Interpreting the Weibull fitting parameters for diffusion-controlled release data

We examine the diffusion-controlled release of molecules from passive delivery systems using both analytical solutions of the diffusion equation and numerically exact Lattice Monte Carlo data. For very short times, the release process follows a t power law, typical of diffusion processes, while the long-time asymptotic behavior is exponential. The crossover time between these two regimes is determined by the boundary conditions and initial loading of the system. We show that while the widely used Weibull function provides a reasonable fit (in terms of statistical error), it has two major drawbacks: (i) it does not capture the correct limits and (ii) there is no direct connection between the fitting parameters and the properties of the system. Using a physically motivated interpolating fitting function that correctly includes both time regimes, we are able to predict the values of the Weibull parameters which allows us to propose a physical interpretation.