Landau theory correlation functions

There exist pre-transition effects in the isotropic phase heralding the I-N phase transition. Such pre-transition effects, which are consistent with the weakly first-order nature of the I-N transition, can be attributed to the development of short-range orientational order, which can be characterized by a position-dependent local orientational order parameter Q(r), where all component indices have been omitted [2]. In the Landau approximation, the spatial correlation function < G(0)G(r) > has the Omstein-Zemike form < G(0)G(r) exp(—r/ )/r, where is the coherence length or the second-rank orientational correlation length. The coherence length is temperature-dependent and the Landau-de Gennes theory predicts... 

Fig. 4.10 a V/Vq plot for BagSi4 as a function of pressure (points) along with a third-order Birch-Mumaghan equation of state (line). The macroscopic order parameter corresponds to spontaneous i c., the Variation of the volume cmrected from the compressibility, b Aspo ,a eous as a function of pressure fits with the theoretical analysis based on the Landau theory of phase transition null before the transition pressure, a jump at the transition and a square-root evolution after the transition. Such a behaviOT is also observed for Si atomic displacement parameters that can be used as microscopic order parameter [82]. The correlation between these physical quantities underlines the relationships between the isostructural transition and disordering of the Si sub-lattice... 

If the correlation function of dielectric constcint (permittivity) h(r) is taken as the order parameter, Equation 7 is similar to Equation 2.3 129. It reveals Landau s mean field theory with a gradient term equivalent to Ornstein-Zernike s approximation (section 2.3). 

This approach (comprising, however, only the LW and EL forces) was developed independently by Derjaguin and Landau (1941) and Verwey and Overbeek (Verwey and Overbeek, 1948, 1999), and became known, after these authors, as the DLVO theory, and the corresponding energy vs. distance plots as DLVO plots. In the absence, or virtual absence, of polar (AB) interactions (i.e., in mainly apolar media), the DLVO theory correlates admirably with the stability of particle suspensions. However, in the cases of particle suspensions in polar and especially aqueous media, disregarding the influence of polar interactions by using simple DLVO plots usually leads to severely unrealistic models (van Oss et ai, 1990a). In other words, in all polar systems one should take into account AG j, as a function of , as ... 

The construction of the phase diagram of a heteropolymer liquid in the framework of the WSL theory is based on the procedure of minimization of the Landau free energy T presented as a truncated functional series in powers of the order parameter with components i a(r) proportional to Apa(r). The coefficients of this series, known as vertex functions, are governed by the chemical structure of heteropolymer molecules. More precisely, the values of these coefficients are entirely specified by the generating functions of the chemical correlators. Hence, before constructing the phase diagram of the specimen of a heteropolymer liquid, one is supposed to preliminarily find these statistical characteristics of the chemical structure of this specimen. Here a pronounced interplay of the statistical physics and statistical chemistry of polymers is explicitly manifested. 

As per the prescription of Li et al., a simple way to get a combined theory is to assume that the total memory function of the correlator of interest is the sum of the mode coupling memory function and the Landau-de Gennes memory... 

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