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...

The properties of template-directed nucleation are studied in the transition region where full nucleation control is lost and additional nucleation beyond the prepatterned structure is observed. To get deeper insight into the microscopic mechanisms, Monte Carlo simulations were performed. In this context, the previously used continuous algorithm [F. Kalischewski, J. Zhu, and A. Heuer, Phys. Rev. B 77, 155401, (2008)] was replaced by a discrete one to reduce simulation time and to allow more detailed calculations. The applied method is based on the assumption that the molecules on the surface occupy the sites of a simple fcc lattice. It is shown that a careful mapping of the continuous Monte Carlo technique onto the discrete algorithm leads to a good reproduction of the former results by means of the latter method. Furthermore, the new method facilitates the calculation of the spatial distribution of nuclei on the surface. This provides a detailed comparison with experimental data.

The nucleation of organic molecules on surfaces, prepatterned with stripes, is investigated with emphasis on anisotropy effects. Representing the molecules as ellipsoids, the related particle-particle interaction is modeled by means of a generalized Gay-Berne potential for similar biaxial particles. The orientation behavior of these ellipsoidal molecules induced by the stripe pattern is studied for the first monolayer by performing kinetic Monte Carlo simulations. It is shown how the properties of the particle alignment depend on energy scales, temperature, and flux. Based on the fact the particles strictly arrange in rows, it is furthermore instructive to analyze the orientation behavior within the different rows. Finally, the transfer of orientation from a preset row of molecules with fixed orientation to other nucleating particles is examined.