Phase Separation

Figure 6A is a general representation of the pressure-composition diagrams for systems that display liquid -liquid phase separation. The binodal boundary represents the equilibrium demixing pressures for a monodisperse polymer system. Below the binodal there is another boundary known as the spinodal boundary. The binodal and the spinodal envelopes determine the metastable region (shaded area in between). They merge at the critical polymer concentration c). Starting from a high-pressure in the one-phase region, phase separation may be induced by reducing the pressure. The equilibrium compositions of the two phases that form when pressure is reduced from P, to Pf are given by the binodals ^ Iband IIbFor the different pressure quench paths I, II and III that end at the same final pressure (Pf), the compositions of the coexisting phases are given by the same binodal compositions, even though the concentrations of the initial one-phase solutions are different. The difference in the initial compositions shows itself in the phase volumes of the coexisting phases rather than the compositions.

Figure 6A is the thermodynamic (equilibrium) picture and does not describe the transient structures that may form along the different pressure reduction paths before final equilibrium conditions are reached. Along the paths I and III, the system enters the metastable regions where the mechanism of phase separation is by nucleation and growth13-5 In solutions of low polymer concentrations along path I, the polymer-rich phase nucleates in the polymer-lean phase, and grows. In contrast, in the more concentrated polymer solutions along path III, the polymer-lean phase nucleates in the polymer-richphase and grows. The particles of polymer-rich phase (path I), or the bubbles of polymer-lean phase (path III) unless frozen may eventually collapse, settling into the two coexisting phases with compositions fixed by the binodal values. These are demonstrated in Figure 6B. Along the path II which corresponds to the critical polymer concentration, the system immediately enters the spinodal region where the phase separation is spontaneous and in the initial stage a co-continuous texture of polymer-rich and polymer-lean phases forms. In time, the structure coarsens and may eventually collapse. At concentrations away from the critical polymer concentrations, entering the spinodal domain may not be readily achievable. This depends on the width of the metastable region and the speed with which it can be traversed.

Polymer concentration, w

Path I Path II Path III

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