Reference Work Entry

Encyclopedia of Colloid and Interface Science

pp 523-524

Flory-Huggins Interaction Parameter

Synonyms

Polymer-solvent interaction

Definition

The Flory-Huggins interaction parameter χ gives a measure of the interaction of the polymer chains with the solvent molecules as well as the polymer-polymer interaction. To understand the meaning of χ, one must consider the free energy of mixing of pure polymer with pure solvent as considered by Flory and Huggins theory. This theory considers the free energy of mixing of pure polymer with pure solvent, ΔGmix, in terms of two contributions, namely, the enthalpy of mixing, ΔHmix, and the entropy of mixing, ΔSmix. The entropy of mixing is determined by the volume fractions of solvent and polymer, whereas the enthalpy of mixing is determined by the dimensionless interaction parameter χ. χkT (where k is the Boltzmann constant and T is the absolute temperature) expresses the difference in energy of a solvent molecule in pure solvent compared to its immersion in pure polymer. χ is usually referred to as the Flory-Huggins interaction parameter. The mixing of a pure solvent with a polymer solution creates an osmotic pressure, π, which can be expressed in terms of the polymer concentration C2 and the volume fraction of the polymer: (π/C2) = RT [(1/M2) + (ν 2 2 )(1/2−χ) C2]; the second term is the second virial coefficient B2. The latter is equal to zero when χ = ½, i.e., the polymer behaves as ideal in mixing with the solvent. This condition was termed by Flory as the θ-point. Under these conditions, the polymer chains in solution have no repulsion or attraction or they adopt their unperturbed dimension. Clearly, when χ < 1/2, B2 is positive and mixing is nonideal leading to positive deviation (repulsion); this occurs when the polymer chains are in “good” solvent conditions. In contrast, when χ > 1/2, B2 is negative and mixing is nonideal leading to negative deviation (attraction); this occurs when the polymer chains are in “poor” solvent conditions (precipitation of the polymer may occur under these conditions). Since the polymer solvency depends on temperature, one can also define a theta temperature θ at which χ = 1/2.

Cross-References

Polymer Solutions

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