Equation of state for polymer liquid crystals: theory and experiment

TL;DR

This paper develops a theoretical model for the free energy of polymer nematic liquid crystals and experimentally measures the equation of state for DNA liquid crystals, confirming the theory across various salt concentrations.

Contribution

It introduces a continuum elastic model for polymer nematic free energy and validates it with extensive osmotic stress measurements on DNA, providing a new method to determine effective charge densities.

Findings

Configurational entropy enhances chain repulsion.

Equation of state is independent of ionic strength at high pressures.

Experimental data aligns well with the theoretical model.

Abstract

The first part of this paper develops a theory for the free energy of lyotropic polymer nematic liquid crystals. We use a continuum model with macroscopic elastic moduli for a polymer nematic phase. By evaluating the partition function, considering only harmonic fluctuations, we derive an expression for the free energy of the system. We find that the configurational entropic part of the free energy enhances the effective repulsive interactions between the chains. This configurational contribution goes as the fourth root of the direct interactions. Enhancement originates from the coupling between bending fluctuations and the compressibility of the nematic array normal to the average director. In the second part of the paper we use osmotic stress to measure the equation of state for DNA liquid crystals in 0.1M to 1M NaCl solutions. These measurements cover 5 orders of magnitude in DNA osmotic pressure. At high osmotic pressures the equation of state, dominated by exponentially decaying hydration repulsion, is independent of the ionic strength. At lower pressures the equation of state is dominated by fluctuation enhanced electrostatic double layer repulsion. The measured equation of state for DNA fits well with our theory for all salt concentrations. We are able to extract the strength of the direct electrostatic double layer repulsion. This is a new and alternative way of measuring effective charge densities along semiflexible polyelectrolytes.