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Fall 2020 CHE 4480 Palmer This wor k by Alycia Palme r is licensed under CC BY 4. 0 1 Electronic Spectra of Conjugated Dyes Particle in a box theory applied to dyes with varying length Objective Students will co llect absorption spectra of several conjugated dyes and use particle in a box (PIB) theory with the energy of maximum absor ption to estimate the length of each dye . The values determined by PIB will be compared to empirically determined lengths. Logistics The duration is one week. Each student will collect the absorbance spectrum of a different dye to maxmax values will be compiled and shared with the class to finish data analysis. Introduction The particle in the box approximation to the Schrodinger equation is the simplest way to model the translational position and potential e nergy of a confined particle. Figure 1 illustrates a particle in an infinitely deep well that cannot escape. Figure 1 . A particle in a 1 D infinite potential well with length L. By restricting the motion to 1dimension, that is translation along the xcoordinate, and not allowing changes in potential energy (V = 0), t he Schrodinger equation reduces to Equation 1. Equation 1
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Fall 2020 CHE 4480 Palmer This wor k by Alycia Palme r is licensed under CC BY 4. 0 2 Where is the reduced Planck Constant , m is the mass of the particle in kg, (x) is the stationary time independent wavefunction, a nd E is the energy of the particle in J. In the particle in the box model, the probability of finding the particle at x = 0 or x = L is zero. Using these boundary c onditions, the Schrodinger equation can be solved to find the allowed energies for the particle for values of n. Equation 2 And for transitions between energy levels, the energy absorbed by the electron can be calculated using Equation 3. Equation 3 If we consider the â€œboxâ€ to be the linear, conjugated part of a dye molecule, we can use the equation above to relate the length of the box to the energy absorbed by the molecules . Cyanine dyes absorb energy with the same magnitude as photons in the visible region, which is why they appear colored to our eyes. Thus we can take an absorption spectrum to determine what energy of photons is being absorbed. Consider the cyanine dye be low, 1,1' diethyl 2,2' carbocyanine, or Dye B. The region between the two nitrogen atoms is conjugated. Dye B has 8 pi electrons between the two nitrogen atoms, including the lone pair of electrons on the neutral nitrogen. Figure 2 . Structure of 1,1â€™ diethyl 2,2â€™ cyanine iodide (Dye B) Resonance in cyanine dyes allows for good porbital overlap in the conjugated pi system, which enables the electrons to move freely in that region. The excellent p orbital overlap makes cyanine dyes good model systems for the particlein the box approximation. Figure 3 . P orbital overlap in the conjugated pi system of Dye B. The length of the linear conjugated system is analogous to the length of the box, shown in Figure 4. Cyanine dyes are model systems for particle in the box because the potential energy doesnâ€™t vary along
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Fall 2020 CHE 4480 Palmer This wor k by Alycia Palme r is licensed under CC BY 4. 0 3 the length of the chain. Figure 4 . Potential energy well for dye B. We can use the number of pi electrons (N) in the conjugated system to determine the quantum numbers ni and nf for an electronic transition . Take for instance a molecule with N= 6 pi electrons , as in Figure 5 . Since each energy level can occupy 2 electrons, the first three energy level s are full . The most likely transition is with nf = ni + 1. Thus in a molecules with 6 pi electrons the HOMO (highest occupied molecular orbital) to LUMO (lowest unoccupied molecular orbital) transition will be from n = 3 4. Figure 5 . Ene rgy diagram for Dye A (left) and Dye B (right). Dye A has 6 pi electrons so that the HOMO has n = 3 and LUMO has n = 4. Dye B has 8 pi electrons, with HOMO (n=4) and LUMO (n=5). Since Dye B is longer than Dye A, its energy levels are spaced more closely to gether. Figure 5 highlights two main relationships from the Schrodinger equation. For the same value of L, as the n =3 4 is lower energy than the n = 4 5 transition. However, for the same value of n, as L increases (as the box gets longer), the energy of that level decreases. Thus longer molecules have energy levels that are spaced more closely together. That is, Dye B has a smaller ween the same energy levels. In this experiment, the cyanine dyes absorbing visible light will cause an electronic transition from the HOMO to LUMO. The energy of the photon is related to its wavelength by Equation 4. Equation 4 In the cyanine dyes, ni (the n value for the HOMO) is equal to the number of pi electrons in the
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Fall 2020 CHE 4480 Palmer This wor k by Alycia Palme r is licensed under CC BY 4. 0 4 conjugated system divided by two since each orbital may occupy two electrons. Equation 5 Using Equations 3, 4, and 5 and assuming nf = ni +1 , the wavelength of maximum a bsorbance can be related to the n value of the HOMO, p. Equation 6 Finally, the length of the box can be solved for, as in Equation 7. Equation 7 With Equation 7, max) to the length of the â€œboxâ€ which we assume to be approximately the length of the conjugated region between the two nitrogen atoms. In order to test this assumption, the length of the conjugated chain will be determined empirically. Because there is resonance in this region , the bond length between carbon atoms will be similar to that of benzene, 0.139 nm , and the N C bond length is 0.134 nm Materials Dye A: 1,1' D iethyl2,2' cyanine iodide (CAS 977968) Dye B: 1,1' D iethyl 2,2' carbocyanine (CAS 605 914) Dye C: 1,1' D iethyl 2,2' dicarbocyanine (CAS 14187316) Dye D: 1,1' Diethyl4,4' cyanine iodide (CAS 472749 5) Dye E: 1,1' Diethyl 4,4' carbocyanine iodide (CAS 4727508) Dye F: 1,1' Diethyl 4,4' dicarbocyanine iodide (CAS 18300317) Dye G: 3,3' D iethylthiacy anine iodide ( CAS 2197015) Dye H: 3,3' D iethylthiatricarbocyanine iodide ( CAS 3071703) Dye I: 3,3' D iethylthiacarbocyanine iodide ( CAS 905975) Dye J: 3,3â€™ Diethylthiadicarbocyanine iodide (CAS 514 738) Ethanol Pre lab question 1. Draw th e chemical structures of the nine dyes used in this lab. Then identify the number of pi electrons in the conjugated portion between the two nitrogen atoms and including the lone pair on the neutral nitrogen. Procedure Obtain the 1.010â€“4M solution of your a ssigned dye, and take an absorption spectrum between 300800 nm. The results from the class will be compiled into a single spreadsheet and be made available on Canvas.
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Fall 2020 CHE 4480 Palmer This wor k by Alycia Palme r is licensed under CC BY 4. 0 5 Spreadsheet Assignment Plot the absorption spectra for each of the dyes and max. Make a table for each of the dyes studied and list the following as columns : number of pi electrons, max value , L calculated from equation 7, and L calculated using the number of pi bonds in the conjugated system . For the last column, estimate the length of the box using the C C bond length of 0.139 nm (the bond length in benzene) and the N C bond length of 0.134 nm. Format Excel to calculate the difference between th e L calculated using PIB theory (Equation 7) and the L calculated empirically using the number of bonds. Compute the percent difference between the two length determinations for each dye. Finally, plot the percent difference as a function of the pvalue. Discussion points Discuss the difference between th e length of the box calculated using PIB theory and the length calculated empirically . How well does PIB theory predict the conjugated pi systemâ€™s length for the various dyes tested? Is there a notable correlation between the percent difference and the p val ue of the dye? References Halpern, A. M.; McBane, G. C. Experimental Physical Chemistry, 3rd Ed.; W. H. Freeman and Company: New York, 2006. Autschbach, J. Why the Particle in a Box Model Works Well for Cyanine Dyes but Not for Conjugated Polyene s . J. Chem. Educ . 200 7, 84 ( 11) , 18401845. Particle in a box Libre text: https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_ Maps/Supplementa l_Modules_(Physical_and_Theoretical_Chemistry)/Quantum_Mechanic s/05.5%3A_Particle_in_Boxes/Particle_in_a_1Dimensional_box (Accessed Feb 6, 2020) Particle in a box lab: https://chem.libretexts.org/Courses/Howard_University/Howard%3A_Physical_Chemistry _Laboratory/13._Particle_in_a_Box (Accessed Feb 6, 2020)
