Dynamical critical phenomena

Hohenberg P C and Halperin B I 1977 Theory of dynamic critical phenomena Rev. Mod. Phys.49 435... 

Nucleation is a term that naturally arises in the study of dynamical critical phenomena, which is concerned not so much with the equilibrium properties of a sys-... 

V. Dynamical Critical Phenomena Genesis of the Modem Mode Coupling Theory... 

In this section we will not discuss the dynamical critical phenomena in detail because they are beyond the scope of this chapter. Instead, this phenomena will be discussed with a view toward understanding the development of the modem mode coupling theory. 

Compared to binary mixtures of low molecular fluids, the critical behavior of polymer blends has been much less explored so far. However, a number of interesting static and dynamic critical phenomena in polymer blends attract increasing attention [4, 5], Neutron, X-ray, and static light scattering experiments belong to the major techniques for characterizing the static properties of polymer blends. Photon correlation spectroscopy (PCS) has traditionally been the method of choice for the investigation of the dynamics of critical [6-9] and noncritical [10-12] polymer blends. 

Hohenberg PC, Halperin BI. Theory of dynamic critical phenomena. Rev. Mod. Phys. 1977 49 435-475. 

Theory of dynamic critical phenomena by P. C. Hohenberg and B. I. Halperin, Rev. Mod. Phys. 49, 435 (1977) details many of the crucial ideas on order parameters and their dynamical evolution in the critical phenomena setting. Their Model A has been introduced here as the Cahn-Allen equation while their Model B we have referred to as the Cahn-Hilliard equation. 

Static and dynamic critical phenomena in solutions of polymers in organic solvents and... 

Beautiful and useful though they are, Eqs. (130) and (136) do not represent the complete solution of a mode-mode coupling problem. Recall that the aim of mode-mode coupling is to predict all dynamical critical phenomena and long-time tails from equilibrium properties and bare transport coefficients. Thus, we have not really completed our calculation of D until 17 is eliminated. To do this, we calculate 17 via mode-mode coupling theory. 

Stoll, E., Binder. K, Schneider, T. (1973). Monte-Carlo investigation of dynamic critical phenomena in the two-dimensional kinetic Ising model. Physical Reoiew B, 8 (7), pp. 3266. 

By virtue of Equation 31, the diffusion coefficient is classified with the parameters characterizing a system in nonequilibrium, i.e. with the dynamic parameters of the system. The behaviour of such parameters near the spinodal and critical point is called dynamic critical phenomena. To describe them, an approach in the fashion of the similarity hypothesis has proved to be very fruitful, this hypothesis in its application to the dynamic parameters being called a dynamic similarity hypothesis (Stanley, 1971). 

For the dynamic critical phenomena, Debye s phenomenological approach, developed for mean-statistical critical phenomena (see siib.section 2.3.5), has turned out to be helpful. Introducing a gradient term into AF heis led (Fixman, 1966 Chu et al., 1972 Tscharnuter et al., 1972) to... 

On the other hand, the renormalization-group theory of dynamic critical phenomena predicts that asymptotically diverge as (Hohenberg Halperin 1977). The two predictions can be reconciled if one considers equation (6.31) as a first approximation to the power law (6.23), with z = 8/15jr = 0.054 as a first-order estimate for the exponent z. Until recently, the theoretical estimates for the exponent z appeared to be consistently lower than the experimental values z 0.065 (Bhattacharjee Ferrell 1983b). But this problem is now resolved, and the most recent theoretical estimate is z = 0.063 (Hao 1991). 

Hao, H. (1991). Aspects of dynamic critical phenomena in a single component fluid. Ph.D. Thesis. College Park, MD University of Maryland. 

The mode-coupling theory of dynamic critical phenomena can be used to generalize the asymptotic equation for the thermal conductivity to give (Chapter 6 Sengers 1985 Mostert etal. 1990)... 

The critical enhancement term AXc (p, T) was based on the theory of dynamic critical phenomena, which predicts that the critical part of the thermal diffusivity kj pep, where c JO is the heat capacity at constant pressure, close to the critical point satisfies a Stokes-Einstein diffusion law of the form (Chapter 6)... 

This crude analysis [8], based on the asymptotic degeneracy of the continuous spectrum as k- k, indicates the existence of longtime tails in the mode-selection problem, with corresponding longtime tails in the resulting pattern (11). Thus even for long duration of experimental measurements the predicted pattern (11) eventually may not be reached. This behavior resembles features in dynamic critical phenomena and in the microscopic dynamics of simple fluids. 

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