Phase transition dynamics is centrally important to condensed matter physics. This 2002 book treats a wide variety of topics systematically by constructing time-dependent Ginzburg-Landau models for various systems in physics, metallurgy and polymer science. Beginning with a summary of advanced statistical-mechanical theories including the renormalization group theory, the book reviews dynamical theories, and covers the kinetics of phase ordering, spinodal decomposition and nucleation in depth. The phase transition dynamics of real systems are discussed, treating interdisciplinary problems in a unified manner. Topics include supercritical fluid dynamics, stress-diffusion coupling in polymers and mesoscopic dynamics at structural phase transitions in solids. Theoretical and experimental approaches to shear flow problems in fluids are reviewed. Phase Transition Dynamics provides a comprehensive account, building on the statistical mechanics of phase transitions covered in many introductory textbooks. It will be essential reading for researchers and advanced graduate students in physics, chemistry, metallurgy and polymer science.

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Highly supercooled liquids with soft-core potentials are studied via molecular dynamics simulations in two and three dimensions in quiescent and sheared conditions. We may define bonds between neighboring particle pairs unambiguously owing to the sharpness of the first peak of the pair correlation functions. Upon structural rearrangements, they break collectively in the form of clusters whose sizes grow with lowering the temperature T . The bond life time τ b , which depends on T and the shear rateγ, is on the order of the usual structural or α relaxation time τα in weak sheaṙ γτα ≪ 1, while it decreases as 1/γ in strong shearγτα ≫ 1 due to shear-induced cage breakage. Accumulated broken bonds in a time interval (∼ 0.05τ b ) closely resemble the critical fluctuations of Ising spin systems. For example, their structure factor is well fitted to the Ornstein-Zernike form, which yields the correlation length ξ representing the maximum size of the clusters composed of broken bonds. We also find a dynamical scaling relation, τ b ∼ ξ z , valid for any T andγ with z = 4 in two dimensions and z = 2 in three dimensions. The viscosity is of order τ b for any T andγ, so marked shear-thinning behavior emerges. The shear stress is close to a limiting stress in a wide shear region. We also examine motion of tagged particles in shear in three dimensions. The diffusion constant is found to be of order τ −ν bwith ν = 0.75 ∼ 0.8 for any T andγ, so it is much enhanced in strong shear compared with its value at zero shear. This indicates breakdown of the Einstein-Stokes relation in accord with experiments. Some possible experiments are also proposed. 64.70Pf, 83.50Gd, 61.43Fs

We review theories and experiments on the effects of shear in fluids undergoing phase transitions. We put emphasis on near-critical fluids and polymer solutions as representative examples, but also discuss related problems in polymer blends, gels, and surfactant systems, etc. In near-critical fluids, convective deformations can drastically alter the critical behaviour, spinodal decomposition, and nucleation. In this case the hydrodynamic interaction suppresses the fluctuations and gives rise to a downward shift of the critical temperature (shear-induced mixing). The rheology in two-phase states, and effects of random stirring are also reviewed. In semidilute polymer solutions near the coexistence curve, on the other hand, the composition fluctuations can be strongly influenced by the viscoelastic stress. In shear flow, this dynamical coupling results in enhancement of the composition fluctuations (shear-induced demixing). They grow, but are eventually disrupted by convective deformations, yielding chaotic dynamical steady states where phase separation is incompletely taking place. Such nonlinear shear regimes are examined using computer simulations based on a viscoelastic Ginzburg-Landau model.

The diffusivity of tagged particles is demonstrated to be very heterogeneous on time scales comparable to or shorter than the $\alpha$ relaxation time $\tau_{\alpha}$ ($\cong$ the stress relaxation time) in a highly supercooled liquid via 3D molecular dynamics simulation. The particle motions in the relatively active regions dominantly contribute to the mean square displacement, giving rise to a diffusion constant systematically larger than the Einstein-Stokes value. The van Hove self-correlation function $G_s(r,t)$ is shown to have a long distance tail which can be scaled in terms of $r/t^{1/2}$ for $t \ls 3\tau_{\alpha}$. Its presence indicates heterogeneous diffusion in the active regions. However, the diffusion process eventually becomes homogeneous on time scales longer than the life time of the heterogeneity structure ($\sim 3 \tau_{\alpha}$).Comment: 4 pages, 5 figure