Rotational diffusion in the rotator phase of n‐alkanes

Spectroscopic analysis in molecular simulations with discretized Wiener-Khinchin theorem for Fourier-Laplace transformation

The Wiener-Khinchin theorem for the Fourier-Laplace transformation (WKT-FLT) provides a robust method to obtain the single-side Fourier transforms of arbitrary time-domain relaxation functions (or autocorrelation functions). Moreover, by combining an on-the-fly algorithm with the WKT-FLT, the numerical calculations of various complex spectroscopic data in a wide frequency range become significantly more efficient. However, the discretized WKT-FLT equation, obtained simply by replacing the integrations with the discrete summations, always produces two artifacts in the frequency-domain relaxation function. In addition, the artifacts become more apparent in the frequency-domain response function converted from the relaxation function. We find the sources of these artifacts that are associated with the discretization of the WKT-FLT equation. Taking these sources into account, we derive discretized WKT-FLT equations designated for both the frequency-domain relaxation and response functions with the artifacts removed. The use of the discretized WKT-FLT equations with the on-the-fly algorithm is illustrated by a flow chart. We also give application examples for the wave-vector-dependent dynamic susceptibility in an isotropic amorphous polyethylene and the frequency-domain response functions of the orientation vectors in an n-alkane crystal.

Study of disorder in different phases of tetratriacontane and a binary alkane mixture, using vibrational spectroscopy

Raman spectroscopy has been used to investigate the monoclinic crystal --> rotator --> melt phase transitions in n-C(34)H(70), for both real-time heating and cooling runs. Changes in band intensity and frequency in the CH2 bending, CH2 twisting, skeletal C-C stretching, and CH3 rocking regions revealed both transitions, particularly when using band components related to gauche bonds. In the room temperature infrared spectrum, the CH2 rocking-twisting and CH2 wagging progressions were observed and indexed for n-C(34)H(70) and a 2:1 (w/w) mixture of C(34)H(70) and C(36)D(74). This led to best estimates for the all-trans crystal core in both cases of 33 to 34 carbon atoms, indicating that the core corresponds to almost the whole of the C(34)H(70) molecule.