NMR of Short-Chain Hydrocarbons in Nematic and Smectic A Liquid Crystals

The proton NMR spectra
of ethane, propane, and n-butane codissolved and
orientationally ordered in two liquid-crystal
solvents that exhibit both nematic (N) and smectic A (SmA) phases
(one of which also has a reentrant nematic (RN) phase) are analyzed
using CMA-ES (covariance-matrix adaptation evolution strategy). To
deal with problems arising from the broad liquid-crystal background
signal, a smoothed experimental spectrum is fitted to a smoothed calculated
spectrum. The ethane and propane dipolar couplings and anisotropic
energy parameters scale with each other, and the n-butane couplings are assumed to behave likewise. This restriction
on the relative values of the n-butane energy parameters
facilitates a fit to the temperature dependence of the n-butane dipolar couplings, in which the six n-butane
energy parameters (three for trans and three for gauche), the isotropic
trans–gauche energy difference Etg, and its temperature coefficient Etg′, and the
methyl CCH angle decrease are obtained. Unlike earlier studies, the
fit does not employ a model for the anisotropic intermolecular potential.
The nematic potential in the SmA phase of the liquid-crystal mixture
6OCB/8OCB is estimated by interpolated values obtained from the ethane
spectra for the N and RN regions. Analysis of results for the SmA
phase involves adding a nematic–smectic coupling prefactor
and a smectic prefactor. Spectra obtained in the liquid-crystal 8OCB
are calculated with no adjustable parameters, scaling the potentials
using the ethane values, and the agreement between experiment and
calculation is outstanding. Conformer populations are affected by
the environment, and the isotropic solute–solvent interactions
result in increased gauche populations, whereas anisotropic interactions
increase the trans probability. The trans probability in the SmA phase
is slightly lower than expected from the nematic results.