Unified Hydrodynamic Theory for Crystals, Liquid Crystals, and Normal Fluids

TLDR

Distinguishing local lattice dilations from mass changes and recognizing vacancy diffusion are essential for linking theories across phases, and the authors aim to clarify how their theory differs from other phenomenological proposals. The authors present a unified hydrodynamic theory applicable to crystals, liquid crystals, glasses, and normal fluids, and seek to explain its distinctions from existing phenomenological models. The theory reduces the number of first‑order elastic constants and transport coefficients as spatial degeneracy increases, and derives formulas for the number, frequencies, lif.

Abstract

A unified hydrodynamic theory is presented that is appropriate for crystals; smectic, cholesteric, and nematic liquid crystals; glasses; and normal fluids. In the theory, the increased spatial degeneracy as the system progresses from crystalline and mesomorphic phases to the isotropic fluid phase is marked by successive reductions in the number of firstorder elastic constants and in the number of transport coefficients. Distinction between local lattice dilations and local mass changes, and recognition of processes like vacancy diffusion that this difference makes possible, are crucial for understanding the connection between theories in different phases. Formulas are derived that give the number of hydrodynamic modes and the frequencies, lifetimes, and intensities of these modes in all of the above systems. In the nematic and cholesteric phases, the results agree with some found previously. In more complex systems, they are new. An attempt is made to explain the differences between the present hydrodynamic theory and other phenomenological proposals.