Understanding the mechanisms of solid-water reactions through analysis of surface topography

The topography of a reactive surface contains information about the reactions that form or modify the surface and, therefore, it should be possible to characterize reactivity using topography parameters such as surface area, roughness, or fractal dimension. As a test of this idea, we consider a two-dimensional (2D) lattice model for crystal dissolution and examine a suite of topography parameters to determine which may be useful for predicting rates and mechanisms of dissolution. The model is based on the assumption that the reactivity of a surface site decreases with the number of nearest neighbors. We show that the steady-state surface topography in our model system is a function of, at most, two variables: the ratio of the rate of loss of sites with two neighbors versus three neighbors (d2/d3) and the ratio of the rate of loss of sites with one neighbor versus three neighbors (d1/d3). This means that relative rates can be determined from two parameters characterizing the topography of a surface provided that the two parameters are independent of one another. It also means that absolute rates cannot be determined from measurements of surface topography alone. To identify independent sets of topography parameters, we simulated surfaces from a broad range of d1/d3 and d2/d3 and computed a suite of common topography parameters for each surface. Our results indicate that the fractal dimension D and the average spacing between steps, E[s], can serve to uniquely determine d1/d3 and d2/d3 provided that sufficiently strong correlations exist between the steps. Sufficiently strong correlations exist in our model system when D>1.5 (which corresponds to D>2.5 for real 3D reactive surfaces). When steps are uncorrelated, surface topography becomes independent of step retreat rate and D is equal to 1.5. Under these conditions, measures of surface topography are not independent and any single topography parameter contains all of the available mechanistic information about the surface. Our results also indicate that root-mean-square roughness cannot be used to reliably characterize the surface topography of fractal surfaces because it is an inherently noisy parameter for such surfaces with the scale of the noise being independent of length scale.