CALCULATION OF THE ABSORBENCY BY INTEGRATION OF THE CONCENTRATION DISTRIBUTION IN LONG OPTICAL-PATH LENGTH THIN-LAYER ELECTROCHEMICAL-CELLS

A theoretical solution of the concentration distribution in long optic al path length thin layer spectroelectrochemical cells is given by a c onvergent infinite summation of terms. At short times a large number o f terms is required to obtain a good approximation. Alternatively, on a timescale at which the boundary of the diffusion layer has not reach ed the celt wall opposite to the electrode the concentration profile o f the thin layer cell is equal to the profile of a semi-infinite bulk electrochemical cell. This profile is described by an error function, for which no analytical solution is available. A new three-parameter e xponential approximation for this error function is presented with an accuracy better than 0.05% for all positive values of x. When the diff usion layer boundary reaches the cell wall the semi-infinite bulk mode l is no longer valid but then the slope of the profile is small enough to he approximated by only the first five terms of the summation.