We report on a large scale computer simulation study of crystal nucleation in hard spheres. Through a combined analysis of real and reciprocal space data, a picture of a two-step crystallization process is supported: First dense, amorphous clusters form which then act as precursors for the nucleation of well-ordered crystallites. This kind of crystallization process has been previously observed in systems that interact via potentials that have an attractive as well as a repulsive part, most prominently in protein solutions. In this context the effect has been attributed to the presence of metastable fluid-fluid demixing. Our simulations, however, show that a purely repulsive system (that has no metastable fluid-fluid coexistence) crystallizes via the same mechanism.The crystallization process in complex fluids is not trivial. For systems such as solutions of proteins, alkanes, and colloids it has been shown that crystal nucleation rates can be enhanced considerably if the supersaturated liquid is quenched to a state that lies close to a metastable fluid-fluid critical point [1][2][3][4][5][6][7][8]. The enhanced nucleation rate is generally attributed to the fact that the density fluctuations occuring in the vicinity of a metastable fluid-fluid critical point enable the system to evolve via a two-step process. First dense, amorphous precursors form and then the crystallization process takes place inside these. The prerequisite of this process scenario, the metastable fluid-fluid critical point, is easily realized in the systems listed above, which exhibit an interplay of repulsive and attractive interactions.However, it is worthwhile asking whether the two-step process occurs more generally. Surprisingly, there have been experiments indicating two-step crystallization occuring also in hard sphere systems, the simplest model system for liquids and crystals (see e.g. Ref.[9]). As the interaction energy between two hard spheres is either zero (no overlap) or infinite (overlap), the phase behaviour of the system is purely determined by entropy. In particular, for one component hard spheres there exists a stable crystalline phase but no metastable fluid-fluid demixing region.The crystallization kinetics in colloidal hard sphere systems has been studied experimentally using predominantly time resolved light scattering [9][10][11][12][13][14][15] and to a lesser extend real-space imaging techniques [16][17][18][19]. In the scattering experiments described in Refs. [9,15,20] the time-evolution of the structure factor has been interpreted using a two-step process model: In the induction stage precursors (compressed, structurally heterogeneous clusters) slowly grow. Then the precursors are converted into highly ordered crystals in a fast, activated process. In Ref. [9] it was suggested that size polydispersity limited growth is responsible for the induction stage. However, later it was argued that the precursor stage behaves in a similar fashion, regardless of polydispersity or of metastability suggesting that the precurs...
The crystallization kinetics of colloidal hard spheres was studied using a special Bragg spectrometer with high sensitivity. In contrast with the classical scenario we observe a two-step nucleation process: the number of crystallites increases slowly at early times, followed by a dramatic reduction at intermediate times, prior to undergoing a rapid increase at late times. We explain these results in terms of a polydispersity limited growth of crystallites, where the crystallization at early times is governed by local fractionation processes, leading to a long delay prior to final crystallization.
We present measurements of effective charges in de-ionized aqueous suspensions of highly charged spherical latex colloids. For crystalline ordered samples the shear modulus G was measured using torsional resonance spectroscopy. It increases with increasing particle number density n. From fits of theoretical expressions based on a Debye–Hückel-type pair interaction potential, an effective charge ZG* was derived. On the other hand the effectively transported charge Zσ* was determined from the n dependence of the suspension conductivity. Both effective charges are independent of n within experimental error. For most species they scale with the ratio of radius to Bjerrum length. For all species, however, Zσ* is found to be systematically larger than ZG* by some 40%.
We present a comprehensive study of the solidification scenario in suspensions of colloidal hard spheres for three polydispersities between 4.8% and 5.8%, over a range of volume fractions from near freezing to near the glass transition. From these results, we identify four stages in the crystallization process: (i) an induction stage where large numbers of precursor structures are observed, (ii) a conversion stage as precursors are converted to close packed structures, (iii) a nucleation stage, and (iv) a ripening stage. It is found that the behavior is qualitatively different for volume fractions below or above the melting volume fraction. The main effect of increasing polydispersity is to increase the duration of the induction stage, due to the requirement for local fractionation of particles of larger or smaller than average size. Near the glass transition, the nucleation process is entirely frustrated, and the sample is locked into a compressed crystal precursor structure. Interestingly, neither polydispersity nor volume fraction significantly influences the precursor stage, suggesting that the crystal precursors are present in all solidifying samples. We speculate that these precursors are related to the dynamical heterogeneities observed in a number of dynamical studies.
Highly cross-linked polystyrene microgel colloids dispersed in an index and density matching solvent provide a system with hard-sphere-like interactions, where gravity effects are effectively minimized. They are a suitable target for time-resolved observations of solidification in purely repulsive systems. We have investigated the crystallization kinetics at increasing undercooling using time resolved light scattering. Crystallization starts always with the formation of compressed, structurally heterogeneous precursor domains. In the coexistence region the precursors, after being converted into true crystallites, start growing fast by assimilating particles from the melt. The resulting polycrystalline material consists of high quality crystals and seems not to undergo long time-scale rearrangements. As the particle concentration grows, the higher undercooling and reduced particle mobility increasingly compromise the conversion-growth process. The growth of crystallites relies then on much slower ripeninglike processes, while refining of the crystal structure is detected up to the longest observed times.
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