STRUCTURE FACTOR SCALING IN AGGREGATING SYSTEMS

We study the structure factor of evolving two-phase systems such as ag gregating colloids and spinodally decomposing fluids. We interpret the total structure factor as described well by the product of cluster-cl uster and single-cluster structure factors, each with their own charac teristic length, the mean cluster nearest-neighbor separation, and the cluster size, respectively. Both length scales are thus relevant to t he total structure factor. For systems with moderate to strong cluster -cluster correlations, this product causes an apparent peak in the str ucture factor. For compact clusters, i.e., clusters with a fractal dim ension equal to the spatial dimension, this peak obeys the experimenta lly observed scaling law. However, for fractal clusters the two length scales evolve differently, hence scaling cannot occur. Despite this, our simulations show an apparent scaling when the system is dense enou gh so that the two length scales are comparable in magnitude. When thi s occurs, each length scale eliminates the individual effect of the ot her from the total structure factor leaving a peak. These results expl ain both the lack of scaling early and the scaling observed latter in experiments on aggregating colloids. An important conclusion is that t he position of this peak q(m) does not represent a true length scale o f the system.