Dependence of crystallization of Brownian particles by sedimentation on the force direction

Abstract

The formation of a large close-packed colloidal crystal with the fcc structure was observed during the sedimentation of colloidal particles in an inverted pyramidal pit [S. Matsuo et al., Appl. Phys. Lett. 82, 4285 (2003)]. Carrying out Brownian dynamics simulations, we confirmed that large grains with the fcc structure are formed when the apex angle of the inverted pyramidal container is suitable and the force direction is parallel to the the center axis [Y. Kanatsu and M. Sato, J. Phys. Soc. Jpn. 84, 044601 (2015)].To form a high-quality colloidal crystal without defects, it is important to investigate in detail how the quality of a colloidal crystal is affected by the force direction and container shape. In this paper, we focus on the effect of the force direction on crystal quality and investigate how the ratio of the number of the hcp structured particles, N hcp , to that of fcc structured particles, N fcc , is affected by the force direction.In our simulation, the ratio of N fcc to N hcp is hardly changed when the force direction deviates from the central axis: N fcc is much larger than N hcp irrespective of the force direction. Thus, our results show that the crystal structure is insensitive to the force direction in forming a colloidal crystal by sedimentation in an inverted pyramidal container.

Effect of direction of an external force on crystallization of colloidal particles in a V-shaped groove by sedimentation

“…We regard the local structure around the ith particle as the fcc structure when −0.18 < w 4 (i) < −0.01 and 0.175 < Q 4 (i) < 0.2. When 0.02 < w 4 (i) < 0.15 and 0.06 < Q 4 (i) < 0.15, 7,8,[10][11][12][13][14][15] the structure is regarded as the hcp structure. When w 4 (i) and Q 4 (i) have other values, we regard the ith particle as a disordered solid.…”

“…The saturated value of N fcc clearly decreases with increasing θ; thus, the dependence of N fcc on θ is different from that in the case of solidification in a pyramidal pit. 7) Figure 4(b) shows the time evolution of the number of particles acting as defects, N defect , which is the sum of the numbers of hcp-structured particles and disordered solid-like particles. We want to know how many defects there are in the ordered region.…”

“…In our previous studies, 7,8,[10][11][12][13][14][15] we neglected the inertial term m€ r i for simplicity, but this term may affect the crystallization of particles. Thus, we take account of the inertial term and carry out simulations using a simple Verlet-type algorithm.…”

“…Owing to the unique stacking on the {100} face, grains with the hcp structure hardly appear, irrespective of the particle size, when the apex angle of the pyramidal pit is suitable. The hcp-structured grains, which act as defects in the fcc-structured crystal, increase in number with increasing deviation of the apex angle 7,8) but their number hardly depends on the inclination of the force direction. 7) In the growth of colloidal particles in a V-shaped groove, 6) the growth interface is directed toward the 〈110〉 direction if the external force bisects the angle between the two walls of the groove.…”

“…The hcp-structured grains, which act as defects in the fcc-structured crystal, increase in number with increasing deviation of the apex angle 7,8) but their number hardly depends on the inclination of the force direction. 7) In the growth of colloidal particles in a V-shaped groove, 6) the growth interface is directed toward the 〈110〉 direction if the external force bisects the angle between the two walls of the groove. It is easily expected that the number of defects increases with increasing deviation of the angle between the walls from a suitable value.…”