Static structure factor of dilute solutions of polydisperse fractal aggregates

Taco Nicolai (1) , Dominique Durand (1) , Jean-Christophe Gimel (1)

1 LPCM - Laboratoire de chimie et physico-chimie macromoléculaire

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 mw∝Rdf*gz 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.

Domaines: Physique [physics]; Matière Condensée [cond-mat]; Matière Molle [cond-mat.soft]

Taco Nicolai, Dominique Durand, Jean-Christophe Gimel. Static structure factor of dilute solutions of polydisperse fractal aggregates. Physical Review B: Condensed Matter and Materials Physics (1998-2015), 1994, 50 (22), pp.16357-16363. ⟨10.1103/PhysRevB.50.16357⟩. ⟨hal-02318707⟩