Phase Separation in a Simple Model with Dynamical Asymmetry

We perform computer simulations of a Cahn-Hilliard model of phase separation which has dynamical asymmetry between the two coexisting phases. The dynamical asymmetry is incorporated by considering a mobility function which is order parameter dependent. Simulations of this model reveal morphological features similar to those observed in viscoelastic phase separation. In the early stages, the minority phase domains form a percolating structure which shrinks with time eventually leading to the formation of disconnected domains. The domains grow as L(t) ~ t^{1/3} in the very late stages. Although dynamical scaling is violated in the area shrinking regime, it is restored at late times. However, the form of the scaling function is found to depend on the extent of dynamical asymmetry.Comment: 16 pages in LaTeX format and 6 Postscript figure

A Viscoelastic model of phase separation

We show here a general model of phase separation in isotropic condensed matter, namely, a viscoelastic model. We propose that the bulk mechanical relaxation modulus that has so far been ignored in previous theories plays an important role in viscoelastic phase separation in addition to the shear relaxation modulus. In polymer solutions, for example, attractive interactions between polymers under a poor-solvent condition likely cause the transient gellike behavior, which makes both bulk and shear modes active. Although such attractive interactions between molecules of the same component exist universally in the two-phase region of a mixture, the stress arising from attractive interactions is asymmetrically divided between the components only in dynamically asymmetric mixtures such as polymer solutions and colloidal suspensions. Thus, the interaction network between the slower components, which can store the elastic energy against its deformation through bulk and shear moduli, is formed. It is the bulk relaxation modulus associated with this interaction network that is primarily responsible for the appearance of the sponge structure peculiar to viscoelastic phase separation and the phase inversion. We demonstrate that a viscoelastic model of phase separation including this new effect is a general model that can describe all types of isotropic phase separation including solid and fluid models as its special cases without any exception, if there is no coupling with additional order parameter. The physical origin of volume shrinking behavior during viscoelastic phase separation and the universality of the resulting spongelike structure are also discussed.Comment: 14 pages, RevTex, To appear in Phys. Rev

Dynamics of Highly Supercooled Liquids:Heterogeneity, Rheology, and Diffusion

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 $\tau_b$, which depends on $T$ and the shear rate \gdot, is on the order of the usual structural or $\alpha$ relaxation time $\tau_{\alpha}$ in weak shear \gdot \tau_{\alpha} \ll 1, while it decreases as 1/\gdot in strong shear \gdot\tau_{\alpha} \gg 1 due to shear-induced cage breakage. Accumulated broken bonds in a time interval ($\sim 0.05\tau_b$) 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 $\xi$ representing the maximum size of the clusters composed of broken bonds. We also find a dynamical scaling relation, $\tau_b \sim \xi^{z}$, valid for any $T$ and \gdot with $z=4$ in two dimensions and $z=2$ in three dimensions. The viscosity is of order $\tau_b$ for any $T$ and \gdot, 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 $\tau_b^{-\nu}$ with $\nu=0.75 \sim 0.8$ for any $T$ and \gdot, 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.Comment: 20pages (including figures

Spinodal decomposition of off-critical quenches with a viscous phase using dissipative particle dynamics in two and three spatial dimensions

We investigate the domain growth and phase separation of hydrodynamically-correct binary immiscible fluids of differing viscosity as a function of minority phase concentration in both two and three spatial dimensions using dissipative particle dynamics. We also examine the behavior of equal-viscosity fluids and compare our results to similar lattice-gas simulations in two dimensions.Comment: 34 pages (11 figures); accepted for publication in Phys. Rev.

Spinodal decomposition with formation of a glassy phase

The consequences of a glass transition occurring in one of the two phases formed by spinodal decomposition of a liquid mixture are investigated by numerical solution of the deterministic Cahn-Hilliard equation for two dimensions with a concentration-dependent mobility. The glass transition is modelled by a rapid decrease of the mobility coefficient with increasing concentration of the glass-forming component. For concentrations of the mixture for which the glassy phase percolates and the liquid phase is confined in droplets, a new coarsening mechanism is found which consists in the migration and eventual coalescence of liquid droplets in the glassy phase. For a particular model of the mobility coefficient the growth law for the characteristic length R(t) shows a pronounced plateau at intermediate times