Detailed Comparison Of Several Ion-Transport Algorithms In A 1-Dimensional Liquid Crystal Model.

In this paper we investigate three one-dimensional ion transport simulation algorithms and compare the results. The ion transport algorithms are incorporated in a one-dimensional Liquid Crystal Display (LCD) model that calculates the director orientation and the influence of ions on the electrical field. The aim is to improve calculation speed and accuracy. The first algorithm is the traditional explicit forward method using finite differences (1). The second algorithm is based on the first, but it assumes an exponential variation, instead of a constant ion concentration in each interval. The third is Monte Carlo based. It does not use any intervals but calculates drift for individual ions and treats diffusion as a random walk. We investigated the frontiers of stability and speed with respect to the accuracy, by varying the time steps and the number of intervals. The main conclusion of our work is that the calculation speed can be improved by using the new algorithms without loss of accuracy. The exponential algorithm proves to be very helpful in the simulation in the case of ions piling up near the alignment layer. The Monte Carlo algorithm is the most appropriate and at the same time a promising candidate for extension to two-dimensional simulations.