Direct imaging of three-dimensional structure and topology of colloidal gels

We present novel measurements of the structure of colloidal gels. Using confocal microscopy, we obtain the precise three-dimensional positions of a large number of particles. We develop quantitative descriptions of the topology of the gel, including the number of bonds per particle, the chemical or bond fractal dimension, the number of flexible pivot points and other topological parameters that describe the chainlike structure. We investigate the dependence of these parameters on the particle volume fraction and the strength of the attraction that holds the particles together. While all samples have approximately the same fractal and chemical dimensions, we find that gels formed with stronger attraction or larger volume fraction have fewer bonds per particle, more filamentous chains and a greater number of flexible pivot points. Finally, we discuss the topological results in the context of the gel's elasticity. Measurements of the elastic constants of individual chainlike segments are explained with a simple model. The distribution of elastic constants, however, has a general form that is not understood.