Temperature fluctuations, mode coupling theory

The temperature dependence of the dynamic fluctuations which contribute to the effective pore size may be estimated by means of mode coupling theory, which views a gel as consisting of N pores of diameter t, over which the density fluctuations are correlated [4, 20, 21]. 

When an atomic system is cooled below its glass temperature, it vitrifies, that is, it forms an amorphous solid [1]. Upon decreasing the temperature, the viscosity of the fluid increases dramatically, as well as the time scale for structural relaxation, until the solid forms concomitantly, the diffusion coefficient vanishes. This process is observed in atomic or molecular systems and is widely used in material processing. Several theories have been developed to rationalize this behavior, in particular, the mode coupling theory (MCT) that describes the fluid-to-glass transition kinetically, as the arrest of the local dynamics of particles. This becomes manifest in (metastable) nondecaying amplitudes in the correlation functions of density fluctuations, which are due to a feedback mechanism that has been called cage effect [2],... 

Based on the ab initio theory of complex electronic ground state of superconductors, it can be concluded that e-p coupling in superconductors induces the temperature-dependent electronic structure instability related to fluctuation of analytic critical point (ACP - maximum, minimum or saddle point of dispersion) of some band across FL, which results in breakdown of the adiabatic BOA. When ACP approaches FL, chemical potential Pad is substantially reduced to IJ-antiadilJ-ad > Pantiad < b(o). Under these circumstances the system is stabilized, due to the effect of nuclear dynamics, in the antiadiabatic state at broken symmetry with a gap in one-particle spectrum. Distorted nuclear structure, which is related to couple of nuclei in the phonon mode r that induces transition into antiadiabatic state, has fluxional character. It has been shown that until system remains in antiadiabatic state, nonadiabatic polaron - renormalized phonon interactions are... 

Figure 2.24 shows the temporal evolution of the compositional structure factor S<(, (a) and the orientational structure factor Ss (b) for the temperature quench into the lu region (T/Tn, = 0.6, (f)Q = 0.55) in Figure 2.22. The structure factor for concentration has a maximum at q, which corresponds to the peak wavenumber of coi(q). With time the corresponding mode grows exponentially and the peak position qm is invariant. Then the time evolution of the structure faaor S<, is lhe same as that of the Cahn-Hilliard theory for isotropic SD [102]. The amplitude of the peak at q = 0 decreases with time because s > 0 and another peak appears at q. In this quench, the concentration fluctuation initially induces the SD and the orientational ordering within the domain subsequently takes place due to the coupling between the two order parameters concentration-induced SD.

---