Phase separation thermodynamic

The spontaneous mixing of the two polymers will transpire at a rate which reflects the degree of miscibility of the system. As X approaches the critical value for phase separation, "thermodynamic slowing down" of the interdiffusion will occur [12]. The rate of increase of the scattering contrast reflects the proximity of the system to criticality, as well as the strong composition dependence of the glass transition temperature of the blend. Extraction of a value for either the self diffusion constants [13,14] or the interaction parameter is not feasible from the presently available data. 

In the above equations Np and Nh are the number of monomer segments that comprise the deuterated and undeuterated polymer chains, respectively. As X approaches Xs> equivalently, as T approaches the UCST, the system experiences large fluctuations in composition. The extent of the "thermodynamic slowing down" should therefore be enhanced. In cases where X > Xs the mixture is unstable and undergoes phase separation. "Thermodynamic slowing down" effects should not, however, be observable when X = 0-... 

In Chap. 8 we discuss the thermodynamics of polymer solutions, specifically with respect to phase separation and osmotic pressure. We shall devote considerable attention to statistical models to describe both the entropy and the enthalpy of mixtures. Of particular interest is the idea that the thermodynamic... 

The title of this chapter is somewhat misleading. In one sense it is too broad, in another sense too restrictive. We shall really discuss in detail only the phase separation and osmostic pressure of polymer solutions a variety of other thermodynamic phenomena are ignored. In this regard the chapter title would better read Some aspects of. . . . Throughout this volume only a small part of what might be said about any topic is actually presented, so this modifying phrase is taken to be understood and is omitted. 

With these remarks, we conclude our discussion of phase separation. In the remainder of the chapter we consider another thermodynamic property of... 

Thermodynamics and kinetics of phase separation of polymer mixtures have benefited greatly from theories of spinodal decomposition and of classical nucleation. In fact, the best documented tests of the theory of spinodal decomposition have been performed on polymer mixtures. 

Compatibility. Clear definition of compatibility is rather difficult. Compatibility has been defined as the ability of two or more materials to exist in close and permanent association for an indefinite period without phase separation and without adverse effect of one on the other [28]. On the other hand, compatibility is easily recognized in solvent-borne adhesives as a homogeneous blend of materials without phase separation. Normally, compatibility is understood as a clear transparent mixture of a resin with a given polymer. But, compatibility is a more complex thermodynamic phenomenon which can be evaluated from specific... 

D. Blankschtein, G. Thurston, G. Benedek. Phenomenological theory of equilibrium thermodynamic properties and phase separation of micellar solutions. J Chem Phys 25 7268-7288, 1986. 

The flow behavior of the polymer blends is quite complex, influenced by the equilibrium thermodynamic, dynamics of phase separation, morphology, and flow geometry [2]. The flow properties of a two phase blend of incompatible polymers are determined by the properties of the component, that is the continuous phase while adding a low-viscosity component to a high-viscosity component melt. As long as the latter forms a continuous phase, the viscosity of the blend remains high. As soon as the phase inversion [2] occurs, the viscosity of the blend falls sharply, even with a relatively low content of low-viscosity component. Therefore, the S-shaped concentration dependence of the viscosity of blend of incompatible polymers is an indication of phase inversion. The temperature dependence of the viscosity of blends is determined by the viscous flow of the dispersion medium, which is affected by the presence of a second component. 

The term compatibility is used extensively in the blend literature and is used synonymously with the term miscibility in a thermodynamic sense. Compatible polymers are polymer mixtures that do not exhibit gross symptoms of phase separation when blended or polymer mixtures that have desirable chemical properties when blended. However, in a technological sense, the former is used to characterize the ease of fabrication or the properties of the two polymers in the blend [3-5]. 

The formation mechanism of structure of the crosslinked copolymer in the presence of solvents described on the basis of the Flory-Huggins theory of polymer solutions has been considered by Dusek [1,2]. In accordance with the proposed thermodynamic model [3], the main factors affecting phase separation in the course of heterophase crosslinking polymerization are the thermodynamic quality of the solvent determined by Huggins constant x for the polymer-solvent system and the quantity of the crosslinking agent introduced (polyvinyl comonomers). The theory makes it possible to determine the critical degree of copolymerization at which phase separation takes place. The study of this phenomenon is complex also because the comonomers act as diluents. 

The mechanism of phase separation proposed here (and also observed experimentally) involves the formation in the first stage of polymer blanks1, the globules size depends on the initial comonomers and the copolymerization conditions. In the case of slow phase separation proceeding near the thermodynamic equilibrium... 

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. 

The presence of ions in an otherwise organic matrix is not thermodynamically stable. As a result these materials undergo slight phase separation in which the ions cluster together in aggregates. These ionic clusters are quite... 

In view of the above developments, it is now possible to formulate theories of the complex phase behavior and critical phenomena that one observes in stractured continua. Furthermore, there is currently little data on the transport properties, rheological characteristics, and thermomechaiucal properties of such materials, but the thermodynamics and dynamics of these materials subject to long-range interparticle interactions (e.g., disjoiiung pressure effects, phase separation, and viscoelastic behavior) can now be approached systematically. Such studies will lead to sigiuficant intellectual and practical advances. 

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