Meyer-Flory-Huggins theory

Gibbs and DiMarzio [47] (GD) first developed a systematic statistical mechanical theory of glass formation in polymer fluids, based on experimental observations and on lattice model calculations by Meyer, Flory, Huggins, and... 

The swelling of vulcanized crosslinked rubber by solvents has long been observed. This behavior was first modeled in the 1940s by Flory and Refiner [47]. They combine the Meyer-Flory-Huggins statistical thermodynamic theory of polymer solutions (Section 3.3) with the molecular theory of crosslinked rubber elasticity [48]. The molecular weight between crosslinks of the vulcanizates was predicted from the swelling to be... 

Statistical thermodynamic theories provide a powerful tool to bridge between the microscopic chemical structures and the macroscopic properties. Lattice models have been widely used to describe the solution systems (Prigogine 1957). Chang (1939) and Meyer (1939) reported the earliest work related with the lattice model of polymer solution. The lattice model was then successfully established by Flory (1941, 1942) and Huggins (1942) to deal with the solutions of flexible polymers by using a mean-field approximation, and to derive the well-known Flory-Huggins equation. 

The lattice theory of flexible chain polymer solutions developed by Meyer [6], Huggins [7], and Flory [8] was hrst extended to polymer blends by Scott [9], The free energy of the mixing of a polymer blend maybe represented according to Scott [9] in the form (compare Eqs.3.21 and 3.22) ... 

Of more interest are intermediate cases. Low molecular weight compounds have easier miscibility than polymers to form solutions than various polymers have to form miscible blends. This is associated with the reduced entropy of mixing in polymer solutions as modeled in the theories of Meyer [7], Huggins [8] and Flory [9,10] (as described in Chapter 3). Thus, benzene is soluble in propyl alcohol, while polystyrene is soluble in benzene but not in alcohol where the endothermic heat of mixing and low entropy of mixing is too unfavorable. If we consider such a ternary system, it often leads to the situation where we have two phases, which are solutions immiscible with each other. The polymer is distributed between the two phases. The polymer in the system cited above, polystyrene, would primarily be in the benzene-rich phase. 

We may represent the phenomena described above in terms of the Meyer-Huggins-Flory theory described in Chapter 3, but for ternary systems. The equations are basically those of Sections 6.2 and 6.3. This has been considered and modeled by Scott [24]. The distribution of the third component between the different phases for non-polar systems is largely determined by the values of the solubility parameters (or parameters) between components as well as the molecular weights. 

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