Colloidal assembly by ice templating - Kumaraswamy, Guruswamy; Biswas, Bipul; Choudhury, Chandan Kumar (Faraday Discussions, 2016)
We investigate ice templating of aqueous dispersions of polymer coated colloids and crosslinkers, at particle concentrations far below that required to form percolated monoliths. Freezing the aqueous dispersions forces the particles into close proximity to form clusters, that are held together as the polymer chains coating the particles are crosslinked. We observe that, with an increase in the particle concentration from about 106 to 108 particles per ml, there is a transition from isolated single particles to increasingly larger clusters. In this concentration range, most of the colloidal clusters formed are linear or sheet like particle aggregates. Remarkably, the cluster size distribution for clusters smaller than about 30 particles, as well as the size distribution of linear clusters, is only weakly dependent on the dispersion concentration in the range that we investigate. We demonstrate that the main features of cluster formation are captured by kinetic simulations that do not consider hydrodynamics or instabilities at the growing ice front due to particle concentration gradients. Thus, clustering of colloidal particles by ice templating dilute dispersions appears to be governed only by particle exclusion by the growing ice crystals that leads to their accumulation at ice crystal boundaries.

Colloidal assembly by directional ice templating - Biswas, Bipul; Misra, Mayank; Bisht, Anil Singh; Kumar, Sanat K.; Kumaraswamy, Guruswamy (Soft Matter, 2021)
We investigate directional ice templating of dilute aqueous colloidal particle dispersions and examine the nature of the assemblies that result. We coat micron-size polystyrene colloids with cross-linkable polymer (polyethyleneimine, PEI), add cross-linker, and subject this dispersion to unidirectional freezing. We work at sufficiently low colloid concentrations, such that the particles do not percolate on freezing. When the aqueous dispersion freezes, ice crystals force polymer-coated particles and cross-linker into close proximity. This results in the formation of cross-linked clusters of particles at ice crystal boundaries. We vary the particle volume fraction from phi similar to 2.5 x 10(-3) to phi similar to 5.0 x 10(-2) and observe that there is a transition from isolated single particles to increasingly large sized clusters. Most of the clusters formed under these conditions are either linear, two-particle wide chains, or sheet-like aggregates. The probability (P-n) of clusters containing n particles (n > 2) obeys a power law P-n similar to n(-eta), where eta strongly depends on the particle concentration in the dispersion, varying from 2.10 (for phi similar to 5.0 x 10(-2)) to 3.03 (for phi similar to 2.5 x 10(-3)). This change in eta is qualitatively different from the case of isotropic freezing, where eta is particle concentration-independent and depends only on the ice nucleation density. To understand the differences between isotropic and directional ice templating, we performed lattice simulations of a highly simplified model, where ice crystals grow at a constant rate to force clustering. We ignore hydrodynamic interactions and ice growth instabilities. Despite ignoring these experimental details, the simulations capture the experimental results, nearly quantitatively. As the ice crystals grow and the space available to the colloids ``closes up'' so that the particles cluster to form aggregates, crystallization protocol-induced differences in the geometry of these ``closed up'' spaces determine the scaling behaviour of P-n.