Flory—Huggins theory polymer blends

The well-known mean-field incompressible Flory-Huggins theory of polymer mixtures assumes random mixing of polymer repeat units. However, it has been demonstrated that the radial distribution functions gay(r) of polymer melts are sensitive to the details of the polymer architecture on short length scales. Hence, one expects that in polymer mixtures the radial distribution functions will likewise depend on the intramolecular structure of the components, and that the packing will not be random. Since by definition the heat of mixing is zero for an athermal blend, Flory-Huggins theory predicts athermal mixtures are ideal solutions that exhibit complete miscibility. 

In polymer solutions or blends, one of the most important thennodynamic parameters that can be calculated from the (neutron) scattering data is the enthalpic interaction parameter x between the components. Based on the Flory-Huggins theory [4T, 42], the scattering intensity from a polymer in a solution can be expressed as... 

Flory-Huggins Theory. The simplest quantitative model foi that iacludes the most essential elements needed foi polymer blends is... 

Note 1 The Flory-Huggins theory has often been found to have utility for polymer blends, however, there are many equation-of-state theories that provide more accurate descriptions of polymer-polymer interactions. 

Flory-Huggins Theory. The simplest quantitative model for AGmx that includes the most essential elements needed for polymer blends is the Flory-Huggins theory, originally developed for polymer solutions (3,4). It assumes the only contribution to the entropy of mixing is combinatorial in origin and is given by equation 3, for a unit volume of a mixture of polymers A. and B. Here, pt and... 

Equation-of-state theories employ characteristic volume, temperature, and pressure parameters that must be derived from volumetric data for the pure components. Owing to the availability of commercial instruments for such measurements, there is a growing data source for use in these theories (9,11,20). Like the simpler Flory-Huggins theory, these theories contain an interaction parameter that is the principal factor in determining phase behavior in blends of high molecular weight polymers. 

The lattice fluid equation-of-state theory for polymers, polymer solutions, and polymer mixtures is a useful tool which can provide information on equa-tion-of-state properties, and also allows prediction of surface tension of polymers, phase stability of polymer blends, etc. [17-20]. The theory uses empty lattice sites to account for free volume, and therefore one may treat volume changes upon mixing, which are not possible in the Flory-Huggins theory. As a result, lower critical solution temperature (LCST) behaviors can, in principle, be described in polymer systems which interact chiefly through dispersion forces [17]. The equation-of-state theory involves characteristic parameters, p, v, and T, which have to be determined from experimental data. The least-squares fitting of density data as a function of temperature and pressure yields a set of parameters which best represent the data over the temperature and pressure ranges considered [21]. The method,however,requires tedious experiments to deter-... 

In this section, we mention very briefly some recent theoretical developments, which go far beyond the simple Flory-Huggins theory. As was emphasized above, the Flory-Huggins theory suffers from two basic defects (i) Using a lattice model where polymers are represented as self-avoiding walks is a crude approximation, which neglects the disparity in size and shape of subunits of the two types of chain in a polymer blend, as well as packing constraints, specific interactions etc. (ii) Even within the realm of a lattice model, the statistical mechanics (involving approximations beyond the mean field approximation) is far too crude. 

In a blend solution, the interaction parameter x of the Flory-Huggins theory is zero (the chain end effect is negligible) and independent of temperature. Otherwise, a temperature-dependent x can lead to a thermorhe-ologically complex behavior of the polymer solution sj tem, which would disallow the apphcation of the time-temperature superposition principle. A theoretical analysis indicates that if M M2, the system is free of the excluded volume effect that will cause the component-two chain to expand in other words, the chain coil remains Gaussian. Here, we consider polystyrene blend solutions with Mi slightly smaller than Mg (= 13,500 for polystyrene). In such a system, the condition M > M2 can be easily satisfied. Furthermore, the solvent, being chains of more than ten Rouse... 

Maier, T. R., Jamieson, A. M., and Simha, R., Phase equilibria in SBR/polybutadiene elastomer blends application of Flory-Huggins theory, J. Appl. Polym. Sci., 51 (6), 1053-1062 (1994). 

Bawendi MG, Freed KF (1988) Systematic corrections to Flory-Huggins theory polymer-solvent-void systems and binary blend-void systems. J Chem Phys 88 2741-2756 Chang TS (1939) Statistical theory of absorption of double molecules. Proc R Soc Ser A 169 512-531... 

The Flory-Huggins theory, originally developed for polymer/solvent systems, was extended to polymer blends and other multicomponent mixtures by R. L. Scott, J. Polym. Sci. 9,423 (1952). 

There have been also some recent theoretical approaches addressing mainly the thermodynamic properties of binary and ternary polymer blends. Campos et al. (1996) extended the Flory-Huggins theory to predict the thermodynamic properties of binary polymer blends and blends in solution. Their approach was applied for PVDF/PS dry blend and in solutirm in dimethylformamide (DMF) with inclusion of an interaction functirai. It could be inferred that this blend behave as slightly incompatible under envirorunental cruiditions, in agreement with previously reported data. That incompatibility was suppressed when a low molar mass component, such as DMF, was added, reaching the semidilute regime (total... 

Buta et al. (2001) tested the Monte Carlo approach for the lattice cluster theory to derive the thermodynamic properties of binary polymer blends. They considered the two polymers to have the same polymerization indices, i.e., M = 40, 50, or 100. The results confirm that this lattice cluster theory had a higher accuracy compared to the Flory-Huggins theory and the Guggenheim s random mixing approximation. However, some predictions for the specific heat were found to be inaccurate because of the low order cutoff of the high temperature perturbative expansion. 

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