STATIC STRUCTURE FACTOR OF DILUTE-SOLUTIONS OF POLYDISPERSE FRACTAL AGGREGATES

We have calculated the z-average static structure factor [S(q)z], z-average radius of gyration (Rgz), and the weight average aggregation number (mw) of fractal aggregates with an aggregate number distribution given by N(m)m-τf(m/m*). Here, q is the scattering wave vector and for the cutoff function f(m/m*) at a characteristic aggregation number m* we have chosen a stretched exponential function. We derive expressions for the prefactors of the scaling relations mwRgzdf* and S(q)z(qRgz)-df* and make explicit the conditions for their validity at finite values of mw and qRgz. For values of τ close to two these conditions are shown to be very difficult to meet in practice. For the case of aggregates formed by a percolation process where τ=2.2 it is shown that attempts to measure df* directly from the slope of log10(mw) vs log10(Rgz) or log10(S(q)z) vs log10(q) are biased by the effect of the internal and/or external cutoff of the fractal regime. © 1994 The American Physical Society.