The self-diffusion coefficients D of compressed supercritical water have been measured as a function of pressure in the temperature range 400 to 700 °C using the NMR spin–echo technique. The experimental diffusion data were compared to theoretical predictions based on a dilute polar gas model using a Stockmayer potential for the evaluation of collision integrals and a temperature dependent hard sphere diameter. The empirical expression ρDαTn, where n = 0.76, fits the experimental data to within±10% over the entire density and temperature region studied. The value of the exponent n = 0.76 agrees favorably with the n values found for diffusion of other gases. The product ρD is density independent under isothermal conditions which indicates that two-body collisions dominate the diffusion behavior. This finding is in agreement with our earlier results for proton relaxation in compressed supercritical water which were analyzed using a binary collision approximation and a collision modulated spin–rotation interaction described by a single correlation function which is an exponential function of time. The hydrodynanic Stokes–Einstein equation appears to hold at densities above ρc. As expected, the diffusion data cannot be described in terms of a hard sphere model but an empirical fit to lnρD = (A/T)+B, where A and B are constants, represents the experimental data well over the range of temperatures and densities studied.

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The distribution of capture zones formed during the nucleation and growth of point islands on a one-dimensional substrate during monomer deposition is considered for general critical island size i. A fragmentation theory approach yields the small and (for i = 0) large size asymptotics for the capture zone distribution (CZD) under the assumption of no neighbourneighbour gap size correlation. These CZD asymptotic forms are different to those of the Generalised Wigner Surmise which has recently been proposed for island nucleation and growth models, and we discuss the reasons for the discrepancies.

The nucleation and growth of point islands during submonolayer deposition on a one-dimensional substrate is simulated for critical island size i=0,1,2,3. The small- and large-size asymptotics for the gap-size and capture-zone distributions (CZDs) are studied. Comparisons to theoretical predictions from fragmentation equation analyses are made, along with those from the recently proposed generalized Wigner surmise (GWS). We find that the simulation data can be fully understood in the framework provided by the fragmentation equations, while highlighting the theoretical areas that require further development. The GWS works well for the small-size CZD behavior, but completely fails to describe the large-size CZD asymptotics of the one-dimensional system.