Growth of phase-separated domains

In a UCST system, when the temperature is reduced to a final value 7/ that is below the critical temperature Tc, a mixture with a concentration 0 not too far from the critical composition phase separate into two phases whose compositions lie on the opposite sides of the binodal envelope line of Fig. 9-1. The dynamics of the separation process of a single phase into these two phases is controlled by Tf, the composition , the rate of the quench dT/dt, the viscous (or viscoelastic) properties of the phases formed, and the interfacial tension F between the two phases. Although a variety of different kinds of behavior can occur, there are two generic types of phase separation, namely, spinodal decomposition (SD) and nucleation and growth (NG). SD occurs when the mixture is quenched into a part of the phase diagram where the mixture is unstable to small variations in composition, leading to immediate growth of phase-separated domains. When the quenched... 

The growth of phase separated domains may be analyzed by examining the shift of wavenumber maximum (qm) and the corresponchng peak intensity (Im) as a function of elapsed time. A power law scheme has been customarily employed for characterizing the phase growth as follow ... 

In the late sage, the following scaling law for the growth of phase-separated domain structure is expected to be satisfied The characteristic length scale L of the structure obeys the power law... 

At higher concentrations of hexane, the metastable region is entered at lower conversions, hence lower viscosity. As the nucleation starts at the point d the diffusion constant is high, leading to a very fast growth of the separated domains immediately after the start of the phase separation. This allows the system to reach the equilibrium concentration after a rather short period. Consequently, the driving force for the phase separation, given by becomes nearly ze-... 

In general, a block copolymer added to immiscible polymer blend significantly suppresses the growth rate of phase-separated domains due to the reduction of interfacial tension resulting from a preferential localization of block copolymer at the interface. However, the retardation effect by the block copolymer is found to be dependent upon the structure of the block copolymer added, such as the interaction energy, the chain length, and the composition of block copolymer. 

A detailed description of AA, BB, CC step-growth copolymerization with phase separation is an involved task. Generally, the system we are attempting to model is a polymerization which proceeds homogeneously until some critical point when phase separation occurs into what we will call hard and soft domains. Each chemical species present is assumed to distribute itself between the two phases at the instant of phase separation as dictated by equilibrium thermodynamics. The polymerization proceeds now in the separate domains, perhaps at differen-rates. The monomers continue to distribute themselves between the phases, according to thermodynamic dictates, insofar as the time scales of diffusion and reaction will allow. Newly-formed polymer goes to one or the other phase, also dictated by the thermodynamic preference of its built-in chain micro — architecture. 

Note 2 Representative mechanisms for coarsening at the late stage of phase separation are (1) material flow in domains driven by interfacial tension (observed in a co-continuous morphology), (2) the growth of domain size by evaporation from smaller droplets and condensation into larger droplets, and (3) coalescence (fusion) of more than two droplets. The mechanisms are usually called (1) Siggia s mechanism, (2) Ostwald ripening (or the Lifshitz-Slyozov mechanism), and (3) coalescence. 

K. Binder and D. Stauffer, Adv. Phys. 25 343 (1976). K. Binder and D. W. Heerman, Growth of Domains and Scaling in the Late Stage of Phase Separation, in Scaling Phenomenon in Disordered Systems R. Pynn and A. Skjeltorp (eds.), Plenum Press, New York, 1985. S. Watanabe, J. Phys. Soc. Japan. 54 1665 (1985). 

In spinodal decomposition, phase separation does not arise due to nucleation and growth of spherical domains, but rather arises from fluctuations in concentration such that phase separation arises in intercoimected regions. Sperling (2001) has highlighted the differences between the two methods of phase separation in terms of... 

In a fundamental study of the factors affecting the growth of the rubber domains in a CTBN-toughened DGEBA epoxy resin cured by piperidine (Manzione and GilUiam, 1981) the kinetics of phase separation were linked to the diffusivity, Uab, of the rabber (A) dissolved in the epoxy resin (B). The relevant dependence on the molar volume of the rubber (proportional to the radius of the rubber molecules when dissolved in the epoxy resin) at the viscosity for the temperature T of reaction is given by the Stokes-Einstein equation ... 

An alternative, and interesting, possibility is to introduce a phase-separating blend as the fluid component (a schematic of this system is shown in Fig. 11). The phase-separating A-B polymer blend will evolve, and phase separate, at its own length- and timescales. However, to minimize the interface between the A and B domains of the polymer blend it may be desirable for the length-scale of phase separation to conform to the wavelength of undulation growth found in... 

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