Phase behavior, of polymer solutions

Before discussing theoretical approaches let us review some experimental results on the influence of flow on the phase behavior of polymer solutions and blends. Pioneering work on shear-induced phase changes in polymer solutions was carried out by Silberberg and Kuhn [108] on a polymer mixture of polystyrene (PS) and ethyl cellulose dissolved in benzene a system which displays UCST behavior. They observed shear-dependent depressions of the critical point of as much as 13 K under steady-state shear at rates up to 270 s Similar results on shear-induced homogenization were reported on a 50/50 blend solution of PS and poly(butadiene) (PB) with dioctyl phthalate (DOP) as a solvent under steady-state Couette flow [109, 110], A semi-dilute solution of the mixture containing 3 wt% of total polymer was prepared. The quiescent... 

Several attempts have been made to explain theoretically the effects of flow on the phase behavior of polymer solutions [112,115-118,123,124]. This has been done by modification of the mean-field free energy. The key point is to include properly the elastic energy of deformation produced by flow. A more rigorous approach originates from Helfand et al. [125, 126] and Onuki [127, 128] who proposed hydrodynamic theories for the dynamics of concentration fluctuations in the presence of flow coupled with a linear stability analysis. 

Now we turn our attention to the phase behavior of polymer solutions and blends and the questions we asked right at the beginning of this chapter will a particular polymer dissolve in a given solvent or mix with another chosen polymer ... 

An important subset of high-pressure phase diagrams is that of polymer-SCF mixtures. This area has not been as extensively studied since it wasn t until about the late 1920s that polymers were accepted as substances having well-defined molecular identities (Munk, 1989). Although it was known for almost 100 years that alcohol-SCF mixtures can exhibit LTV behavior near the critical point of the SCF solvent (Kuenen and Robson, 1899), it wasn t until the early 1960s that similar phenomena were discovered for nonpolar polymer-solvent mixtures (Freeman and Rowlinson, 1960). The scientific interest in the high-pressure phase behavior of polymer solutions was initially driven by the... 

Often r is approximated by the ratio of the molar volumes of pure liquid polymer and pure solvent. The segment fractions of solvent and polymer are then equal to the volume fractions of solvent and polymer, and p. Equation (27) is derived using many assumptions and approximations (for a discussion, see Ref. 8), but on the basis of this rather simple expression many features of the phase behavior of polymer solutions can be explained. The expressions for the mole fraction based activity coefficients of solvent and polymer are Eqs. (30) and (31), respectively. 

Furthermore, the phase behavior of polymer solutions and mixtures is more complex than that of small molecule mixtures. Whereas most small molecule solutions exhibit only an upper critical solution temperature phase transition, at which phase separation occurs with cooling, polymer mixtures commonly exhibit a lower critical solution temperature phase transition, at which phase separation occurs with heating. 

In this chapter, we have seen how classical and statistical thermodynamics coupled with simple ideas of lattice theory can be used to predict the phase behavior of polymer solutions. For polymers dissolved in low-molecular-weight solvents, the Flory-Huggins theory and its various modifications can adequately explain data obtained for quiescent solutions. More recently, the theory has been applied to predict the shift in the binodal under the influence of an imposed shear deformation [33]. For macromolecular solvents, however, development of the theory has not reached the same stage of maturity as for low-molecular-weight solvents. This remains an area of current and active research. 

Of course, nanocomposites are not the only area where mesoscale theories are being used to predict nanostructure and morphology. Other applications include—but are not limited to—block copolymer-based materials, surfactant and lipid liquid crystalline phases, micro-encapsulation of drugs and other actives, and phase behavior of polymer blends and solutions. In all these areas, mesoscale models are utilized to describe—qualitatively and often semi-quantitatively—how the structure of each component and the overall formulation influence the formation of the nanoscale morphology. 

Table I. Phase behavior of polymer/surfactant-cosurfactant aqueous solutions as observed in polarized light...

Using Flory-Huggins theory it is possible to account for the equilibrium thermodynamic properties of polymer solutions, particularly the fact that polymer solutions show major deviations from ideal solution behavior, as for example, the vapor pressure of solvent above a polymer solution invariably is very much lower than predicted from Raoult s law. The theory also accounts for the phase separation and fractionation behavior of polymer solutions, melting point depressions in crystalline polymers, and swelling of polymer networks. However, the theory is only able to predict general trends and fails to achieve precise agreement with experimental data. 

A number of important characteristics of polymers, such as molecular weight, chain length, branching, and chain stiffness, can be explored when the individual molecules are separated froni each other. Such studies therefore employ dilute solutions of polymers. However, the dissolution of a polymer also brings with it many new problems. For a correct interpretation of the behavior of polymer solutions it is essential to understand the thermodynamics of polymer-solvent interaction. We will therefore explore some of the basic underlying thermodynamic principles of polymer solutions in this chapter. A major part of the chapter will be concerned with methods of studying polymer solutions that deal with equilibria and can be fully described by thermodynamic relations. These include vapor pressure, osmotic pressure, and phase separation in polymer-solvent systems. 

Liquid-liquid demixing in solutions of polymers in low molar mass solvents is not a rare phenomenon. Dembcing depends on concentration, temperature, pressure, molar mass and molar mass distribution function of the polymer, chain branching and end groups of the polymer, the chemical nature of the solvent, isotope substitution in solvents or polymers, chemical composition of copolymers and its distributions, and other variables. Phase diagrams of polymer solutions can therefore show a quite complicated behavior when they have to be considered in detail (see Ref la). 

Phase Behavior of Polymer Systems in High Pressure Fluids The basic description and definitions of the different phenomena associated with phase equilibria in polymer solutions are described in Section 25.2.5. Topics such as construction and interpretation of binary... 

Phase separation is frequently observed in polymer solutions and it is mainly due to their low entropy of mixing. At a state of equilibrium each species of the mixture is partitioned between two phases, namely, the supernatant (extremely dilute) and precipitated (moderately dilute) phases [78]. Theoretical models and experimental techniques have been developed to predict the solubility behavior of polymer solutions, polymer blends, and other related systems [79, 80]. Simple theories only permit a rather qualitative description of this phenomenon [78]. Refined and improved theoretical and semiempirical models allow a more accurate prediction of the demixing phenomena and related thermodynamic properties [57, 81]. 

HA4 Haschets, C.W. and Shine, A.D., Phase behavior of polymer-supercritical chlorodifluoro-methane solutions, Macrowo/ecM/es, 26, 5052, 1993. 

Adidharma and Radosz provides an engineering form for such a copolymer SAFT approach. SAFT has successfully applied to correlate thermodynamic properties and phase behavior of pure liquid polymers and polymer solutions, including gas solubility and supercritical solutions by Radosz and coworkers Sadowski et al. applied SAFT to calculate solvent activities of polycarbonate solutions in various solvents and found that it may be necessary to refit the pure-component characteristic data of the polymer to some VLE-data of one binary polymer solution to calculate correct solvent activities, because otherwise demixing was calculated. GroB and Sadowski developed a Perturbed-Chain SAFT equation of state to improve for the chain behavior within the reference term to get better calculation results for the PVT - and VLE-behavior of polymer systems. McHugh and coworkers applied SAFT extensively to calculate the phase behavior of polymers in supercritical fluids, a comprehensive summary is given in the review by Kirby and McHugh. They also state that characteristic SAFT parameters for polymers from PVT-data lead to... 

Kirby, C.F. McHugh, M.A. Phase Behavior of Polymers in Supercritical Fluid Solvents. Chem. Rev. 1999, 99, 565 Kauffman, J.F. Quadrupolar Solvent Effects on Solvation and Reactivity of Solutes Dissolved in Supercritical CO2 J. Phys. Chem. A 2001, 105, 3433. 

Haschets, C.W., T.A. Blackwood, and A.D. Shine, Phase-behavior of polymer-Hcfc compressed solvent solutions. Abstracts of Papers of the American Chemical Society, 1993. 205 p. 28. 

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