Absorption Spectra of Conjugated Dyes

Abstract: The absorption spectra of a series of three diphenyl dyes and three polymethine dyes were measured and interpreted by ultra-violet spectroscopy. The spectrums of these dyes were compared to the estimated wavelength of absorbance through the particle-in-a-box model. Maximum wavelengths of 523, 604, 707, 330, 354 and 375 and box lengths of 1.053, 1.284, 1.535, 0.707, 0.867, and 1.011 nm, for 1,1’-diethyl-2,2’-cyanine iodide, 1,1’-diethyl-2,2’-carbocyanine chloride, 1,1’-diethyl-2,2’-dicarbocyanine iodide, 1,4-diphenyl-1,3-butadiene, 1,6-diphenyl-1,3,5-hexatriene, and 1,8-diphenyl-1,3,5,7-octatetraene were experimental obtained. Both spectral and physical measurements proved Kuhn’s free-electron model is most accurate for 1,4-diphenyl-1,3-butadiene, 1,6-diphenyl-1,3,5-hexatriene, and 1,8-diphenyl-1,3,5,7-octatetraene, but an adjustment with an empirical parameter α to 1.2 was required for more reliable predictions of 1,1’-diethyl-2,2’-cyanine iodide, 1,1’-diethyl-2,2’-carbocyanine chloride, and 1,1’-diethyl-2,2’-dicarbocyanine iodide. The more polarizable end group compounds like the polymethine dyes retained higher wavelengths of absorption.
Introduction:
Determination of the box length in the one-dimensional particle-in-a-box model can be found through the absorption spectra of polymethine dyes. The length of the box is more easily visible in a new series of diphenyl dyes, which are less hazardous, as well as less expensive. These new compounds are 1,4-diphenyl-1,3-butadiene, 1,6-diphenyl-1,3,5-hexatriene, 1,8-diphenyl-1,3,5,7-octatetraene. The π electrons along the polymethine chain involved in electronic transitions give rise to the visible bands in the absorption spectrum.1 Polymethines are very important organic compounds, and their absorption maximums can be calculated by making a model of the dye that is analogous to the free-electron gas model.2 In this experiment, the conjugated π electron system of each dye is modeled after the particle-in-a-box theorem, which enabled the prediction of absorbance at a maximum wavelength. Kuhn proposed this in the simple free-electron model. Since each conjugated dye is considered a one-dimensional box of length L, the quantum mechanical solution for the energy level in Kuhn’s model can be calculated by E = h2n28mL2 n=1, 2, … (1) where h is Plank’s constant, n is the quantum number, and m is the mass of the electron. Only two electrons are allowed to occupy each energy level (with opposite spins), which is stated by the Pauli exclusion principle. This means a system with N π electrons will have the ground state of a molecule with N/2 lowest levels filled and the remaining levels will remain empty. A one-electron jump from the highest energy level (n1= N/2) to the lowest unoccupied energy level (n2= N/2+1) signals the molecule absorbed light. The calculation for the energy change of this transition is ΔE = h28mL2(n22-n12)= h28mL2(N+1) (2) with a wavelength corresponding to ΔE, and the speed of light, c, is λ = 8mcL2h(N+1) (3) From Kuhn’s assumption, L was said to be the length of the methine chain between the nitrogen atoms with one additional bond distance on each side of the nitrogen atoms. Therefore, the number of carbon atoms in the methine chain, denoted by p, gives the number of π electrons N=p+3. Based on the above, the length of the one-dimensional box is L=(p+3)l, where l is the bond length between atoms on a benzene molecule. Equation 3 can be rewritten as λ (nm) = 8mcl2(p+3+α)2h(p+4) = 63.7 (p+3+α)2p+4 (4) where l=0.139 pm and α is a constant for a series of dyes.3
Experimental:
The following polymethines were dissolved in methanol and the diphenyls were dissolved in cyclohexane to give dilute solutions: 1,1’-diethyl-2,2’-cyanine iodide, 1,1’-diethyl-2,2’-carbocyanine chloride, 1,1’-diethyl-2,2’-dicarbocyanine iodide, 1,4-diphenyl-1,3-butadiene, 1,6-diphenyl-1,3,5-hexatriene, and 1,8-diphenyl-1,3,5,7-octatetraene. The concentrations of 1,1’-diethyl-2,2’-cyanine iodide, 1,1’-diethyl-2,2’-carbocyanine chloride, 1,1’-diethyl-2,2’-dicarbocyanine iodide were 1.00 × 10-6 M, 5.02 × 10-7 M and 1.00 × 10-6 M, respectively and were made together by Groups B, C, and D. The concentrations of 1,4-diphenyl-1,3-butadiene, 1,6-diphenyl-1,3,5-hexatriene, and 1,8-diphenyl-1,3,5,7-octatetraene were 5.30 × 10-6 M, 5.20 × 10-6 M, and 5.00 × 10-6 M, respectively and were made by Group A. Each solution was made dilute enough to be perceived accurately with a smooth maximum absorbance below 1 Au. Shown in Figure 1 and Figure 2, absorbances were taken between 190 and 1100 nm for the polymethine dyes and between 330 and 425 nm using an Agilent 8435 UV-Vis Spectrophotometer with disposable plastic cuvettes and methanol and cyclohexane as the blanks.
Raw Data:
Table 1. Experimental and theoretical wavelengths for 1,1’-diethyl-2,2’-cyanine iodide, 1,1’-diethyl-2,2’-carbocyanine chloride, 1,1’-diethyl-2,2’-dicarbocyanine iodide, 1,4-diphenyl-1,3-butadiene, 1,6-diphenyl-1,3,5-hexatriene, 1,8-diphenyl-1,3,5,7-octatetraene. The percent difference between the two wavelengths and the empirical parameter α are present as well. Dye | λexperimental (nm) | λtheoretical (nm) | Percent difference between λexp and λcal (%) | α | 1,1’-diethyl-2,2’-cyanine iodide | 523 | 485 | 7.3 | 1.3 | 1,1’-diethyl-2,2’-carbocyanine chloride | 604 | 612 | 1.3 | 1.3 | 1,1’-diethyl-2,2’-dicarbocyanine iodide | 707 | 739 | 4.3 | 1.3 | 1,4-diphenyl-1,3-butadiene | 330 | 319 | 3.3 | 0 | 1,6-diphenyl-1,3,5-hexatriene | 354 | 328 | 7.3 | 0 | 1,8-diphenyl-1,3,5,7-octatetraene | 375 | 453 | 17.2 | 0 |

Figure 1. Absorption spectra of the polymethine dyes, 1,1’-diethyl-2,2’-cyanine iodide (blue), 1,1’-diethyl-2,2’-carbocyanine chloride (green), 1,1’-diethyl-2,2’-dicarbocyanine iodide (red).

Figure 1 shows the absorbance spectra of the three conjugated polymethine dyes. There is a general increase in the wavelength of absorbance with a decrease in the number of π electrons in the methine chain. The longest wavelength of absorbance corresponds to the dye with the least π electrons (3 e-), 1,1’-diethyl-2,2’-cyanine iodide, and the shortest wavelength of absorbance corresponds to the dye with the most π electrons (10 e-), 1,1’-diethyl-2,2’-dicarbocyanine iodide. 1,1’-diethyl-2,2’-cyanine iodide, 1,1’-diethyl-2,2’-carbocyanine chloride, 1,1’-diethyl-2,2’-dicarbocyanine iodide have a maximum wavelength of absorption at 523 nm, 604 nm, and 707 nm, respectively. Three trials of each polymethine dye were taken, but the maximum wavelengths for the second and third trials were exactly the same as the first trial so they are not added to the figure.
Figure 2. Absorption spectra of the diphenyl dyes 1,4-diphenyl-1,3-butadiene (blue), 1,6-diphenyl-1,3,5-hexatriene (red), 1,8-diphenyl-1,3,5,7-octatetraene (green).

Figure 2 shows the absorbance spectrum the three conjugated diphenyl dyes. There is a general increase in the wavelength of absorbance with an increase in the number of π electrons in the methine chain. The longest wavelength of absorbance corresponds to the dye with the most π electrons (8e-), 1,8-diphenyl-1,3,5,7-octatetraene, and the shortest wavelength of absorbance corresponds to the dye with the least π electrons (4e-), dyes 1,4-diphenyl-1,3-butadiene. 1,4-diphenyl-1,3-butadiene, 1,6-diphenyl-1,3,5-hexatriene, and 1,8-diphenyl-1,3,5,7-octatetraene have a maximum wavelength of absorption at 330 nm, 354 nm, and 375 nm, respectively. Three trials of each diphenyl dye were taken, but the maximum wavelengths for the second and third trials were exactly the same as the first trial so they are not added to the figure.
Data Analysis: Equation (3) was used to calculate the wavelengths of the polymethine and diphenyl dyes. These numbers were then compared to the wavelengths that were observed experimentally. However, an empirical parameter α was used if the observed wavelengths differed greatly from the calculated ones. For the diphenyl dyes, the theoretical wavelength were within 10% of the experimental wavelength, except for 1,8-diphenyl-1,3,5,7-octatetraene in which the difference was about 17%. For the polymethine dyes, the theoretical wavelengths required a parameter α, and this α was obtained by using Equation (4) with each of the experimental wavelengths and then averaging the values because the original calculated theoretical absorption maximums were four times larger than the experimental absorption maximums.2 Then the theoretical wavelengths were calculated again with the parameter. For example, the calculation for the new theoretical wavelength with the parameter α of 1,1’-diethyl-2,2’-cyanine iodide was found by λ = 63.7(1+3+1.3)2(1+4)
The difference between the experimental wavelengths and theoretical wavelengths was minimized to less than 10% but as low as 1.3% for 1,1’-diethyl-2,2’-carbocyanine chloride. Microsoft Excel 2010 assisted in calculation all of the values present in Table 1. These values proved parameterizing a model in this fashion are valid.
Error Analysis: We had a 97% confidence limit for our empirical parameter α. The determination of our lengths of the boxes from the particle-in-a-box model proved to be exactly the same from literature results for the lengths of the boxes in the polymethine dyes, 1,1’-diethyl-2,2’-cyanine iodide, 1,1’-diethyl-2,2’-carbocyanine chloride, and 1,1’-diethyl-2,2’-dicarbocyanine iodide, which gives a percent error of 0%. For the diphenyl dyes, 1,4-diphenyl-1,3-butadiene, 1,6-diphenyl-1,3,5-hexatriene, and 1,8-diphenyl-1,3,5,7-octatetraene, our percent error was less than 3% because our box length results were extremely close to literature results. Figures 3 and 4 show the accuracy of our results.
Figure 3. Wavelength of maximum absorbance (nm) as a function of the number of π electrons in the chain of the polymethine dyes. Figure 3 shows a positive correlation between the wavelength of absorbance and the number of π electrons in the polymethine dyes, 1,1’-diethyl-2,2’-cyanine iodide, 1,1’-diethyl-2,2’-carbocyanine chloride, and 1,1’-diethyl-2,2’-dicarbocyanine iodide. The shortest wavelength (523 nm) corresponds to 1,1’-diethyl-2,2’-cyanine iodide with the least number of π electrons, and the longest wavelength (707 nm) corresponds to 1,1’-diethyl-2,2’-dicarbocyanine iodide with the most π electrons.
Figure 4. Wavelength of maximum absorbance (nm) as a function of the number of π electrons in the chain of the diphenyl dyes. Figure 3 shows a positive correlation between the wavelength of absorbance and the number of π electrons in the diphenyl dyes, 1,4-diphenyl-1,3-butadiene, 1,6-diphenyl-1,3,5-hexatriene, and 1,8-diphenyl-1,3,5,7-octatetraene. The shortest wavelength (330 nm) corresponds to 1,4-diphenyl-1,3-butadiene with the least number of π electrons, and the longest wavelength (375 nm) corresponds to 1,8-diphenyl-1,3,5,7-octatetraene with the most π electrons.
Discussion:
A simple formula to find the absorbance wavelength of each dye was found by assuming the potential energy along the methine chains is constant with addition of the particle-in-a-box model. After all, analysis of the polymethine and diphenyl dyes using Kuhn’s free-electron model seem to be the most accurate model to determine the length of the box in these compounds. The diphenyl dyes, 1,4-diphenyl-1,3-butadiene, 1,6-diphenyl-1,3,5-hexatriene, and 1,8-diphenyl-1,3,5,7-octatetraene, had experimental wavelengths in precise accordance with the theoretical wavelength without addition of a parameter α. A longer wavelength corresponds to larger energy transition, which means the number of π electrons present in each dye has an effect on the wavelength of absorbance. According to Figures 3 and 4, there is a correlation between the wavelength of absorbance and the number of π electrons. The end groups in the diphenyl dyes are not as polarizable as the polymethine dyes because theoretical wavelength was accurate in comparison to the experimental wavelength without the use of the parameter. Polymethine dyes contain polarizable end groups, therefore, the use of the correction parameter α was used for these compounds. The theoretical and experimental wavelengths differed by less than 10% when the average value of α, 1.2, was calculated from the experimental wavelengths to retrieve new theoretical wavelengths. The longest wavelength of absorbance corresponded to the compound with the highest number of π electrons, 1,1’-diethyl-2,2’-dicarbocyanine iodide. Therefore, the smallest wavelength of absorbance corresponds to the compound with the least number of π electrons, 1,1’-diethyl-2,2’-cyanine iodide. As in the polymethine dyes, the presence of nitrogen atoms on the polymethine chain made it apparent that the more polarizable dyes need an empirical parameter to calculate precise theoretical wavelengths. The longer the conjugated system, the lower the energy of light absorbed by the molecule.
Conclusion:
Ultimately, use of Kuhn’s free-electron model, which simulates the particle-in-a-box, grants for acceptable predictions for the theoretical wavelengths of maximum absorbance with knowledge of the number of π electrons in compounds like polymethine and diphenyl dyes. The theoretical wavelengths obtained by the particle-in-a-box model were compared to the recorded visible spectra of three conjugated polymethine dyes and three conjugated diphenyl dyes, which proved the polymethine dyes containing more polarizable end groups needed the empirical parameter α and the diphenyl dyes did not. Overall, the free-electron model is an appropriate model to predict agreeable absorption wavelengths.

References
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2. H. Kuhn. J. Chem. Phys. 17, 1198 (1949)
3. Garland, C., Niber, J., Shoemaker, D. Experiments in Physical Chemistry XIV, 8th ed., The
McGraw-Hill Companies: New York, NY, 1994.