Computer simulations of the spatial statistical analysis of single nuncleus growth on microelectrodes

Abstract

The theoretical model was that of a single nucleus growing as a circular monolayer to cover a circular microelectrode. Random numbers were used to simulate the radial positions that might be obtained from a collection of experimental current-time transients. Given this set of radial positions, both a cumulative density distribution (CDD) and a site density function (SDF) can be calculated. Since these are calculated from a finite sample of values, there will be deviations from the theoretical CDD and SDF determined from geometric considerations alone. Computer simulations were conducted to determine the limits of deviation that could arise from sampling. The confidence limits on the CDD were found to be elliptical with the minor axis proportional to the inverse square root of the sample size. The confidence limits on the SDF were not symmetrical about the expected theoretical value for the site density. A simple case of non-random nucleation was also simulated. None of the tests for non-random nucleation was found to be very sensitive to its presence or amount. It was found that for a given sample of radial positions, the localised non-random sites would be added to whatever spatial pattern of random sites was present on the rest of the electrode.