Modeling back-relaxation in ionic polymer metal composites: The role of steric effects and composite layers

Ionic polymer metal composites (IPMCs) are a new class of active materials that are gaining traction as soft actuators in medical and industrial applications. IPMCs can undergo large deformations under modest voltage inputs, in dry and wet environments. Past studies have demonstrated that physical and geometric properties of all the IPMC constituents (ionomer, electrodes, and counterions) may all influence the time scales of the transient response and severity of the back-relaxation. In this study, we present a detailed mathematical model to investigate how the finite size of the counterions and the presence of metal particles in the vicinity of the electrodes modulate IPMC actuation. We build on previous work by our group on thermodynamically consistent modeling of IPMC mechanics and electrochemistry, which attributes IPMC actuation to the interplay between Maxwell stress and osmotic forces. To gain insight into the role of physical and geometric parameters, the resulting nonlinear partial differential equations are solved semianalytically using the method of matched asymptotic expansions, for the initial transient and the steady-state. A numerical solution in COMSOL Multiphysics^® is developed to verify semianalytical findings and further explore IPMC actuation. Our model can successfully predict the entire response of IPMCs, from the initial bending toward the anode to the steady-state toward the cathode. We find that the steric effect can abolish the back-relaxation of IPMCs by restraining the counterions' concentration near the electrodes. We also find that increasing the thickness of the ionomer-metal composite layers may enhance IPMC actuation through increased osmotic forces and Maxwell stress.