Dendritic Growth of Hard Sphere Crystals

Abstract

Recent observations of the disorder−order transition for colloidal hard spheres under microgravity revealed dendritic crystallites roughly 1−2 mm in size for samples in the coexistence region of the phase diagram. Order of magnitude estimates rationalize the absence of large or dendritic crystals under normal gravity and their stability to annealing in microgravity. A linear stability analysis of the Ackerson and Schätzel model for crystallization of hard spheres establishes the domain of instability for diffusion-limited growth at small supersaturations. The relationship between hard sphere and molecular crystal growth is established and exploited to relate the predicted linear instability to the well-developed dendrites observed.

Tuning the structure of non-equilibrium soft materials by varying the thermodynamic driving force for crystal ordering

“…2g), indicative of the front propagation being controlled by the rate of particle diffusion. This mode can be identified with the 'slow' mode described by Russel et al 7 and is also responsible for the appearance of the dendritic structures shown in Fig. 2b-d where the same 'diffusive' growth kinetics is exhibited.…”

“…This dynamic density adjustment (trapping) mechanism in crystal growth is well established in the rapid solidification of alloys where this phenomenon is associated with solute trapping, 37,38 making this mode of crystal growth an analogue of the fast or ''diffusionless'' crystal mode defined by Russel et al 7 We believe, furthermore, that this is the first demonstration of such a dynamic trapping of a conserved field in simulations based on microscopic theory. The next question is how these distinct slow and fast growth modes contribute to the progressive morphology changes seen in Fig.…”

“…Numerous theoretical methods have been previously introduced to describe colloidal crystal growth, including adaptations 6,7 of the classical Wilson-Frenkel (WF) type crystal growth model, cluster dynamics, 8 a simple field theoretical model, 9 and density functional theory (DFT).…”

Entropically driven self-assembly of colloidal crystals on templates in space

“…Their rich phenomenology derives from a fascinating interplay of physical, chemical and hydrodynamic mechanisms whose realization provides a unique opportunity for the study of statistical mechanics in classical many-body systems. Recent experimental and theoretical progress relevant to the present proposal includes studies of the role of entropy and interparticle interaction in affecting self-assembly 1 and directed assembly in systems of monodisperse hard-spheres, [2][3][4][5][6][7][8][9][10][11][12] particle suspensions with added particles or polymers, monodisperse emulsions with added polymer, 41,43 binary emulsions, 38 suspensions of rod-like particles in mixtures of spheres, [53][54][55][56][57][58][59][60] liquid crystal emulsions, [61][62][63] and charged-stabilized particle suspensions. [64][65][66][67][68][69][70][71] Research on these substances is also driven by a variety of practical applications (see for example [72] and references therein) ranging from the prospect of using these materials as templates for photonic materials [73][74][75] and lithography, 76,77 to their uses in ceramics and as biochemical sensors.…”

Anisotropic diffusion limited aggregation in three dimensions: Universality and nonuniversality

“…The tendency of snow crystals to grow six arms is well known, and lately this has been replicated in controlled laboratory studies [17]. Cubic crystalline anisotropy also produces striking anisotropic "dendrite" growth: succinonitryl is the classical example [18,19], and lately colloidal crystal exemplars have been observed in growth under microgravity [20,21]. The manner in which surface tension and its anisotropy select the morphology of growing tips has been the subject of intense analytical study [22].…”