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The adsorption of large rod-like molecules or crystallites on a flat crystal face, similar to Buffon's needle, requires the rods to "land," with their binding sites in precise orientational alignment with matching sites on the surface. An example is provided by long, helical antifreeze proteins (AFPs), which bind at specific facets and orientations on the ice surface. The alignment constraint for adsorption, in combination with the loss in orientational freedom as the molecule diffuses toward the surface, results in an entropic barrier that hinders the adsorption. Prior kinetic models do not factor in the complete geometry of the molecule, nor explicitly enforce orientational constraints for adsorption. Here, we develop a diffusion-controlled adsorption theory for AFP molecules binding at specific orientations to flat ice surfaces. We formulate the diffusion equation with relevant boundary conditions and present analytical solutions to the attachment rate constant. The resulting rate constant is a function of the length and aspect ratio of the AFP, the distance threshold associated with binding, and solvent conditions such as temperature and viscosity. These results and methods of calculation may also be useful for predicting the kinetics of crystal growth through oriented attachment. [ABSTRACT FROM AUTHOR]

One-dimensional (1D) nucleation is important in crystal growth, amyloid fibril formation, and supramolecular polymerization. The nucleation rate can be readily calculated, but there is no consensus on the critical length. In this work, we employ a splitting probability to derive an analytical expression for the critical length, which corresponds to a 50% survival probability. For a 1D nucleus on a crystal step, this critical length depends on the supersaturation (driving force) and is nearly independent of the kink (surface) energy. [ABSTRACT FROM AUTHOR]

Crystal growth rates depend on the density of kink sites along step edges, ρ. The supersaturation-dependence of the kink density, ρ(S), is often ignored despite available nonequilibrium models for centrosymmetric crystals. The aim of this work is to derive ρ(S) from a rather simple one-dimensional nucleation framework in a manner that accounts for multiheight kinks. These become more prevalent at higher S and/or lower kink energies where the step front roughens (i.e., higher ρ). We arrive at a density of kinetic kinks that contribute to the step velocity and make comparisons with other models and simulations. Our model almost entirely eliminates systematic errors in predicted step velocities and crystal growth rates. [ABSTRACT FROM AUTHOR]

Crystals with asymmetric growth units present a ubiquitous challenge for modeling crystal growth. We derive the crystal step edge velocity for steps with alternating rows of growth units (i.e., a row of A followed by a row of B growth units). We construct a free energy model for 1D nucleation of this two-tiered row and show that a single anisotropic interaction parameter and the supersaturation characterize the edge stability. A Fokker–Planck model captures the kinetics of nucleation and seamlessly connects the stable and unstable regimes, whereas previous models diverge near the transition between these cases. The 1D nucleation model leads to an expression that predicts the step velocity as a function of supersaturation and edge stability. We show that the model is in excellent agreement with kinetic Monte Carlo simulations. • Crystal growth models are important for screening and discovery. • Complex crystal step edges exhibit stable and unstable behavior. • 1D nucleation rate is derived along a complex crystal step. • Crystal step velocity is determined from 1D nucleation. • Anisotropic spirals and nuclei are predicted by the model. [ABSTRACT FROM AUTHOR]

Many molecular crystals are comprised of centrosymmetric dimer motifs. In several cases, these are thought to grow by direct incorporation of dimerized units rather than from monomers. In this work, we model the effects of the dimerization kinetics in the boundary layer close to the crystal surface on the rate of crystal growth. We identify three dimensionless parameters that relate diffusivity through the boundary layer, dimerization kinetics, and dimer incorporation kinetics to estimate the extent to which dimerization kinetics impede the crystal growth from dimers. • We develop an analytical growth model for crystals that grow from dimer units. • Nondimensionalization yields parameters reminiscent of those used in catalysis. • We quantify how crystal growth rates are impeded by finite dimerization kinetics. • We give simple rules for conditions under which growth impedance is significant. [ABSTRACT FROM AUTHOR]

Nucleationkinetics, induction times, and metastable zone widthsare often modeled in quiescent, quasi-steady, and/or spatially uniformconcentration fields. However, freezing an aqueous solution can concentratethe solute and effectively increase the supersaturation. During thefreezing process, a boundary layer of giant supersaturation developsahead of the moving ice front. We develop stochastic models of nucleationin the boundary layer when the growing ice perfectly excludes thesolute for a one-dimensional system. The models make three simplifyingassumptions: quasi-stationary nucleation kinetics, nuclei that aresmall compared to the boundary layer thickness, and a constant solventcrystallization growth velocity. Whether heterogeneous on the icesurface, or homogeneous in the boundary layer, the models suggestthat nucleation is dramatically accelerated by the growing ice. Formethane hydrates, which form at conditions similar to that of ice,induction times for hydrate nucleation can be reduced by as much as10105times because of the moving supersaturation zone. [ABSTRACT FROM AUTHOR]

Almost all molecules are non-centrosymmetric, which produces interaction anisotropy within a crystal lattice. This anisotropy generates multiple types of kink sites on each crystal step and repeating patterns of rows with different growth units from the perspective of the lattice interaction environment, even for pure molecular crystals. As a result, unstable edge rows may be generated that dissolve under conditions of crystal growth. A method to account for edge surface structures, considering such effects, is required to accurately model the step velocity, which is vital for a mechanistic description of crystal growth. We classify both thermodynamic and kinetic contributions to step row instability and develop expressions for kink densities and step velocities that capture these important non-centrosymmetric phenomena. To demonstrate the utility of our framework, we consider in depth the case of an alternating-row A-B step. Our mechanistic predictions compare favorably to kinetic Monte Carlo simulations across a wide range of interaction anisotropy. [ABSTRACT FROM AUTHOR]

The central kinetic processes defining layer-by-layer crystal growth or dissolution are the attachment and detachment rates of growth units at kink sites; the net balance of these activated processes leads to either crystal growth or dissolution. Various sets of rate expressions for attachment and detachment processes have been used in the literature, in each case attempting to most appropriately capture the underlying surface chemistry. We examine these proposals with specific attention to thermodynamics and detailed balance criteria and then recommend which expressions to adopt. [ABSTRACT FROM AUTHOR]