RELATING SOLUBILITY TO CLUSTER CHEMISTRY
IN SUPERCRITICAL SOLUTIONS
Kent Allen Stephens
B.S., Texas Christian University, 1993
A thesis submitted to the
University of Colorado at Denver
in partial fulfillment
of the requirements for the degree of
Master of Science
This thesis for the Master of Science
Kent Allen Stephens
has been approved
Stephens, Kent Allen (M.S., Chemistry)
Relating Solubility to Cluster Chemistry in Supercritical Solutions.
Thesis directed by Professor Larry Anderson
and Senior Professional Research Assistant Jeff Boon
Currently there are a few techniques being used to look at the extent of clustering in
supercritical solutions. These techniques although useful are not universally applicable
and require expensive instrumentation. This paper looks at a new technique that is
capable of measuring this extent of clustering. The use of viscosity and solubility data
in calculation of the extent of clustering in a supercritical solution was looked at in this
research. The viscosity of a fluid provides a means of calculating the effective
diameters of the species in the fluid. In a supercritical solution the viscosity of the
clustered species can be estimated through a combination of overall solution viscosity,
pure solvent viscosity and solute solubility. From the effective cluster sizes the extent
of clustering of solvent molecules around a solute can be estimated from a packing
density model. This information could then be used to further the understanding of
molecular interactions in supercritical solutions. A better understanding of this would
lead to improved equations of state for supercritical fluids in general.
This abstract accurately represents the content of the candidates thesis. I recommend
I dedicate this thesis work to my parents and my grandmother for all their help over
1 Introduction...................................................... 1
1.1 Benefits of SCFs.................................................. 1
1.2 Problems with SCFs................................................ 2
2 Solubility and clustering......................................... 5
2.1 Clustering........................................................ 6
2.1.1 Categories of clustering.......................................... 6
2.2 Solubility vs. clustering......................................... 8
2.3 Current research into clustering........................................ 10
2.3.1 Solvatochromic shifts vs. clustering extent............................. 10
2.3.2 Rotational relaxation via fluorescence measurements..................... 12
2.4 Goal of this research................................................... 14
3 Theoretical Background.................................................. 16
3.1 Hard sphere approximation............................................... 16
3.1.1 Viscosity and effective diameter........................................ 17
3.1.2 Viscosity of mixtures................................................... 18
3.1.3 Molecular weight of clusters............................................ 19
3.1.4 Effective diameter of clusters........................................ 19
3.1.5 Cluster extent vs. ratio.............................................. 21
4 Instrumental section.................................................. 22
4.1 Solubility measuring.................................................. 22
4.1.1 Dynamic systems....................................................... 23
4.2 Instrumentation used in this study.................................... 24
4.2.1 Initial problems with instrumentation................................. 25
4.3 Solute selection...................................................... 27
4.3.1 Scrubber solvent choice............................................... 28
4.3.2 Experimental procedure................................................ 29
4.3.3 Viscosity calibration................................................. 30
4.3.4 Problems with instrumentation......................................... 35
5 Experimental results.................................................. 37
6 Detection limit....................................................... 38
7 Future work........................................................... 40
8 Conclusion............................................................ 42
The state of matter known as supercritical fluid has been studied since the late
1800s. Included in these early studies was the phenomenon of solubility in a
supercritical fluid (or SCF). However, most researchers at that time did not realize
what they were working with. One such researcher, Professor William Ramsay of the
chemistry Department, University College, Bristol, referred to it as a hot liquid in a
famous debate over the phenomenon of solubility in SCFs. The lack of technology to
produce this state of matter slowed the continuation of any research for a long time.
Subsequently, WWD and the following cold war kept most of the research very
secretive for another long period.
The cold war is now over, and SCFs have now become one of the fastest
growing areas of scientific research. This is mainly due to their many unique physical
properties and their enhanced ability to dissolve solutes. This solubility enhancement,
the same phenomenon studied in the late 1800s, is still an area of much debate and
research. Although it is easier to achieve the necessary conditions for the supercritical
state, research in the area is still hampered by the high cost of the instrumentation, the
hazards inherent with the work, and the lack of a completely accepted theoretical basis
for research in the area. The work described in this thesis is designed to help solve the
1.1 Benefits of SCFs
Some of the reasons for increased interest in SCFs is because of their
attractiveness as an alternative solvent in separation processes. One reason is the fact
that more environmentally benign solvents can be used in place of organic solvents in l
many of these processes. Some of the more common SCFs used are CO2 and water,
with C02 being the most common. Although CO2 is a greenhouse gas, both of these
compounds are generally considered to be more environmentally friendly than the
alternative organic solvents. Also the fact that they are able to be recycled in most
processes, makes them even more appealing.
The fact that the physical properties of an SCF can be varied over a continuum
by simple adjustments of the temperature and pressure also make it an attractive
alternative. For example, in SCF-chromatography, adjusting the conditions of the
eluent, makes it possible to achieve the same effect as a gradient type of eluent system
in HPLC. This feature is also attractive in the extraction process. Here the extracted
substance can be easily recovered from the supercritical solvent by rapidly changing
the solvent pressure and/or temperature conditions. Besides being faster, this type of
extraction has the added benefit of recovery of a pure substance, without residual
1.2 Problems with SCFs
A supercritical fluid is one of the five states of matter, along with solid, liquid,
gas, and plasma. It has physical properties that parallel both liquids and gases as well
as some unique properties, as can be seen in Table l.l1. The diffusivity and the
viscosity of this state are very similar to that of gases, but the solvating ability and
density are more closely related to liquids. Along with these properties SCFs also
have a high compressibility and a unique type of solute-solvent clustering. Because of
these widely varied physical properties, as well as the fact that each of these properties
varies with temperature and pressure conditions, none of the accepted equations of
state (EOS) for other states of matter work adequately for SCFs.
Table 1.1 Properties of SCFs
Density (e/cm3) Viscosity (CD) Diflusivity (m2/s)
Gas (0.6-2)xl0'3 (l-3)xl0'2 (0.1-0.4)xl0
SCF at the critical pt. 0.2-0.5 (l-3)xl02 7x10-
Liquid 0.6-1.6 0.2-0.3 (0.2-2)xl0'9
There are currently a large number of researchers working on an improved
EOS for this state of matter. Besides improving the equation of state, many scientists
are also looking at improving the mixing rules for existing equations of state. The
biggest problem is in developing an EOS that accurately represents multiple
component systems, which is why the mixing rules are also considered.
The intermolecular interactions in a supercritical solution are not completely
understood. The mixing rules which include the van der Waals interaction constant,
an, do not fully describe the phase behavior of a system. In a paper by Debenedetti
and Mohamed3, the Lorentz-Berthelot mixing rules, equation 1.1, were evaluated for
their ability to describe an SCF binary system. The authors noted that, when using the
van der Waals model to predict a near-critical system, there was a very high deviation
of the Lorentz-Berthelot an value. Many other groups have found similar results with
different mixing rules as well as various equations of state.3"7 A better understanding
of the precise molecular interactions would be of immeasurable value in developing
more adequate equations of state and mixing rules.
One way of approaching this problem is by looking at one of the physical
properties of these systems in more depth. In this research the property of solute-
solvent clustering is being studied, and the instrumentation is being developed.
2.0 Solubility and Clustering
It has been shown that the solubility of a solute in an SCF can be enhanced by
as much as 6 orders of magnitude over the predicted gas phase solubility2. This is
generally attributed to the liquid-like density of the solvent in the supercritical phase.
It has been demonstrated that the solubility of a solute, in an SCF, increases rapidly
with increasing density of the solvent8. Supercritical fluids have several anomalies
associated with them, such as retrograde solubility. Retrograde solubility is a
characteristic of SCFs where the solubility of a solute in the fluid decreases with
increasing temperature in some regions. This anomaly and others associated with
supercritical fluids can be explained by looking at the density of the solvent. The
solubility is shown to increase rapidly with increasing pressure at a fixed temperature.
This is due to the high isothermal compressibility factor of SCFs. As the pressure
increases the density increases along with it, and thus increasing the solvating power of
the solvent. It has also been shown that, at low pressures, an increase in the
temperature causes a slight drop in the density of the fluid8. With this drop in fluid
density comes a decrease in solvating power, and the resulting observations are a
decreasing solubility with increasing temperature. This is the cause of the retrograde
solubility phenomenon of supercritical solutions in the vicinity of the critical point.
Figure 2.1 Diagram of solute-solvent cluster
There is another factor that helps contribute to the enhanced solubility, other than
solvent density, and that is the clustering phenomenon. In an SCF solution the
density of the solvent molecules in the bulk solution often differ from their density in
the localized region surrounding the solute molecule, as can be seen in Figure 2.1.
This density enhancement or regression is known as the solute-solvent clustering.
2.1.1 Categories of clustering
There are three main categories of clustering; attractive, weakly-attractive,
and repulsive. In the attractive system there is a large number of excess solvent
molecules surrounding the solute. It has been calculated that there may be as many as
100 molecules of solvent, in excess of the bulk, surrounding a given solute molecule.8
A weakly-attractive system has a slight excess of solvent molecules, with respect to
the bulk, surrounding the solute. In the repulsive system there is actually a decreased
number of molecules in the region localized about the solute. Most systems seem to
fall within the attractive category and are thus more convenient to discuss.
The clustering effect was first discovered by measurements of the solute partial molar
volumes in supercritical solutions. The partial molar volume, V, is an intensive
property of matter that for an ideal gas is equal to the volume, V, divided by the
number of moles, n, of the substance. In a binary system the sum of the individual
partial molar volumes times the respective number of moles of each substance gives
the overall volume of the system.
In early measurements of partial molar volumes it was noted that in some
systems the partial molar volume of the solute was a large negative value, up to
-10,000 cc/mole.9 These values could only be explained by a large number of solvent
molecules condensing around the solute. Debenedetti et. al2 then defined the
following relationship between the partial molar volume and the extent of clustering.
Where VT is the partial molar volume at infinite dilution, or dilute enough to where
there are no solute-solute interactions. The value, p, is the solvent density, k is
Boltmanns constant, Kt is the solvents isothermal compressibility, T is the
temperature, and t, is the number of excess solvent molecules surrounding the solute
with respect to the bulk.
In an attractive type system the addition of solute attracts solvent molecules to
it, causing a pressure decrease at constant volume:
where xx is the mole fraction of the solute. In a repulsive type of system the solute will
repel the solvent molecules, resulting in an increase in pressure. In this case the solute
is surrounded by an area of reduced solvent density and the value of 2, becomes
negative. This pressure-mole fraction relationship can be used to help determine
cluster types in a system.
2.2 Solubility vs. clustering
Although there is not a straight-forward relationship between the clustering
and solubility, it is thought by some that this clustering effect is responsible for the
enhanced solubility of solutes in SCFs, in the region near the critical point. In fact,
increased solubility in this region is thought to be dependent upon an attractive type of
It is believed that the increased interactions between the solvent and solute
with increasing solvent density, is the chief reason for the increase in solubility; but the
clustering about a solute molecule generally decreases with increasing bulk solvent
density. In an attractive system, one where the localized density of solvent is
enhanced, this would mean that as the number of solvent molecules clustering around
the solute decreased, the solubility increased. Although at first this seems contrary to
the theory of increased interactions paralleling increased solubility it does not however
threaten it. Since the clustering is defined as the excess number of local solvent
molecules with respect to the bulk, as the bulk density increases it can be reasoned that
the solvent clusters are simply absorbed into the bulk solution or the bulk density
gradually becomes equal to the cluster solvent density. The number of solvent
molecules in contact with the solute does not decrease, the nature of them just shifts.
Solubility is very dependent on the intermolecular interactions in solution.
Thus, the solubility of a compound in solution begins to shed some light on the
solvating mechanism. Since clustering has been credited with some of the solubility
enhancement, it is an area worthy of study. The type of clustering in the solution may
be of importance. For example a compound that induces a repulsive type cluster
experiences very different intermolecular forces with the solvent than does a solute
that induces an attractive type cluster. The extent and the persistence of a cluster
should also be considered. As previously mentioned the extent of clustering declines
as the density of the bulk solution increases. It would be interesting to look at the
diminishing effect on these clusters in two similar systems.
Knowledge of the type of molecular interactions present in a binary
supercritical system could prove to be very beneficial in the development of a new
equation of state for these solutions. The predominant theory now is that the
intermolecular forces at work in the solvating process and the cluster formation in
SCFs are the van der Waals long range forces.11 These forces include dipole-dipole,
dipole-induced dipole, and dispersion forces. The nature of the electric dipole
moments in a solution govern which of these forces are felt. It has been suggested by
some that the dielectric constant of an SCF varies with temperature and pressure
conditions.12 It would at first appear so since the solubility in the system is very
dependent on experimental conditions, but this can also be explained by the increased
molecular interactions, as described above.
The van der Waals forces are not all of equal strength. The dipole-dipole
forces are the strongest attractive forces and the dispersion forces the weakest. It has
also been suggested by some that hydrogen bonding may exist in supercritical systems,
although this is not yet confirmed. Hydrogen bonds are even stronger forces than the
dipole-dipole forces. The type of bonding undergone in the system may account for
the type or extent of clustering.
2.3 Current research into clustering
The nature of these clusters and in fact the solvating mechanism in SCFs is
under considerable debate.2 In recent articles the presence or absence of hydrogen
bonding in supercritical water has been debated.(12'14) Researchers are looking at
whether or not these type of bonds exist in clusters of water molecules in the fluid.
While some experiments have seemed to provide evidence for it, others have had
opposing results and still other results have been inconclusive. Spectroscopic
evidence13 supports the presence of hydrogen bonding while neutron diffraction
experiments oppose it. Obviously the presence or absence of hydrogen bonding could
go a long way toward explaining the interactions of supercritical water in solutions.
There are other groups who are attempting to measure the extent of clustering
in a system and derive some results about the intermolecular forces from this
information. This type of research can presently be divided into two main groups.
The first group is using the solvatochromic shift of a solute in supercritical solutions to
estimate the clustering extent.(15'19> The other group is using the rotational relaxation
time of various species in solution.20,21
2.3.1 Solvatochromic shifts vs. clustering extent
By using the shift in the position of maximum absorbance in spectra versus
solvent density, some idea of the solvent strength can be determined. The solvent
strength is dependent upon the type of forces involved in the solvating process.
Determining the solvent strength can then lead to a better understanding of the types
of forces involved.
In the spectroscopic shift, or solvatochromic, method a linear relationship of
solvation energy is used.15 The shift in the absorption maximum is linearly related to
the hydrogen bond abilities, and polarity/polarizability of the solvent. A term n* is
used to represent the polarity/polarizability term. The 7t* term correlates the solvent
effect on the solutes p7t* and 7t7t* electronic transitions, and is thus measurable.
By using a system that minimizes the hydrogen-bonding interactions and
charge transfer interactions, a simple equation relating the wavenumber of the
maximum absorbance, Vmax, to a reference wavenumber of a standard solution, vG,
could be derived.15
Vmax= V0 + S7t* (2.4)
The term s in equation 2.4 represents the susceptibility of the spectroscopic shift to
changing the %* value and is dependent upon the solute of interest. For this reason the
s value must be determined experimentally for each different system.
Once the value of tc* is found a solvation model can be employed to estimate
the density of the solvent surrounding the solute. This then gives an estimation of the
extent of interaction between solute and solvent. The problem with this is that the
solvation model and the solvatochromic behavior only reflect the solvent environment
in the immediate vicinity of the solute. Partial molar volume data appears to suggest
that these solvent interactions in the clusters would extend over a larger volume. This
means that this type of measurement is only accurate for small cluster sizes covering
only the first solvation shell in the cluster.15 This method also requires some
knowledge of the solute solvent interaction parameters prior to performing the
experiment. These values are not available for all substances.
The main problem with this type of measurement is that it is not applicable to
compounds containing certain types of functional groups. Since the compounds which
are most susceptible to large solvatochromic shifts are also those with functional
groups that experience charge transfer and/or hydrogen bonding, this method has a
limited range of application.20
2.3.2 Rotational relaxation via fluorescence measurements
Another method of measuring cluster sizes has just recently been tested. This
method uses the measurements of molecular rotational relaxation of solutes in
supercritical solutions. The rotational relaxation time is related to the fluorescence
lifetime of the molecule, since the rotation is a nonradiative way for the molecule to
relax it will affect the fluorescence lifetime. The proposed relationship between the
local solvent density and the fluorescence lifetime states that, by increasing the
viscosity of the surrounding solute, the non-radiative pathways for molecular
relaxation are slowed, thus increasing the lifetime.20 As the density of the solution
surrounding the molecule increases the solute-solvent friction increases and thus the
fluorescence lifetime also increases. The group of Kauffinan and Anderton20 have
derived an equation relating the measured rotational correlation time, the
experimentally derived rotational correlation time at a fluid viscosity of zero, and the
local solvent density. This gives a direct way of measuring the fluid density
surrounding the solute.
This relationship is not intuitively obvious when looking at the possible
mechanisms for the relaxation of an excited molecule. The lifetime of the excited state
of a molecule in inversely related to the einstein coefficient for spontaneous emission,
A2i, and the rate constants for internal conversions times the concentration of other
species available for collisional quenching, k[M], Collisional quenching occurs when
the excited molecule collides with another species that has an appropriate energy level
to absorb the energy of the excited species. As the density of the localized solvent
increases the number of collisions should increase, concentration of M goes up. This
increased number of collisions should decrease the lifetime of the fluorescence state, or
if the concentration becomes high enough it should prevent fluorescence activity
altogether. The experimental evidence of Kauffman and Anderton20 seems to suggest
the opposite is true though. Apparently the lifetime, as they are measuring it, is
directly related to the speed at which the molecule rotates, and thus increases with
increasing viscosity of the surrounding solvent.
This method however also has some limitations. The first being that it only
measures the density of the localized solvent, or solvent in the immediate vicinity of
the solute, and not the extent of the clustering or solvent shell. This method also
requires that certain solute specific constants be known for it to work. One of these
constants is the van der Waals volumes of the solute. In the present research these
volumes were estimated using a group contribution method. These methods work
well for organic compounds but would limit the ability of this method to inorganic
solutes. The most important limitation of this method is that large solute molecules
are needed in order for the technique to work. Since the method depends on the
solvent viscosity to increase the fluorescence lifetime, at the low fluid viscosity of the
supercritical fluid the lifetime is much shorter. For small molecules the lifetime would
be expected to be on the order of a picosecond or less.21 Thus large molecules are
used to create longer, more easily measured lifetimes.
Despite their limitations both of these methods are capable of providing some
useful information on the nature of the solvating mechanism in supercritical solutions.
A current literature search though only turned up one group using any of the current
methods to compare similar solute structures.
The group of Anderton and Kauffman20 are measuring experimentally the
solute-solvent interaction parameters for structurally similar molecules. By measuring
the rotational correlation time of a particular solute in supercritical CO2 and relating it
to the local solvent density, they have a means to compare solute-solvent interactions.
Figure 2.2 Structures of DPB and HMS
In their study they used diphenylbutadiene (DPB) and 4-(hydroxymethyl) stilbene
(HMS) as the solutes. The structures of these molecules are shown if Figure 2.2.
They have determined from their study, that in supercritical CO2 solvent, the local
solvent density about the HMS is much greater. They have then paralleled these
findings to the rotational correlation times of both solutes in room temperature hexane
and ethanol. The results suggested similar local densities in the nonpolar hexane, but
different effects in ethanol. In the ethanol solvent, the HMS experienced a much
greater rotational friction. The most obvious conclusion is that the hydroxyl group on
the HMS molecule is creating the added solute-solvent interactions. The same can be
concluded from the SCF CO2 system. Since both molecules contain similar conjugated
7C electron systems it can be reasoned that the hydroxyl group on HMS causes the
One problem with a direct comparison of these two systems may arise in the
difference between the diameter of the two solutes. An increase in solute diameter
with respect to the solvents results in a loss of the van der Waals attractive behavior.22
This is because the attractive or repulsive behavior in a van der Waals system is
dependent on the ratio of solute to solvent specific energies, which are based upon the
These results still appear to hold some promise in describing the molecular
interactions of the clustering in these systems. Further work needs to be added before
anything conclusive can be drawn from these results.
2.4 Goal of this research
This project was designed to resolve some of the problems associated with the
methods described in sections 2.3.1 and 2.3.2. These previously described methods
have several inherent problems. The major problem is that they are restrictive in the
type of systems applicable to their method. By designing a method to look at cluster
sizes that would allow for a wider range of solute types more information could be
gathered to advance the research.
In designing this method several factors needed to be considered. Among
these factors were how to estimate the cluster size, developing the instrumentation to
measure these cluster sizes, and how to estimate the extent of clustering from these
The rest of this thesis will describe the development of this method. Section
three will cover the derivation of pertinent equations. These equations were derived
from using a hard sphere approximation for the clusters. Included in this section will
be the measurement of cluster diameters from viscosity measurements and calculations
of the clusters molecular weight and diameter from a cluster extent parameter, Â£. The
cluster extent parameter simply describes the number of excess solvent molecules in
the vicinity of the solute.
After the derivation of the calculations the design of the instrumentation will be
covered. This section encompassed the majority of the actual work on this project.
Most of the problems with the research was in this section and will be described in
3. Theoretical background
The estimation of the cluster sizes was made by measuring the viscosity of the
solution. The viscosity measurements were made using a dynamic flow solubility
measuring technique. The instrumentation used will be described later in section four.
3.1 Hard sphere approximations
If the attractive forces at work in the cluster formation are strong enough, then
the clusters may be approximated to act as hard spheres. This approximation is the
most crucial one to the validity of this experiment. It is known that the clusters
formed in these solutions are dynamic in nature, suggesting that no permanent bond is
made between the solute and solvent. This would suggest that the clusters may not be
a very rigid entity, but in an attractive system the extension of the cluster over several
solvation levels indicates that the forces holding the molecules together are very
Another means of verification is by looking at the expansion of supercritical
fluids or solutions through a restrictor. When the fluid, at a high pressure, is rapidly
expanded through the restrictor to a region of lower pressure the expanding fluid is
accelerated to form a supersonic jet.23 As this jet continues to expand it spreads out
and the fluid goes to the gas phase. Several groups have studied the nature of this
expansion jet for supercritical solutions in order to better understand many deposition
processes, such as RESS (rapid expansion of supercritical solutions).2425 A group at
Battelle, Pacific Northwest Laboratories,26 has discovered many features of the
expansion process. One of these features is that the expansion jet, under appropriate
conditions, can contain small droplets of the solvent mixed with the solute. These
solvent droplets prevent solute molecules from interacting within the jet stream. It
may be argued that these solvent droplets are the solvent clusters that have not had
sufficient time to expand to the gas phase. If this is true then this would also lend
validity to the hard sphere assumption.
Measurement of the size of the cluster can nOw be reduced to the measurement
of a hard sphere. Viscosity values are related to the effective diameter of the
molecules from which they are measured. The effective size of molecules can then be
found by measuring the viscosity of the solutions. In this study for the SCFs, the
method of finding effective diameters of a gas were used since the viscosity of SCFs is
similar to that of gases.
3.1.1 Viscosity and effective diameter
If M is the molecular weight of the molecules in a fluid, R is the universal gas
constant, T is the system temperature (in K), and Na is avogadros number; then the
viscosity (ri) is related to the effective diameter (a) in gases by the equation:
The effective diameter of a hard sphere can be calculated with equation 4.1 if the
viscosity is known. The viscosity can be measured experimentally using a form of
Poiseuilles Law, where the molar flow rate of a fluid (<|)m) is measured at a known
system pressure and temperature combination. The viscosity then has the following
relationship to the molar flow rate:
Where pi is the system pressure or high end pressure, p2 is atmospheric pressure, and
T is the temperature, and K is equal to a geometry constant for the experimental
instrumentation. The constant K is dependent upon the radius, r, and the length, L, of
the flow restrictor, described in section four, as shown in equation 3.3.
K= 7tr4 (3.3)
3.1.2 Viscosities of mixtures
Equation 3.2 only describes the viscosity of the bulk solution. To gain any
insight into the cluster sizes in the solution the viscosity of the pure clusters needs to
be known. From Hirschfelder, Curtis, and Bird27 a method of combining the
viscosities of the individual components of a mixture is found. If a new constant K is
then the viscosity of the pure components in the mixture, rji, is found to be
proportional to a ratio of the square root of the components molecular weight and the
effective diameter squared.
The viscosities of the pure components can then be combined along with the mole
fractions of each component, x;, to give a good estimate of the viscosity of the
1 - Xi + x?
1/2 _ 1/2 1/2
Tlsol 111 T]2
In the case of a supercritical solution the subscript sol represents the solution, 1
represents the pure solvent, and 2 the pure clusters.
The values of r]soi, r|i, xi, and X2 can be found experimentally, thus making it
possible to calculate the viscosity of the pure clusters from equation 3.6. Equation 3.5
can then be used to calculate the ratio between the molecular weight and the cluster
3.1.3 Molecular weight of clusters
A relationship between the cluster size and its molecular weight needs to be
found, before any useful data can come from equation 3.7. Since we know that the
ratio, (M21/2/a22), should change as more and more solvent molecules begin to cluster
around the solute, a relationship between this ratio and the number of clustered solvent
molecules, clustering extent would provide the information needed.
First the molecular weight of various cluster sizes was calculated by simply
adding the weight of the solute with the weight of the solvent multiplied by the
clustering extent, In the present work caffeine was used as a solute and carbon
dioxide as the solvent so the values of Msoiute=194.19 g/mole and Msoiv=44 g/mole
were used in the following equation.
M2= Msolule+E, Msolv (3.8)
The values of M2 calculated for various clustering extents can be found in Table 3.1.
3.1.4 Effective diameter of clusters
A model was used to describe the packing of the solvent molecules in the
cluster formation. The packing model gave a mathematical relationship between the
effective size of each of the individual components and the overall cluster size. This
relationship could then be used to calculate cr2.
Table 3.1 Relationship between Â£ and M2
20 1074 g/mole 32.8 (g/mole)
40 1954 44.2
60 2834 53.2
80 3714 60.9
120 5474 74
Villarica et. al.28 proposed the use of a ballistic model to accomplish this goal. In then-
work a ballastic model, one in which the effective size of the individual components
could be reduced to simple hard spheres, was used to calculate the effective radius of
clusters. In this model the radius of the cluster, Ri2, was estimated to be an average of
the contribution of the individual components.
The value of R2 is the effective radius of the solute and Ri is the combination of all the
solvent molecules in the cluster. The value of Ri needs to be calculated separately
from the radius of the individual solvent molecules, Ro, and the clustering extent using
The cluster diameter can then be calculated as two times the Ri2 value. An
example of possible g2 values corresponding to various cluster extents are shown in
3.1.5 Cluster extent vs. ratio
A plot of clustering extent versus the ratio (M21/2/a22) then gives a means of
finding the extent of clustering value. A plot of 2, vs. (M21/2/o22) is shown in figure 3.1.
From this plot a best fit line for the data is shown to be an exponential function. Using
experimentally determined ratios the extent of clustering can be found.
Table 3.2 Relationship between 2, and a2
s R, a?
20 9.066 Angstroms 15.666 Angstroms
40 11.42 18.022
60 13.08 19.675
80 14.39 20.991
120 16.47 23.074
Figure 3.1 Molecular weight effective
diameter ratio vs. clustering extent
4. Instrumental section
4.1 Solubility measuring
There are two main techniques for measuring of SCF solubility: static and
dynamic. In a static type of measurement the system is closed to the outside. The
system is allowed to come to equilibrium before measurements are taken. The
solution is measured without disturbing the system in any way. In this type of set-up
the sample can be measured again using either on-line or off-line sampling. On-line
sampling is generally done by some means of spectroscopy where a spectral cell is
placed in line with the solution cell and the concentration of solute in the solution is
then measured. In an off-line sampling technique a small portion of the solution is
taken from the bulk, usually by means of a sampling loop, and then analyzed by some
method. In off-line sampling it is very important to extract a very small sample of the
solution so as not to disturb the equilibrium. For this reason a very sensitive
measuring technique is needed for off-line sampling.
The on-line measuring method also has some inherent problems. One major
problem is that the effect of the SCF on the spectral absorption properties and the
band shape of the solute need to be known thoroughly. Adjustments for these effects
needs to then be made. Also since the solution being measured is a saturated one, the
solid solutes may fall out of solution and cling to the spectral windows giving
erroneously high results. The last major concern with this method is that the spectral
cells are usually custom made to handle the extreme conditions of the experiment.
This last problem with the static system measurements is also the first benefit of a
dynamic type of measurement.
4.1.1 Dynamic Systems
Dynamic systems are the easiest and probably the most common type for SCF
solubility measuring. The main reason is that the equipment used is of a common
variety. Very few special parts are needed and the sampling technique is simple,
relative to static systems. The most common type of sampling method used is a
A gravimetric set up consists of eight main regions or components. The first is
the source for the SCF. Since most SCFs used are gases in their natural state, the
source is usually a gas tank. From there the fluid is pressurized to the critical state
with some form of pump and passed into a heated region, where it becomes
supercritical. The fluid is often pumped through an extended piece of plumbing within
the heated region to allow the temperature to equilibrate, prior to entering the solution
cell. This region of plumbing is referred to as the pre-heater coil, since the plumbing is
generally coiled to allow a longer length of it within the heated region. From the pre-
heater coil the solution passes into a solution cell, where the solute of interest is
located. The solution is then passed out of the cell and through some form of
restrictor, often a needle valve. The restrictor is used to allow control of the pressure
and flow rate of the solution. The solution undergoes a rapid expansion upon flowing
through the restrictor. During this expansion the solute drops out of solution and is
collected in a trap. The expanded solvent, if now in the gas state, can leave the trap to
be measured by a flow meter for solubility calculation. If the expanded solvent is not
of a gaseous nature then another method of measuring the solvent needs to be found.
Gravimetric type of sampling techniques also have some inherent
disadvantages. Some of the disadvantages include:
solute buildup in various pieces of equipment can cause stoppage of
entrainment of liquid solutes in the SCF solution
if the SCF phase is denser than the liquid solute then risk of the
solute being pushed out of the solution cell exists
if multiple component mixtures are used risk of depleting one or
more of these during a run exists
if a liquid solute is used the solubility of the SCF in the liquid may
interfere with results
4.2 Instrumentation used in this study
In the present work the sampling was done via a gravimetric method. This was
done since it was the simplest way to proceed, it didnt require any additional
equipment other than what was on hand, and only the first major disadvantage listed
above would be of any concern.
The solute being used was a solid at room temperature and at the temperatures
used during the experimental runs so the problems associated with liquids were not of
a concern. Also there were no multi-component systems tested so that wasnt a
concern. This left only the problem of solute buildup. This did at times present some
problems, as will be mentioned later.
The exact experimental apparatus is shown in Figure 4.1. The solvent being
used for this research was CO2, thus a liquid withdrawal cylinder was used as the
solvent source. A liquid withdrawal cylinder draws the CO2 from the bottom of the
tank where it is in the liquid form. A more conventional pump can then be used to
pressurize the system. Two separate piston pumps were used. After the first failed a
second was utilized. First a Milton Roy mini-pump and then an SSI HPLC pump.
The plumbing was HPLC tubing of 1/16" O.D.. A gutted Hewlett Packard GC oven
model number 5880A was utilized as the heated extraction region. The pre-heater coil
was designed by coiling the tubing in several loops inside the oven. This gave an extra
length of tubing for the solvent to pass through and equilibrate before entering the
solution cell. The solution cell was made from a gutted gel-permeatation
chromatography column. The type of restrictor used also varied throughout the
experiment. Initially, a needle valve was used but it was replaced later by a
thermospray 37 micron sapphire aperture. The collection trap, a liquid scrubber
assembly, was connected to the restrictor apparatus with tygon tubing. The scrubber
was then connected via tygon to a stoppered erlenmeyer flask. The stopper had two
holes one for a long piece of glass tubing to allow the incoming gas to bubble through
a solution, the other as an exhaust for outgoing gas. The gas then proceeded through
another length of tubing to a wet test flow meter, where the volume of gas flowing
through the scrubber assembly was measured.
4.2.1 Initial problems with instrumentation
The initial changes to the setup were made to remedy problems with the
pressurizing step. At first an ordinary gas cylinder was used to feed the C02 directly
into the liquid end of the piston pump. However, the pump was not able to pressurize
the gas. The reason was thought to be that the gaseous C02 would simply leak around
the seals and check valves. If this were true then the problem would simply increase as
the pressure did, making it impossible for the pump to create any kind of pressure. A
liquid feed cylinder was then used.
The mini-pump was able to pressurize the liquid C02 because of the
compounds higher viscosity and lower diflusivity in this state. The pressure achieved
with the liquid C02 was well above the critical pressure, 1070.9 psi. The pump
however was only able to maintain this pressure for a few minutes. It was determined
that the loss in pressurizing ability was due to the liquid end of the pump vapor
Figure 4.1 Instrumental design
1. liquid feed gas cylinder
2. piston pump
3,4. shut off valves
5. preheater coil
6. solution cell
8. pressure guage
9. flow restrictor
11. flow meter
The pump vapor locked when the liquid CO2 heated up too much and was
converted to the gaseous state. The pump was not able to pressurize the gaseous form
of the solvent and the run ended. The heat used to evaporate the liquid solvent was
generated by the mechanical motion of the piston and the heat coming off the electrical
motor of the pump. A means to negate these heating effects and keep the liquid end of
the pump at a low enough temperature to prevent vapor locking was needed.
The theory of vapor locking was tested by using a bag of ice strapped to the
liquid end of the pump. The pump was able to maintain the system pressure over time.
The next step was to find a more practical and permanent means of cooling the pump.
A thermoelectric (Peltier) heat pump was used. With a Peltier heat pump, heat is
absorbed or liberated when a current flows across two unlike materials. The material
on one side of this junction absorbs heat and the other material liberates it, thus the
The Peltier was connected to a 5V,3Amp power source. It was then thermally
connected to the liquid end of the pump using thermal grease and a small piece of
metal. To dissipate the heat created at the hot side of the pump heat sinks were
attatched with thermal grease and a fan was located to circulate air through the sink
fins. Several 10 minute runs were made to test the performance of the modified set
up. The set up proved to be a sufficient way to cool the pump and prevent vapor
locking. The next step was to test the system as a means of measuring solubility in an
4.3 Solute selection
Before tests of the instrument could proceed, first a suitable solute had to be
located. The criteria for solute suitability included:
1. It needed to be a solute with a well established solubility in the SCF
2. It needed to be one of relatively low toxicity, even though the
solute was being scrubbed out of the gaseous solvent.
3. The solute needed to be one that could be measured by some
4. It needed to be stable at the temperatures being utilized in the
Caffeine appeared to be a good choice as the solute. The caffeine/C02 system is one
of the most thoroughly studied binary systems in supercritical technology. There have
been numerous reports of the solubility in this system by various techniques. Data
from Johannsen et. al.29 was used in this study as a comparison. Caffeine has a strong
absorption band in the UV region, s=509 wt%/cm at X212 nm.30 This absorption
would allow for a quick and simple means of measuring the amount of solute
Two alternative solutes were also considered at the same time, but were not
utilized immediately. They were both members of the xanthine family of compounds,
theobromine and theophylline. Both of these compounds have the same attractive
attributes as caffeine.
4.3.1 Scrubber solvent choice
The first step in verifying the solubility methodology was to determine the
exact procedure of collecting the solute and quantifying the amount collected. The
method of collection was pre-determined to be a gravimetric type trap, as previously
described in section 4.1.1. The trap was a liquid scrubber type, so a suitable solvent
for the trap needed to be determined. The solute needed to be appreciably soluble in
the solvent and the solvents UV cut-off needed to be low enough so as not to
interfere with detection of the solute. Water was chosen as the solvent for caffeine.
Caffeine solubility in water is lg in 46 ml of solution/1 At the low solution
concentrations used in this experiment that was more than adequate. Also waters UV
cutoff is 191nm32 which would prevent it from interfering with the detection of the
caffeine at the 272nm peak. Several standard solutions were made up using water as
the solvent and measured on a Perkin Elmer model 552A UV-Vis spectrometer. The
solutions were tested at not only the 272 nm region but also at 2 less intense
wavelengths. At the 2 more intense wavelengths the relative error of concentration
values was less than 2.3 %, on all runs. This accuracy was considered to be
4.3.2 Experimental procedure
The actual solubility runs were conducted next. This process went through
several alterations in an attempt to maximize the detection level. The final test
procedure used was as follows:
Started by recording initial settings on the flow meter.
Attach exhaust tubing, from the expansion nozzle, to the pre-scrubber unit.
The pre-scrubber was used to collect all the solute that exited the
expansion orifice before the temperature and pressure conditions were
The solution cell was removed from the oven, and a known amount of
solute was added to the cell preceded by a small plug of glass wool and
followed by another.
Replace column in the oven.
Start the temperature control on the oven and heat tape. Record
Start the thermoelectric heat pump and cooling fan.
When the temperature was reached the gas was turned on and pump set to
desired setting. The setting was recorded.
While the pressure is building up, the pressure was recorded the
atmospheric pressure and room temperature.
When the pressure is stabilized at the appropriate amount, the exhaust
tubing was switched from the pre-scrubber to the scrubber set-up.
Recorded the pressure range during the run.
Started the timer when the scrubber set-up is connected.
Recorded volume of gas flow periodically.
Allow to run until the pre-determined volume of gas has gone through the
Remove exhaust tubing and return to the pre-scrubber.
Shut off pump and gas, and allow the pressure to vent.
Turn off oven, heat tape, and heat pump.
Record the final flow meter settings, and calculate the volume of gas
Collect scrubber solutions in a volumetric flask.
Measure solution absorbance with the UV-Vis spectrometer, and calculate
The concentration was recorded as a mole fraction of solute to gaseous
molecules so no conversion was needed for the SCF density. The molar flow rate of
the solvent was determined from a plot of gas volume (from flow meter) vs. time. The
viscosity was then determined from equation 4.2. The geometry of the expansion
orifice was first calibrated using N2 and C02 gases and the same equation.
4.3.3 Viscosity calibration
Several calibration runs were conducted using various expansion set-ups as
well as a few viscosity runs using pure SCFs. With the first expansion set-up used,
the needle valve, very linear flow rates were observed (R2>0.997) but the flow rate
values did not change significantly with changing experimental temperature and
pressure. It was later determined that this was due to an inadequate length to diameter
ratio, L/D. In expansion orifices with a sharp edge geometry the length to diameter
ratio is very critical in determining the maximum flow rate and flow type.
For L/D ratios between zero and three the fluid flow is in the form of a free
streamline jet. At these values a critical flow rate is reached. This was the problem
with the needle valve assembly. Figures 4.2 and 4.3 show flow rate plots for two runs
of CO2 through the needle valve. Both runs were done at the same pressure, 640 psi,
but different temperatures. The flow rates, which are the slopes of these plots, do not
change significantly for the change in temperature. Table 4.1 lists the experimental
results for the runs used to determine that a critical flow had been reached. The run
time for the first two runs was 30 minutes. When this failed to produce acceptable
results the run time was increased to one hour. The first and third runs were used to
C02 viscosity 21'C
C02 viscosity 74'C
Table 4,1 viscosity results using the needle valve as a restrictor
Gas Pressure (psi) Temp (C). Flow rate (Liter/min) K ('molesKmt>oise') seckPa2 viscosity (mpoise) %error in viscosity
n2 1580 21.3 0.0113 3.33xl0"12
n2 1570 75 0.0090 0.183 6.6
n2 1570 21 0.0088 2.64xl012
n2 1550 75 0.0084 0.151 22.9
(N 8 860 21.6 0.0022 0.191 28.4
co2 860 74 0.0023 0.155 11.3
calculate the geometry constant, K, which was then used to calculate the viscosity for
the subsequent runs.
For ratios of three to twelve the jet slowly breaks up. Above twelve the jet is
completely broken up and laminar flow sets in. Laminar flow is necessary for viscosity
The next two expansion devices used, the syringe needle and the sapphire
aperature, both solved the problem of the free jet expansion. The main concern now
was in increasing the L/D value even further to slow the flow rate down to a workable
level. A workable level in this case was one where the flow rate was low enough that
the piston pump being used was still able to keep the system pressurized. The first
needle used was a 27 gauge Hamilton needle. It was determined to have an interior
diameter which was much too large. Next a 30 gauge needle was tried but again the
flow was not optimal. The last expansion device tried was a 77 micron sapphire
aperature. This gave a much lower flow rate than the 30 gauge syringe needle. The
flow rate for the syringe was 4.95 ml/min (liquid phase) and the flow rate through the
aperature for an equivalent run, same pressure and temperature was 2.256 ml/min.
Several calibration runs using both CO2 and N2 gases were made to determine
the value of the geometry constant, K, in equation 4.2. Plots were made of the volume
of gas in liters expanded during the run versus time to find a flow rate. This value was
then converted to a molar flow rate for calculation of K. Two of these plots are
shown in figures 4.4 and 4.5. The R2 values of these plots were very typical of all the
plots made. The results for all the calibration runs performed with the sapphire
aperature are shown in table 4.2. Also shown in the table is the average of the K
values along with the standard deviation. Two averages are shown the first including
all the data and a second which omits the first C02. This run failed a 90% confidence
Figure 4.6 shows a sample calculation for the geometry constant.
Figure 4.4 Calibration plot using
77micron aperature and N2 gas
0 5 10 15
Figure 4.5 Calibration plot of
77micron aperature and C02 gas.
Table 4.2 Viscosity results using sapphire aperature
Gas Pressure (psi) Temp (C). Flow rate (Liter/min) K (molesKmDoisel sec*kPa2 Average and Std. Dev. of K values values with first C02 run omitted
n2 1450 40.1 1.1907 4.638xlO'n ave=5.93xl0'13 ave=4.95xl0'
n2 1440 30.8 1.1032 4.144xl013 o=2.53xl013 a=9.20xl0"14
n2 1330 24 0.9801 4.159xl0'13
co2 780 88.2 0.6374 1.082xl0"12
co2 900 60.5 0.5693 6.190xl0'13
co2 780 40.3 0.4402 5.640xl0'13
Figure 4.6 Sample calculation for the geometry constant, K.
gas flow rate = 0.5693 L/min (C02): measured experimentally
1. 0.5693 L/min 1.975 g/L mole/44g min/60sec = 4.259x10"* moles/sec
1.975 g/L is the C02 density in the gas phase
the molecular weight of C02 is 44g/mole
2. Temp = 60.5 C = 333.65 K
3. q = 0.168 mpoise
This is the viscosity for C02 gas at 60.5
4. P2 = 900 psi 6.895xl03 Pa/psi = 6.21xl03 kPa
900psi is the system pressure
5. 4.259x10"* moles/sec = K (P22 / (q Temp))
K = 6.19xl0"13 moles Ki poise
4.3.4 Problems with the instrumentation
Problems arose when the SCF solutions were run through the instrumentation.
Either the expansion orifice or the tubing leading to it was always plugged up when
the solutions were used. This was due to a lack of control over the temperature of the
expansion set-up. During the rapid expansion of the solution through the orifice, a
dramatic drop in the temperature of the expansion unit was created. The heat tape
applied to the expansion unit was meant to compensate for this by adding heat to the
unit and maintaining the temperature of the experimental conditions. If the expansion
unit cooled too much, then the solution could drop below the critical point and deposit
the solute along the way. If too much heat was applied then, because of the
retrograde solubility of SCFs, again the solute could fall out of solution. Once the
solute falls out of solution, for whatever reason, it can then begin to clog the
passageway and prevent the solution from reaching the expansion orifice. If no
solution is undergoing expansion then there is no cooling effect upon the expansion
unit. The heat applied becomes too great and the solute buildup in the unit can get
cooked on, making it very hard to remove. Although careful monitoring of the
units temperature was made, adequate control of the temperature was not possible
To prevent the problem of plugging, it is suggested by Taylor33 that any
attempt at this type of extraction should make use of an electronically controlled
restrictor to control temperature. This more precise control of the restrictor
temperature virtually eliminates plugging. Several restrictors of this type are
5. Experimental results
As mentioned previously in section 3.1, the assumption of a hard sphere cluster
is dependent upon the clustering type being attractive. This assumption was not
known previously, but was assumed from the solubility data, and later backed up with
experimental data. As was mentioned in section 2.1.1, for an attractive type system
there is a reduction in solvent pressure as the solute becomes solvated. This fact
provided a means of testing the cluster type of the CCVcaffeine system.
In a few early runs a static equilibration step was used. During this step the
solution cell was pressurized and closed off at both ends with shut-off valves. The cell
was then heated to supercritical conditions. As the solution came to equilibrium and
the solute was dissolved a small drop in pressure was observed. For operating
pressures of approximately 2700 psi and temperatures of 40 C, a drop of around 300
psi was observed.
The drop in pressure in an attractive system is due to the condensing of solvent
molecules around the solute, creating a negative partial molar volume. The partial
molar volume in turn affects the total volume of the system as seen in eqn. 2.1. The
total volume of the system is not only dependent upon the partial molar volume but
also the number of moles of the substance. When coupled with the low mole fraction
solubility of caffeine this drop in pressure would appear sufficient to conclude that the
system was attractive.
6. Detection Limit
The detection limit of the method described above is dependent upon several
factors. First the type of expansion device used. Secondly, the time limit of individual
runs and lastly the packing model used in the estimation of the effective diameter.
The expansion nozzle as mentioned in section 4.2 had a large impact on the
detection limit of the instrumentation. The standard deviation of the measured
viscosity is highly dependent upon the geometry constant, K in equation 3.2, and thus
the geometry of the restrictor. The geometry constant not only affects the standard
deviation of the viscosity directly, but also affects the flow rate variable. The
geometry constant is dependent upon a ratio of the radius of the restrictor to fourth
power divided by the restrictor length. By reducing this ratio the geometry constant
and the flow rate both decrease. Both values then affect the detectable change in the
The time limit used in an individual run affects the detection limit also. By
increasing the time used during a run, the standard deviation of the flow rate is directly
affected. Since this value is dependent upon the inverse of the time variable,
increasing the time then decreases the standard deviation of the flow rate. This in turn
decreases the standard deviation of the measured viscosity.
Lastly the type of packing model used in the study also proved to have a
tremendous effect on the detectable change in cluster extent. In the first model used,
the simple geometric model, the detection limit was calculated to be +17 It was
known that the first model would only provide a lower limit on the cluster sizes, a,
since it was an overly simple model, thus it was only meant to be temporary. The final
model used, the ballistic model, provided a much better detection limit. Using the
ballistic model the detectable change of cluster extent was calculated to be less than
The reliability of this detection limit, however, depends heavily on the accuracy
of the packing model. A model that predicts a looser or tighter packing could affect
the detection limit of the technique either way slightly. Since the interactions of the
solvent and solute in supercritical solutions are not well understood the accuracy of
the packing model can only be estimated at this time. Even with the uncertainty of the
detection limit of Â£, the technique could still be used as a semi-quantitative means of
measuring these values, and thus a valuable way to compare the difference in
clustering in like systems such as the xanthines.
7. Future Work
7.1 System comparison
There is very little work currently being done to compare the clustering extent
of systems with similar solutes and the same solvent. Information of this type would
be of tremendous assistance in the study of intermolecular forces in supercritical
By looking at the cluster sizes of a group of compounds whose structures only
differ by a functional group type or location some evidence may be provided toward
the solvating mechanism, as was suggested by the Anderton and Kauffman paper.20 A
very useful group of compounds for this type of research would be the xanthines.
The xanthines include the three compounds caffeine, theophylline and
theobromine. The structures of each of these compounds are identical in every way
except in the theophylline and theobromine one of the three methyl groups, on
caffeine, has been replaced with a hydrogen. From the solubility data alone a
dramatic difference can be seen.29 There is roughly an order of magnitude difference
between the solubility of caffeine and theophylline in the supercritical CO2, with
caffeine being the greater. Theobromine is about another order of magnitude less than
theophylline. This demonstrates that not only is there a vast difference in the solubility
when a methyl group is replaced by a hydrogen, as is the case between caffeine and the
other two, but also there is a large difference in solubilities depending on which methyl
group is replaced.
Solvents are able to solvate a molecule when the intermolecular forces between
the solvent and solute are like enough to take the place of solute-solute forces. In the
case of the xanthines a large difference in the solubility of each solvent can also be
seen in liquid solvents of known polarities. These values can be seen in table 7.1. In
the highly polar water solvent caffeine is the most soluble and theobromine the least,
but in the non-polar solvent hexane the theophylline is the most soluble and the
caffeine is the least. This gives us some valuable information about the types of
interactions these compounds are capable of. The next step would then be to compare
it to supercritical data. From table 7.1 it can be seen that the solutes solubility in
supercritical CO2 parallels the trend of their solubilities in water. This type of
comparison is too simple though since it neglects to take into account the size of the
clusters involved in the solvating process.
Table 7,1 Physical properties of xanthines28
mole fraction mole fraction
m.p.__________solubility in SCF CQ> in liquid water in liquid hexane
Caffeine 508-11K 1300-5000 mg/Kg C02 0.6915
Theophylline 547-48 K 40-140 mg/Kg C02 0.4237
Theobromine 618-23 K
4-20 mg/Kg C02 0.0310
Although no data was obtained from this research it may still be considered
successful. The theoretical work supporting this research is strong and helps lend
validity to the technique. It has been shown that the technique is theoretically capable
of predicting cluster extents in supercritical solutions with good accuracy. This type
of data would be invaluable in the study of interactions in supercritical solutions.
The instrumental work also proved to be helpful in some areas. With some
slight variations to the current instrumentation the method of analysis proposed in this
research should be successful. As mentioned before in section 4.3.3, an easier
controlled restrictor nozzle would be able to eliminate many of the problems with the
current instrumentation. Also a better pressurizing system might be available. It is
possible that switching from the current reciprocating piston pump to a dual syringe
pump, also available through Isco, Inc., that a better control of the system pressure
could be achieved.
Also in comparison to the other current methods of measuring solute-solvent
interactions, this method is more universally applicable. It requires less expensive
instrumentation, it is less restrictive on the type of system being investigated, and it
provides a direct measurement of the cluster dimensions where the other current
techniques only provide indirect measurements of localized solvent densities.
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