The transport of charge due to electric stimulus is the primary mechanism of actuation for a class of polymeric active materials known as ionomeric polymer transducers (IPTs). A two-dimensional ion hopping model has been built to describe ion transport in the IPT. In a Monte Carlo simulation, a square lattice of 50nm × 50nm is investigated containing 200 cations and 200 anions. Step voltages are applied between the electrodes of the IPT, causing the thermally-activated hopping between multiwell energy structures. The energy barrier height includes three parts: intrinsic energy, energy height due to the electric field and energy height due to ion-ion interactions. Periodic boundary conditions have been applied in the direction perpendicular to the electric field. The influence of the electrodes on both faces of IPT is formulated by the method of image charges. The charge density profile over the material has been calculated by the ion distribution in steady state. The Monte Carlo simulation is repeated multiple times to obtain an average result of the charge density. The averaged profile shows regions of cation depletion close to the anode, charge neutrality in the central part and ion accumulation close to the cathode, which qualitatively agrees with the results from conventional continuum models. To quantatively examine the Monte Carlo simulation of the ion hopping model, comparisons with a computational model of transport and electromechanical transduction are performed. This computational model is based upon a coupled chemo-electrical multi-field formulation and computes the spatio-temporal charge density profile to an applied potential at the boundaries. It can be seen that both methods, the statistical theory and the continuum theory, match quite well and are both able to represent the actual behavior inside the IPT. Moreover, experiments are performed to validate the current density calculated by the Monte Carlo simulation. The active material is Nafion 117 (Dupont) in the form of a cantilevered transducer with conductive electrodes on both surfaces and with mobile Na+ counter-ions. Voltage inputs are provided by a dSPACE DS 1102 DSP and amplified using an HP power amplifier. The current is measured by placing a small resistor in series with the sample, between the sample and ground. The voltage across the resistor is amplified and measured by dSPACE. The electrical current is calculated by dividing the voltage drop across the resistor by its resistance. Current density in both simulation results and experimental results exhibits an exponential decay over time.
A Monte Carlo simulation of ion transport at finite temperatures
