Monte-Carlo Simulation of Ion Transport at the Polymer-Metal Interface

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. Continuum-based models of ion transport have been developed for the purpose of understanding charge transport due to diffusion and migration. In this work a two dimensional ion hopping model has been built to describe ion transport in ionomeric polymer transducer (IPT) with Monte-Carlo simulation. In the simulation, cations are distributed on 50nm × 50nm × 1nm (or 50nm × 10 nm × 1nm) lattice cells of IPT while the same number of negative charges are uniformly scattered and fixed as background. In the simulation, thermally activated cations are hopping between multiwell energy structures by overcoming energy barriers around with a hopping distance of 1nm during each time step. A step voltage is applied between the electrodes of the IPT. In one single simulation step, coulomb energy, external electric potential energy and intrinsic energy of the material are calculated and added up for the energy wells around the cations. And then hopping rates in every potential hopping direction are obtained. Due to the random nature of the ion transitions, a weighting function from Monte-Carlo algorithm is added in to calculate the ion hopping time. Finally hopping time is compared, the minimum hopping time is chosen and one hopping event is completed. Both system time and ions distribution are updated before the next simulation loop. Periodic boundary conditions are applied when ions hop in the direction perpendicular to the electric field. The influence of the electrodes on both faces of IPT is presented by the method of image charges. The charge density at equilibrium state is compared with the result from a continuum-based model. The property of charge density has charge neutrality over the central part of the membrane and the charge imbalance over boundary layers close to the anode and cathode. Electric field distribution is obtained after charge distribution. After it is demonstrated that ion hopping model leads to the results qualitatively matching the property of IPT, the paper uses the model to analyze the polymer-metal interface when the electrode shape inside transducer varies.