Testing Assumptions about Solute Concentration Dependence in Liquid Crystal NMR

The NMR spectra of four solutes, used as probes of liquid crystal orientational order, were analyzed. For
each solute, samples were prepared at different solute concentrations, and the concentration dependence was
used to extrapolate zero-concentration properties. The mean-field (Maier−Saupe) model when applied to
solutes neglects solute−solute interactions and assumes all solutes in a mixed-solute sample see the same
average environment. The first assumption is only valid as one approaches zero concentration, while experiments
are typically carried out at concentrations between 0 and 10 mol %. The solute concentration dependence has
in the past been “scaled out” using an internal solute reference as an orientational standard. We measured the
concentration dependence of the orientational order parameter and calculate the corresponding interaction
energies based on a mean-field interaction potential for a solute. We find agreement at the 3% level between
experiments for different solutes while using (i) the zero-concentration values as solute-dependent orientational
references and (ii) scaling to either order parameters or interaction energies; these two scalings gave equivalent
but not identical results. We find, too, that errors inherent in the experiment and the calculations will limit
attempts to refine the theory to push the comparisons beyond the 2% level.