Multicomponent polymers thermodynamics

Koningsveld, R. Kleintjens, L.A., "Liquid-liquid Phase Separation in Multicomponent Polymer Systems. 22. Thermodynamics of Statistical Copolymers," Macromolecules, 18, 243 (1985). 

Kambour RP, Bendler JT, Bopp RC (1983) Phase behavior of polystyrene, poly(2,6-dimethyl-l,4-phenylene oxide), and their brominated dtaivatives. Macromolecules 16 753-757 Koningsveld R, Kleijens LA (1971) Liquid-liquid phase separation in multicomponent polymer systems. X. Concentration dependence of the pair-interaction parameter in the system cyclohexane-polystyrene. Macromolecules 4 637-641 Maron SH (1959) A theory of the thermodynamic behavior of non-electrolyte solutions. J Polym Sci 38 329-342... 

This chapter summarizes the thermodynamics of multicomponent polymer systems, with special emphasis on polymer blends and mixtures. After a brief introduction of the relevant thermodynamic principles - laws of thermodynamics, definitions, and interrelations of thermodynamic variables and potentials - selected theories of liquid and polymer mixtures are provided Specifically, both lattice theories (such as the Hory-Huggins model. Equation of State theories, and the gas-lattice models) and ojf-lattice theories (such as the strong interaction model, heat of mixing approaches, and solubility parameter models) are discussed and compared. Model parameters are also tabulated for the each theory for common or representative polymer blends. In the second half of this chapter, the thermodynamics of phase separation are discussed, and experimental methods - for determining phase diagrams or for quantifying the theoretical model parameters - are mentioned. 

Koningsveld R., Kleintjens L.A. and Leblans-Vinck A.M., (1985), Liquid-Liquid phase separation in multicomponent polymer systems XXIV Thermodynamics of polymer blends, Ber Bunsenges. Phys. Chem. 89, 1234. 

Many multicomponent polymer systems may be, and are, used as matrices for composite materials. The concept of hybrid matrices was put forward. These matrices are polymer alloys of miscible and immiscible polymers (both linear and cross-linked). Because a structure of alloys of immiscible polymers is formed during the phase separation, it is very important to establish the influence of the interface with solid on these processes, on the thermodynamic state of filled pol3mier alloys, and, correspondingly, on their viscoelastic properties. The interface with solid in hybrid matrices affects both the structure formed during phase separation and the properties of composites based on filled hybrid matrices. Here the solid phase plays not only the traditional role of reinforcement but also the new role of a regulator of the phase structure, due to the phase border influence on the phase separation and thermodynamic stability or instability of the system. 

Flory PJ, Orwoll RA, Vrij A (1964) Statistical thermodynamics of chain molecule liquids. I. An equation of state for normal paraffin hydrocarbons. J Am Chem Soc 86 3507 3514 Nose T (1976) Theory of liquid liquid interface of polymer systems. Polym J 8 96 113 de Gennes P G (1977) Qualitative features of polymer demixtion. J Phys Lett 38 L441 L443 Ouhadi T, Fayt R, Jerome R, Teyssie Ph (1986) Molecular design of multicomponent polymer systems. 9. Emulsifying effect of poly(alpha methylstyrene b methlyl methacry late) in poly(vinylidene fluoride)/poly(alpha methylstyrene) blends. Polym Commun 27 212 215... 

Relations 22 and 23 emphasize that the surface composition of a typical multicomponent polymer may differ drastically from that of the bulk, even for a true solution. Lower surface energy components adsorb preferentially at the surface, thereby lowering the overall surface tension of the mixture. In terms of adhesion, the manifestation of surface segregation is a generally weaker interface, since lowering the surface energy will decrease the thermodynamic work of adhesion. 

It is evident that the contribution of the elastic energy in multicomponent polymer systems is small at the onset of phase separation. It increases with growth in the composition difference of phase-separated microregions. As a result, the system is stabihzed when the thermodynamic force of phase separation is balanced by the elastic forces from entanglements of the network fragment. The system remains in a state of incomplete phase separation. The stability limit of such a polymer system will be characterized by the curve below the chemical spinodal. For the system with UCST the real spinodal is located below the chemical spinodal. It is important to note that for some systems, including IPNs, the real spinodal is so removed from the chemical one that the unstable state cannot be reached. 

Multicomponent polymer blends can offer a vast array of possible morphologies. Three factors can have an important effect on morphology formation in immiscible multicomponent polymer blends thermodynamic properties of the blend, and more specifically the interfacial tensions of the different polymer pairs [1-5] viscosity of the constituents [6] and elasticity of the constituents [7, 8]. 

Unfortunately, relatively little work has been done on the solution thermodynamics of concentrated polymer solutions with "gathering". The definitive work on the subject Is the article of Yamamoto and White (17). The corresponding-states theory of Flory (11) does not account for gathering. We therefore restrict our consideration here to multicomponent solutions where the solvents and polymer are nonpolar. For such solutions, gathering Is unlikely to occur. 

Equilibrium phenomenon, operative in polymer solutions, in multicomponent solvents, and in polymer networks swollen by multicomponent solvents, that produces differences in solvent composition in the polymer-containing region and in the pure solvent which is in thermodynamic equilibrium with that region. 

It is the intent of this doeument to define the terms most commonly encountered in the field of polymer blends and eomposites. The scope has been limited to mixtures in which the eomponents differ in ehemical composition or molar mass or both and in which the continuous phase is polymeric. Many of the materials described by the term multiphase are two-phase systems that may show a multitude of finely dispersed phase domains. Hence, incidental thermodynamic descriptions are mainly limited to binary mixtures, although they can be and, in the scientific literature, have been generalized to multicomponent mixtures. Crystalline polymers and liquid-crystal polymers have been considered in other documents [1,2] and are not discussed here. 

The objective of this review is to characterize the excimer formation and energy migration processes in aryl vinyl polymers sufficiently well that the excimer probe may be used quantitatively to study polymer structure. One such area of application in which some measure of success has already been achieved is in the analysis of the thermodynamics of multicomponent systems and the kinetics of phase separation. In the future, it is likely that the technique will also prove fruitful in the study of structural order in liquid crystalline polymers. 

Among other approaches, a theory for intermolecular interactions in dilute block copolymer solutions was presented by Kimura and Kurata (1981). They considered the association of diblock and triblock copolymers in solvents of varying quality. The second and third virial coefficients were determined using a mean field potential based on the segmental distribution function for a polymer chain in solution. A model for micellization of block copolymers in solution, based on the thermodynamics of associating multicomponent mixtures, was presented by Gao and Eisenberg (1993). The polydispersity of the block copolymer and its influence on micellization was a particular focus of this work. For block copolymers below the cmc, a collapsed spherical conformation was assumed. Interactions of the collapsed spheres were then described by the Hamaker equation, with an interaction energy proportional to the radius of the spheres. 

Third, a serious need exists for a data base containing transport properties of complex fluids, analogous to thermodynamic data for nonideal molecular systems. Most measurements of viscosities, pressure drops, etc. have little value beyond the specific conditions of the experiment because of inadequate characterization at the microscopic level. In fact, for many polydisperse or multicomponent systems sufficient characterization is not presently possible. Hence, the effort probably should begin with model materials, akin to the measurement of viscometric functions [27] and diffusion coefficients [28] for polymers of precisely tailored molecular structure. Then correlations between the transport and thermodynamic properties and key microstructural parameters, e.g., size, shape, concentration, and characteristics of interactions, could be developed through enlightened dimensional analysis or asymptotic solutions. These data would facilitate systematic... 

The basic issue confronting the designer of polymer blend systems is how to guarantee good stress transfer between the components of the multicomponent system. Only in this way can the component s physical properties be efficiently used to give blends with the desired properties. One approach is to find blend systems that form miscible amorphous phases. In polyblends of this type, the various components have the thermodynamic potential for being mixed at the molecular level and the interactions between unlike components are quite strong. Since these systems form only one miscible amorphous phase, interphase stress transfer is not an issue and the physical properties of miscible blends approach and frequently exceed those expected for a random copolymer comprised of the same chemical constituents. 

The design engineer dealing with polymer solutions must determine if a multicomponent mixture will separate into two or more phases and what the equilibrium compositions of these phases will be. Prausnitz et al. (1986) provides an excellent introduction to the field of phase equilibrium thermodynamics. 

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