DFT optimized electronic energy as a function of the dihedral angle centered on the symmetric, center bond of isoprene.
DFT optimized electronic energies, including zero point corrections, vs isoprene end-to-end distance as measured between the midpoints of the double bonds.
Distribution of contour lengths for chains constructed of 78 isoprene end-to-end distances randomly chosen from Boltzmann-weighted minimum energy rotational conformations (shown in Fig. 2) at temperatures 200, 250, 300, 350, and 400 K.
Most probable contour length for chains constructed of 78 isoprene end-to-end distances as a function of temperature, normalized to a single isoprene unit. Note that the contour length contracts with increasing temperature.
(a) Boltzmann-weighted end-to-end distance distribution for kinks of one and two isoprene units obtained from MD simulations. (b) Boltzmann-weighted end-to-end distance distribution for kinks composed of three, four, and five isoprene units obtained from MD simulations.
Distributions of contour lengths for chains containing isoprene units constructed from kinks of order 1–5 with kink end-to-end distances chosen randomly from the Boltzmann distributions shown in Figs. 5(a) and 5(b). Each chain is composed of only a single kink size comprised of between one and five isoprene units.
Distribution of contour lengths for chains randomly constructed from 78 single isoprene kink end-to-end distances, using DFT-B3lYP (blue) and MD-CHARRM force field (red). Note the close agreement of the two methods.
Least-squares fit to the derivative (with respect to chain contour length) of the natural logarithm of the distribution function shown in Fig. 8.
DFT/B3LYP 6-31g(d) optimized parameter values for isoprene minimum energy rotational conformations.
Parameters for chains constructed from single kink type, 78 total isoprene units. : entropic force constant . : most probable chain length. Modulus: predicted initial tensile modulus for a network (see text).
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