MOLECULAR FLUCTUATIONS IN THE PACKING OF POLYMERIC LIQUID-CRYSTALS

Recent measurements of forces between DNA polyelectrolytes have shown a direct and continuous coupling between intermolecular forces and molecular disorder in lattices of interacting particles. Over a wide range of conditions the work of assembly is dominated by the configurational entropy of molecules restricted by repulsive forces from their neighbors. This observed entropic force decays half as fast as what is predicted from the decay lengths for an electrostatic double layer or hydration forces between parallel molecules. It cannot be fit by the traditional model of flexible molecules with an effective hard wall radius. In this paper we develop a statistical mechanical model of a Gaussian randomly walking polymer surrounded by an effective “tube” of its neighbors, a model that can be solved in strict formal analogy to the problem of a bounded two-dimensional quantized oscillator. The doubling of the underlying exponential decay length emerges naturally. One may also extract the underlying direct intermolecular force through which molecular motion is restricted. © 1990, American Chemical Society. All rights reserved.