# Tonnishtha Dasgupta MSc

Ornstein Laboratory, room 16

Princetonplein 1, 3584 CC Utrecht

P.O. Box 80 000, 3508 TA Utrecht

The Netherlands

phone: +31(0)30 253 2467

secretariat: +31(0)30 253 2952

e-mail: t.dasgupta@uu.nl

## Research

Promotor: Prof.dr.ir. M. Dijkstra

Employed since: July 2014

Funded by FOM

## Sedimentation in Colloidal Systems: Theory and Simulations

Photonic crystals, which show a band gap in the visible region, have numerous interesting applications. Intriguingly two such structures, diamond and pyrochlore, can be self-assembled into the Laves MgCu2 structure from a simple binary colloidal hard-sphere mixture. Binary hard-sphere mixtures have been known to form the Laves phase at specific pressures and composition at size ratios between 0.76 and 0.84. Our broad objective is to stabilize the Laves phase through sedimentation of binary colloidal mixtures. While for pure colloidal systems under gravity the entire equation of state can in principle be obtained from a single simulation, the correlation between sedimentation equilibria and bulk properties of a binary mixture is not trivial. In this regard one can construct a stacking diagram, which comprises a set of all possible stacking sequences of phases in a sedimentation column. We construct a stacking diagram for a size ratio of 0.82 from the corresponding bulk phase diagram of a binary hard-sphere colloidal mixture (shown in Figure 1). We also perform event-driven brownian dynamics simulations on sedimenting mixtures of binary hard spheres to obtain the phases as predicted by our stacking diagram.

Figure 1: Stacking diagram representing the various stacking sequences in a sedimenting binary hard-sphere colloidal mixture with a small sphere to large sphere size ratio 0.82. Phases: L = fcc (large spheres), S = fcc (small spheres), Lav = laves phase, F = binary fluid mixture. s (on x-axis) = ratio of gravitational length of the large species to the small species. a (on y-axis) = chemical potential (large species) – s * chem. pot. (small species).

[1] D. Heras et al., Soft Matter 9, 8636-8641 (2013)

[2] A.-P. Hynninen et al., Nature materials 6, 202-205 (2007)

**Event driven Brownian dynamics (EDBD), Theoretical free-energy calculations, Band structure calculations**

The hard-sphere model is extremely interesting because despite its simplicity, it has been thought to represent many prime features of the intermolecular repulsive forces in real fluids when studying equilibrium and non-equilibrium phenomena. To make things more interesting, this highly theoretical model can be realized experimentally through colloidal systems. Specifically, our research interest lies in photonic crystals which show a bandgap in the visible region. Two such structures are the diamond and pyrochlore structures (Figures 1b and c).

Interestingly these structures can be assembled into the MgCu_{2} structure from a binary colloidal mixture. Binary hard-sphere mixtures have been known to form the Laves phase at specific pressures and composition at size ratios between 0.76 and 0.84. The Laves phase structures class under three broad structural prototypes, cubic MgCu_{2} (Figure 1a), hexagonal MgZn_{2} and hexagonal MgNi_{2}. In the size ratios discussed above, the Laves phase formed by the assembling binary spheres are constituted of a mix of all three structures because their free energies are very similar.

Therefore growing pure MgCu_{2} crystals poses a big challenge. Hynninen et.al [1] discussed a template-directed approach to growing the pure MgCu_{2}. This is the main objective that we are looking at with template-directed sedimentation of binary hard-sphere mixtures.

[1] A.-P. Hynninen, J. H. Thijssen, E. C. Vermolen, M. Dijkstra, and A. Van Blaaderen, *Nature Materials* **6**, 202 (2007)