Absorption Spectrum of a Conjugated Cyanine Dyes
Introduction
Since cyanine dyes have a long conjugation in its structure, these structures have been known to have several functions that include light-energy conversion, nonlinear optics, sensitization2,3, aggregation3, etc.2 Cyanine dyes are particles with a positive charge in its structure delocalized through a string of double bond carbons with amino end groups.1, 2 In this experiment, three solutions of cyanine dyes were studied through spectroscopy. The family of cyanine dyes studied for this experiment were: 1,1’-diethyl-2,2’-cyanine iodide (p = 3), 1,1’-diethyl-2,2’-carbocyanine iodide (p = 5), and 1,1’-diethyl-2,2’-dicarbocyanine iodide (p = 7). The number of carbons in the conjugated carbon chain is noted as “p” in both equation 1 and 2 below. A particle-in-a-box model is a standard model in quantum chemistry that confines conjugated electron movement to the borders of the molecule itself, and models the distance of the conjugated string as the sides of an inelastic box.1 According to Kuhn, the particle-in-a-box model can be used for predicting the wavelength of maximum absorbance (λmax) for a series of conjugated dyes.1 It is useful to determine a semi-empirical equation that can be used for a series of dye molecules because this empirical parameter may be adjusted to achieve the best fit to the data.1 The following equation represents the free electron model, which is used for calculating the maximum wavelengths for each dye, on which the empirical parameter, α, is equal to zero:
Equation 1: λ (in nm)= 63.7 〖(p+3)〗^2/(p+4)
To determine the theoretical maximum wavelength of each dye, the following equation is used:
Equation 2: λ (in nm)= 63.7 〖(p+3+α)〗^2/(p+4)

Equation 2 is also used to determine the best value of empirical parameter for the series of dyes studied. The maximum wavelengths for a series of these cyanine dyes are obtained from the spectra, and then compared with those expected based on the particle-in-a-box model. Subsequently, based on the results we will know whether the free-electron model is useful in estimating the maximum wavelengths for the series of conjugated cyanine dyes.

Results and Discussion
The experimental maximum wavelengths of solutions 1-3 were determined through spectroscopy. The calculated maximum wavelengths for the three solutions were determined by using Equation 1, where empirical parameter is equal to zero for the free electron model. The empirical parameter, α, for each dye was calculated by using Equation 2 with the experimental values of maximum wavelengths obtained from the spectroscopy. In addition, the theoretical maximum wavelengths of the cyanine dyes were determined using Equation 2, where it was estimated that the best empirical parameter is equal to 1 for the series of dyes studied in this experiment.
Table 1: Collected and calculated data for the Absorption Spectrum of the three conjugated cyanine dyes.
Solution Compound Experimental Values of λmax (nm) Calculated Values of λmax (nm) Calculated Values of α Theoretical Values of λmax (nm)
1 1,1’-diethyl-2,2’-cyanine iodide 524 328 1.59 446
2 1,1’-diethyl-2,2-carbocyanine iodide 605 453 1.25 573
3 1,1-diethyl-2-2’-dicarbocyanine iodide 707 579 1.05 701
Based on Table 1, it shows that the experimental maximum wavelengths of the cyanine dyes increases as its conjugated chain between the amino end groups increased. Therefore, the shortest wavelength between the three cyanine dyes is found to be 1,1’-diethyl-2-2’-cyanine iodide, which is observed to have its maximum wavelength at 524 nm; whereas, the longest wavelength between the three dyes is found to be 1,1’-diethyl-2,2’-dicarbocyanine iodide, which was observed to have its maximum wavelength at 707 nm (Table 1) . In Table 1, the intermediate molecule among the three conjugated cyanine dyes is observed to be 1,1’-diethyl-2,2’-carbocyanine iodide, which was observed at 605 nm.
In terms of the empirical parameters of each dye, it was observed that as the experimental maximum wavelengths for each dye increases, its empirical parameter decreased (Table 1).
Meanwhile, when it was estimated that the best fit empirical parameter for the series of dyes is equal to 1, the theoretical maximum wavelengths for solutions 1-3, are as follows: 446 nm, 573 nm, and 701 nm, respectively. On the other hand, the theoretical maximum wavelengths are much smaller compared to the observed wavelengths by spectroscopy when the empirical parameter was altered to be equal to 1 for this series of conjugated cyanine dyes. Additionally, based on Table 1, the calculated maximum wavelengths for each dye from the free electron model is also much smaller compared to the experimental maximum wavelengths.
Based on these results, the particle-in-a-box model shows how the conjugated chain influences the maximum wavelengths of these cyanine dyes because without the alteration of the empirical parameter, it shows that the free electron model do not agree well with the observed maximum wavelengths for the series of conjugated cyanine dyes. On the other hand, when there was a configuration with the semi-empirical equation, the errors between the theoretical and experimental maximum wavelengths were minimized.
In terms of potential sources of errors for this experiment, one may consider that it has to do with the methanol, but since a blank was taken before observing the maximum wavelength of each dye, methanol does contribute to the potential source of errors in this experiment. In addition, it was observed that as the string of conjugated chain increases between the amino end groups, the errors between the theoretical and experimental maximum decreased. Therefore, one may consider that there exists some type of spectral split in which the apparatus measures the maximum wavelengths for the series of conjugated cyanine dyes because it has been known that in ethanol solution, conjugated cyanine molecules undergo systematic shift when the conjugation length is changed.2

Conclusion
The particle in a box model shows that the length between the conjugated chains of the cyanine dye influences its maximum wavelengths. In addition, the free electron model for which the empirical parameter was equal to zero, it shows large differences between the experimental and calculated maximum wavelengths for each of the conjugated cyanine dyes. It was observed that 1,1’-diethyl-2,2’-dicarbocyanine iodide have the longest wavelength among the three conjugated cyanine dyes, which was observed to have its maximum wavelength at 707 nm (Table 1). In addition, the intermediate compound was determined to be 1,1’-diethyl-2,2-carbocyanine iodide , which was observed to have its maximum wavelength at 605 nm; whereas, the shortest wavelength among the three cyanine dyes is 1,1’-diethyl-2,2’-cyanine iodide, which was observed to have its maximum wavelength at 524 nm (Table 1). In addition, it was also determined that a configuration in the semi-empirical equation (Eq.2) was needed for minimizing the differences between the experimental and theoretical maximum wavelengths for the series of conjugated cyanine dyes. Although the particle-in-a-box model do not completely agree with the experimental maximum wavelengths obtained from the spectroscopy, it shows that particle-in-a-box model shows the trend in which conjugated chains between the amino end groups affect the maximum wavelengths for the series of cyanine dyes.
Since we now know that there exist some errors in the approximation based on the particle-in-a-box model, we can thereby further investigate other models in physical chemistry that has a more reliable approximation results of the maximum wavelengths for the series of conjugated dyes. In addition, since we used methanol as a solvent in this experiment, we can also further investigate the effect of conjugated cyanine dyes in ethanol just as mentioned in the dye aggregation experiment by McArthur, et. al.3

References Garland, C.W.; Nibler, J.W. and Shoemaker, D.P. Experiments in Physical Chemistry, 8th Ed.; McGraw-Hill: New York, 2009, pp. 393-398. Guarin, C.A; Villabona-Monsalve, J.P.; López-Arteaga, Rafael, and Peon, Jorge. Dynamics of the Higher Lying Excited States of Cyanine Dyes. An Ultrafast Fluorescence Study. J. Phys. Chem. B 2013, 117, 7352-7362. McArthur, E.A; Godbe, J.M; Tice, D.B; and Weiss, E.A. A Study of the Binding of Cyanine Dyes to Colloidal Quantum Dots Using Spectral Signatures of Dye Aggregation. J. Phys. Chem. C 2012, 116, 6136-6142.