Microscopic order-macroscopic disorder parameters

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... 

Basic to the thermodynamic description is the heat capacity which is defined as the partial differential Cp = (dH/dT)n,p, where H is the enthalpy and T the temperature. The partial differential is taken at constant pressure and composition, as indicated by the subscripts p and n, respectively A close link between microscopic and macroscopic description is possible for this fundamental property. The integral thermodynamic functions include enthalpy H entropy S, and free enthalpy G (Gibbs function). In addition, information on pressure p, volume V, and temperature T is of importance (PVT properties). The transition parameters of pure, one-component systems are seen as first-order and glass transitions. Mesophase transitions, in general, were reviewed (12) and the effect of specific interest to polymers, the conformational disorder, was described in more detail (13). The broad field of multicomponent systems is particularly troubled by nonequilibrium behavior. Polymerization thermodynamics relies on the properties of the monomers and does not have as many problems with nonequilibrium. 

Figure 1. Deuteron NMR line shapes. Top static powder pattern for a macroscopically disordered sample in the absence of molecular motions (77 = 0 case). Middle , motionally narrowed powder pattern for a macroscopically disordered mesophase with axially symmetric molecular motions (( ]) = 0). The ratio of the peak splittings in the top and middle spectra defines the microscopic order parameter. Bottom , doublet spectrum of a macroscopically aligned mesophase. If the microscopic order parameter is known, the angle between the director and the magnetic field can be obtained from the splitting.

As it is known [5], the intensity of the scattered light gives us an information about the system s disorder, e.g., presence therein of pores, impurities etc. Since macroscopically liquid is homogeneous, critical opalescence arises due to local microscopic inhomogeneities - an appearance of small domains with different local densities. In other words, liquid is ordered inside these domains but still disorded on the whole since domains are randomly distributed in size and space, they appear and disappear by chance. Fluctuations of the order parameter have large amplitude and involve a wide spectrum of the wavelengths (which results in the milk colour of the scattered light). 

In contrast to LCs, for LCEs the situation remained elusive for several years. For the nematic LCEs, the early experimental studies reported a continuous or supercritical-like evolution of the order parameter [15-18]. Most of the characterizing techniques employed in these studies, such as the thermoelastic response, birefringence and X-ray scattering [17-20], are sensitive to macroscopic or collective rather than local or microscopic quantities. These techniques detect a smooth temperature dependence of the averaged order parameter without any discontinuity at the phase transition. It was, therefore, generally accepted that the phase transition in LCEs is supercritical [15, 21, 22], which was supported by some theoretical predictions about the possible existence of a critical point [22-24]. Nevertheless, there were also ideas that the continuous phase transition is a manifestation of the heterogeneous nature of LCEs [2] and the effects of quenched disorder [25]. 

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