Binary polymer solutions coexistence curve

Figure 9 Coexistence curve of binary polymer solutions with different chain lengths. From bottom to top the chain lengths are 1, 2, 4, 8,16, 32, 64,100, 200, and 600, respectively.

Figure 10 Coexistence curve of binary polymer solutions with chain length r2 = 18 and 60. Open squares MC data solid line this work dash line Flory-Huggins theory dotted line Freed theory.

Turbidity measurements use the onset of two-phase separation when adding a non-solvent to a dilute polymer solution in a good solvent. Two different non-solvents have to be used one having a solubility parameter above that of the (good) solvent, and another having a solubility parameter below that of the solvent. A series of experiments has to be done to find the solvent-polymer pair with 62 = di. Liquid-liquid equilibrium (LLE) curves of binary polymer solutions ean also be applied for the determination of solubility parameters of polymers. An appropriate thermodynamic model relating cloud-point or coexistence data with Xh is necessary, however. 

Figure 1, Liquid-liquid equilibria in a polymer/solvent solution ethylene-polyethylene binary coexistence curve (constant T and molecular weight)...

Certain principles must be obeyed for experiments where liquid-hquid equilibrium is observed in polymer-solvent (or supercritical fluid) systems. To understand the results of LLE experiments in polymer solutions, one has to take into account the strong influence of polymer distribution functions on LLE, because fractionation occurs during demixing. Fractionation takes place with respect to molar mass distribution as well as to chemical distribution if copolymers are involved. Fractionation during demixing leads to some effects by which the LLE phase behavior differs from that of an ordinary, strictly binary mixture, because a common polymer solution is a multicomponent system. Cloud-point curves are meastrred instead of binodals and per each individual feed concentration of the mixture, two parts of a coexistence curve occur below (for upper critical solution temperature, UCST, behavior) or above the cloud-point curve (for lower critical solution temperature, LCST, behavior), i.e., produce an infrnite number of coexistence data. 

Physically speaking, LCST represents the shared minima of the spinodal and coexistence curves in a binary system, namely polymer and solvent (Schattling et al., 2014). Typically, this phase transition phenomena are fully reversible and the polymer solution can recover the initial state. 

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