Solution-diffusion-mechanics model: Derivation, generalization, and non-equivalence of molecular simulations and experiments
Viatcheslav Freger
Abstract
The solution-diffusion (SD) model has faithfully served membrane research for decades, however, recently reported discrepancies between molecular dynamics and experiments reignited a debate on its validity. This study places on a solid foundation the picture of SD as mechanical-transport coupling put forward recently. The full set of coupled relations is rigorously derived using a variational approach. The approach is also generalized to the case of coupled solvent and solute transport and the result is equivalent to the classical irreversible thermodynamics relations, the Spiegler-Kedem model, augmented with a pressure-stress relation. This suggests a more general interpretation of SD, whereby what differentiates SD form the pore-flow is the nature of the driving force or “solution”, when the single-phase membrane phase exchanges both mechanical and chemical energy with the permeating solvent, rather than “diffusion”, i.e., specific mechanism behind solvent-membrane friction. Using a numerical solution, the paper also analyzes the cases of the supported and open films, representative of experiments and molecular simulations. This demonstrates that MD simulations agree with the SD model predictions and the basis for its rejection is removed, once the transport and mechanical boundary conditions are aligned in both types of computations. The presented study then closes a critical gap between simulations and real-world processes and applications, opening opportunities for new insights, modeling, and design of next-generation materials. • Solution-diffusion model is generalized to include coupling to mechanics. • All coupled relations are derived from a general variational principle. • For multiple permeants, derivation yields Spiegler-Kedem model coupled to mechanics. • Different coupling makes molecular dynamics and experimental data non-equivalent. • SD and pore-flow models are distinct by “solution” rather than “diffusion”.