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 transient gel-like 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. This unique feature originates from the difference in mobility between two components of a mixture. 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: It suppresses short-wavelength concentration fluctuations in the initial stage, and causes the volume shrinking of a more viscoelastic phase. We also propose a simple general law of the stress division between the two components of a mixture, as a straightforward extension of that obtained in polymer mixtures. 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 parameters. We show that this feature leads to a phenomenon of ``order-parameter switching'' during viscoelastic phase separation, even if it is driven by a single thermodynamic driving force. The physical origin of volume shrinking behavior during viscoelastic phase separation and the universality of the resulting spongelike structure are also discussed.