Equation of state for polymer liquid crystals: Theory and experiment

The first part of this paper develops a theory for the free energy of lyotr opic polymer nematic liquid crystals. We use a continuum model with macrosc opic elastic moduli for a polymer nematic phase. By evaluating the partitio n function, considering only harmonic fluctuations, we derive an expression for the free energy of the system. We find that the configurational entrop ic part of the free energy enhances the effective repulsive interactions be tween the chains. This configurational contribution goes as the fourth root of the direct interactions. Enhancement originates from the coupling betwe en bending fluctuations and the compressibility of the nematic array normal to the average director. In the second part of the paper we use osmotic st ress to measure the equation of state for DNA liquid crystals in 0.1M to 1M NaCl solutions. These measurements cover five orders of magnitude in DNA o smotic 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 fluctua tion enhanced electrostatic double layer repulsion. The measured equation o f state for DNA fits well with our theory for all salt concentrations. We a re able to extract the strength of the direct electrostatic double layer re pulsion. This is an alternative way of measuring effective charge densities along semiflexible polyelectrolytes. [S1063-651X(99)11401-6].