IRREVERSIBLE AGGREGATION KINETICS - POWER-LAW EXPONENTS FROM SERIES

The kinetics of irreversible aggregation are studied using power series in time for general sum and product kernels of the type (i(alpha)+j(alpha)) and (ij)alpha. Assuming a power-law form for the asymptotic behavior of the first moment of the cluster distribution, M0 is similar to t-gamma, we are able to determine the exponent gamma by inverting the series to give t as a function of the first moment. Exact solutions are known for alpha=0 and 1. Our numerical method gives gamma as a function of alpha for alpha in the range from 0 to 1 for the sum kernel. For the product kernel we are able to determine gamma near alpha=0 and 1, but a power-law form does not seem to fit the series well in the midrange near alpha=1/2. For the product kernel we clearly detect the onset of the gelation transition at alpha=1/2.