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## Flory-Huggins solution theory
## Additional recommended knowledgeA change, denoted by Δ, is the value of a variable for a solution or mixture minus the values for the pure components considered separately. The objective is to find explicit formulas for Δ The result obtained by Flory and Huggins isThe right-hand side is a function of the number of moles ## DerivationWe first calculate the
From statistical mechanics we can calculate the entropy change, the increase in spatial uncertainty, as a result of mixing solute and solvent. where These are also the probabilities that a given lattice site, chosen at random, is occupied by a solvent molecule or a polymer segment, respectively. Thus For a small solute whose molecules occupy just one lattice site, In addition to the entropic effect, we can expect an The total number of such contacts is where The enthalpy change is equal to the energy change per polymer monomer-solvent interaction multiplied by the number of such interactions The polymer-solvent interaction parameter It depends on the nature of both the solvent and the solute, and is the only Assembling terms, the total free energy change is where we have converted the expression from molecules The value of the interaction parameter can be estimated from the Hildebrand solubility parameters δ where This treatment does not attempt to calculate the conformational entropy of folding for polymer chains. (See the random coil discussion.) The conformations of even amorphous polymers will change when they go into solution, and most thermoplastic polymers also have lamellar crystalline regions which do not persist in solution as the chains separate. These events are accompanied by additional entropy and energy changes. More advanced models exist, such as the Flory-Krigbaum theory. ## References and footnotes-
**^**"Thermodynamics of High Polymer Solutions," Paul J. Flory*Journal of Chemical Physics,*August 1941, Volume 9, Issue 8, p. 660 Abstract. Flory suggested that Huggins' name ought to be first since he had published several months earlier: Flory, P.J., "Thermodynamics of high polymer solutions,"*J. Chem. Phys.***10**:51-61 (1942)*Citation Classic*No. 18, May 6, 1985 -
**^**"Solutions of Long Chain Compounds," Maurice L. Huggins*Journal of Chemical Physics,*May 1941 Volume 9, Issue 5, p. 440 Abstract -
**^**We are ignoring the*free volume*due to molecular disorder in liquids and amorphous solids as compared to crystals. This, and the assumption that monomers and solute molecules are really the same size, are the main*geometric*approximations in this model. -
**^**For a real synthetic polymer, there is a statistical distribution of chain lengths, so*x*would be an average. -
**^**The enthalpy is the internal energy corrected for any pressure-volume work at constant (external)*P*. We are not making any distinction here. -
**^**In fact, two of the sites adjacent to a polymer segment are occupied by other polymer segments since it is part of a chain; and one more, making three, for branching sites, but only one for terminals.
Categories: Polymer chemistry | Solutions | Free energy | Thermodynamics | Statistical mechanics |
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This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Flory-Huggins_solution_theory". A list of authors is available in Wikipedia. |