Sorption–deformation coupling in soft nanoporous materials: insights from a three-phase poromechanics theory

Abstract We develop a large-strain poromechanics theory for the coupled sorption–deformation behaviours exhibited by many soft nanoporous materials. Instead of modelling sorption as a molecular mixing process as in classical gel theories, we interpret it as a nanopore-level phenomenon that alters pore-scale interactions and thereby affects the macroscopic response of the porous solid. The proposed theory primarily follows the poromechanics formulation of Coussy (Coussy 2004 Poromechanics. Chichester: John Wiley & Sons, Ltd) and its enrichment with surface thermodynamics (Zhang 2018 J. Mech. Phys. Solids114, 31–54). Specifically, we treat the system as a three-phase mixture by separately listing the balance laws of the solid, the bulk fluid and the sorbed excess phases, which are then combined to deduce the free energy imbalance of the system. Examining individual dissipation terms leads to the general forms of transport laws, reaction kinetics, constitutive relations of the porous solid and the equations of state (EOS) of the bulk and the excess fluids. We demonstrate that, in the presence of sorption, the equivalent pore pressure that drives changes of fluid-accessible porosity is no longer solely the bulk fluid pressure, as assumed in traditional poromechanics theories, but includes an additional disjoining pressure arising from the sorbed excess. We confirm that the disjoining pressure isotherm and the sorption isotherm are fundamentally the two sides of the same coin, both characterized by the free energy potential of the excess phase. A simple four-parameter model for amorphous cellulose (AC) interacting with water vapour is constructed using only elementary, textbook-level constitutive laws for the individual phases. Despite its simplicity, the model exhibits remarkable predictive capability in capturing the complex, nonlinear sorption–deformation coupling of the material. Finally, we show that the chemomechanical formulation of Gurtin et al. (Gurtin et al. 2010 The mechanics and thermodynamics of continua. Cambridge University Press) and the gel theory of Hong et al. (Hong et al. 2008 J. Mech. Phys. Solids56, 1779–1793) can be retrieved by reducing the ‘resolution’ of the proposed theory through eliminating the porosity terms and combining the bulk fluid and the sorbed excess phases. The modularity and versatility of the proposed theory make it well-suited for applications beyond polymeric materials, extending to a broad class of nanoporous systems with diverse microstructures and physicochemical interactions with surrounding fluids.