Physical gels are characterized by dynamic cross-links that are constantly created and broken, changing its state between solid and liquid under influence of environmental factors. This restructuring ability of physical gels makes them an important class of materials with many applications, such as in drug delivery. In this article, we present a thermodynamic model for physical gels that considers both the elastic properties of the network and the transient nature of the cross-links. The cross-links' reformation is captured through a connectivity tensor M at the microscopic level. The macroscopic quantities, such as the volume fraction of the monomer φ, number of monomers per cross-link s, and the number of cross-links per volume q, are defined by statistic averaging. A mean-field energy functional for the gel is constructed based on these variables. The equilibrium equations and the stress are obtained at the current state. We study the static thermodynamic properties of physical gels predicted by the model. We discuss the problems of un-constrained swelling and stress driven phase transitions of physical gels and describe the conditions under which these phenomena arise as functions of the bond activation energy Ea, polymer/solvent interaction parameter χ, and external stress p.

Original languageEnglish (US)
Pages (from-to)2083-2099
Number of pages17
JournalJournal of the Mechanics and Physics of Solids
Issue number12
StatePublished - Dec 2010


  • Free energy
  • Phase transition
  • Physical gels
  • Reformation
  • Thermodynamics

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


Dive into the research topics of 'A thermodynamic model of physical gels'. Together they form a unique fingerprint.

Cite this