Colloidal Crystallization in 2D for Short-Ranged Attractions: A Descriptive Overview

Abstract

With the aid of 2D computer simulations, the whole colloidal crystallization process for particles interacting with a short-ranged attractive potential is described, emphazising the visualization of the different subprocesses at the particle level. Starting with a supercooled homogeneous fluid, the system undergoes a metastable fluid-fluid phase separation. Afterwards, crystallite nucleation is observed and we describe the obtainment of the critical crystallite size and other relevant quantities for nucleation. After the crystal formation, we notice the shrinking and eventual disappearance of the smaller crystals, which are close to larger ones; a manifestation of Ostwald ripening. When two growing crystal grains impinge on each other, the formation of grain boundaries is found; it is appreciated how a grain boundary moves, back and forth, not only on a perpendicular direction to the boundary, but with a rotation and a deformation. Subsequently, after the healing of the two extremes of the boundary, the two grains end up as a single imperfect grain that contains a number of complex dislocations. If these dislocations are close to the boundary with the fluid, they leave the crystal to make it more perfect. Otherwise, they migrate randomly inside the grain until they get close enough to the boundary to leave the grain. This last process of healing, trapping and getting rid of complex dislocations occurs preferentially for low-angle grain boundaries. If the angle between the symmetry axes of the two grains is not low, we end up with a polycrystal made of several touching crystal grains.

Real-Space Mapping of the Two-Dimensional Phase Diagrams in Attractive Colloidal Systems

“…Regarding a repulsive system, the transition order is proven to depend on the softness of the pair potential [7,8]. Compared with repulsive systems, attractive systems are more analogous to real materials and have been more intensively studied with simulations [9][10][11][12][13][14] and tested with several theories [15][16][17], but the topic of transition order remains a subject of debate [2,18]. Moreover, although widely reported in simulations, equilibrium 2D vapor-liquid coexistence has not heretofore been observed in colloidal experiments due to the challenges of realizing the long-range attraction.…”

“…Moreover, a dense fluid may offer an intrinsic free-energy advantage for crystallization of a hard sphere [29] where the (metastable) critical point does not exist and even appears below the triple temperature in a Lennard-Jones simulation [28]. Additionally, because nucleation experiments test only one possible route on the phase diagram plane, the exact condition under which two-step nucleation occurs remains elusive [18,33]. At last, to offer a clear insight into the role that the metastable fluid-fluid regime plays in the assistance of crystallization nucleation, it is desirable, under some conditions, to witness a full fluid-fluid phase separation with any given shape of droplets of dense fluid, instead of a dense region, inside the dilute fluid before crystallization begins [18,30].…”

Heterogeneous Nucleation of Colloidal Crystals on a Glass Substrate with Depletion Attraction

“…The boundaries of all the islands are rough and the facet boundary is not observed. The rough boundary was reported for subcritical and supercritical nuclei, − in which fractal dimension was calculated to obtain line tension. We have applied CNT to the rough islands assuming that islands have circular shapes with smooth boundaries.…”

Phase diagrams and crystal-fluid surface tensions in additive and nonadditive two-dimensional binary hard-disk mixtures

“…Complementary, dedicated simulation or experimental results on this are clearly desirable, also in view of the relevance of the surface tension for nucleation processes, see Ref. [31] for a review on more qualitative results on 2D crystal and defect formation. The observed decrease in surface tension should lead to a considerable decrease in the time scales of crystal nucleation.…”