Field induced assembly of paramagnetic colloidal particles

The assembly of paramagnetic colloidal particles in the presence of an external magnetic field is studied with optical video microscopy. The first half of this thesis concerns chain formation, which occurs at relatively low surface coverages, and the second half concerns network formation, happening at relatively high surface coverages. First, we study the irreversible aggregation kinetics of two-dimensional paramagnetic colloidal particles in the presence of an in-plane magnetic field at low packing fractions. In particular, we study the packing fraction and field dependence of the mean cluster size. We compare experimental results to the predicted scalings for diffusion limited and deterministic aggregation respectively. It is shown that the aggregation kinetics for our experimental system is consistent with a deterministic mechanism. Next, we establish a direct relation between the distribution of coordination numbers of particles and the mean cluster size using simple statistical considerations. Empirically, a shifted geometric distribution of cluster sizes is observed, consistent with a discrete compound Poisson growth process. This is corroborated by simulations in which the initial spatial distribution of particles is controlled. The generality of our approach is demonstrated by applying it to a more complex clustering processe in two dimensions. Then we investigate the structural properties of magnetorheological networks. The size distributions, orientational ordering and spatial distribution of voids is investigated and compared to random fiber theory. In the fiber phase, the segment length distribution is characterised, as well as the distributions of fiber widths and orientations. These network properties are interrelated such that the entire growth process of fibrous networks can be summarised in terms of a single length scale. We follow this length scale in time for a range of fields and concentrations, investigating the dynamics of the network coarsening. Finally, we propose a link between random fiber theory and the coordination number statistics of particles that make up the network. We show that the fraction of particles with a coordination number less than 6 is key in quantitatively predicting the area of voids. Additionally, we show that clusters of 2 and 4 coordinate particles correspond to segments of the network, 6 coordinate particles represent a population of filled voids, and that singly coordinated particles are a sensitive diagnostic tool to probe the initial aggregation mechanism.</p