Entropy-driven crystal formation on highly strained substrates

Abstract

In heteroepitaxy, lattice mismatch between the deposited material and the underlying surface strongly affects nucleation and growth processes. The effect of mismatch is well studied in atoms with growth kinetics typically dominated by bond formation with interaction lengths on the order of one lattice spacing. In contrast, less is understood about how mismatch affects crystallization of larger particles, such as globular proteins and nanoparticles, where interparticle interaction energies are often comparable to thermal fluctuations and are short ranged, extending only a fraction of the particle size. Here, using colloidal experiments and simulations, we find particles with short-range attractive interactions form crystals on isotropically strained lattices with spacings significantly larger than the interaction length scale. By measuring the free-energy cost of dimer formation on monolayers of increasing uniaxial strain, we show the underlying mismatched substrate mediates an entropydriven attractive interaction extending well beyond the interaction length scale. Remarkably, because this interaction arises from thermal fluctuations, lowering temperature causes such substratemediated attractive crystals to dissolve. Such counterintuitive results underscore the crucial role of entropy in heteroepitaxy in this technologically important regime. Ultimately, this entropic component of lattice mismatched crystal growth could be used to develop unique methods for heterogeneous nucleation and growth of single crystals for applications ranging from protein crystallization to controlling the assembly of nanoparticles into ordered, functional superstructures. In particular, the construction of substrates with spatially modulated strain profiles would exploit this effect to direct self-assembly, whereby nucleation sites and resulting crystal morphology can be controlled directly through modifications of the substrate.thermodynamics | colloids | tunable depletion interaction C rystal growth typically initiates at surfaces where the barrier for nucleation is significantly lower than in bulk (1)(2)(3)(4)(5). If the surface is regular, lattice mismatch between the crystallizing material and the underlying substrate can strongly affect the resulting crystal morphology (6-10). In many systems of interest, including nanoparticles and globular proteins, the interparticle interactions extend only a small percent of the particle diameter (11-15). Consequently, even a small lattice mismatch should strongly frustrate particle configurations due to the competition between in-plane and substrate bonds. These effects are even more dominant at large mismatch, where particles at adjacent lattice sites are separated by distances greater than the interaction length. Overcoming these effects, however, is technologically important for many applications, including protein crystallization and assembly of photonic as well as photovoltaic devices (10,16). Experimentally, these effects are difficult to study in situ at the nanometer scale due to rap...

Crystallization kinetics of colloidal model suspensions: recent achievements and new perspectives

“…Centrifugation onto templates was studied by Jensen et al [352] and also the nucleation mechanism on 111 fcc templates [353], which differs from that observed for flat walls [338]. Still different and more complex are the observations made for AS on structured and strained substrates [354] Seeding has been investigated with seeds of various sizes with either smooth or structured surfaces. At least two factors determine whether a large impurity with smooth surface can function as a seed for heterogeneous nucleation: timescales and surface curvature [355].…”

Ionic-Liquid-Functionalized Mineral Particles for Protein Crystallization

“…Therefore, even the small lattice mismatch between the protein and a substrate can strongly frustrate crystal formation as a result of the competition between intermolecular protein interactions and protein−substrate attraction. 7 Disordered solids are supposed to be more effective in protein nucleation because of the possibility that some fraction of the solid binding sites will be located just at the right distance to fit the protein− protein spacing in the crystal. The same probability-based reasoning was given to the fact that a wide distribution of pore sizes is a necessary parameter for an effective protein nucleant.…”

“…1−6 Very recently, nonporous ordered surfaces have also been found to be prone to induce crystal growth in model systems where the crystal contacts are governed by short-range interactions (as for proteins). 7 The requirement for those surfaces to act as nucleants is the presence of surface strain. Otherwise, crystalline solids were shown to be ineffective in promoting nucleation, except in those rare cases where the crystal lattice spacing of the substrate corresponded to that of the protein (epitaxy).…”

Tasas de difusión y de deposición en un modelo de epitaxia coloidal

“…Gracias a que tanto el alcance como la intensidad de las interacciones entre las partículas coloidales, y por lo tanto el comportamiento de fases, pueden ser ajustadas con relativa facilidad a través de múltiples factores físico-químicos, estos sistemas han permitido explorar una variedad de fenómenos incluyendo nucleación, cristalización, gelificación y vitrificación. Adicionalmente, dado el tamaño y las escalas temporales características de estos sistemas, las posiciones individuales de las partículas pueden rastrearse de manera precisa a través de métodos ópticos como la dispersión dinámica de luz (DSL) y la microscopia confocal de fluorescencia (3,4) .…”

“…De igual manera, este tipo de sistemas se puede emplear para estudiar la dinámica de procesos de relajación en sustratos deformados (strained layers ) (4,10) y gracias a los avances en la síntesis de coloides con formas e interacciones anisotrópicas, se espera que nuevas fronteras puedan alcanzarse en relación a la epitaxia molecular. En este ámbito, se puede considerar que el método más conveniente para estudiar los efectos inducidos por el sustrato en la formación de monocapas coloidales, es crear el sustrato mediante el empleo de pinzas ópticas, las cuales consisten en campos de luz extendidos creados convenientemente, por ejemplo, a través de la interferencia de haces láser.…”