Incompressible mixtures

Let us consider die scattered intensity from a binary incompressible mixture of two species (containing molecules of particle 1 and molecules of particle 2) as in (B 1.9.112) we can rewrite the relationship as... 

The multicomponent RPA formalism [11-15] is applied, here, to a ternary incompressible mixture [11-16] of homopolymers (A, B, C). Assuming that component C is the matrix component, one is left with 2x2 matrices for components A and B ... 

In the case of a binary incompressible mixture of stiff homopolymers (components are named A and B), the above equations simplify. Assuming that component A is flexible (freely-jointed chains) and B is rigid (rigid rod polymers) and imposing the incompressibility condition, the following result can be obtained ... 

In incompressible mixtures we find from (3.87), presuming constant thermal conductivity,... 

SIMPLIFICATION OF THE MASS TRANSFER EQUATION FOR PSEUDO-BINARY INCOMPRESSIBLE MIXTURES WITH CONSTANT PHYSICAL PROPERTIES... 

Restriction to a (chemically) non-reacting incompressible mixture mixture density (4.404) is constant because the composition is fixed (wp = const.). 

The time evolution of phase separation by spinodal decomposition is described by a diffusion equation for the density (pure fluid) or species concentration (mixture) [101,103,105]. To illustrate the basic aspects of the theory, we consider the onedimensional, pure fluid case. Generalization to more dimensions, and extension to binary incompressible mixtures involve just a change of notation. For a pure fluid, the diffusion equation reads... 

In order to obtain the specific form of T(q), we now apply the random phase approximation (RPA) [22-26] to our system. The RPA provides a classical treatment of concentration fluctuations for incompressible mixtures of very large molecular weight molecules. It assumes a self-consistent potential uniformly acting on all species of monomers to ensure the incompressibility condition. The details of the RPA method, as applied to our polydisperse block copolymer blend, are given in Appendix 5.B. The result leads to... 

Equation (1.7) describes the spinodal curve in the plane of variables (x, <)>)- The maximum of the spinodal curve for such a binary incompressible mixture yields the critical point, that is ... 

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