Suppression of self-stratification in colloidal mixtures with high Péclet numbers.

The non-equilibrium assembly of bimodal colloids during evaporative processes is an attractive means to achieve gradient or stratified layers in thick films. Here, we show that the stratification of small colloids on top of large is prevented when the viscosity of the continuous aqueous phase is too high. We propose a model where a too narrow width of the gradient in concentration of small colloids suppresses the stratification.

Stratification in binary colloidal polymer films: experiment and simulations.

When films are deposited from mixtures of colloidal particles of two different sizes, a diverse range of functional structures can result. One structure of particular interest is a stratified film in which the top surface layer has a composition different than in the interior. Here, we explore the conditions under which a stratified layer of small particles develops spontaneously in a colloidal film that is cast from a binary mixture of small and large polymer particles that are suspended in water. A recent model, which considers the cross-interaction between the large and small particles (Zhou et al., Phys. Rev. Lett., 2017, 118, 108002), predicts that stratification will develop from dilute binary mixtures when the particle size ratio (α), initial volume fraction of small particles (ϕS), and Péclet number are high. In experiments and Langevin dynamics simulations, we systematically vary α and ϕS in both dilute and concentrated suspensions. We find that stratified films develop when ϕS is increased, which is in agreement with the model. In dilute suspensions, there is reasonable agreement between the experiments and the Zhou et al. MODEL: In concentrated suspensions, stratification occurs in experiments only for the higher size ratio α = 7. Simulations using a high Péclet number, additionally find stratification with α = 2, when ϕS is high enough. Our results provide a quantitative understanding of the conditions under which stratified colloidal films assemble. Our research has relevance for the design of coatings with targeted optical and mechanical properties at their surface.

Nucleation of crystals that are mixed composites of all three polymorphs in the Gaussian core model.

We present results of computer simulations of homogeneous crystal nucleation in the Gaussian core model. In our simulations, we study the competition between the body-centered-cubic (bcc), face-centered-cubic (fcc), and hexagonal-close-packed crystal phases. We find that the crystal nuclei that form from the metastable fluid phase are typically "mixed"; they do not consist of a single crystal polymorph. Furthermore, when the fcc phase is stable or fcc and bcc phases are equally stable, this mixed nature is found to persist far beyond the size at the top of the nucleation barrier, that is, far into what would be considered the growth (rather than nucleation) regime. In this region, the polymorph that forms is therefore selected long after nucleation. This has implications. When nucleation is slow, it will be the rate-limiting step for crystallization. Then, the step that determines the time scale for crystallisation is different from the step that controls which polymorph forms. This means that they can be independently controlled. Also between nucleation and polymorph selection, there is a growing phase that is clearly crystalline not fluid, but this phase cannot be assigned to any one polymorph.

Computer simulation of epitaxial nucleation of a crystal on a crystalline surface.

We present results of computer simulations of crystal nucleation on a crystalline surface, in the Lennard-Jones model. Motivated by the pioneering work of Turnbull and Vonnegut [Ind. Eng. Chem. 44, 1292 (1952)], we investigate the effects of a mismatch between the surface lattice constant and that of the bulk nucleating crystal. We find that the nucleation rate is maximum close to, but not exactly at, zero mismatch. The offset is due to the finite size of the nucleus. In agreement with a number of experiments, we find that even for large mismatches of 10% or more, the formation of the crystal can be epitaxial, meaning that the crystals that nucleate have a fixed orientation with respect to the surface lattice. However, nucleation is not always epitaxial, and loss of epitaxy does affect how the rate varies with mismatch. The surface lattice strongly influences the nucleation rate. We show that the epitaxy observed in our simulations can be predicted using calculations of the potential energy between the surface and the first layer of the nucleating crystal, in the spirit of simple approaches such as that of Hillier and Ward [Phys. Rev. B 54, 14037 (1996)].

Freezing in the bulk controlled by prefreezing at a surface.

We use Monte Carlo simulations of the Lennard-Jones model to study the nucleation of a crystal phase at a flat surface. Our motivation is the observation that crystal phases almost always nucleate at a surface. We find that a surface phase transition (prefreezing) can control nucleation of the bulk crystal. This finding should be general and so surface phase behavior should be considered whenever nucleation of bulk phases at surfaces is considered. Also, nucleation of the bulk crystal transforms smoothly into the nucleation of a surface crystal layer as the bulk transition is crossed.

Two-step vapor-crystal nucleation close below triple point.

We present the results of Monte Carlo simulations of crystal nucleation from the vapor phase. We studied the Lennard-Jones system at conditions close to, but below, the triple point. This system is expected to show surface melting. The nucleation pathway that we observe consists of two distinct steps. In the first step, a liquid droplet nucleates from the vapor. Its nucleation rate depends strongly on the vapor supersaturation. In the second step, the final crystal phase nucleates in the liquid droplet, provided that this liquid droplet exceeds a minimum size. Our simulations show that within a liquid droplet the crystal nucleation rate does not depend on the vapor supersaturation. In a recent independent study Chen et al. [J. Phys. Chem. B 112, 4069 (2008)] investigated the same phenomenon using umbrella sampling to compute free energy barriers and hence nucleation rates. We use a different numerical approach where we focus on computing the nucleation rates directly using forward-flux sampling. Our results agree with the findings of Chen et al. and both methods observe two-step nucleation. This finding indicates that this nucleation process can be described with a quasiequilibrium theory. Due to different cutoffs for the interaction potential the results cannot be compared quantitatively.

Miscibility gap in the microbial fitness landscape.

It is shown from molecular statistical considerations that a demixing instability exists in the moment space of a microbial protein expression profile. Although avoidance of demixing is generally requisite for biological function, a comparison with proteomic and genomic data suggests that many microbes lie close to the onset of this instability. Over evolutionary time scales, straying too close or into the immiscible domain may be associated with intracellular compartmentalization.

Protein crystals and charged surfaces: interactions and heterogeneous nucleation.

As proteins typically have charges of around 10, they will interact strongly with charged surfaces. We calculate the electrostatic contribution to the interaction of crystals of protein with charged surfaces. The surfaces repel like-charged crystals and attract oppositely charged crystals, with free energies that can be easily several kT per protein molecule brought into contact with the surface. This means that oppositely charged surfaces can act as a nucleant, they can induce nucleation of a protein crystal by lowering the free energy barrier to heterogeneous nucleation of the crystal from a dilute solution.

Phase separation in mixtures of colloids and long ideal polymer coils.

Colloidal suspensions with free polymer coils which are larger than the colloidal particles are considered. The polymer-colloid interaction is modeled by an extension of the Asakura-Oosawa model. Phase separation occurs into dilute and dense fluid phases of colloidal particles when polymer is added. The critical density of this transition tends to zero as the size of the polymer coils diverges.

Homogeneous nucleation of a noncritical phase near a continuous phase transition.

Homogeneous nucleation of a new phase near a second, continuous, transition, is considered. The continuous transition is in the metastable region associated with the first-order phase transition, one of whose coexisting phases is nucleating. Mean-field calculations show that as the continuous transition is approached, the size of the nucleus varies as the response function of the order parameter of the continuous transition. This response function diverges at the continuous transition, as does the temperature derivative of the free-energy barrier to nucleation. This rapid drop of the barrier as the continuous transition is approached means that the continuous transition acts to reduce the barrier to nucleation at the first-order transition. This may be useful in the crystallization of globular proteins.

Low-temperature interface between the gas and solid phases of hard spheres with a short-ranged attraction.

At low temperature, spheres with a very short-ranged attraction exist as a near-close-packed solid coexisting with an almost infinitely dilute gas. We find that the ratio of the interfacial tension between these two phases to the thermal energy diverges as the range of the attraction tends to zero. The large tensions when the interparticle attractions are short ranged may be why globular proteins only crystallize over a narrow range of conditions.

Spontaneous patterning of quantum dots at the air-water interface.

Nanoparticles deposited at the air-water interface are observed to form circular domains at low density and stripes at higher density. We interpret these patterns as equilibrium phenomena produced by a competition between an attraction and a longer-ranged repulsion. Computer simulations of a generic pair potential with attractive and repulsive parts of this kind, reproduce both the circular and stripe patterns. Such patterns have a potential use in nanoelectronic applications.