Flory compensation temperature

While the Flory-Krigbaum potential is a qualitatively reasonable form for polymers in a good solvent, it completely misrepresents the shape of the potential of mean force near the Flory temperature. The potential of mean force is positive and repulsive for small values of the center-of-mass separation, just as it was for the overlap of two subchains. For the overall excluded volume to vanish, the potential of mean force must be negative for small degrees of overlap. The Flory compensation temperature is a balance... 

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. 

Following Flory (1969), a 0 solvent is a thermodynamically poor solvent where the effect of the physically occupied volume of the chain is exactly compensated by mutual attractions of the chain segments. Consequently, the excluded volume effect becomes vanishingly small, and the chains should behave as predicted by mathematical models based on chains of zero volume. Chain dimensions under 0 conditions are referred to as unperturbed. The analogy between the temperature 0 and the Boyle temperature of a gas should be appreciated. 

The lateral forces depend on temperature at high temperatures the repulsion interactions between particles prevail on the contrary, at low temperatures the attraction interactions prevail, so that there is a temperature at which the repulsion and attraction effects exactly compensate each other. This is the 0-temperature at which the second virial coefficient is equal to zero. It is convenient to consider the macromolecular coil at 0-temperature to be described by expressions for an ideal chain, those demonstrated in Sections 1.1-1.4. However, the old and more recent investigations (Grassberger and Hegger 1996 Yong et al. 1996) demonstrate that the last statement can only be a very convenient approximation. In fact, the concept of 0-temperature appears to be immensely more complex than the above picture (Flory 1953 Grossberg and Khokhlov 1994). 

When the temperature of a polymer solution diminishes, the attractive long-range forces become more efficient than the hard-core repulsive forces. At a temperature Tf recognized by Paul Flory in 1942, attractions and repulsions compensate. In this case, for a temperature slightly smaller than TF, the solution separates into two phases and this phenomenon is called demixtion. 

FIG U RE 10.4 Comparison between experimental (o) and calculated (solid lines) solubilities of phenacetin (S is the mole fraction of phenacetin) in the mixed solvent water/dioxane is the mole fraction of dioxane) at room temperature. The solubility was calculated using Equation 10.29. 1-activity coefficients expressed via the Flory-Huggins equation, 2-activity coefficients expressed via the Wilson equation. (From C. Bustamante, and P. Bustamante, 1996, Nonlinear Enthalpy-Entropy Compensation for the Solubility of Phenacetin in Dioxane-Water Solvent Mixtures, Journal of Pharmaceutical Sciences, 85, 1109. Reprinted from E. Ruckenstein, and I. L. Shulgin, 2003c, Solubility of Drugs in Aqueous Solutions. Part 2 Binary Nonideal Mixed Solvent, International Journal of Pharmaceutics, 260, 283, With permission from Elsevier.)... 

As explained previously, the Rg of polymer chains in organic solvents depends on the sign and magnitude of the interactions between the chain segments and the molecules of the surrounding liquid. The attractive and repulsive interactions compensate at the theta temperature Tq), at which = 0, and Rg corresponds to the dimension of a volume-less polymer coil. Similarly, as the concentration of polymer increases, excluded-volume effects are screened and diminished, and, in the limit of the bulk polymer, the conformation of a single chain can be described as an unperturbed random walk, as originally predicted by Flory [11], and one of the first applications of SANS was to confirm this prediction for the condensed amorphous state (see Section 7.1.2). 

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