The elastic constants of condensed matter: A direct‐correlation function approach

We describe a simple, systematic and physically transparent method for calculating the elastic constants of condensed matter. This approach is equally useful when applied to such diverse materials as alkali halides and nematic and smectic A liquid crystals, as we report in this paper. Our analysis involves regarding the periodic density of the ordered phase to be representable as a small perturbation to the uniform density distribution of the corresponding fluid phase. We implement this idea by making use of recent work on the density wave theory of freezing and the statistical mechanics of nonuniform systems. The theory makes the role of the structure of the medium explicit while leaving the role of the intermolecular potential implicit. We find, for example, that the elastic constants of an alkali halide crystal can be expressed in terms of the curvatures of the Fourier transforms of the charge–charge and number–number direct correlation functions of the corresponding fluid evaluated at the reciprocal l...

[1]  Y. Singh.  Molecular theory of liquid crystals: application to the nematic phase , 1984 .

[2]  S. Rice,et al.  Crystallization of the classical one-component plasma , 1984 .

[3]  D. Oxtoby,et al.  A systematic density functional approach to the mean field theory of smectics , 1983 .

[4]  W. Gelbart,et al.  On the stretching of alkyl chains by nematics , 1983 .

[5]  D. Oxtoby,et al.  A molecular theory for the solid–liquid interface , 1981 .

[6]  W. Gelbart,et al.  A van der Waals picture of the isotropic-nematic liquid crystal phase transition , 1980 .

[7]  A. Poniewierski,et al.  Statistical theory of the elastic constants of nematic liquid crystals , 1979 .

[8]  M. Yussouff,et al.  First-principles order-parameter theory of freezing , 1979 .

[9]  A. Wulf.  Short‐range correlations and the effective orientational energy in liquid crystals , 1977 .

[10]  T. Faber.  A continuum theory of disorder in nematic liquid crystals. - II. Intermolecular correlations , 1977, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[11]  P. Gennes,et al.  The physics of liquid crystals , 1974 .

[12]  J. Straley.  Frank Elastic Constants of the Hard-Rod Liquid Crystal , 1973 .

[13]  Richard G. Priest,et al.  Theory of the Frank Elastic Constants of Nematic Liquid Crystals , 1973 .

[14]  W. G. Hoover,et al.  ADIABATIC ELASTIC CONSTANTS FOR ARGON. THEORY AND MONTE CARLO CALCULATIONS , 1969 .

[15]  F. Stillinger.  Molecular Distribution and Elasticity in Crystals , 1966 .

[16]  J. Nehring,et al.  On the Elastic Theory of Uniaxial Liquid Crystals , 1971 .

[17]  J. Lebowitz,et al.  Statistical Thermodynamics of Nonuniform Fluids , 1963 .

[18]  M. Born,et al.  Dynamical Theory of Crystal Lattices , 1954 .