Flory theta temperature

J. O. Park and G. C. Berry, Moderately concentrated solutions of polystyrene. III. Viscoelastic properties at the Flory theta temperature , Macromolecules, 22, 3022 (1989). 

It is well established that the excluded volume effect vanishes under a special condition of temperature or solvent, which is usually known as the Flory theta temperature or solvent. Thus, light scattering measurements performed on solutions under theta conditions can furnish direct knowledge of the unperturbed dimensions [see, for example, Outer, Carr and Zimm (207) Shultz (233) and Notley and Debye (207)]. Viscosity measurements, though less directly, can also furnish similar knowledge with the aid of the Flory-Fox equation (103,109), which may be written... 

The difference between a and aJy is caused by the non-Gaussian character of the chain, but it is rather small and negligible for most purposes. These equations can be effectively applied to systems in poor solvents near the Flory theta temperature, but not to systems in good solvents because of slow convergence of the series [see, for example, Kurata, Yamakawa and Teramoto (75 )]. 

Krigbaum, W. R. Geymer, D. 0., "Thermodynamics of Polymer Solutions. The Polystyrene-Cyclohexane System Near the Flory Theta Temperature," J. Am. Chem. Soc., 81, 1859 (1959). 

Most polymers are more soluble in their solvents the higher the solution temperature. This is reflected in a reduction of the virial coefficient as the temperature is reduced. At a sufficiently low temperature, the second virial coeflicient may actually be zero. This is the Flory theta temperature, which is defined as that temperature at which a given polymer species of infinite molecular weight would be insoluble at great dilution in a particular solvent. A solvent, or mixture of solvents, for which such a temperature is experimentally attainable is a theta solvent for the particular polymer. 

The parameter will vary with PS molecular weight and with the free energy of dilution (Flory, 1953), kT jj2 — Q/T)v, where is the entropy of dilution, 9 is the Flory theta temperature, and V2 is the volume fraction of solute. 

At high temperatures, the repulsive core is dominant, and the local minimum may be neglected completely. This is the excluded volume effect, and corresponds to what is called a good solvent [10,11]. There exists a critical temperature called the Flory theta temperature, where the excluded volume effect and the attractive part compensate each other. Such solutions are said to be in a theta solvent [12-14]. For still lower temperatures, the attractive part of the potential becomes dominant, and although two monomers are not allowed to be in the same location, they tend to be in the vicinity of each other. As a consequence, the chain tends to collapse on itself [15-17]. Solvents in which this happens are known as poor solvents. 

KIN Kinsinger, J.B. and Wessling, R.A., The Flory (theta) temperature of atactic and isotactic polypropylene,/. Amer. Chem. Soc., 81, 2908, 1959. 

Thermodynamic and conformational characteristics are represented in the fimc-tions P(q, c) and F(q, c). Some theories of moderately concentrated stdutions of flexible chains give H(q, c) equal to unity for all q and c [14, 24, 25], but the exact behavior is not yet settled. The behavior of H(q, c) is contidered below for solutions at the Flory Theta temperature, and for sotutimis in good solvent ie., systems for which /2 is large. Further, as discussed below, the principal effect on P(q, c) appears to be that of the concentration dependence Re, rather than any appreciable change in the functional form of P(q, cX... 

Data on dilute solutions in both a good solvent and at the Flory Theta temperature have been analyzed using this relation [73]. The function Ayjfq), found to be independent of q for small q and to tend to proportionality with q for large q, was fitted by the semi-empirical relation... 

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