Concentration-induced spinodal

The crucial question is at what value of <)> is the attraction high enough to induce phase separation De Hek and Vrij (6) assume that the critical flocculation concentration is equivalent to the phase separation condition defined by the spinodal point. From the pair potential between two hard spheres in a polymer solution they calculate the second virial coefficient B2 for the particles, and derive from the spinodal condition that if B2 = 1/2 (where is the volume fraction of particles in the dispersion) phase separation occurs. For a system in thermodynamic equilibrium, two phases coexist if the chemical potential of the hard spheres is the same in the dispersion and in the floe phase (i.e., the binodal condition). 

In flow the challenge has been to write convincing equations that couple concentration and composition gradients to elastic stresses and the bulk flow field. When done within a two-fluid model for polymer solutions transitions in light-scattering patterns seen in experiment may be explained. Extensions to polymer blends are potential candidates as explanations of shear-induced shifts of the spinodal and biphasic islands seen experimentally. - ... 

Spinodal decomposition is the second mechanism of liquid-liquid phase separation. Here, the solution spontaneously separates into interconnected regions of high and low polymer concentration with intertwined networks. The authors report that for chemically Induced systems (polymer/solvent/nonsolvent), the nucleation and growth kinetics are much too rapid to permit spinodal decomposition. 

Some of the basic features of pressure-induced phase separation have already been discussed in connection with Figure 5. The figure demonstrates three different paths corresponding to three different polymer concentrations in which the system pressure has been reduced from an initial pressure of Pi to a final pressure of Pf. Paths AB and A B take the system to the metastable regions, while path A B takes the system inside the spinodal envelop. Once the phase separation is complete, the two phases that coexist in equilibrium will have the same phase compositions (specified by the binodals) irrespective of which path has been followed. Phase volumes of polymer-rich and polymer-lean phase will however depend on the path. What is not described in Figure 5 is the transient structures that form along these paths. These are demonstrated in Figure 16. 

A direct link between theoretical and experimental work on depletion-induced phase separation of a colloidal dispersion due to non-adsorbing polymers was made by De Hek and Vrij [56, 109]. They mixed sterically stabilized silica dispersions with polystyrene in cyclohexane and measured the limiting polymer concentration (phase separation threshold). Commonly, one uses the binodal or spinodal as experimental phase boundary. A binodal denotes the condition (compositions, temperature) at which two or more distinct phases coexist, see Chap. 3. A tie-line connects two binodal points. A spinodal corresponds to the boundary of absolute instability of a system to decomposition. At or beyond the spinodal boundary infinitesimally small fluctuations in composition will lead to phase separation. De Hek and Vrij [56] used the pair potential (1.21) to estimate the stability of colloidal spheres in a polymer solution by calculating the second osmotic virial coefhcient B2 ... 

A homogeneous mixture quenched from a stable phase into a thermodynamically unstable state within a phase diagram develops into an inhomogeneous system. Spinodal decomposition (SD) is induced by the instability of an order parameter, which is usually concentration [101]. In the early stages, the SD is interpreted within the framework of the Cahn theory for an isotropic SD [102,103]. In contrast, in the late stages, the SD is governed by diffusion or hydrodynamic processes and exhibits slow coarsening [104]. There are two types of order parameters that describe a system. One is a conserved order parameter such as concentration of binary mixtures. The other is a non-conserved order parameter such as the polarization of a ferroelectric... 

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