.19008E-09
2.45529 0.0428529 5.74192E-05 4.30E-10 9.46916E-10 7.94E-10 9.22291E-10 1.46839E-09 3.60667E-09 2.5565E-09 5.02926E-09
2.54189 0.0443643 5.94441E-05 4.43E-10 9.89412E-10 8.67E-10 9.18745E-10 1.45409E-09 3.48187E-09 2.7494E-09 4.91171E-09
2.63155 0.0459292 6.15405E-05 5.10E-10 9.02269E-10 9.71E-10 9.05277E-10 1.43009E-09 3.46921E-09 2.9895E-09 4.91136E-09
2.72436 0.0475491 6.37105E-05 5.77E-10 7.96037E-10 9.64E-10 8.47565E-10 1.37219E-09 3.86188E-09 2.99E-09 5.45826E-09
2.82046 0.0492263 6.59574E-05 5.38E-10 7.59388E-10 8.53E-10 7.64402E-10 1.39166E-09 4.21183E-09 2.6705E-09 5.90639E-09
2.91994 0.0509626 6.82833E-05 4.96E-10 7.13426E-10 7.85E-10 7.47531E-10 1.54479E-09 4.12371E-09 2.5199E-09 5.50397E-09
3.02294 0.0527603 7.06914E-05 4.47E-10 6.81698E-10 8.03E-10 8.00649E-10 1.81631E-09 3.64429E-09 3.0108E-09 4.98188E-09
3.12957 0.0546213 7.31843E-05 4.00E-10 6.53426E-10 8.03E-10 8.74287E-10 1.95951E-09 3.11702E-09 3.3721E-09 4.91964E-09


Angles Adjusted Data (Light Intensity in Micros Watts)
Angle, 0 n Angle, 0 [radiants] q-vector Blank lppm 2ppm 5ppm lOppm 20ppm 40ppm 80ppm
3.23996 0.056548 7.57651E-05 3.59E-10 6.9318E-10 7.40E-10 9.37038E-10 1.96222E-09 3.0828E-09 3.1885E-09 4.9769E-09
3.35425 0.0585427 7.8437E-05 2.98E-10 8.00385E-10 6.51E-10 9.4172E-10 1.74718E-09 3.40447E-09 2.9668E-09 4.56965E-09
3.47257 0.0606078 8.1203E-05 2.41E-10 8.71695E-10 6.43E-10 8.92852E-10 1.63104E-09 3.31016E-09 3.2454E-09 4.54988E-09
3.59507 0.0627458 8.40666E-05 2.06E-10 8.87712E-10 6.17E-10 8.47104E-10 1.35536E-09 3.27658E-09 3.861E-09 4.34692E-09
3.7219 0.0649594 8.70313E-05 2.42E-10 8.96334E-10 6.27E-10 7.87233E-10 1.21704E-09 3.41517E-09 4.6952E-09 3.86341E-09
3.8532 0.067251 9.01005E-05 2.56E-10 7.98837E-10 6.62E-10 7.85148E-10 1.40074E-09 3.46899E-09 4.9813E-09 3.54429E-09
3.98913 0.0696235 9.32777E-05 2.41E-10 6.33669E-10 7.65E-10 8.76628E-10 1.81558E-09 3.29359E-09 4.1511E-09 3.50821E-09
4.12987 0.0720798 9.65672E-05 2.24E-10 5.3461E-10 7.59E-10 9.43324E-10 1.81369E-09 2.97278E-09 3.5502E-09 4.53272E-09
4.27558 0.0746229 9.99727E-05 2.12E-10 4.90837E-10 6.88E-10 9.5355E-10 1.59202E-09 2.82447E-09 3.6783E-09 5.29806E-09
4.42643 0.0772558 0.000103498 1.88E-10 4.27424E-10 7.08E-10 1 08051E-09 1.55221E-09 2.68768E-09 4.0382E-09 6.07329E-09
4.58261 0.0799816 0.000107148 1.69E-10 3.96366E-10 7.59E-10 1.00036E-09 1.5096E-09 2.8077E-09 4.0465 E-09 7.03336E-09
4.7443 0.0828037 0.000110927 1.70E-10 4.77577E-10 7.23E-10 9.42163E-10 1.44165E-09 2.70722E-09 3.7694E-09 7.05094 E-09
4.91171 0.0857255 0.000114838 1.79E-10 5.09182E-10 8.18E-10 9.06643E-10 1.41312E-09 2.58557E-09 3.3979E-09 6.43679E-09
5.08503 0.0887505 0.000118888 1.66E-10 4.76079E-10 7.79E-10 8.26906E-10 1.49502E-09 2.96347E-09 3.54E-09 6.07189E-09
5.26448 0.0918825 0.000123081 1.35E-10 4.18227E-10 6.17E-10 7.74724E-10 1.34151E-09 2.99181E-09 3.6721E-09 5.6315E-09
5.45027 0.0951252 0.000127421 1.26E-10 4.51708E-10 4.98E-10 6.4521E-10 1.15731E-09 3.03776E-09 3.4344E-09 5.2.9622E-09
5.64263 0.0984825 0.000131915 1.32E-10 4.42697E-10 4.30E-10 7.25282E-10 1.13949E-09 3.16623E-09 3.7006E-09 4.95973E-09
5.84178 0.1019583 0.000136567 1.37E-10 4.67422E-10 4.53E-10 8.5844E-10 1.2576E-09 3.11198E-09 4.348E-09 4.71529E-09
6.04798 0.1055572 0.000141383 1.30E-10 4.98364E-10 4.74E-10 8.31839E-1C 1.31557E-09 2.75602E-09 3.5579E-09 4.57672E-09
6.26147 0.1092833 0.000146368 1.20E-10 4.46405E-10 4.76E-10 8.46361E-10 1.42327E-09 2.69854E-09 3.154E-09 5.22048E-09
6.48251 0.1131411 0.00015153 1.29E-10 4.241E-10 4.79E-10 7.7979E-10 1.32852E-09 2.71432E-09 3.4504E-09 5.20992E-09
6.71138 0.1171357 0.000156874 1.25E-10 4.09707E-10 5.38E-10 6.46949E-10 1.22177E-09 3.15032E-09 3.3289E-09 4.99809E-09
6.94834 0.1212714 0.000162406 1.28E-10 3.88576E-10 5.88E-10 6.22712E-10 1.13763E-09 3.22724E-09 3.4649E-09 4.77114E-09
7.19369 0.1255536 0.000168133 1.38E-10 3.51665E-10 5.08E-10 7.45272E-10 1.08968E-09 2.9502E-09 3.4203E-09 4.50915E-09
7.44772 0.1299872 0.000174062 1.24E-10 3.30934E-10 4.71E-10 6.70459E-10 1.13448E-09 2.68309E-09 2.95E-09 4.69667E-09
7.71076 0.1345781 0.000180201 1.07E-10 3.08727E-10 5.42E-10 6.29909E-10 1.24494E-09 2.79227E-09 2.9856E-09 4.24005E-09
7.98311 0.1393316 0.000186555 1.03E-10 3.12077E-10 5.66E-10 6.56656E-10 1.38422E-09 2.70696E-09 2.4311E-09 3.69826E-09
8.26512 0.1442536 0.000193134 1.15E-10 2.72144E-10 4.71E-10 7.04121E-10 1.3432E-09 2.71967E-09 2.1674E-09 3.78759E-09
8.55712 0.1493499 0.000199945 1.09E-10 2.79289E-10 4.45E-10 7.12343E-10 1.21577E-09 2.58856E-09 2.5517E-09 3.75129E-09
8.85948 0.1546271 0.000206996 1.10E-10 2.69958E-10 4.06E-10 7.18194E-10 1.11488E-09 2.50329E-09 2.5851E-09 3.76395E-09
9.17256 0.1600914 0.000214296 1.14E-10 2.74164E-10 4.27E-10 7.07951E-10 9.27161E-10 2.68202E-09 2.5011E-09 4.00889E-09
9.49676 0.1657497 0.000221853 1.02E-10 2.58073E-10 4.09E-10 7.25061E-10 9.69959E-10 2.46697E-09 2.0624E-09 4.48736E-09


Angles Adjusted Data (Light Intensity in Micros Watts)
Angle, n Angle, 0 [radiants] q-vector Blank lppm 2ppm 5ppm lOppm 20ppm 40ppm 80ppm
9.83248 0.1716091 0.000229677 9.94E-11 2.70044E-10 3.76E-10 6.70133E-10 9.80759E-10 2.41336E-09 2.1649E-09 3.78012E-09
10.18012 0.1776766 0.000237776 9.00E-11 2.94011E-10 3.21E-10 6.93954E-10 1.14405E-09 2.31685E-09 2.1535E-09 3.22991E-09
10.54012 0.1839598 0.000246162 9.32E-11 2.79761E-10 3.32E-10 6.20484E-10 1.11027E-09 2.27086E-09 1.9488E-09 3.09208E-09
10.91292 0.1904664 0.000254842 8.54E-11 2.74477E-10 3.17E-10 5.54103E-10 8.88829E-10 2.12442E-09 1.7773E-09 2.69468E-09
11.29899 0.1972046 0.000263829 7.70E-11 2.61479E-10 2.96E-10 5.56573E-10 8.43115E-10 2.12042E-09 2.0577E-09 2.6037E-09
11.69882 0.2041829 0.000273133 8.26E-11 2.66511E-10 3.08E-10 6.39771E-10 7.81404E-10 2.03543E-09 2.1608E-09 2.84539E-09
12.11289 0.2114098 0.000282765 7.18E-11 2.5C602E-10 3.01E-10 5.63593E-10 8.35363E-10 1.82777E-09 1.8827E-09 2.57131E-09
12.54174 0.2188947 0.000292737 6.32E-11 2.48555E-10 2.93E-10 5.21892E-10 8.09451E-10 1.72901E-09 1.5663E-09 2.28516E-09
12.98589 0.2266465 0.00030306 5.72E-11 2.48741E-10 2.78E-10 4.41671E-10 7.53954E-10 1.48153E-09 1.4717E 09 2.12408E-09
13.44591 0.2346754 0.000313748 6.09E-11 2.21009E-10 2.51E-10 4.37566E-10 6.93037E-10 1.46791E-09 1.4476E-09 2.16666E-09
13.92239 0.2429915 0.000324812 5.43E-11 1.77764E-10 2.34E-10 4.15854E-10 6.69699E-10 1.53452E-09 1.5888E-09 2.10699E-09
14.41592 0.2516053 0.000336266 4.89E-11 1.76212E-10 2.09E-10 3.71846E-10 6.39937E-10 1.4279E-09 1.4678E-09 1.85178E-09
14.92714 0.2605277 0.000348125 5.25E-11 1.75779E-10 2.10E-10 3.44461E-10 6.42462E-10 1.26471E-09 1.1616E-09 2.10624E-09
15.45671 0.2697705 0.000360402 4.27E-11 1.72848E-10 1.79E-10 3.26038E-10 5.99456E-10 1.28203E-09 1.4042E-09 1.82886E-09
16.0053 0.2793452 0.000373111 4.21E-11 1.56903E-10 1.67E-10 2.73261E-10 4.59837E-10 1.20614E-09 1.2643E-09 1.69966E-09
16.57362 0.2892642 0.000386269 3.74E-11 1.284E-10 1.66E-10 2.71606E-10 3.89908E-10 1.01877E-09 1.0582E-09 1.63518E-09
17.16242 0.2995407 0.00039989 3.22E-11 1.23611E-10 1.36E-10 2.6102E-10 3.64076E-10 9.41621E-10 9.8671E-10 1.33238E-09
17.77247 0.3101881 0.000413993 3.33E-11 1.16423E-10 1.21E-10 2.54119E-10 3.60723E-10 1.06919E-09 1.047E-09 1.18024E-09
18.40457 0.3212203 0.000428592 3.22E-11 1.04707E-10 1.16E-10 2.1727E-10 3.78074E-10 9.20217E-10 8.7427E-10 1.44398E-09
19.05955 0.3326519 0.000443706 3.56E-11 9.05291E-11 1.17E-10 1.95072E-10 3.51888E-10 7.77187E-10 7.9857E-10 1.34267E-09
19.73829 0.3444981 0.000459354 2.95E-11 8.34181E-11 1.08E-10 1.81709E-10 3.1686E-10 6.90367E-10 8.2306E-10 1.14496E-09
20.44171 0.3567751 0.000475553 2.80E-11 7.91784E-11 1.02E-10 1.60496E-10 2.85013E-10 6.8906E-10 8.3391E-10 1.02703E-0S
21.17075 0.3694993 0.000492323 2.63E-11 6.93415E-11 9.56E-11 1.61312E-10 2.95325E-10 5.63353E-10 8.4452E-10 9.41743E-10
21.92642 0.3826882 0.000509685 2.72E-11 5.50617E-11 7.41E-11 1.22986E-10 2.37099E-10 5.22379E-10 6.3649E-10 8.70152E-10
22.70975 0.3963599 0.000527659 2.25E-11 5.03133E-11 5.87E-11 1.26156E-10 2.21662E-10 5.16606E-10 6.2615E-10 8.59306E-10
23.52185 0.4105337 0.000546267 2.32E-11 5.17093E-11 5.46E-11 1.03978E-10 2.2594E-10 4.49537E-10 6.1505E-10 8.00903E-10
24.36384 0.4252292 0.000565531 2.40E-11 4.41223E-11 4.41E-11 9.21473E-11 1.85196E-10 4.13316E-10 5.9641E-10 6.77451E-10
25.23694 0.4404677 0.000585474 2.48E-11 3.28496E-11 4.22E-11 7.93828E-11 1.72449E-10 3.74092E-10 5.3851E-10 6.87417E-10
26.14241 0.4562711 0.000606121 1.92E-11 3.64066E-11 3.64E-11 6.52591E-11 1.42199E-10 3.21725E-10 5.4293E-10 7.41688E-10
27.08155 0.4726622 0.000627495 1.66E-11 2.55845E-11 2.89E-11 6.20215E-11 1.34896E-10 2.70706E-10 4.2639E-10 6.25141E-10
28.05578 0.4896657 0.000649624 2.05E-11 2.1142E-11 2.46E-11 4.8519E-11 1.03273E-10 2.57269E-10 3.394E-10 5.37883E-10
29.06655 0.507307 0.000672533 1.77E-11 1.96923E-11 1.97E-11 4.09015E-11 8.33198E-11 2.17645E-10 3.6611E-10 4.54482E-10


Angles Adjusted Data (Light Intensity in Micros Watts)
Angle, 0 n Angle, [radiants] q-vector Blank lppm 2ppm 5ppm lOppm 20ppm 40ppm 80ppm
30.1154 0.5256129 0.00069625 1.46E-11 1.82279E-11 1.09E-11 3.28307E-11 7.29882E-11 1.9346E-10 3.2854E-10 4.12501E-10
31.20397 0.544612 0.000720803 1.13E-11 1.29891E-11 9.22E-12 2.80675E-11 7.33026E-11 1.60003E-10 2.844E-10 3.48483E-10
32.33398 0.5643344 0.000746222 1.17E-11 9.32213E-12 9.32E-12 2.48885E-11 5.99128E-11 1.37745E-10 2.8563E-10 3.28433E-10
33.50725 0.5848118 0.000772537 8.03E-12 7.61525E-12 7.62E-12 1.96652E-11 4.77818E-11 9.99985E-11 2.1246E-10 2.88782E-10
34.72573 0.6060783 0.000799781 8.29E-12 7.71217E-12 3.57E-12 1.60017E-11 3.67255E-11 8.23179E-11 2.0666E-10 2.35674E-10
35.99145 0.6281693 0.000827985 8.55E-12 3.52617E-12 3.53E-12 1.20779E-11 3.34572E-11 7.19397E-11 1.7884E-10 2.21594E-10
37.30662 0.6511234 0.000857184 4.41E-12 6.14696E-12 1.74E-12 1.05568E-11 3.26061E-11 6.78847E-11 1.6049E-10 2.0018E-10
38.67356 0.674981 0.000887413 4.55E-12 6.25217E-12 1.71E-12 1.07988E-11 2.44387E-11 6.53585E-11 1.381E-10 1.83571E-10
40.09476 0.6997856 0.000918707 4.69E-12 6.35414E-12 1.67E-12 1.10403E-11 2.04125E-11 4.85294E-11 1.3757E-10 1.46938E-10
41.5729 0.725584 0.000951105 6.64E-100 4.82816E-12 4.83E-12 9.65631E-12 2.41408E-11 4.82815E-11 1.207E-10 1.25532E-10
43.11082 0.7524258 0.000984646 6.83E-100 4.97251E-12 4.97E-12 9.94501E-12 1.98901E-11 4.47526E-11 1.1437E-10 1.14368E-10
44.71162 0.780365 0.001019369 7.04E-100 5.11896E-12 5.12E-12 1.02379E-11 2.04759E-11 4.09517E-11 1.0238E-10 1.07498E-10
46.37863 0.8094598 0.001055317 7.24E-100 5.26721E-12 7.24E-100 5.26721E-12 1.58016E-11 4.21377E-11 8.9542E-11 9.48096E-11
48.11544 0.8397728 0.001092533 7.44E-100 7.4449E-100 7.44E-100 5.41693E-12 1.62508E-11 4.33354E-11 S.6671E-11 8.12538E-11
49.92598 0.8713727 0.001131061 7.65E-100 7.6521E-100 7.65E-100 5.5677E-12 1.11354E-11 2.78385E-11 8.3515E-11 7.23799E-11
51.81451 0.9043338 0.001170948 7.86E-100 7.8601E-100 7.86E-100 7.8601E-100 1.14381E-11 2.28762E-11 6.8628E-11 6.86283E-11
53.78571 0.9387377 0.001212241 8.07E-100 8.0681E-100 8.07E-100 8.0681E-100 5.87038E-12 2.34816E-11 5.2833E-11 5.28334E-11
55.84472 0.9746742 0.001254991 8.28E-100 8.2752E-100 8.28E-100 8.2752E-100 6.02104E-12 1.8U631E-11 4.8168E-11 4.81683E-11
57.99721 1.0122423 0.001299248 8.48E-100 8.4802E-100 8.48E-100 8.4802E-100 6.17022E-12 1.23404E-11 4.3191E-11 3.08511E-11
60.2495 1.0515521 0.001345066 8.68E-100 8.6819E-100 8.68E-100 8.6819E-100 8.6819E-100 6.31699E-12 3.1585E-11 3.15849E-11
62.60861 1.0927264 0.0013925 8.88E-100 8.8788E-100 8.88E-100 8.8788E-100 8.8788E-100 6.46026E-12 1.9381E-11 2.58411E-11
65.08246 1.1359032 0.001441606 9.07E-100 9.0692E-100 9.07E-100 9.0692E-100 9.0692E-100 9.0692E-100 1.3197E-11 1.97961E-11
67.67999 1.1812387 0.001492444 9.25E-100 9.2508E-100 9.25E-100 9.2508E-100 9.2508E-100 9.2508E-100 1.3462E-11 2.01926E-11
70.41142 1.2289111 0.001545075 9.42E-100 9.4212E-100 9.42E-100 9.4212E-100 9.4212E-100 9.4212E-100 1.371E-11 2.05647E-11
73.28846 1.2791249 0.001599562 9.58E-100 9.5776E-100 9.58E-100 9.5776E-100 9.5776E-100 9.5776E-100 1.3937E-11 1.39374E-11
76.32474 1.332118 0.00165597 9.72E-100 9.7165E-100 9.72E-100 9.7165E-100 9.7165E-100 9.7165E-100 1.4139E-11 1.41395E-11
79.53623 1.3881691 0.001714368 9.83E-100 9.8337E-100 9.83E-100 9.8337E-100 9.8337E-100 9.8337E-100 7.155E-12 1.431E-11
82.94193 1.4476098 0.001774825 9.92E-100 9.9242E-100 9.92E-100 9.9242E-100 9.9242E-100 9.9242E-100 7.2209E-12 1.44417E-11
86.56472 1.5108394 0.001837414 9.98E-100 9.982E-100 9.98E-100 9.982E-100 9.982E-100 9.982E-100 9.982E-100 7.26294E-12
90.43268 1.578348 0.001902211 1.00E-99 9.9997E-100 1.00E-99 9.9997E-100 9.9997E-100 9.9997E-100 IE-99 7.2758E-12
94.58093 1.6507486 0.001969292 9.97E-100 9.9681E-100 9.97E-100 9.9681E-100 9.9681E-100 9.9681E-100 9.968E-100 7.25277E-12
99.05445 1.7288263 0.002038739 9.88E-100 9.8754E-100 9.88E-100 9.8754E-100 9.8754E-100 9.8754E-100 9.875E-100 9.8754E-100


Angles Adjusted Data (Light Intensity in Micros Watts)
Angle, n Angle, 0 [radiants] q-vector Blank lppm 2ppm 5ppm lOppm 20ppm 40ppm 80ppm
103.9126 1.8136172 0.002110635 9.71E-100 9.7066E-100 9.71E-100 9.7066E-100 9.7066E-100 9.7066E-100 9.707E-100 7.06256E-12
109.2368 1.9065411 0.002185066 9.44E-100 9.4417E-100 9.44E-100 9.4417E-100 9.4417E-100 9.4417E-100 9.442E-100 9.4417E-100
115.1439 2.0096403 0.002262122 9.05E-100 9.0524E-100 9.05E-100 9.0524E-100 9.0524E-100 9.0524E-100 9.052E-100 6.58656E-12
121.814 2.1260547 0.002341896 8.50E-100 8.4976E-100 8.50E-100 8.4976E-100 8.4976E-100 8.4976E-100 8.498E-100 8.4976E-100
129.5516 2.2611016 0.002424483 7.71E-100 7.7105E-100 7.71E-100 7.7105E-100 7.7105E-100 7.7105E-100 7.711E-100 7.7105E-100
138.9598 2.4253066 0.002509982 6.57E-100 6.5659E-100 6.57E-100 6.5659E-100 6.5659E-100 6.5659E-100 4.7773E-12 4.77734E-12
151.6614 2.6469911 0.002598496 4.75E-100 4.7468E-100 4.75E-100 4.7468E-100 3.45378E-12 1.03613E-11 1.3815E-11 2.07227E-11


APPENDIX B AutoCAD Drawings of SLS Column & Holder
78


COLUMN CLAMP MATERIAL: ALUMINUM AND/OR SATIN LESS STEEL


JE-
I A A
COLUMN CAP (QUANTITY x2) MATERIAL: PVC, ACRYLIC, OR OTHER MATERIALS
0 1 2
SCALE (INCHES)
TITLE: CONCEPTUAL SKETCH
DATE: 10/03/08 SCALE: AS NOTED


1
SCALE (INCHES)
MATERIAL: ALUMINUM AND/OR STAINLESS STEEL
TITLE: COLUMN CLAMP
DATE: 10/03/08 SCALE: AS NOTED




0,070


threaded pressure
TRANSDUCER PORTS (X3, 1/4 20 TPI)
MATERIAL: OPTICAL GRADE GLASS
TITLE:
SLS COLUMN
DATE:
9/19/08
SCALE:
AS NOTED


I
3


4
T
3


2
1
1
REVISION HISTORY
ZONE REV DESCRIPTION DATE APPROVED
1 HRG3
S-
DRAWN HRG3 10/7/2008 Community College of Denver
CHECKED
TITLE
QA
MFC
APPROVED HRG3
SIZE DWG NO REV C SLS Assembly i

1 1 SHEET 1 OF 4
2 i r


Full Text

PAGE 1

IN SITU MEASUREMENTS OF AGGREGATE STRUCTURES FRACTAL DIMENSIONS INSIDE INDEX MATCHED GRANULAR MEDIA by Orion Taiyo Cannon B.S., Colorado School of Mines, 2005 A thesis submitted to the University of Colorado Denver in partial fulfillment of the requirements for the degree of Master of Science Civil Engineering 2009

PAGE 2

This thesis for the Master of Engineering Degree by Orion Taiyo Cannon Has been approved by Dr. David Mays, Assistant Professor Dr. NienYin Chang, Dean and Professor Dr. Arunprakash Karunanithi Assistant Research Professor Date

PAGE 3

Cannon, Orion Taiyo (M.S. Civil Engineering-Water Resources Specialty) In Situ Measurements of Aggregate Structures Fractal Dimensions inside Index Matched Granular Media Thesis directed by Assistant Professor Dr. David C Mays ABSTRACT Clean water is a valuable resource that is crucial to a healthy society. Water treatment, therefore, is an important civil engineering task that has great social significance. One of the most simple, yet effective, components within a water treatment process is a granular media filter. A nearly perfectly optically transparent granular filter was prepared using a polymer material called Nafion inside a solution of deionized water and isopropyl alcohol per procedures developed by Adam Kanold, a former graduate student at UC Denver. Test tube samples were prepared to which 0.1 and 1.0 IJm polystyrene micro spheres of varying concentrations were added. The concentration of polystyrene micro spheres ranged from 0 to 200 ppm. To half of the samples Nation was added to effectively simulate conditions similar to a granular sand bed. The other half of the samples were left as simple in-suspension samples To each of these two sets of samples calcium nitrate was added to half to induce aggregation/flocculation of the polystyrene micro spheres in suspension. Measurements of fractal dimensions of aggregated/flocculated polystyrene micro spheres inside the samples were made using a static light scattering apparatus The fractal dimensions of aggrega t ed/flocculated polystyrene micro spheres inside the optically transparent granular filter media (Nation) were found to be similar to those aggregated/flocculated micro spheres in suspension The similarity of fractal dimensions of aggregated/flocculated micro spheres, both inside granular filter media and in simple suspension, were observed for nearly all samples

PAGE 4

These results suggest it is possible to accurately measure the fractal dimensions of aggregated structures in situ inside an optically transparent granular filter. Using optically transparent granular media together with a light scattering apparatus will make it possible to learn how the fractal dimension of aggregated/flocculated structures made of suspended solids affects the clogging of granular media filters over time. This abstract accurately represents the contents of the candidate's thesis. Signed Dr. David Mays

PAGE 5

ACKNOWLEDGEMENT Thank you to everyone who assisted in so many ways to keep this research project going forward. A partial list showing those who gave a significant amount of their time is shown below This project would not have taken form without their help Thank you for your time and energy you put into this project! Helen Frey Benjamin Gilbert Rick Glesner Tim Lei David Mays Randy Ray Larry Scherrer Randy Tagg Sam Wheeler UC Denver Lawrence Berkley National Laboratory Community College of Denver Program Chair CAD UC Denver Department of Electrical Engineering UC Denver Department of Civil Engineering UC Denver Machine Shop Colorado Advanced Photonics Technology Laboratory UC Denver Department of Physics l,JC Den v er

PAGE 6

TABLE OF CONTENTS Figures ....... .. .. .. ........ ... ........................................... .. .... .... xiii Tables .......... .......... ......................................... ........................ ..... x Chapter 1. Introduction .................. ...................... .. .. .............. ... ..... 1 1.1 Background .............. .. .. ............ .. .. ................................ .. l 1.2 Motivation and Purpose ofStudy .. .. .. .. ................ ..... .. .. ...... ...... 2 2 Granular Media and Other Types of Filters .... ............................. .... 5 2.1 Common Applications of Granular Media Filters ........ .. ................. 5 2.2 Service Cycles of Granular Filter Media Filters ........... .. .. .. ....... ...... 6 2.3 Other Types of Filters and Their Applications ...... ........ ...... .. .......... 7 3. Fractal Dimension and Static Light Scattering ........ .. ..................... 9 3 1 Background of Light Scattering ................. .. .. ............. .. .. ........... 9 3.2 Fractal Dimension ....... ... ........................ ............... .. ......... ... 1 0 3.3 Using Light Scattering to Measuring the Fractal Dimensions of Fractal Aggregate Structures ................ ....................................... .. .. 14 3.4 Light Scattering Procedures .. .. .. ........... ..................... . .... 16 3.4.1 Sample Preparation ......................................... .............. ....... 16 3.4.2 Measurements ................. .. ..................................... .. .......... 16 3.4.3 Interpretation of Data .... .. .................................. .. ............... .. 17 4. Optical Refractive Index Matching .. ............ .............................. 22 4.1 Index of Refraction ......................... .. .. ............................. ..... 22 4.2 Optical Index Matching .. .. ............. .. ................... ................. ... 24 4.3 Refraction ....................................... ............ ................. ...... 25 4 4 Snell's Law ....... .. .................... .. .. .. ............................ .... 31 4.5 Works by Adam Kanold ..................... .................. .. ................ 33 5 Experimental Methods ... ......... .. ............................. ..... .......... 34

PAGE 7

5.1 Experiments with Compositions ofDI Water and IPA ...................... 34 5 2 Preparation of Index Matched Granular Filter Media ............ ............ 34 5 3 Preparation of Colloid Suspension Using Micro spheres ......... ...... ... 35 5 3 Preparation of Colloid Suspension Using Micro Sphres .... ...... ... .. .35 5.3.l Sizes and Concentrations ............ ...... .. .. .. .. .. ....................... 35 5.3.2 Stable and Aggregated Micro Spheres ......................................... .36 5.4 Static Light Scattering ......... .. .. .. .. .. .. ..... .............................. 39 5.4.l Static Light Scattering Apparatus ............. .. ............................. .. 39 5.4.2 Scanning Samples Using the SLS Apparatus ........... ..................... .41 5.5 Data Reduction ....................................... .. .. ...... ............... 42 5.6 Interpretation of Data ......... .............................. .. ...... .......... .45 5.6.l Scaling Method .................. .. ....... ...................................... .45 5.6 2 Model Fitting Method ................... .. .. ................... ................ .47 6. Experimental Results ............... ................. ..................... ...... .48 6.1 Qualitative Observations .................................. ..... ................ .48 6.2 Quantitative Results .. ..................... .. .. ...................... ... .... .49 6.2.1 Scaling Approach ........... .. ..... ...... ................. ........................ 50 6.2.2 Form Fitting Approach ...... .. .................................... ........... 55 7 Conclusion ... ..... ................................................................ 61 7.1 Application of Light Scattering in Civil Engineering ................ ..... .... 61 7.2 Problems Encounered ....................................................... .... 61 7.3 Future Work ................... ................ .. ...................... ............ 62 Appendix A Detailed Static Light Scattering Data ........ .. ............ ................... 65 B AutoCAD Drawings of SLS Column ....................... ............... .. 78 Bibliography ................................. ......................... .............. .. ... 85 VII

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LIST OF FIGURE S FIGURE 2.1 Schematic Diagram of How Granular Media Filters Work ................... 6 2.2 Picture of a Hand Operated Backpacking Pump .. .. ...... .. .. .. ........ 8 3.1 Illustration of a Colloidal Fractal Aggregate .. .. .. .. ............ .... .. 11 3.2 lllustration of Various Colloidal Fractal Aggregates with Varying Fractal Dimensions .... . .......... ............ .. .. .. .. .. .. ...... .. .. .. .. .. 13 3.3 Scatter Plot of Scattered Light Intensity vs. q-vector. .. . ...... ..... . 15 3.4 Scatter Plot of I vs. q-vector (Stable Aggregated Micro Spheres) ...... 19 4 1 Illu s tration of Light Refraction .. ............... ............ .. .. . .. ... 25 4.2 Conceptuallllustration of Light Bending ................................ .. ... 27 4.3 Relationship of Wavelength and Refractive Index ..................... ...... .29 4.4 Outward Movement of Concentric Waves .. .. .. ......... ............. 30 4.5 lllustration of Snell's Law .................. .................. .. ...... .. ...... .32 4.6 Nafion inside Di f ferent Fluids ............... ...... .. .. ............ ...... 34 5 1 Schematic Diagram Showing the P a th of Laser Beam ........ .. ...... .40 5.2 Photograph of a Sample Test Tube and the SLS Light Detector. ........ .. .42 5.3 Intensity vs. q-vector Scatter Plot Made using a 2 ppm Sample .. .. ...... .44 5.4 Ideal Scatter Plo t. .. . .. .. .. . ....................... ........... .... .. . .44 6.1 Theoretical Scatter Plot of Stable Micro Spheres in Suspension ........ .. .49 6.2 Light Intensity vs. q-vector Plot 1 !..1m, Aggregated Micro Spheres ....... 51 6 3 ZoomIn of! vs. q, 1 !..1m, Aggregated Micro Spheres ........ .. ............. 52 6.4 Inten s ity vs q-vector Plot I !..1m, Stable Micro Spheres .. ..... ..... ..... 53 6.5 Zoom-In of! vs. q, 1 !..1m, Stable Micro Sph e res ....... ................ .... 54 6 6 Non-Linear L e ast Squares Fit Plot, 1 ppm Stable Micro Spheres .......... 56 6 7 Non-Linear Least Squares Fit Plot 2 ppm Stable Micro Spheres ... ... 57 VIII

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6.8 Non-Linear Least Squares Fit Plot 1 ppm, Aggregated Micro Spheres ................................ ....................... 58 6.9 Non-Linear Least Squares Fit Plot, 2 ppm, Aggregated Micro Spheres ... .. ........... .......................... .. .. ....... 59

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LIST OF TABLES TABLE 4 1 Common Transparent Materials and Their Refractive Indices .............. 23 4.2 List of Common Solvents, Their Densities, and Refractive Indices ... .... 24 5.1 Compositions Samples ........ ... .. .. ... .. .. .. .. ............................ .38 5 2 List of Concentrations Prepa r ed ........... ... .. .. ............. ... ....... .. 39 6.1 Summary of Fracta l Dimensions Measured Using the Form Fitting Approach .. .. .. .. .. ... .. .. .. ....... ...... ........ ...................... ..... 55 6.2 Summary of Fractal Dimen sions and Primary Particle Radii Calculated Using the Non-Liner Least Squares Fit Approach ...... .. .. ..... ......... 60 x

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Granular media filters, such as sand filters are used to remove suspended solids for the purpose of water treatment. Granular media filters are used in water treatment plants and in fac ilities with swimming pools Clogging of granular media filters is affected by the amount of suspended solids it removes from water as well as the morphology of these suspended solids. Small suspended particles corne together to form larger aggregated s tructures when chemically induced with alum or salts Fractal aggregate structures are formed when uniformly sized particles corne to g e t h e r to form lar g er structures Static light scattering is an analytical method that is used in the areas of polymer science and physics to study small-scale particles in suspension, such as proteins and polymers. Sorensen (2001) Bushell et al. (2002), and Teixeira (1988) have shown that light scattering can be used to quantify the fractal dimension, a g eometric scaling factor of aggregated fractal structures, using static light scattering. By m a king an op t ically transparent granular filter by following procedures developed by Kanold (2008) the fractal dimension of aggregated structures were measured inside th e granular filter media via light scattering Measurements of fractal dimensions were made on aggregated structures in suspension for comparison purpos e s as well. The measured values of fractal dimensions of aggregated structures in suspen s ion were found to be very close to those in s ide granular filter media The text has been written in a way that first introduces the reader to several concepts tha t were import a nt in the research project. These concepts

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include: (1) granular filter media, (2) light scattering, and (3) optical index matching. Experimental procedures and experimental results follow those sections. Granular media filters are a vital component in water treatment systems. They are designed to filter out suspended solids and other objects from water. The clogging of granular media filters depends not only on the quantity of suspended solids it removes, but the morphology of those structures as well. has been shown that clay, which i s composed of particles which have a sheet-like configuration, has much lower permeability than does silt. The shape of the particles has an effect on how water is able to travel through the pore spaces between individual particles and hence affect the permeability (Mays and Hunt 2007). a similar way, it will be beneficial to study how the fractal dimension of aggregated structures affect clogging of gr anular media filters. This research project is a pilot project to accomplishing that goal, and it focuses on in situ measurement of fractal aggregates inside a transparent granular filter. The motivation of the project is to learn if i t is possible to measure the fractal dimension of aggregated structures inside granular filter media. Past projects have measured the fractal dimensions of aggregate structures in suspension, and have found values to be between 1.8 and 2.2 (Bushell et al. 2002). is of interest to find out how the values of fractal dimensions of aggregate structures inside a granular filter media compare to values measured previously using classical methods. A previous study researched the correlation between aggregate structure morphology and clo gg ing of granular filter media. this study deposits that 2

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caused clogging and were trapped inside granular filter media were collected and used it to prepare suspended solid samples with. The samples were analyzed and the results showed that the fractal dimension of aggregate structures had no correlation with clogging (Veerapaneni and Wiesner 1997). However, there are good reasons to believe that the aggregate structure deposits were significantly disturbed during sample preparation, and the fractal dimension of the deposits may not have been preserved. If so, the fractal dimensions of the prepared samples that were measured will not have been representative of what existed in situ. That is another reason for the motivation of measuring the fractal dimension of aggregate structure deposits in situ 3

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Granular media filters are used in both drink i ng w ater and waste water treatment. Granular media filters are essentially containers with an inlet and an outlet that is filled with variou s grain sizes of ag g regates. The sand and gravel aggregates are held in place inside a container usually by a screen that allows for water to pass through but not the sand and gravel. Raw water from wells streams and lakes is treated in several steps before being distributed for the purpose of municipal use. Some of these treatment steps include hardness treatment, removal of iron and manganese and disinfection. One of the final steps in water treatment is a filtration process which removes suspended solids in water by passing it through a porous granular filter media. Suspended solids that naturally exist in water, such as small debris and vegetation, become trapped between grains of sand and gravel as water passes through a porous granular media filter. Water that goes through these treatment processes is clean and safe for consumption Granular media filers are also used in places such as recreational centers where there a re swimming pools. Water in pools is continual1y cycled through porous granular media filters to remove solids. 4

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2.2 Service Cycles of Granular Filter Media Filters There are two stages that granular media filters cycle through. The first stage is the actual removal of suspended solids from water, or the production stage. Water is actively being treated when porous granular media filters are in this stage. The amount of suspended solids that accumulate within a granular media filter is nearly proportional to the duration in which this granular media filter remains in operation the more water that is processed, the more solids accumulate. Unless the driving head is continually increased, the rate at which water can pass through a granular media filter decreases as suspended solids accumulate and pore spaces become clogged. As pore spaces within granular media filters become clogged the paths which water travels through become increasingly restricted. To address this problem granular media filters need to be backwashed periodically to remove suspended solids, clear out the pore spaces, and increase the rate of flow. The process of backwashing is the second stage in a regular cycle of filter operation Clean, treated water is pumped through the filter body in a direction that is opposite to regular flow Clean, treated water is pumped vigorously to fluidize the granular media and solids trapped inside the filter body.

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Illustration of how granular media filters works Solids and other material trapped inside a filter body become mobilized and carried away with the clean water vigorously flowing in the backwards direction during backwashing This water used for backwashing which contains fluidized solids is either routed to directly to a waste water treatment plant or recycled and reused for conservation purposes. Backwashing effectively removes most trapped solids from within the filter body, and restores the filter to a near original operational state of working The frequencies at which filters used in water treatments plants are backwashed vary with many factors. Some of these include the type of filter used, age of the filer extent of clogging, grain size of sand used inside the filter, and the morphology of solids deposited inside the filter (Weisner 1999), (Mays 2009) 6

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Clogging of granular media filters is affected not only by the quantity of suspended solids trapped inside the filter body, but also by their morphology as well. The fractal dimension of aggregate stmctures has been shown to affects how granular media filters become clogged (Weisner 1999), (Mays 2009). 2.3 Types In addition to porous granular media filters, there exists a wide variety of filters for many applications. One of these filters currently under intense research is membrane filters which are used for many purposes including separating salts dissolved in sea water from pure water. This process of separating salts from sea water using membrane filters is called desalination by reverse osmosis Relatively inexpensive backpacking filers, such as one shown in Figure 2.2 are designed to treat water from lakes, ponds, streams and creeks These filters filter out both pathogens, such as bacteria, viruses, and protozoa, as well as suspended solids at once. These filters clog after certain use, and will stop working at that time. Once these filters clog, the inner filter cartridges must be replaced. 7

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A hand operated backpacking and camping water filter. (Backcountrygear.com)

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3. Fractal Dimensions and Static Light Scattering 3.1 Background of Light Scattering Light interacts with matter in several ways there is reflection, refraction, and absorption. Beams of light can reflect off of a surface of an object, go through an object such as glass, or simply become absorbed and change to heat. There are two broad categories of light scattering static and dynamic light scattering both utilize the ways in which light interacts with matter Both methods measure the scattered light from small suspended particles within a sample cell to determine certain physical characteristics of those particles. Light scattering is used in the fields of physical chemistry and polymer science. In static light scattering a single light detector, which can take measurements about a sample at different angles, is used to make these measurements. In comparison, dynamic light scattering machines have multiple light detectors that can detect very rapid changes in scattered light at different angles simultaneously Static light scattering machines are used to obtain the root mean square radius (or radius of gyration) and the average molecular weight. In addition to the above mentioned physical parameters, Sorensen (2001) and Bushell et al. (2002) have successfully used static light scattering to measure the fracta l dimension, a geometric scaling factor used to characterize the relative mass-length scaling of aggregate structures 9

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Fractal aggregates are intricate structures composed of individual suspended solid particles that have come into contact with one another through one of two processes. These two processes are called diffusion limited aggregation (DLA) and rate limited aggregation (RLA) respectively, and discussed later. One process by which drinking water is treated prior to distribution is flocculation and filtration. Small suspended solids in water are made to stick to one another by inducing a flocculating agent, such as alum. The purpose of using alum is to make suspended solids more chemically attractive toward one another, and ultimately causing them to form larger structures. These larger structures are either settled or filtered and separated from clean water. Aggregate structures, such as one shown in Figure 3.1, form through continued collision of suspended particles with one another and sticking together. An aggregate structure will continue to grow as long as the collision processes of suspended solids continue. Fractal aggregates have what is called a fractal dimension, a relative measurement of a structure's radius of gyration in proportion to the number of particles comprising the structure. The fractal dimension of an aggregate structure can vary anywhere from a one dimensional string (fractal dimension = 1) to a solidly compacted structure without gaps inside (fractal dimension = 3). The fractal dimension of an aggregate structure can never be less than one or greater than 3 Most aggregate structures composed of suspended solid particles will have fractal dimensions between 1.8 and 2.2. According to Bushell et al. (2002) equation 3.1 describes the relationship between the radius of gyration of aggregate structures, the number of particles, and the fractal dimension. 10

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(Eq.3.1) = Number of colloidal particles in an aggregate structure = Structure prefactor, a constant =Radius of gyration, the root means-square distance ofthe colloidal particles from the center of mass = Colloidal particle radius =Fractal dimension An illustration of an aggregate structure composed of uniformly sized spherical colloids. (Astronomy and Astrophysics website)

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The first process whereby particles come into contact is when all collisions lead to aggregation, which is called diffusion limited aggregation (DLA) When aggre g ates or clusters join together th i s process of aggregation is called Diffusion Limi t ed C luster Aggregation (DLCA). The s econd process in which individual suspended solid parti c les stick together and form aggregate structures is when collisions mayor may not lead to aggregation, which is called rate limited aggregation (RLA). Clusters can also join together through a process called Rate Limited Cluster Aggregation (RLCA). What makes the RLCA process different from the prev i ou s aggregation is the charge and affinity which individual particles carry that controls the probability with which they stick to one another. As discussed earlier, fracta l d i mensions can only be between 1 and 3 In general, the more int ricate and strung out a structure is, the lower its fractal dimension will be. Converse ly, a densely packed structure with little voids will have a greater fractal dimension Some examples of fractal aggregates with various fractal dimensions are shown on Figure 3.2.

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a o_ a a -t_ 2. 8 1.0 2.06 D f = 1.8 1.2 = 1.0 = 3. 84 ". lOA 29. 1 iJAggreg a te structures with 1 16, 125, 1000, and 3375 particle s (sorted by rows from top to bottom), and fractal dimensions of 1.2, 1.8, 2.4, and 2.8 (sorted by columns from right to l eft) (Astronomy Astrophysics website) 13

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Unlike in the process of imaging which disturbs fractal aggregates during sample preparation light scattering can be us e d to take measurements on fractal aggregates that are in suspension without disturbing samples. The theory behind light scattering is that multiple light waves in phase with one another will experience constructive interference and vice versa. Depending on how light passe s through fractal objects and the size of t he primary particles that make up the fractal structures, light waves will either (1) add constructively, (2) add des t ructively, or (3) experience a mixture of both which cancels out to approximately zero net interference effect. Sorensen (2001) derived three theoretical scenarios in which how scattered light will behave. The scenarios are broken up into three by the primary particle size and the radius of gyration as they relate to the scattering wave vector, q. The three theoretical scenarios of light scattering and their intensities are as foll ows : ex ex ex I( q) = con st ant I(q) q D I(q) _q-4 Intensity of scattered light from a sample forq
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= Refractive index offluid used in sample R=Radius of gyration a=radius of primary part i cle Dm= Mass fractal dimension Above equations are gra phically represented in a log of light intensity vs. log of q-vecto r plot as shown in Figure 3.3 q 3.3 Intensity vs q-vector plot showing three zones and their theoretical scattering patterns on a log-log scale. Dm=mass fractal dimension R = average radius of gyration of aggregate structures a =primary suspended particles size 15

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Samples containing suspended solid particles are prepared by either dissolving or placing in suspension within a so l ute. is extremely important to keep all samples clean because any foreign particles, such as dust, will interact with light and give false readings. Test tubes used to hold samples are cleaned with care using soap and water followed by rinsing using a solvent, such as acetone. is also important to keep the solute used for sample preparation as clean as possible Usually a solvent will be filtered multiple times through a filter paper or similar w i th openings equal to or less than 0.2 /lm in s i ze. This ensures there are no particles in suspension that will affect the light scattering measurements. Samples prepared for this rese a rch project were given a minimum of 24 hours prior to being placed for measurement. This ensured particles in suspension had time to come in contact with one another and form aggregate structures There are various types of static light scattering devices, and each has slightly different measurement procedures. The fundamental concept of sample measurements is the same however scattered light from samples are measured as accurately as possible at either one or multiple angles. First, samples are placed in a sample holder. If necessary, samples are aligned within the sample holder. 16

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A carefully aligned beam of light is passed through a test tube containing the sample solution/mixture. is common to use a laser beam because of its high quality of focus The intensity of the scattered light from the sample is measured at various angles For our project, a measurement was taken every 1110 ofa degree from approximately 0 to 155 degrees A computer with data acquisition software is typically used to record and store collected light intensity data Stored data is easily converted to spreadsheet or other desired format for analysis. 3.4.3 Collected data consists of intensity of scattered light in j.lW as a function of angle, 8. In other words the brightness of scattered light has been recorded from some starting angle, to the ending angle, There are several steps that are required in order to calculate and obtain meaningful results from collected data. Fractal Dimension (Scaling Approach): (1) Samples with multiple dilutions of suspended solids were prepared. A blank solution with no suspended solids was also prepared. The purpose of preparing mUltiple dilutions was to measure each sample and see how the concentration of suspended soli d s affected measurements The possibility of multiple scattering was a source of concern and it was of interest to find out if multiple scattering became a factor at a certain concentration of suspended solids. could be concluded that multiple scattering was a factor if in fact there was mUltiple scattering observed for samples with a certain concentration or greater suspended solids but not for other samples. What are 17

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called Mie humps as shown in Figure X.x can be observed when multiple scatt e ring is not a significant factor. Mie humps are characteristic signs that are observable on a scattering plot and are caused by light refracting off of uniformly sized spherical particles in suspension (2) The intensity of scattered l i ght at angles from to are measured u s ing a static light scattering apparatus. ( 3 ) The mea s ured intensity from the blank sample is subtracted from the measured intensity of the dilute sample at each angle at which measurements were made (4) The adjusted data is normalized to account for the differences in scattering volume at each angle by dividing the adjust e d intensity by the sine of the scattering angle (5) Convert values of S to q vec t or values for each data point using the equation: = 4;rXsin(8 / 2) (6) Plot a log-log plot of q vs. adjusted normalized intensity of scattered light. (7) The slope of the linear region a s shown on Figure 3.4 is the calculated fractal dimension of aggregate st r uctures in suspension

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a Theor e tical intensity vs. q-v ector plo ts. Stable colloids in suspension (top) and aggregated structures in suspension (bottom). From Sorensen (2001) Fractal Dimension (Form Fitting Approach): (1) Collect data of scattered light intensity vs. angle 8, in the same way as described in steps (1)-(5) above. (2) Simultaneously fit the collected data p o ints to a series of equations using a non-linear least squares fit. The equations to which the data points are fit are: a (Sorensen 2001) = Scattering vector [nm-']

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B=Scattering angle [degr e es] =Wavelength of incident beam [nm] = (Teixeira 1988) l(q)= Intensity of scattered light [mW, or =Number of scattering particles [unit less] = Scattering volume of the sample [cm3 ] = Form Factor of primary particle [cm2 ] factor of fractal aggregates [unit less] c. = (Teixeira 1988) = Volum e o f uniform s ph e r es/ primary particles [cm3 ] = Density of pri m ary particles 1988) = Fractal dimension [unit less] =Gamma function of the argument .; = Upper lim i t of fractal correlations [nm] e. = I).;z 2 (Teixeira 1988) = Radius of gyration of aggregate structure [nm] 20 (Tei x e i ra

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(3) This method yields the primary particle radius, the radius of gyration of the fractal aggregate structure and the fractal dimension simultaneously. Through a process of iteration, a relatively simple computer program will simultaneously and repeatedly fit three variables into the above shown equations until the sum of difference in calculated values compared to empirical values are minimized The three values found through this process oftrial and error are the primary particle radius the radius of gyration ofthe aggregate structure and the fractal dimension of the aggregate structure. The average molecular weight and the radius of gyration can also be calculated using static light scattering The procedures include preparation and scanning of multiple samples with various concentrations followed by a process of linear interpolation. Details on these procedures can be found in several texts, including Huglin (1972)

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The index of refraction is a measure used to characterize the optical property of transparent materials quantitatively describes how fast light travels through a given material compared to the vel o city at which light travels through a vacuum. Materials, such as air, water, and glass each have different indices of refraction, indicating light travels at different velocities through each. The index of refraction, of a given material is the ratio of two velocities the velocity at which light travels through a v a cuum is compared to the velocity at which light travels through a given material, and is shown in Equation X.I. (Eq.4 .1) m a t e rial =Index of refraction of material, a = Speed of light in a vacuum =Speed oflight through material a For example, the index of refraction of glass is the velocity at which light travels through a vacuum divided by the velocity at which light travels through common glass. Given that light travels through a vacuum at approximately 3.00x108 or 300 million meters per second and the index of refraction of crown glass is known to be 1 .52 (Huglin 1972), the velocity at which light travels 22

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through glass is calculated to be approximately 1.97xl 08 or roughly of the velocity in a vacuum. Table 4 1 shows an abbreviated list of common transparent materials and their indices of refraction Common transparent materials and their indices of refraction (www.en.wikipedia.orglwiki/List_oCrefractive_indices) Diamond 2.42 Eye, Cornea 1.38 Eye, Lens 1.41 Fused Silica 1.57 Glass, Crown 1.52 G lass, Pyrex 1.47 Lucite 1.50 Nylon 1.53 Obsidian 1.50 Plastic 1.46-1.55 Polystyrene 1.49 Table 4.2 shows an abbreviated list of solvents and their indices of refraction (Johnson and Smith 1972) As shown in the list wavelength oflight has a small effect on the effective indices of refraction. 23

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A brief list of solvents, their densities, and indices of refraction. @ @ @ Acetic Acid 1.0437 1.3713 1.3789 Acetone 0.7846 1.3581 1.3647 Benzene 0.8737 1.5020 1.5196 Carbon Tetrachloride 1.5844 1.4596 1.4691 CycIohexane 0.7738 1.4253 1.4328 Ethyl Alcohol 0.7852 1.3612 1.3677 Methyl Alcohol 0.7866 1.3284 1.3337 Isopropyl Alcohol 0.7809 1 3772 1.3835 Toluene 0.8623 1.4980 1.5151 Water 0.9970 1.3340 1.3390 Optical index matching is a process where a pair of transparent materialsa solid and a liquid are selected and matched according to their indices of refraction, n. A transparent solid material with a given index of refraction, when submerse d in a liquid with the same index of refraction, will effectively appear to disappear. Optic index matching, in another sense, is a way of carefully choosing a solid and a liquid according to their indices of refraction such that light travels through both materials without changing its velocity. Light travels linearly through a homogenous material, given the temperature and density of the material 24

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is constant. Similarly, given a pair of index matched materials, such as glass and toluene, light travels linearly through both without refraction, or bending. The reason why light experiences refracti on at the interface of two different transparent materials is because light experiences a change in speed at the interface. Figure 4.1 illustrates how the trajectory of light changes between air and water. Normal line A simple illustration that demonstrated refraction oflight 25

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The velocity at which light travels through a given material is dependent on the index of refraction of that material. The velocity oflight will decrease as it leaves a material with a relatively low index of refraction and enters a material with a relatively lar g e index of refraction. As an example, as light travels from air a material with an index of refraction of approximately 1.0003, into common glass, a material with an index of refraction of approximately 1.52, the velocity of light will decrease from approximately 2.98x 1 08 to 1.97x 1 08 In a similar way as illustrated in Figure 4.1, light experiences diffraction or bending in order to keep its continuity at the interface of two transparent materials. Just as it is imposs i ble for only a portion of a barrel to roll and travel at a different rate than the remainder of the barrel, so also light must adjust its course oftravel at the interface of two transparent materials. This is illustrated in Figure 1.2. 26

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A conceptual illustration showing how the direction of travel of a barrel changes as it travels from one surface to another. (Serway Beichner 2000) Since light has a wave nature it must have both amplitude and a frequency The amplitude of light waves is associated with the intensity or brightness of light, and the frequency describes its color. Equation X.2 describes the relationship between frequency and time. = (Equation 4.2) = Frequency 27

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A wavelength is the distance a wave will travel in the time it takes to complete one wave cycle. Wavelengths will change as it leaves one medium and enters another. The wave frequency, however, remains the same in both media (Figure 4.3) 28

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An illustration of how wavelength of a given incident light differs in two different media. (Serway Beichner 2000) Light traveling from a source will undergo some amount of refraction at all angles, except when traveling at a normal angle to a given material which it enters. This is qualitatively illustrated in Figure 4.4. 29

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Concentric rings represent waves traveling in an outward direction from a given source. As shown the directions in which waves travel undergo refraction at all angles except when normal to the material which it enters (en.wik i pedia org / wiki / List _ofJefractive_ indices) 30

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The distances between concentric rings shown in Figure 4.4, which represent single wavelengths oflight, changes at the interface oftwo media with differing indices of refraction. The velocity and wavelength at which light travels through each material is different the frequency however, remains unchanged. Energy is conserved because the frequency oflight, which is associated with the energy of light is unchanged. If the distances between concentric circles did not change at the interface of two transparent m a terials with differing indices of refraction, then the frequency of light must change. This would violate the principle of conservation of energy. If this were hypothetically possible, the color of the incident beam would change as it left one transparent material and entered another. Some portion oflight will reflect at the interface of two transparent materials. The angle of reflection will be the same as the angle of incidence. The remaining portion of light will experience refraction at the same interface of two transparent materials Figure 4 5 illustrates the paths of incident, reflected, and refracted light at the interface of two transparent materials. 31

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1 9i The relationship between incident angle reflection angle, and refraction angle are illustrated (Serway Beichner 2000). Snell's Law relates the angle of refraction to the angle of incidence and indices of refraction of the two transparent materials as shows in Equation X.3. (Equation 4.3) 32

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Snell's Law shows that the path oflight will remain unchanged and will not experience refraction at the interface of two transparent materials when n and n the indices of refraction of those materials are the same. also shows that at an angle of 0 degrees, light traveling normal to the interface of the two transparent materials will not experience refraction. Adam Kanold, a previous University of Colorado Denver graduate student under Dr. David Mays' guidance, experimented with several combinations of transparent solids and liquids in search of an index matched pair. The purpose of the search was to make an optically transparent granular media filter. Some of the solids that were tested include fused silica, polished glass, and a polymer material called Nafion. After experimentations with several solid-liquid combinations, Kanold found Nafion to be nearly invisible when it was boiled in isopropyl alcohol for a couple of hours, then placed in a mixture of 40% isopropyl alcohol and 60% deionized water (Kanold 2008). Photograph shows four glass containers from left to right with (1) water, (2) index matched granular filter media, (3) non index matched granular filter media, and (4) dry Nafion in bottle. 33

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5. Experimental Methods 5.1 Experiments with Compositions ofDI Water and IPA Following the procedures developed by Kanold (2008) for making index matched Nation submersed in a mixture of deionized water (DI) and isopropyl alcohol (IPA), several batches of index matched Nation were prepared. To verify that the mixture developed by Kanold was the best possible, 6 additional Nation samples were prepared with slightly varied proportions of 01 water and IP A. The six different percent OI water to percent IPA compositions (by volume) were: 60:40 58:42, 56:44 54:46 52:48, and 50:50. The samples were given approximately 3 days time to reach an equilibrium state after preparation. After waiting for 3 days after preparation of these 6 samples, the Nation sample made using 58% DI and 42% IPA appeared to be best index matched based on visual inspection Through this experimentation, it was observed that Nation's refractive index varied by with the fluid is has absorbed. Additionally, it was observed that the fluid which Nation has absorbed required some time to reach a state of equilibrium with the surrounding fluid. Thus samples of Nation were given a minimum of 3 days to reach an equilibrium state before tinal observations were made. 5.2 Preparation of Index Matched Granular Filter Media Approximately 500 mL of filtered deionized water was prepared by running deionized water through a vacuum filter apparatus using 0.2 )..tm filter 34

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paper. The use of improperly purified fluids has lead to calculated values of average molecular weight using light scattering that are lower than actual values (Huglin 1972). To minimize the chance of this, the filtration process was repeated at least twice to ensure removal of particulates that could distract from getting accurate light scattering results Approximately 500 cc of filtered isopropyl alcohol was prepared in the same way by using a vacuum filter and 0.2 filter paper. After filtered deionized water and isopropyl alcohol were prepared, Nafion of desired grain sizes were allowed to soak in a solution of 58% deionized water and 42% isopropyl alcohol for at least one day. After soaking the Nafion for at least a day the mixture of i s opropyl alcohol and water was decanted and replaced with a fresh, clean batch of the same solution of 58% deionized water and 42% isopropyl alcohol for at least an additional day. The Nafion was observed to swell slightly during the soaking process. During the same time, the Nafion reached an equilibrium state where its index of refraction was approximately the same as that of the mixture of 58% deionized water and 42% isopropyl alcohol. 5.3 Preparation of Colloid Suspension Using Micro spheres Quality controlled uniformly-sized polystyrene micro spheres were used to simulate suspended solids in suspension. Two different sizes of polystyrene micro spheres were chosen 1.0 and 0.1 diameter micro spheres were used to prepare samples with. The two sizes were never mixed; samples were kept monodisperse meaning all the suspended solid micro spheres were the same size. This simplified the analysis of data simpler. In addition to samples with various concentrations of suspended solids, blank samples containing no suspended solids were prepared. These were used as controls 35

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Index matched Nafion was decanted and placed into eight 10 mL glass test tubes until the test tubes were approximately half filled. A solution of filtered 58% DI and 42% IP A containing various concentrations of 1.0 Ilm polystyrene micro spheres were prepared using the method of multiple dilutions. Using the method of multiple dilutions made it possible to accurately prepare samples with very small concentrations The concentrations of micro spheres used for each set of measurements were as follows: 0 1, 2, 5, 10, 20, 40, and 80 ppm. Samples with various concentrations were prepared to find out if multiple scattering occurred within test tubes, and if so at what concentration it became a significant factor that affected the measurements. Another purpose for preparing a set of eight samples for each composition was to find out at what concentration multiple scattering became a factor. 5.3.3 Stable and Aggregated Micro Spheres Similarly to above mentioned 16 samples of varying concentrations and sizes of micro spheres an additional 16 samples were prepared with 0.1 M Ca(N02 ) 3 added to induce chemical aggregation of micro spheres Calcium Nitrate was chosen as the aggregation inducing agent following work by other researchers who used it to induce aggregation of colloidal micro spheres (Veerapaneni and Wiesner 1997) The O.lM solution of Calcium Nitrate was prepared by adding approximately 0 .05 moles of calcium nitrate to 500mL ofDI solution. The volume ofNafion in test tubes were not counted as part of the total makeup volume of the O.lM Ca(N03h Using the equation shown below (Snoeylink and Jenkins 1980)), the ionic strength of these samples were calculated to be equal to 0.25 M: 36

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Where = calculated ionic strength, in M C = concentration of ionic species, i in M Z = charge of ionic spec i es i (Eq 5.1) Samples prepared, including those with and without calcium nitrate, with and without micro spheres and with and without nation are summarized in Table 5 .1. 37

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Table 5.1 Compositions of sample s use d for each concentration of suspended colloid s pre pared. Size of Sample Micro Micro Nation Ca(N02}3 No. Spheres Spheres (Jim) No --No No Yes 1.0 No No 3 No --No Yes Yes 1.0 No Yes 5 No -Yes No Yes 1.0 Yes No 7 No Yes Yes 8 Yes 1.0 Yes Yes 9 No -No No 10 Yes 0.1 No No No -No Yes Y es 0.1 No Yes 13 No -Yes No Yes 0.1 Yes No 15 No -Yes Y es Yes 0.1 Yes Yes 38

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total of seven sub-samples each with varying concentrations were prepared for samples containing micro spheres. In other words samples 2, 4, 6, 8, 10, 12, 14 and 16 were prepared w i th differing concentrations to measure the effects of multiple scattering. An example of this is summarized in Table 5.2. Table 5.2 Concentration series from 1 to 80 ppm Sample Concentration of No. Micro Spheres (ppm) 2-1 2-2 2 2-3 5 2-4 10 2-5 20 2-6 40 2-7 80 5.4 Static Light Scattering 5.4.1 Static Light Scattering Apparatus A static light scattering apparatus was constructed by Dr. Lei a professor of electrical engineering at the University of Colorado Denver. A schematic diagram of how the apparatus works is shown in Figure 5.J. 39

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A simplified schematic drawing of the SLS apparatus built by Dr. Lei The apparatus is essentially composed of Helium-Neon laser (source of incident light beam) a sample holder with adjustments in the x and y-axis and a light sensor that is aimed at the center of the sample test tube. The light sensor is mounted on a rotating arm which is able to rotate the sensor about the sample test tube from 0 to 155 degrees. The angle of the rotating arm is controlled by a motor and is controlled using a computer software program LabView. addition to the components mentioned above several additional components added by Dr Lei has improved the functionality of the instrument significantly. These components include: (1) Polarizer (2) Signal noise filter (3) A second He-Ne laser used for aligning the sample test tube (4) A photo detector to measure the power of the incident beam (5) Mirrors to adjust and fine-tune the path ofthe laser beam (6) Lenses to account and correct for the curvature of the sample test tube 40

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(7) A protective, movable mirror to protect the light sensor from direct exposure Samples were brought to the Colorado Advanced Photonics Laboratory (CAPT Lab) to be scanned using the static light scattering apparatus All the instruments that are part of the static light scattering apparatus were turned on. The laser was warmed up for approximately 15 minutes in order to stabilize its power output. The alignment of the laser beam was checked prior to starting the measurement process each day. If necessary, the alignment of the beam was fine tuned using the 4 mirrors, which are placed in line with the path of the laser beam following exact procedures outlined by Dr. Mays. Test tube sample were gently inverted back and forth 25 times to mix the contents well without stirring air bubbles into the solution. A single sample was placed into the sample holder at a time in a position that is straight and vertical as possible by visual inspection. Once the sample was placed in the sample holder, its x and y axis were adjusted, if necessary, by slowly turning the adjustment knobs until both the incident beam and the secondary beam entered the sample test tube squarely in the center of the test tube. The power / intensity of light passing through the sample was recorded both prior to starting a scan and after completion of the scan. A light curtain used to block outside light from coming in was closed. The scattering intensity of light in W was measured from 0 to 155 degrees, initially with constant angular spacing in increments of 0.1 degrees. The Lab View program used to control the angular position ofthe light sensor and record data was later modified such that it could take measurements in q-vector units. Data of scattering angle, e, in degrees vs. scattered light intensity in W were recorded using data acquisition

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instrumentation and computer software, Lab View The light transmission intensity through the sample was measured again after completion ofthe scan. The process was repeated for each sample. Test tube sample (center), and light detector (rear) are shown in photograph. Data points collected using Lab View was analyzed using a spreadsheet program, and using a MatLab script written by Dr. David Mays. The first step 42

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with the analysis of data was to convert the angles in degrees to a q-vector value by using equation 5 2 show below. After this conversion step, data points were plotted with q-vector values on the x-axis and the log of intensity of scattered light in on the y-axis. Next, a data points collected from a blank sample with no micro spheres were plotted in the same way. Thirdly, the light intensity values of the blank sample were subtracted from the light intensity value of the colloidal sample of interest. This was done to subtract out the amount of scattering that are caused by the glass test tube, internal reflections, and other factors other than scattering caused by the actual micro spheres which are of interest. This is similar to pushing the "tare" button on an electronic scale that is used to subtract out the mass of a container that is used in order to get only the mass of the material of interest. The adjusted values of the log of light intensity vs. angle were plotted on a graph for visual inspection. The raw, unadjusted intensity, the blank intensity and adjusted intensity vs. q-vector values are illustrated on Figure 5.3. 43

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Figure 5.3 Intensity vs. q-vector plot showing scattered light intensity from blank and adjusted/unadjusted scattered light intensity from 2 ppm sample. 44

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The units of the x-axis were converted from angle in degrees to the magnitude of the scattering wave vector, using the following equation from Sorenson (2001): = sine Where A = wavelength of the light source, in nm e = angle in degrees (Eq 5 2) The fractal dimension primary particle size, and average aggregate size were estimated by visual inspection of the plots showing light intensity vs. q-vector. According to Sorensen (2001), log-log plots oflight intensity vs. scattering vector, q for samples containing aggregated micro spheres look like one shown in Figure 5.4. 45

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An ideal scatter plot with three regions labeled 1,2, and 3. As seen in the figure, there are three linear regions which are of importance, which are labeled 1,2 and 3. The first region is the linear region where the measured light intensity stays constant with q, followed by a region with a negative slope. According to Sorensen (2001) the slope of this region is equal to the fractal dimension of the aggregate structures formed by micro spheres in the sample. The value of q at which the transition in slope occurs is the inverse of the radius of gyration of the fractal structure. Lastly, there is a region with a slope of -4 The value of q at which the slope transitions from -0 to -4 labeled as a I is the inverse of the primary particle radius.

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This method is the simpler of the two methods. The fractal dimension and the average radius of gyration of aggregate structures in suspension can both be found by visual inspection. This approach, however, can be problematic because of its simplicity Scatter plots created such as one shown in Figure 5.3 are rarely as distinct as one shown above. The exact location where the slope transitions from one region is not clear, therefore room for interpretation exists. With the method of non-linear least squares fit, or the model fitting approach described in the following section there is not room for interpretation. The second, and possibly more accurate method, is one of fitting the data points to a series of model equations simultaneously using a non-linear least squares fit method. Sorensen (2001) Bushell et al. (2002), and Teixeira (1988) use similar equations to model the structure factor, particle factor, fractal dimension, and primary particle radius. non-liner least squares fit program will go through a process of iteration to minimize the difference between the models and collected data until optimum values are calculated. The primary particle radius, the radius of gyration of the fractal aggregate, and the fractal dimension are calculated simultaneously at once. This method requires some time for the computers to run through the process of iterations in order to optimize the fit. 47

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6. This research project relied heavily on instrumentation and quantitative outputs for the results. was unlike testing soils i n a laboratory where senses such as touching seeing, smelling and even listening to how soils behave are in tune with the testing procedures and help technicians characterize soils. There were very little signs that colloidal samples exhibited which helped characterize fractal aggregate structures of samples. For this reason it was important to make careful observations on each colloidal sample and run the experimental procedures as identically and me t hodically as possible from one sample to another. Aggregation was observed inside the test tubes of those samples which contained calcium nitrate. These aggregated structures were usually observed to stick to one side of the test tubes instead of settling. The aggregated structures were big enough that they were visible to the naked eye Samples without calcium nitrate remained cloudy appearance for several days, possibly even a couple of weeks Eventually, however, particles were observed to settle to the bottom ofthe test tube. was unclear exactly when the particles settled and the appearance of the mixture was noticed being clear. These same samples (stable colloids) at high concentrations yielded a gentle glow when incident beam passed through it. The scattered light appeared nearly uniform at all angles. This may be a sign that multiple scattering of light was taking place within the sample test tube Incident light may have scattered off multiple colloids before exiting the test tube. These samples showed no sign of 48

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Mie humps on a scatter plot. Mi humps are sharp humps that are generally characteristics of uniformly sized spherical suspended colloids (Bushell 2002) and are illustrated on a scatter plot in Figure 6.1. tD 'tJ fO ... A theoretical plot of stable spherical particles in suspension The sharp humps, called Mei humps, are characteristics of scattering caused by spherical colloids. Illustration taken from Bushell (2002) Fractal dimensions were measured and calculated for each concentration series of samples. Results obtained using both the scaling and the form fitting approaches are summarized below. 49

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Samples of aggregated diameter colloids in suspension had a range of calculated fractal dimensions from 1.8 to 2.1. Aggregated structures with the same concentrations and sizes of colloids inside granular filter media had calculated fractal dimensions between 1 5 and 2.2. Plots in Figures 6.2 through 6.5 show adjusted intensity vs. q for samples with various concentrations of micro sphere colloids. High concentration samples scattered more light than those with low concentrations as shown in the figures below The calculated fractal dimensions, however, were not affected greatly by the sample concentrations 50

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' .=. c .: 'C 1/1 :c .,F.. -,l-t+ ---,,\ I __ ----------Figure 6.2 I vs, q-vector plot for aggregated samples in suspension with various concentrations of micro sphere colloids. 51

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a c: 'C = 2E_14x1 .n43 = 8E-15X-18807 4E_15X-1 .8952 Y 1E-15x-1 .9569 6E_16x1 9ne :c y 4E_16x-1.9172 = 5E_17x-2.o751 y = 2E_17x2 .136 q Figure 6.3 A zoom-in plot showing linear sections of I vs q plot above Best fit equations for each concentration are shown to the left The exponents of those equations show the calculated values. 52

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-1-----+1-11 .= S "C S I vs. q plot for aggregated samples with various concentrations of micro sphere colloids in granular filter media. 53

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1 7496c: 'tI :c = 1 4885 = 1 9527 = 1 9155 = 2 2192 = 2 2144 = 2 .16504 q Figure 6.5 A zoom-in plot showing only linear sections of I vs. q plot above. Exponents ofthe best-fit equations to the left are the negative ofthe calculated fractal dimensions -D 54 __ LJ

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Calculated results from the plots above are summarized in Table 6 1 Table 6.1 Summary of measured fractal dimensions for each concentration series using 111m diameter suspended colloids Sample Aggregated Aggregated Concentration Colloids in Colloids in (ppm) suspension granular media 2.14 2.17 2 2.08 2.21 5 1.92 2.21 10 1.98 1.92 20 1.96 1.95 40 1.90 1.49 60 1.81 80 1.88 1.75 100 1.77 6.2.2 Form Fitting Approach Several sets of data were analyzed by Dr. David Mays using a non-linear least squares fit script with software, MatLab The equations used for running the non-linear least squares fit are summarized in Section 3.4.3. The fractal dimension, D, and the primary particle radius, r, were fitted simultaneously. Resulting primary particle radii had a range of 531 nm to 535nm. Given the fact that 1000nm diameter colloids with a coefficient of variation of 3 .2% were used to prepare the samples with, the calculated results were very close to actual 55

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values. Code used for the analysis is attached in Appendix X. Figures 6.6 through 6 9 show the resulting plots from the analysis. '; 1 10 .3 t t 1 Non-linear least squares fit plot of aggregated, 1 ppm sample in suspension Fitted results are D=1.8 and r=531nm. From Mays et al. (2009) 56

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Non-linear least squares fit plot of aggregated 2ppm sample in suspension. Fitted results are D=2.3 and r=535nm. From Mays et al. (2009) 57

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10" Non-linear least squares fit plot of 1 ppm aggregated sample inside a granular filter media. Fitted results are D=2.3 and r=535nm From Mays et al. (2009) 58

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ti4 I., 't +t: H+ -0 Non-linear least squares fit plot of2ppm, aggregated sample inside a granular filter media. Fitted results are D=2.3 and r=535nm. From Mays et al. (2009) 59

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Result s that were calculated using the form fitting approach are summarized in Table 6.2. Summary of calculated fractal dimensions and primary particl e radii. 2.1 2.3 2.7 531 535 535 535 60

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7. CONCLUSION 7.1 Application of Light Scattering in Civil Engineering Light sc a ttering has been shown to be eff ective in measuring fractal dimensions of aggregate structures in suspension as well as inside index matched granular media Experimentation with the light scattering has shown that it can be a practical tool in water treatment research. In addition there is some possibility that light scattering can be used to study small particle soils such as silts and clays in the field of soil science ASTM D 422 method utilizes a hydrometer to measure the specific gravity of soil-water mixture at given time intervals to estimate the relative gradation of soils passing the #200 sieve. The test assumes there is a direct relationship between particle size and time it takes for the particles to settle Light scattering can potentially be used to supplement existing tests used to better and more quickly characterize small particles in soils 7.2 Problems Encountered Many problems having to do with minor details were encountered throughout the duration of the research project. A few examples include (1) sample preparation and mUltiple scattering, (2 ) calibration of the static light scattering apparatus and (3) difficulty interpreting collected data Sample preparation and multiple scattering was a source of uncertainty in terms of if the samples were yielding good data or not. Because there was nothing to compare

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the collected data to it was very hard to tell if the samples were of good quality or not. Samples of various concentrations as described in chapter section 5.3 were prepared and data were collected for each sample using the SLS apparatus By so doing, it was found that samples with concentrations in the range of 1-10 ppm lead to collection of clear data. The best sets of data were usually obtained using the 2 ppm sample. Similarly, it was hard to found out if the light scattering apparatus was calibrated correctly or not because there was nothing to compare sets of data that were obtained. Dr. Tagg in the physics department provided some reassurance regarding the functionality of the static light scattering apparatus. His experience in the field of light scattering allowed to project to continue forward after experiencing some difficulty. 7.3 is of interest to learn how the fractal dimensions of aggregate structures affect clogging of granular filters. Basic, foundational laboratory procedures were established during the approximately 17 months of preliminary research. was found that in-site measurements fractal dimensions of aggregate structures inside index matched granular media was possible dureing. This was a very important step to establish before proceeding to more specific phases ofthe project. Proposed future work involves measuring the fractal dimension of aggregate structures inside an index matched filter body as water containing suspended solids is passed through. Figure 7 1 shows an apparatus that was built by Randy Ray at the University of Colorado Denver s machine shop. 62

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A glass flow-through column with transducer ports held in place by an apparatus built by Randy Ray at the University of Colorado-Denver. 63

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The above shown apparatus is designed in a way such that raw water entering the top and exiting at the bottom is filtered while the hydraulic head at various points along the filter body is measured in real-time The glass body allows for visual inspection of the filter body as it clogs as well as the use of static light scattering method to measure the fractal dimension of aggregated structures inside the filter body. This apparatus will make it possible to measure the fractal dimension of aggregate structures inside the filter body, and find how that affects clogging over time 64

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APPENDIX A Detailed Static Light Scattering Data (Samples with Nation and Calcium Nitrate) 65

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e e o o

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e e

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e e 3.23996 0 056548 3.35425 0.0585427 3.47257 0.0606078 3.59507 0.0627458 3 7219 0.0649594 3 8532 0.067251 3.98913 0 0696235 4.12987 0.0720798 4.27558 0 0746229 4.42643 0 0772558 4.58261 0.0799816 4.7443 0 0828037 4.91171 0.0857255 5 .08 503 0 0887505 5 26448 0 0918825 5 45027 0 0951252 5 64263 0.0984825 5 84178 0 .1 0 1 9583 6 04798 0 1055572 6.26147 0 .1 092833 6.48251 0.1131411 6.71138 0.1171357 6 .94834 0.1212714 7.19369 0 .12 55536 7.44772 0.1299872 7.71076 0 .13 45781 7 98311 0.1393316 8 26512 0.1442536 8 55712 0 1493499 8.85948 0.1546271 9 .172 56 0.1600914 9.49676 0 .1 657497 7.57651E-05 7 8437E-05 8.1203E-05 8.40666E-05 8 70313E-05 9.01005E-05 9.32777E-05 9.65672E-05 9.9972 7 E-05 0.000103498 0 000107148 0 000110927 0.000114838 0 000118888 0.000123081 0 000127421 0.000131915 0 000136567 0 000141383 0.000146368 0.00015153 0 000156874 0 000162406 0.000168133 0 000174062 0.000180201 0 000186555 0 000193134 0 000199945 0.000206996 0.000214296 0 000221853 6.35E-09 5 .0 9E-09 3.97E-09 3 .28E -09 3.73E-09 3 81E-09 3.46E-09 3.11E-09 2.84E-09 2.44E-09 2.11E-09 2 06E -0 9 2.10E-09 1 .87E -09 1.47E-09 1.33E-09 1.35E-09 1.35E-09 1.24E-09 1.10E-09 1.14E-09 1.07E-09 1.06E-09 1.11E-09 9.60E-I0 8.00E -1 0 7.42E-I0 8 00E-I0 7.35E-1O 7.13E 10 7.13E-I0 6.18E 10 1 1.26E-08 1.40E -08 1.46E-08 1.44E-08 1.40E-08 1.21E-08 9.35E-09 7 65E-09 6 80E-09 5 73E-09 5.13E-09 5.94E-09 6 13E-09 5.54E-09 4.6 9E-09 4 88E-09 4.63E -09 4.73E-09 4 86E-09 4.21E-09 3 89E-09 3 63E-09 3 34E-09 2 95E-09 2 68E-09 2.41E-09 2.35E-09 2 01E -09 1.99E-09 1.86E-09 1.83E-09 1.67E-09 2 5 1.35E-08 1.69E-08 1.14E-08 1.64E-08 1.09E-08 1.50E-08 1.00E-08 1.37E-08 9 90E-09 1.24E-08 1.01E-08 1.19E-08 1.12E-08 1.28E -08 1.08E-08 1.33E-08 9.44E-09 1 30E-08 9.36E-09 1.42E-08 9 67E-09 1.27E-08 8.91E-09 1.16E-08 9.73E-09 1.08E-08 8 .95E-09 9.50E -09 6.86E-09 8.58E-09 5.37E-09 6.92E-09 4 50E-09 7 51E-09 4.58E-09 8 .5 7E-09 4.63E-09 8 03E-09 4.48E-09 7.88E-09 4.37E-09 7 04E-09 4.73E-09 5.66E-09 4 99E-09 5 28E-09 4.20E 09 6 09E-09 3 75E-09 5.30E-09 4 15E-09 4 80E-09 4.18E-09 4.83E-09 3.39E-09 5 01E-09 3.10E-09 4.90E-09 2.74E-09 4 77E-09 2.79E -09 4.55E-09 2.58E-09 4.50E-09 10 3 51E-08 3 02E 08 2.72E-08 2.18E-08 1.90E-08 2.11E -08 2.63E 08 2.54E-08 2.16E-08 2.03E-08 1.91E-08 1.76E-08 1.67E-08 1.70E-08 1.48E-08 1.23E-08 1.17E-08 1.25E-08 1.2 6E-08 1.32E-08 1.19E-08 1.06E-08 9 53E -09 8.84E-09 8.88E-09 9 39E -09 1.01E-08 9.46E-09 8.28E-09 7.35E-09 5.93E -09 5.98E-09 20 5.49E-08 5.85E -08 5.49E-08 5 25E-08 5.29E-08 5.19E-08 4.76E-08 4.15E -08 3 81E 08 3 50E-08 3.53E-08 3 29E-08 3.04E-08 3 .36E-08 3 27E-08 3.21E-08 3.23E-08 3.07E-08 2 63E-08 2.49E 08 2.42E-08 2.71E-08 2.68E -08 2.37E-08 2 08E -08 2 09E-08 1.96E-08 1.90E-08 1.75E-08 1.64E-08 1.69E-08 1.51E-08 40 5 68E-08 5 lOE-08 5.38E-08 6 18E-08 7.26E-08 7.44E-08 5.99E-08 4.95E-08 4 95E -08 5.25E-08 5.08E-08 4 .5 7E-08 3 99E-08 4.01E-08 4.02E-08 3.63E-08 3.78E-08 4 29E-08 3.39E -08 2.90E-08 3.07E-08 2.86E-08 2.88E-08 2.75E-08 2.29E-08 2.24E-08 1.76E-08 1.52E-08 1.73E-08 1.69E-08 1.58E-08 1.26E -08 80 8 84E-08 7.84E-08 7.54E-08 6.95E-08 5 98E-08 5.30E-08 5.07E-08 6 32E-08 7.13E-08 7.89E-08 8.82E-08 8.54E-08 7.54E-08 6.87E-08 6.15E-08 5.59E-08 5.06E-08 4.65E-08 4.36E-08 4 80E-08 4.63E-08 4.29E-08 3 96E-08 3 .61 E-08 3.64E-08 3.17E-08 2.67E -08 2.65E-08 2.53E -08 2.45E-08 2.53E-08 2.73E -08

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e e 9 83248 0 1716091 10 18012 0 1776766 10.54012 0 1839598 10 91292 0.1904664 11.29899 0 1972046 11.69882 0.2041829 12 11289 0 2114098 12.54174 0 2188947 12 98589 0.2266465 13.44591 0 2346754 13.92239 0 2429915 14 41592 0.2516053 14 92714 0 2605277 15 45671 0 2697705 1 6 0053 0 2793452 16.57362 0 2892642 17 16242 0 2995407 17 77247 0 3101881 18.40457 0.3212203 19.05955 0 3326519 19.73829 0.3444981 20.44171 0.3567751 21.17075 0.3694993 21.92642 0.3826882 22.70975 0.3963599 23. 52185 0.4105337 24.36384 0.4252292 25.23694 0.4404677 26.14241 0.4562711 27.08155 0.4726622 28 05578 0 4896657 29. 06655 0.507307 1 0.000229677 5 82E-10 1.68E -09 0 000237776 5.09E-1O 1.75E-09 0 000246162 5 09E -1O 1.62E -09 0 000254842 4.51E-1O 1.54E-09 0 000263829 3 93E-1O 1.41E-09 0.000273133 4 07E-10 1.40E-09 0 000282765 3.42E-10 1.27E-09 0.000292737 2.91E 10 1.21E-09 0 00030306 2.55E 10 1.16E -09 0.000313748 2.62E 10 1.01E 09 0 000324812 2.26E -1O 7 93E -10 0.000336266 1.96E-1O 7.57E 10 0 000348125 2.04E-1O 7 35E -10 0.000360402 1.60E -10 6.91E-1O 0.000373111 1.53E-10 6 .l1E-10 0.000386269 1.31E-1O 4.87E -1O 0 00039989 1.09E 10 4.51E-1O 0.000413993 1.09E-10 4 15E-10 0 000428592 1.02E-10 3 64E-10 0.000443706 1.09E 10 3 13E 10 0.000459354 8.73E 11 2 .76E10 0.000475553 8 00E 11 2.55E-10 0.000492323 7.28E 11 2 18E-10 0 000509685 7 28E-11 1. 75E10 0.000527659 5 .82E-ll 1.53E 10 0.000546267 5 .82E-l1 1.53E-10 0 000565531 5.82E 11 1.31E -1O 0.000585474 5.82E -ll 1.02E 10 0 000606121 4.37E 11 1.02E 10 0.000627495 3 .64E-ll 7 .28E-ll 0.000649624 4 .37E-ll 6.55E 11 0 000672533 3 64E-11 5.82E -ll 2 5 10 20 40 80 2 30E -09 4 02E-09 5.84E -09 1.42E-08 1.28E-08 2.22E 08 1.91E-09 4 02E-09 6 56E-09 1.32E-08 1.23E -08 1.84E -08 1.91E -09 3.49E-09 6 16E-09 1.25E-08 1.07E-08 1.70E-08 1.76E-09 3.01E-09 4.78E -09 1. 13E -08 9.47E -09 1.43E-08 1.59E 09 2 92E-09 4.38E-09 1.09E-08 1.06E-08 1.34E -08 1.60E-09 3 24E-09 3 94E-09 1.01E-08 1.07E-08 1.41E-08 1.51E -09 2 76E-09 4 05E-09 8.78E-09 9 04E-09 1.23E-08 1.41E -09 2.47E-09 3 79E-09 8 03E -09 7.28E-09 1.06E -08 1.30E-09 2 02E-09 3.41E -09 6 65E-09 6 .61E-09 9.51E-09 1. 14E09 1.94E 09 3.04E -09 6.37E-09 6.29E -09 9.38E -09 1.03E 09 1 78E-09 2 84E-09 6.43E-09 6 .66E-09 8 81E -09 8 88E-10 1.54E -09 2 62E-09 5 78E-09 5.94E -09 7.49E 09 8 .66E-1O 1 39E-09 2.55E-09 4 .96E-09 4.56E-09 8.23E-09 7.13E-10 1 27E-09 2.29E-09 4 85E -09 5.31E-09 6 90E-09 6.48E-10 1.03E 09 1.71E -09 4.42E -09 4 63E-09 6.21E-09 6.18E-10 9 90E-10 1.40E-09 3.61E -09 3.75E -09 5 77E 09 4.95E-10 9.17E 10 1. 27E-09 3 .22E-09 3.38E -09 4.55E-09 4.29E-10 8.66E -1O 1.22E -09 3.54E -09 3.46E-09 3.90E-09 4 00E-10 7.20E 10 1.23E-09 2.95E-09 2.80E-09 4 61E 09 3 93E-10 6 33E-10 1. 11E-09 2.42E -09 2.48E-09 4 15E-09 3.49E 10 5.68E-1O 9 68E 10 2.07E-09 2.47E 09 3.42E 09 3.20E-10 4.87E-1O 8.44E 10 2 00E -09 2.42E -09 2 97E-09 2.91E 10 4 73E-10 8.44E-10 1.59E-09 2.36E -09 2 63E -09 2.26E 10 3.57E-10 6.62E 10 1.43E-09 1.73E-09 2.36E-09 1.75E-10 3.49E-10 5.97E-10 1.36E-09 1.64E-09 2 25E-09 1.60E 10 2.84E-10 5 89E 10 1.15E-09 1.56E -09 2 03E -09 1 31E 10 2.47E-10 4.73E-10 1.03E-09 1.47E-09 1.67E-09 1 24E-10 2 11E-10 4 29E 10 9.02E -10 1.29E -09 1. 64E -09 1.02E 10 1.67E-10 3 42E 10 7 49E-1O 1.25E-09 1.70E-09 8.00E-11 1.53E-10 3 13E-10 6.l1E-1O 9.53E -10 1.39E-09 7.28E-11 1.24E-1O 2.40E-10 5.68E-1O 7.42E -1O 1.16E-09 5.82E-ll 1.02E-10 1.89E-10 4.66E-1O 7.71E -10 9.53E-10

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e e o o o o o o o o o o o o o o o o o o o o o o o

PAGE 81

e e

PAGE 82

*Notes : (1) Fluid is 0.1 M Calcium Nitrate in 58% C (2) The concentration of IlJm m icrospher. (3) Adjusted sample intensities are shown (4) Samples contain Nafion Angles Angle, e [radiants] 0.43401 0 0075749 0.44931 0 0078419 0.46516 0.0081186 0.48156 0 0084048 0.49854 0 0087012 0.51612 0 009008 0.53432 0.0093256 0.55317 0 0096546 0.57268 0 0099952 0.59287 0.0103475 0.61378 0 0107125 0 63542 0.0110902 0.65783 0 0114813 0.68103 0 0118862 0.70505 0 0123054 0 72991 0 0127393 0 75565 0 0131886 0 7823 0 0136537 0.80989 0 0141352 0 83845 0.0146337 0.86802 0 0151498 0 89863 0.0156841 0.93032 0.0162371 0.96313 0.0168098 0 99709 0 0174025 1.03226 0.0180163 q vector 1.01505E-05 1.05083E-05 1.0879E-05 1.12625E-05 1.16597E-05 1 20708E-05 1.24965E-05 1.29373E-05 1.33936E-05 1.38658E-05 1.43548E-05 1.48609E-05 1.5385E-05 1.59276E-05 1.64894E-05 1. 70708E-05 1.76728E-05 1.8296E-05 1.89413E-05 1.96092E-05 2.03008E-05 2.10167E-05 2.17578E-05 2.25251E 05 2.33193E-05 2.41418E-05 7.57E-I02 7.5748E-I02 7.84E-I02 7.8419E-I02 5.91E-14 8.1185E-I02 1.83E-13 8.4047E-102 3.80E-13 8.7011E-I02 7 86E 13 9 0079E-I02 1.49E-12 9.3255E-I02 2.46E-12 9 6545E-I02 3.78E-12 9 995E-I02 7.00E 12 1.0347E-I0l 1.37E-11 1.0712E-I0l 2.24E-11 1.109E-I0l 3 53E 11 1.1481E -I01 5.77E-11 1.1886E-I0l 9.40E-11 1.2305E -I01 1.34E-I0 1.2739E-I0l 1.70E -I0 1.3 188E-I0l 1.92E-I0 1.3653E-I0l 2.02E-I0 1.4135E-I0l 2 06E -I0 1.4633E -I0l 2 09E-I0 1.5149E -I0l 2 lOE-I0 1.5683E-I0l 2.15E-I0 1.6236E-I0l 2.32E-I0 1.6809E -I0l 2.67E-I0 1.7402E-I0l 2.99E-I0 1.8015E-I0l 7 57E-102 7.5748E-I02 7.5748E-I02 7.84E -I02 7 8419E-I02 7 8419E -I02 8.12E -I02 8.1185E-I02 8 1185E-I02 8.40E-102 8.4047E-I02 8.4047E-I02 8 70E-I02 8 7011E-I02 8 7011E -I02 9 01E -I02 9 0079E-I02 9.0079E-I02 9.33EI 02 9.3255E-I02 9.3255E-I02 9.65E -I02 9 6545E-I02 9 6545E-I02 9 .99E-I02 1.03E-I01 1.07E-I01 l.11E-I01 9 995E-I02 9.995E-I02 1.0347E-101 1.0347E-I01 1.0712E-I0l 1.0712E-101 1.109E-101 1.109E-I01 1.15E-101 1.1481E-I01 1.1481E-I0 1 1.19E -I01 1.1886E-I01 1.1886E-I0l 1.23E -I0l 1.2305E-101 1.2305E-I0l 1.27E-I0l 1.2739E-101 1.2739E-I0l 1.32E -I01 1.3188E-101 5 67058E 14 1.37E -I0l 1.3653E-101 1.95063E 12 1.41E-I01 1.4135E-I0l 5 47393E 12 1.46E-I01 1.4633E-101 8 26806E 12 1.51E-101 1.5149E-101 1.23776E-11 1.57E -I01 1.5683E-I01 2.52333E-11 1.62E -I01 1.6236E-101 5.3685E 11 1.68E-101 1.6809E-101 9.90826E-11 1. 74E-I01 1. 7402E-I01 2 09076E-I0 1.80E-I01 1.55841E-12 4.6545E-1O 20ppm 40ppm 7.5748E-I02 7.575E-I02 7.8419E-I02 7.842E-I02 8.1185E-I02 8 118E -I02 8 4047 E-I 02 8.405E -I02 8 7011E1 02 8.701E -I02 9 0079E -I02 9.008E -I02 9 3255E-I02 9.326E-I02 9 6545EI 02 9.654E-I02 9.995E-I02 9.995 E-I 02 1 0347E-101 1.035E -I01 1.0712E-I0l 1.071E -I01 1 109E-101 1.109E-I01 1.1481E-101 1.148E-101 1.1886E-I01 1 .189E-I0l 1.2305E-I01 1.231E-I0l 1.2739E-I01 1.274E -I0l 1.3188E-I01 1.319E-I01 1.3653E-I0l 1.365E-I0l 1.4135E-101 l.413E-I01 1.4633E-101 1.463E-I01 1.5149E-I0l 1.515E-I0l 1.5683E-101 2.427E-13 1.6236E-101 4.0679E-12 1.6809E-101 1.5061E-11 1.7402E-I01 4.3464E-11 1.8015E-I01 1. 118E-I0 80ppm 7.5748E-I02 7.8419E-I02 8.1185E-I02 8.4047E-102 8 7011E-I02 9.0079E-I02 9.3255E-I02 9 6545E-I02 9 995E-I02 1 0347E-I01 1 0712E-I01 1.109E-I0l 1.1481E-I0 1 1.1886E-I01 1.2305E-I0l 1.2739E -I01 1.3188E-I0l 1.3653E-I01 1 .4135E-I0l 1.4633E-I01 1.5149E-I01 1.5683E-I01 1 6236E-I0l 1.6809E-I0l 1.7402E-I01 1 8015E-I01

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1.10635 0.0193095 1.14537 0.0199905 1.18576 0.0206954 1.22758 0.0214253 1.27087 0.0221809 1.31569 0.0229631 1.36209 0.023773 1.41012 0.0246112 1.45985 0.0254792 1.51134 0 0263779 1.56464 0.0273081 1.61982 0 0282712 1.67695 0 0292683 1. 73609 0.0303005 1.79731 0.031369 1.8607 0.0324753 1.92633 0.0336208 1.99426 0.0348064 2.0646 0.0360341 2.13742 0.037305 2.2128 0 0386206 2.29085 0.0399829 2.37164 0.0413929 2.45529 0.0428529 2.54189 0.0443643 2 63155 0 0459292 2.72436 0.0475491 2 82046 0 0492263 2.91994 0 0509626 3 02294 0.0527603 3.12957 0.0546213 2.49931E-05 2.58746E -05 2 67871E-05 2 77317E -05 2 87097E 05 2.97221E-05 3 07703E-05 3 18554E-05 3.29786E -05 3.41416E-05 3.53457E 05 3.65922E -05 3.78826E -05 3.92186E -05 4.06016E -05 4.20332E -05 4.35156E-05 4.50503E-05 4.66388E-05 4.82836E-05 4.99864E 05 5.17491E 05 5.35741E 05 5.54632E-05 5 74192E-05 5.94441E -05 6.15405E-05 6.37105E -05 6.59574E-05 6 82833E-05 7 06914E -05 7 31843E-05 1ppm 3.01E-10 1.8651E -101 2 86E-10 1.9308E-101 2 91E 10 2.18767E 12 3.18E-10 1.48063E-11 3 26E-10 5 42674E-11 3 07E 10 1.05667E 10 3 04E -10 1.65271E-1O 3.16E 10 1.94682E-1O 3.27E 10 2.18098E-10 3.49E 10 2.55634E-10 3.58E-10 3 09701E -1 0 3 58E-1O 3.45241E-10 3.45E 10 3.74848E-1O 3.40E-10 4 25701E 10 3.44E 10 4.95022E 10 3.49E 10 5 29898E -10 3.44E 10 5.35497E-1O 3.48E-10 5.42516E-1O 3 25E-10 5 31567E-10 3 24E-10 4.88213E 10 3.34E-10 5.17512E-10 3 39E-10 6 1592E 10 3.84E-10 7.19892E 10 4.18E-10 8.17339E-10 4.30E-10 9.46916E 10 4 43E-10 9.89412E -10 5.10E-10 9.02269E-1O 5 77E-10 7 96037E 10 5.38E-10 7.59388E 10 4 96E-10 7.13426E 10 4.47E-10 6 81698E-10 4.00E-10 6.53426E 10 2ppm 5ppm 10ppm 20ppm 40ppm 80ppm 1.87E-101 1.02559E-11 8.32878E-1O 1.8651E-101 1.8965E-10 1.8651E 101 1.93E-101 3.7469E-11 1.32545E-09 1 9308E-101 2.8515E-1O 1.9308E-101 2.00E 101 9 25066E-11 1.78849E-09 2 07E 101 1.82239E 10 2.04689E -09 2 14E-101 2 66262E-10 2 15676E-09 1.90E 12 3.41597E-10 2.24274E-09 1 69E-11 4 62145E 10 2.31522E-09 3 90E-11 6.3935E 10 2.33829E-09 5 82372E-12 5.5675E-1O 3.91986E-11 9.4367E-10 2.21992E 10 1.3506E-09 5 80916E 10 1.7681E-09 8.33531E-10 2.4472E-09 1 12051E-09 3 007E-09 1.9989E 101 2 0694E-101 2.1424E 101 2.2179E-101 2.2961E-101 2 3771E-101 9.17E-11 8 37981E-10 2.28365E -09 1.45804E 09 3 149E-09 2.4609E-101 2.36E-10 1.0275E -09 2.16713E-09 1.80104E -09 3.1865E-09 1.52148E-11 4.27E-10 1.16655E -09 2 03952E-09 2.06254E -09 3.3698E-09 8 84359E-11 5.77E-10 1.26568E-09 2 15095E-09 2 27412E-09 3.5283E-09 2.8584E-10 6.69E-10 1.35365E-09 2.36083E-09 2.61978E-09 3.5093E-09 6.56004E-10 6 86E -1O 1.44561E-09 2 .43913E-09 3 0351E-09 3.4644E-09 1.33276E-09 7.29E -10 1.5639E-09 2 .45819E-09 3.32229E-09 3.5328E-09 2.65592E-09 8 34E -10 1.4847E-09 2.47236E-09 3. 28866E-09 3 698E-09 4 18776E-09 9.55E 10 1.32197E 09 2 40588E-09 1.0 1E-09 1. 09013E-09 2 39031E-09 9.64E-10 9 79728E-10 2.40829E-09 8.6 1 E -1O 1.0683E-09 2.37711E-09 8.07E 10 1.12565E-09 2.2 7707E-09 7.96E-10 1.10334E-09 2.01693E-09 7.73E-10 1.03254E-09 1.63603E-09 7.56E-10 9.35064E-10 1.46619E-09 7.94E-10 9 22291E-10 1.46839E-09 8.67E-10 9 18745E-10 1.45409E-09 9 71E-10 9 05277E-10 1.43009E -09 9 64E-10 8.47565E-10 1.37219E -09 8.53E-10 7.64402E-10 1.39166E -09 7 85E-10 7.47531E-10 1.54479E-09 8.03E -1 0 8.00649E 10 1.81631E-09 8 03E-10 8.74287E 10 1.95951E-09 3.4241E-09 4 0275E-09 3.11793E-09 4 2462E-09 2 94076E-09 3.8047E-09 2 89323E-09 3.2012E-09 2.93459E-09 3.054E-09 3 096E-09 2.9971E-09 3 24611E 09 2 9893E-09 3.4901E-09 2.7554E -09 3 60667E-09 2.5565E-09 3.48187E-09 2.7494E -09 3.46921E-09 2 9895E-09 3 86188E 09 2 99E-09 4 21183E-09 2.6705E-09 4 12371E-09 2 5199E-09 3 64429E-09 3.0108E-09 3 11702E-09 3.3721E -09 5.0195E-09 5.35704E-09 5.4267E-09 5.38161E -09 5 65046E -09 5.41454E-09 5.26802E-09 5 19008E-09 5 02926E-09 4.91171E-09 4 91136E-09 5.45826E-09 5.90639E-09 5.50397E-09 4.98188E-09 4.91964E 09

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3 23996 0 056548 3.35425 0 0585427 3.47257 0 0606078 3.59507 0.0627458 3.7219 0.0649594 3.8532 0 067251 3.98913 0.0696235 4.12987 0.0720798 4.27558 0.0746229 4.42643 0.0772558 4.58261 0 0799816 4.7443 0.0828037 4.91171 0.0857255 5.08503 0.0887505 5 26448 0.0918825 5.45027 0.0951252 5.64263 0 0984825 5.84178 0.1019583 6.04798 0 1055572 6 26147 0.1092833 6.48251 0.1131411 6 71138 0.1171357 6.94834 0 1212714 7 19369 0 1255536 7.44772 0 1299872 7.71076 0 1345781 7 98311 0.1393316 8 26512 0.1442536 8.55712 0 1493499 8.85948 0.1546271 9 17256 0.1600914 9.49676 0.1657497 7.57651E-05 7.8437E-05 8.1203E-05 8.40666E-05 8 70313E-05 9.01005E-05 9.32777E-05 9 65672E-05 9.99727E-05 0 000103498 0 000107148 0.000110927 0 000114838 0.000118888 0.000123081 0 000127421 0 000131915 0.000136567 0.000141383 0 000146368 0.00015153 0.000156874 0 000162406 0.000168133 0 000174062 0 000180201 0.000186555 0.000193134 0.000199945 0 000206996 0 000214296 0 000221853 1ppm 3.59E 10 6.9318E-10 2.98E-10 8.00385E-10 2.41E-10 8.71695E-10 2.06E -10 8 87712E-10 2.42E-10 8.96334E 10 2.56E -1O 7.98837E-1O 2.41E-10 6.33669E -10 2.24E-10 5.3461E-10 2.12E-10 4.90837E-10 1.88E-10 4.27424E-10 1.69E -10 3.96366E -10 1.70E-10 4.77577E-10 1.79E-10 5 09182E-10 1.66E-10 4 76079E-10 1.35E-10 4.18227E 10 1.26E-10 4.51708E-10 1.32E-1O 4.42697E-10 1.37E-10 4.67422E-10 1.30E-1O 4 98364E-10 1.20E-1O 4.46405E-10 1.29E -10 4 241E-10 1.25E-10 4 09707E-10 1.28E-10 3.88576E-10 1.38E-10 3.51665E-10 1.24E-10 3.30934E-10 1.07E-10 3.08727E-10 1.03E-1O 3 12077E-10 1.15E-10 2 72144E 10 1 09E-10 2 79289E-10 1.10E-10 2.69958E-10 1.14E -10 2.74164E-10 1.02E-10 2.58073E-10 2ppm 5ppm lOppm 20ppm 40ppm 80ppm 7 40E-10 9.37038E -1O 1.96222E-09 3.0828E-09 3 1885E-09 4.9769E-09 6.51E-10 9.4172E 10 1.74718E-09 3.40447E-09 2.9668E-09 4.56965E-09 6.43E-1O 8 92852E-10 1.63104E-09 3.31016E-09 3 2454E -09 4.54988E -09 6.17E-10 8.47104E-10 1.35536E-09 3.27658E-09 3 861E-09 4.34692E -09 6.27E-10 7.87233E-10 1.21704E-09 6 62E-10 7 85148E-10 1.40074E-09 7.65E-1O 8.76628E-10 1.81558E-09 7.59E-10 9.43324E 10 1.81369E-09 6.88E-10 9.5355E-10 1.59202E-09 7 08E-10 1.08051E-09 1.55221E-09 7.59E-10 1.00036E-09 1.5096E-09 7.23E-10 9.42163E-10 1.44165E-09 8.18E-1O 9 06643E-10 1.41312E-09 7 79E-10 8.26906E 10 1.49502E-09 6.17E-10 7 74724E -1 0 1.3 4151E-09 4 98E-10 6.4521E-10 1 .15731E-09 4 30E-10 7.25282E-10 1.13949E-09 4.53E-10 8.5844E-10 1.2576E-09 4 74E-10 8.31839E-10 1.31557E -09 4.76E-10 8 .4 6361E-1O 1.42327E-09 4.79E-10 7 7979E-10 1.32852E-09 5 38E-10 6.46949E-1O 1.22177E-09 5.88E-10 6.22712E-10 1. 13763E-09 5 08E-10 7 45272E-1O 1.08968E-09 4.71E-10 6.70459E-10 1. 13448E-09 5.42E-10 6 29909E-10 1.24494E-09 5.66E-I0 6.56656E-10 1.38422E-09 3 41517E-09 4.6952E-09 3.46899E-09 4.9813E-09 3 29359E-09 4.1511E-09 2.97278E-09 3 5502E-09 2 82447E-09 3.6783E-09 2 68768E-09 4.0382E -09 2.8077E-09 4.0465E-09 2.70722E-09 3.7694E-09 2.58557E-09 3.3979E-09 2.96347E-09 3.54E-09 2.99181E-09 3.6721E-09 3.03776E-09 3.4344E-09 3.16623E-09 3 7006E -09 3 11198E-09 4.348E -09 2 75602E-09 3.5579E-09 2.69854E -09 3.154E-09 2.71432E-09 3.4504E-09 3.15032E-09 3.3289E-09 3 22724E-09 3.4649E -09 2.9502E-09 3.4203E-09 2.68309E-09 2.95E-09 2 79227E-09 2 9856E 09 2 70696E -09 2.4311E-09 3 86341E -09 3.54429E-09 3.50821E-09 4.53272E-09 5 .2 9806E-09 6 07329E-09 7 03336E-09 7 05094E-09 6.43679E-09 6 07189E-09 5.6315E -09 5.29622E-09 4.95973E-09 4.71529E-09 4.57672E-09 5 22048E-09 5 20992E-09 4.99809E -09 4.77114E-09 4.50915E-09 4.69667E-09 4.24005E-09 3.69826E-09 4.71E -I0 7 04121E-10 1.3432E-09 2 71967E-09 2 1674E-09 3.78759E-09 4 45E -I0 7.12343E -I0 1.21577E-09 2.58856E-09 2.5517E-09 3.75129E-09 4.06E-I0 7.18194E 10 1.11488E-09 2.50329E-09 2.5851E-09 3 76395E-09 4.27E -1O 7 07951E-10 9 27161E-1O 2 68202E-09 2.5011E-09 4 00889E-09 4.09E-I0 7 25061E-10 9 69959E-10 2.46697E-09 2.0624E-09 4.48736E-09

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9.83248 10.18012 0.1776766 10.54012 0.1839598 10.91292 0 1904664 11.29899 0.1972046 11.69882 0 2041829 12.11289 0.2114098 12 54174 0 2188947 12 98589 0 2266465 13.44591 0 2346754 13.92239 0.2429915 14.41592 0.2516053 1 4.92714 0.2605 2 77 15.45671 0.2697705 16.0053 0.2793452 16.57362 0 2892642 17 16242 0.2995407 17 77247 0.3101881 18.40457 0.3212203 19 05955 0.3326519 19 73829 0.3444981 20.44171 0.3567751 21.17075 0.3694993 21.92642 0 3826882 22.70975 0.3963599 23.52185 0.4105337 24.36384 0.4252292 25 23694 0.4404677 26 14241 0.4562711 27 08155 0.4726622 28 05578 0.4896657 29.06655 0.507307 0.000229677 0 000237776 0 000246162 0.000254842 0 000263829 0 000273133 0.000282765 0.000292737 0.00030306 0.000313748 0.000324812 0 000336266 0 000348125 0.000360402 0 000373111 0 000386269 0.00039989 0.000413993 0.000428592 0.000443706 0.000459354 0.000475553 0 000492323 0.000509685 0.000527659 0 000546267 0 000565531 0 000585474 0.000606121 0 000627495 0 000649624 0 000672533 1ppm 9 94E-11 2.70044E-10 9 00E-11 2.94011E -10 9.32E-11 2 79761E-1O 8.54E-11 2.74477E -1O 7.70E-11 2.61479E-1O 8.26E-11 2 66511E-1O 7.18E-11 2.50602E-10 6.32E 11 2 .48555E-1O 5.72E-11 2.48741E-10 6 09E 11 2 21009E-10 5.43E 11 1.77764E-10 4.89E-11 1.76212E-1O 5.25E-11 1.75779E-10 4.27E-11 1.72848E-10 4.21E-11 1.56903E-10 3 74E-11 1.284E-1O 3 .22E11 1.23611E-1O 3 33E-11 1.16423E -1O 3.22E -ll 1.04707E 10 3.56E 11 9.05291E-ll 2 95E-11 8.34181E-ll 2.80E-11 7 91784E-11 2 63E-11 6.93415E -ll 2 72E-11 5.50617E-ll 2.25E-11 5.03133E-ll 2.32E 11 5 17093E-11 2.40E-11 4.41223E-11 2 48E-11 3 .28496E-ll 1.92E-11 3 64066E-11 1.66E-11 2 .55845E-ll 2 05E-11 2 .1142E-ll 1.77E-11 1 96923E-11 2ppm 5ppm 10ppm 20ppm 40ppm 3.76E-1O 6.70133E-10 9 80759E -10 2.41336E-09 2 1649E-09 3 21E-10 6.93954E-1O 1.14405E-09 2.31685E 09 2.1535E-09 3.32E 10 6 20484E-10 1. 11027E -09 2 27086E-09 1.9488E-09 3.17E-10 5.54103E 10 8 88829E-10 2 12442E -09 1.7773E-09 2.96E-10 5.56573E-10 8.43115E-10 2 12042E-09 2 0577E -09 3 08E-10 6.39771E-1O 7.81404E-10 2.03543E-09 2.1608E-09 3.01E-10 5.63593E-10 8.35363E 10 1.82777E-09 1.8827E-09 2 93E-10 5 21892E-10 8 09451E-10 1.72901E-09 1.5663E-09 2 78E-10 4 41671E-10 7 53954E -10 1.48153E-09 1.4717E 09 2.51E-10 4 37566E -10 6.93037E-10 1.46791E-09 1.4476E-09 2.34E-1O 4 15854E-10 6 69699E-10 1.53452E-09 1.5888E-09 2 09E-10 3 71846E 10 6.39937E-10 1.4279E-09 1.4678E-09 2 10E-1O 3.44461E-10 6 42462E-10 1.26471E-09 1.1616E-09 1.79E-10 3.26038E-1O 5.99456E-1O 1.28203E-09 1.4042E-09 1 67E-10 2.73261E-10 4.59837E -1O 1.20614E 09 1.2643E-09 1.66E-1O 2 71606E-10 3.89908E 10 1.01877E-09 1.0582E-09 1.36E-10 2.6102E-10 3.64076E-10 9.41621E1 0 9.8671E-10 1.21E 10 2.54119E-10 3.60723E-10 1.06919E-09 1.047E-09 1.16E-10 2 1727E-10 3 78074E-10 9.20217El 0 8.7427E-1O 1.17E-lO 1.95072E-1O 3 51888E-10 7 77187E-10 7 9857E-1O 1.08E-10 1.81709E-1O 3.1686E-10 6 90367E-1O 8 2306E-10 1 02E-10 1.60496E -1O 2.85013E -10 6.8906E-10 8.3391E-1O 9.56E-11 1.61312E-10 2.95325E-10 5.63353E-1O 8 4452E-10 7.41E-ll 1.22986E 10 2.37099E-10 5.22379E-10 6 3649E-10 5.87E-ll 1.26156E-1O 2 21662E-10 5.16606E-10 6.2615E-1O 80ppm 3 78012E-09 3.22991E-09 3 09208E-09 2 69468E -09 2.6037E-09 2.84539E-09 2.57131E-09 2.28516E-09 2 12408E -09 2.16666E -09 2 10699E-09 1.85178E -09 2 10624E 09 1.82886E-09 1.69966E-09 1. 6 3518E-09 1.33238E-09 1.18024E-09 1.44398E-09 1.34267E -09 1. 14496E -09 1.02703E -09 9.41743E-10 8 70152E -1O 8.59306E-10 5.46E-ll 1.03978E-1O 2.2594E-10 4.49537E -1O 6 1505E-1O 8.00903E-1O 4.41E-11 9 21473E -ll 1.85196E 10 4.13316E-10 5.9641E-1O 6.77451E -10 4 22E-11 7.93828E -ll 1.72449E-10 3.74092E -10 5.3851E-10 6.87417E -10 3 64E-11 6.52591E 11 1.42199E10 3.21725E-10 5.4293E-10 7 41688E -1O 2 89E-11 6 20215E -ll 1.34896E-10 2.70706E-10 4 2639E-10 6 25141E -10 2.46E-11 4.8519E-11 1.03273E-10 2.57269E-10 3.394E-10 5 37883E-10 1.97E-ll 4.09015E-11 8 33198E -ll 2 17645E-10 3.6611E-10 4.54482E-10

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30.1154 0.5256129 31.20397 0.544612 32.33398 0.5643344 33.50725 0.5848118 34.72573 0 6060783 35.99145 0.6281693 37.30662 0.6511234 38.67356 0 674981 40 09476 0 6997856 41.5729 0.725584 43 .11 082 0 7524258 44.71162 0.780365 46.37863 0 8094598 48.11544 0.8397728 49 92598 0 8713727 51.81451 0 9043338 53.78571 0 9387377 55.84472 0 9746742 57.99721 1.0122423 60.2495 1.0515521 62.60861 1.0927264 65 08246 1.1359032 67 67999 1.1812387 70.41142 1.2289111 73.28846 1.2791249 76.32474 1.332118 79.53623 1.3881691 82.94193 1.4476098 86.56472 1.5108394 90.43268 1.578348 94.58093 1.6507486 99.05445 1.7288263 0.00069625 0 000720803 0.000746222 0.000772537 0 000799781 0.000827985 0.000857184 0.000887413 0.000918707 0 000951105 0.000984646 0.001019369 0.001055317 0.001092533 0.001131061 0.001170948 0.001212241 0 001254991 0 001299248 0 001345066 0.0013925 0 001441606 0 001492444 0.001545075 0 001599562 0 00165597 0 001714368 0.001774825 0.001837414 0.001902211 0.001969292 0.002038739 1.46E-11 1.82279E-11 1.13E-11 1.29891E-11 1.17E-11 9.32213E 12 8 03E-12 7 61525E-12 8.29E-12 7 71217E-12 8.55E-12 3 52617E-12 4 .4 1E-12 6.14696E 12 4.55E-12 6.25217E -12 4.69E 12 6.35414E-12 6 .64E-l00 4 82816E 12 6.83E-l00 4 .9 7251E-12 7.04E-l00 5.11896E-12 7.24E-l00 5.26721E-12 7.44E-l00 7.4449E-100 7 .65E-l00 7.6521E-l00 7.86E-l00 7.8601E-l00 8 .07E-l00 8.0681E-l00 8.28E-l00 8.2752E-l00 8.48E-l00 8.4802E-l00 8.68E-100 8.6819E-l00 8.88E-l00 8.8788E-l00 9 .07E-l00 9.0692E 100 9.25E-l00 9 2508E-l00 9.42E-l00 9.4212E-100 9.58E -l00 9.5776E-l00 9.72E-l00 9 .7165E-l00 9.83E -l00 9.8337E-l00 9.92E -l00 9.9242E -l00 9.98E -l00 9 .982E-l00 1.00E-99 9 .9997E-l00 9.97E-l00 9 .9681E-l00 9 .88E-l00 9.8754E-l00 5ppm 10ppm 1 09E-11 3.28307E -11 7.29882E -11 9 .22E-12 2.80675E-11 7.33026E-11 9.32E-12 2 48885E -11 5.99128E-11 7 62E-12 1.96652E-11 4.77818E-11 3.57E-12 1.60017E -11 3 67255E-11 3.53E-12 1.20779E-11 3.34572E-11 1.74E-12 1.05568E-11 3.26061E-11 1.71E-12 1.07988E-11 2.44387E-11 1 .6 7E-12 1.10403E-11 2.04125E-11 4.83E-12 9 65631E -12 2 41408E-11 4.97E-12 9 94501E-12 1.98901E-11 5.12E-12 1.02379E-11 2.04759E-11 7.24E-l00 5.26721E-12 1.58016E-11 7.44E-l00 5.41693E-12 1.62508E 11 7.65E-l00 5.5677E -1 2 1.l1354E-11 7.86E-l00 7 8601E -l00 1.14381E-11 8 07E-l00 8.0681E-l00 5.87038E-12 8 .28E-l00 8.2752E-l00 6.02104E-12 8.48E-l00 8.4802E-100 6.17022E-12 8.68E-l00 8.6819E-l00 8 .6819E-l00 8.88E-l00 8 .8788E-l00 8 .8788E-l00 9 .07E-l00 9.0692E-l00 9 0692E-l00 9 25E-100 9 .2508E-l00 9.2508E-l00 9.42E-l00 9.4212E-l00 9.4212E-l00 9.58E-100 9.5776E-l00 9.5776E-l00 9 72E-100 9 .7165E-l00 9.7165E-l00 9 83E 100 9.8337E-l00 9.8337E-l00 9 92E-100 9 .9 242E -l00 9.9242E-l00 9.98E -l00 9 .982E-l00 9.982E-l00 20ppm 40ppm 1.9346E-l0 3.2854E-1O 1.60003E-l0 2.844E-l0 1.37745E-l0 2.8563E-l0 9.99985E-11 2.1246E -l0 8 23179E-11 2 .0666E-l0 7 .1 9397E-11 1.7884E-l0 6.78847E-11 1.6049E-l0 6.53585E 11 1.381E-l0 4.85294E-11 1.3757E-l0 4.82815E-11 1.207E-l0 4.47526E-11 1.1437E-l0 4.09517E-ll 1.0238E-l0 4.21377E-11 8.9542E-11 4.33354E-11 8.6671E-11 2.78385E 11 8.3515E-11 2.28762E-11 6.8628E-11 2.34816E-11 5 2833E-11 1.80631E-11 4.8168E-11 1.23404E-11 4.3 1 91E-11 6.31699E-12 3 1585E-11 6.46026E-12 1.9381E-11 9 0692E-100 1.3197E-11 9.2508E-l00 1.3462E-11 9.4212E -l00 1.371E-11 9.5776E-l00 1.3937E-11 9.7165E -l00 1.4139E-11 9.8337E -l00 7.155E 12 9.9242E-l00 7.2209E-12 9 .982E-l00 9.982E -l00 1.00E-99 9.9997E-100 9.9997E-l00 9 9997E-l00 lE-99 80ppm 4.12501E-l0 3.48483E -l0 3 .28433E-l0 2 .88782E-l0 2 .35674E-l0 2 21594E -1O 2 .0018E-l0 1.83571E-1O 1.46938E-l0 1.25532E-l0 1.14368E-l0 1.07498E-l0 9.48096E-11 8 12538E -11 7 23799E-11 6 86283E-11 5 28334E-11 4 81683E-11 3 08511E-11 3.15849E-11 2.58411E-11 1.97961E-11 2 01926E-11 2.05647E-11 1.39374E-11 1.41395E-11 1.431E-ll 1.44417E 11 7 26294E-12 7 2758E-12 9.97E-l00 9.9681E-l00 9.9681E-l00 9.9681E-l00 9 .968E-l00 7.25277E-12 9.88E -l00 9.8754E-l00 9.8754E-l00 9.8754E -l00 9.875E-l00 9 8754E-100

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Ippm 2ppm 5ppm lOp pm 20ppm 40ppm 80ppm 103.9126 0 002110635 9.71E-I00 9.7066E-I00 9.71E-I00 9.7066E-I00 9 7066E-I00 9.7066E-I00 9.707E-I00 7.06256E 12 109.2368 1.9065411 0.002185066 9 44E-I00 9.4417E-I00 9.44E-100 9.4417E-I00 9.4417E-I00 9.4417E-100 9.442E-I00 9.4417E-I00 115.1439 2.0096403 0.002262122 9.05E -I00 9 0524E -I00 9.05E-I00 9.0524E-I00 9.0524E-I00 9.0524E -I00 9.052E-I00 6.58656E-12 121.814 2 1260547 0.002341896 8.50E-100 8.4976E-100 8.50E-I00 8 4976E -I00 8.4976E -I00 8.4976E -I00 8.498E-I00 8.4976E-I00 129.5516 2 2611016 0.002424483 7.71E-I00 7.7105E-I00 7.71E-I00 7.7105E-I00 7.7105E-100 7.7105E-I00 7 711E-I00 7.7105E-I00 138 9598 2.4253066 0.002509982 6.57E -I00 6.5659E-I00 6.57E-100 6.5659E -I00 6.5659E-I00 6.5659E-I00 4 7773E-12 4 77734E-12 151.6614 2.6469911 0.002598496 4.75E-I00 4.7468E-100 4.75E-I00 4 7468E-I00 3.45378E-12 1.03613E-11 1.3815E-11 2.07227E-11

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APPENDIX B AutoCAD Drawings of SLS Column Holder 7 8

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,---L ___ x2) o 2 CONCEPTUAL SKETCH 10/03/08 AS NOTED

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----...,-.C \.000 I T ONoT TBD r +---. ___ ._---'_ LT------,---l 1 __ --2000-1-------4 .500 -----L; r---------+ F 0.000 o 2 10/03/08

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1--1-----1-0,610 -1.750-1 1--2,000 [ 0,250

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+ (THREADS DD)

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4 o C B 4 MFG 10/ 7 / 2008 C A REV

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4 c A QA APPROVED 1 2 3 4 S 6 C QTY 2 1 2 1 B 10/ 7 / 2008 TITlE REV

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BIBLIOGRAPHY Backcountrygear.com, "Katadyn Hiker", (September 22, 2009) Bushell, G.c., Yan, Y. D. Woodfield D ., Raper, 1. and Amal, R. (2002) "On techniques for the measurement of the mass fractal dimension of aggregates," 95, 1-50 Huglin, M. B. (1972) "Light Scattering from Polymer Solutions" Academic Press, London and New York Mays, D.C. (2009), "Contrasting clogging in granular media filters, soils, and dead-end membranes", submitted Mays, D.C. and Hunt (2007), "Hydrodynamic and chemical factors in clogging by montmorillonite in porous media", 41(16),5666-5671. Min, M., Dominik, c., Hovenier, 1. W., Koter, A. de., and Waters, B. F. M., (2006) "The amorphous silicate features of fractal aggregates and compact particles with complex shapes", (September 22, 2009) 85

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Mokhtari, T., Sorensen, C. M., and Chakrabarti (2005) "Multiple Scattering Effects on Optical Structure Factor Measurements," 44, 7858. Russo, P S., (1997), "Gunnier Plot: a Light Scattering Primer", (July 2, 2009) Sorensen, C.M. (2001), "Light scattering by fractal aggregates: A review." Aerosol Science and Technology 35(2), 648-687 Teixeira, J. (1988) "Small Angle Scattering by Fractal Systems," 21, 781-785 Veerapaneni V. and M .R. Wiesner, "Deposit Morphology and Headloss Development in Packed Bed Filters," Environmental Science and Technology, 31(10):2738-2744, 1997 Wiesner, M.R. "Morphology of Particle Deposits," Journal of Environmental Engineering, 125(12), 1124-1132, 1999. Wikipedia.com, (2009), "Refractive Index", < http :// en.wik ipe dia.org/wiki / List of refractive indic es> (July 2, 2009) 86