A universal expression for chemical potential in vulcanized-rubber swelling and permeation

Abstract

This study examines the swelling behavior of rubber materials in non-polar solvents, neglecting complex factors such as ions and specific functional groups. A universal expression for the chemical potential μ during the swelling of vulcanized rubber is employed to analyze the effects of bulk modulus (K), Flory–Huggins interaction parameter (χ), and solubility parameter (δ) on swelling thermodynamics and kinetics. The theoretical analysis reveals that a higher K significantly improves swelling resistance by maintaining a more negative equilibrium μ. In contrast, a larger χ value, indicative of stronger hydrophobicity, accelerates the approach to swelling equilibrium while suppressing the ultimate degree of swelling. Analysis of solubility parameters further corroborates the “like-dissolves-like” principle, demonstrating that a closer match between the δ values of the rubber and solvent leads to more pronounced swelling. To validate the theoretical framework, high-temperature diesel immersion experiments were performed on fluororubber specimens. The results confirm that specimens with superior swelling resistance exhibit higher hardness—which reflects a higher K—and lower linear swelling ratios, in full agreement with the chemical potential model. Furthermore, to establish a generalized μ expression for vulcanized elastomers, closed-form analytical solutions for μ were derived within both the Mooney–Rivlin and Gent–Gent constitutive frameworks. In summary, the developed theoretical framework effectively describes and predicts rubber swelling behavior, elucidates the role of key material parameters, and provides a solid theoretical foundation for designing and selecting swelling-resistant rubber materials in engineering applications.