# Experimental observation of the crystallization of hard sphere colloidal particles by sedimentation onto flat patterned surfaces

Original entry: Tom Kodger, APPHY 226, Spring 2009

## Reference

I.B. Ramsteiner, K.E. Jensen, D.A. Weitz, F. Spaepen. *PRE* **79**, 011403 (2009);

## Keywords

Colloidal crystal, patterned substrate, bond order parameter, template

## Abstract

We present a confocal microscopy study of 1.55 μm monodisperse silica hard spheres as they sediment and crystallize at the bottom wall of a container. If the particles sediment onto a feature less flat wall, the two bottom layers crystallize simultaneously and layerwise growth follows. If the wall is replaced by a hexagonal template, only layerwise growth occurs. Our results complement earlier numerical simulations and experiments on other colloidal systems.

## Capillarity In Action

While this paper contains very little capillarity, except for basic sedimentation concepts, the paper contains several useful experimental approaches, such as a bond order parameter, that could be used in other capillarity analyses. On a technical basis, the crystallization kinetics of sedimenting and templated colloidal sized particles is critical toward inexpensive photonic crystals.

Briefly, the experiment system contains monodispersed silica spheres (1.55μm) at low volume fraction in a fluorescent DMSO/water solution. Due to a density difference between the 2 components, these spheres slowly sediment according to,

<math>u_0=\frac{1}{18}\sigma^2\Delta\rho g/\eta \approx 4.7mm/h</math>

The authors index match using DMSO, to minimize van der Waals. As a result the inverse gravitational length, <math>g^*=m^*g\sigma/k_B T \approx 7</math> where <math>m^*=(\frac{1}{3}\pi\sigma^2)\Delta\rho</math> is the relative particle mass.

The particles are sedimented at the slow rate described above onto either a flat or templated substrate. The substrate is templated with a [111] oriented single crystal, made with reactive ion etching. A Leica SP5 confocal is used to observe the particles while they sediment slowly approximately every ~15sec per z-stack. The 3D dimensions are 93 X 93 X 16μm. Density profiles and bond order parameters are measured with time.

The authors define a 6th-order bond parameter to define crystalline particles as such,

<math>\psi_j^{(6)}=\frac{1}{N} \sum_{k=1}^{N_j}e^{i6\theta_{jk}}</math>

where θ_{jk} is the angle between r_{jk}=r_{j}-r_{k}. As seen in Fig.1 the order parameter varies from 0 to 1, with 1 having 6 perfect nearest neighbors. In Fig.1, the increasing gray scale shows increasing crystallinity. The authors then extend this parameterization into the z-dimension by defining,

<math>\psi^{(6)}(z)=\left \langle | \psi_j^{(6)} \right | \rangle_{\Delta z}</math>

By employing this layerwise crystallinity analysis, the authors were able to quantitatively study the crystallization process on an entire layer basis. What they found is graphically represented in Fig. 2. If a flat surface is used, the first two layers crystallize at approximately the same density <math>N/\sigma^2</math>, while with the templated surface the layers crystalize in a sequential fashion Fig.2(b). These results match recent colloidal particle simulations {Ref.1,2}

## References

[1] J. Hoogenboom, P. Vergeer, and A. v. Blaaderen, *J. Chem. Phys.* 119, 3371 (2003).

[2] M. Marechal and M. Dijkstra, *Phys. Rev. E* 75, 061404 (2007).