Chain conformation from the direct calculation of the Raman spectra of the liquid n-alkanes C12–C20

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Abstract
The aim of the present work is to extend the capability of vibrational spectroscopy to determine quantitative information about conformation in assemblies of flexible chains. We have explored methods for simulating, by direct calculation, the isotropic Raman spectra of the liquid n-alkanes and have applied them to C12H26, C16H34 and C20H42 in the frequency region 0–1500 cm–1. The method involves summing the individually calculated spectra of the conformers making up an ensemble. To calculate individual spectra we have used a previously established valence force field and intensity model. Conformers were generated in a Monte Carlo calculation with conditional probabilities based on the rotational-isomeric-state model. One of the two parameters adjusted was the trans/gauche energy difference. A value of 800 cal mol–1 was required for an optimum fit between the calculated and observed spectra of C12 and C16. A substantially improved fit was attained by including torsional fluctuations about C—C bonds. For this a second parameter, the standard deviation of the displacements in the torsion angles, was adjusted, and its value estimated to be 10 ± 2°. The calculated spectra based on these parameters show essentially all the features in the observed spectra. The isotropic Raman spectra and the density of states and scattering density functions are discussed. Progression bands are found in the density-of-states function of the liquid that are closely related to those found for ordered chains. Examples are presented illustrating how spectral simulation by direct calculation might be used to analyse conformation in chain assemblies.