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This study presents a population balance model for the kinetics of nucleation and growth in covalent organic framework (COF) synthesis. The model incorporates second-order nucleation and first-order growth rates, consistent with proposals in the literature. Despite having non-linear terms, an implicit analytic solution is derived and then converted to explicit solutions for the monomer concentration and size distribution of COF flakes as a function of time. For experimental definitions of the induction time and the initial growth rate based on yield (y) vs time (t) curves, the model predicts power-law relationships: t ind = 0.409 k N − 1 / 3 k G − 2 / 3 c A 0 − 1 and d y / d t max = 0.965 k N 1 / 3 k G 2 / 3 c A 0 , respectively. We discuss the implications for the interpretation of Arrhenius plots. We also discuss key discrepancies with experiments, including the predicted attainment of 100% yield instead of 30%–40% as observed and the value of the yield at the inflection point in the yield vs time curve. We suggest extensions to the model, including nucleation and growth kinetics with equilibrium solubility limitations and two-dimensional nucleation for the formation of multilayer COF particles. [ABSTRACT FROM AUTHOR]

This work reexamines seeded simulation results for NaCl nucleation from a supersaturated aqueous solution at 298.15 K and 1 bar pressure. We present a linear regression approach for analyzing seeded simulation data that provides both nucleation rates and uncertainty estimates. Our results show that rates obtained from seeded simulations rely critically on a precise driving force for the model system. The driving force vs. solute concentration curve need not exactly reproduce that of the real system, but it should accurately describe the thermodynamic properties of the model system. We also show that rate estimates depend strongly on the nucleus size metric. We show that the rate estimates systematically increase as more stringent local order parameters are used to count members of a cluster and provide tentative suggestions for appropriate clustering criteria.

Magic clusters are metastable faceted nanoparticles that are thought to be important and, sometimes, observable intermediates in the nucleation of certain faceted crystallites. This work develops a broken bond model for spheres with a face-centered-cubic packing that form tetrahedral magic clusters. With just one bond strength parameter, statistical thermodynamics yield a chemical potential driving force, an interfacial free energy, and free energy vs magic cluster size. These properties exactly correspond to those from a previous model by Mule et al. [J. Am. Chem. Soc. 143, 2037 (2021)]. Interestingly, a Tolman length emerges (for both models) when the interfacial area, density, and volume are treated consistently. To describe the kinetic barriers between magic cluster sizes, Mule et al. invoked an energy parameter to penalize the two-dimensional nucleation and growth of new layers in each facet of the tetrahedra. According to the broken bond model, barriers between magic clusters are insignificant without the additional edge energy penalty. We estimate the overall nucleation rate without predicting the rates of formation for intermediate magic clusters by using the Becker–Döring equations. Our results provide a blueprint for constructing free energy models and rate theories for nucleation via magic clusters starting from only atomic-scale interactions and geometric considerations. [ABSTRACT FROM AUTHOR]

Anti-freeze proteins (AFPs) protect organisms at freezing conditions by attaching to the ice surface and arresting its growth. Each adsorbed AFP locally pins the ice surface, resulting in a metastable dimple for which the interfacial forces counteract the driving force for growth. As supercooling increases, these metastable dimples become deeper, until metastability is lost in an engulfment event where the ice irreversibly swallows the AFP. Engulfment resembles nucleation in some respects, and this paper develops a model for the "critical profile" and free energy barrier for the engulfment process. Specifically, we variationally optimize the ice–water interface and estimate the free energy barrier as a function of the supercooling, the AFP footprint size, and the distance to neighboring AFPs on the ice surface. Finally, we use symbolic regression to derive a simple closed-form expression for the free energy barrier as a function of two physically interpretable, dimensionless parameters. [ABSTRACT FROM AUTHOR]

Nucleation and crystal growth are important in material synthesis, climate modeling, biomineralization, and pharmaceutical formulation. Despite tremendous efforts, the mechanisms and kinetics of nucleation remain elusive to both theory and experiment. Here we investigate sodium chloride (NaCl) nucleation from supersaturated brines using seeded atomistic simulations, polymorph-specific order parameters, and elements of classical nucleation theory. We find that NaCl nucleates via the common rock salt structure. Ion desolvation-not diffusion-is identified as the limiting resistance to attachment. Two different analyses give approximately consistent attachment kinetics: diffusion along the nucleus size coordinate and reaction-diffusion analysis of approach-to-coexistence simulation data from Aragones et al. ( J. Chem. Phys. 2012, 136, 244508 ). Our simulations were performed at realistic supersaturations to enable the first direct comparison to experimental nucleation rates for this system. The computed and measured rates converge to a common upper limit at extremely high supersaturation. However, our rate predictions are between 15 and 30 orders of magnitude too fast. We comment on possible origins of the large discrepancy.

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]

In the theory of solidification, the kinetic coefficient multiplies the local supercooling to give the solid–liquid interface velocity. The same coefficient should drive interface migration at the coexistence temperature in proportion to a curvature force. This work computes the ice–water kinetic coefficient from molecular simulations starting from a sinusoidal ice–water interface at the coexistence temperature. We apply this method to the basal and prismatic ice planes and compare results to previous estimates from equilibrium correlation functions and simulations at controlled supercooling. [ABSTRACT FROM AUTHOR]

The copper hydride clusters [Cu14 H12 (phen)6(PPh3)4][X]2 (X=Cl or OTf; OTf=trifluoromethanesulfonate, phen=1,10-phenanthroline) are obtained in good yields by the reaction of [(Ph3P)CuH]6 with phen, in the presence of a halide or pseudohalide source. The complex [Cu14H12 (phen)6(PPh3)4][Cl]2 reacts with CO2 in CH2Cl2 , in the presence of excess Ph3 P, to form the formate complex [(Ph3P)2Cu(κ(2)-O2CH)], along with [(phen)(Ph3 P)CuCl].

Author(s): Laura Lupi [1]; Arpa Hudait [1]; Baron Peters [2]; Michael Grnwald [1]; Ryan Gotchy Mullen [2]; Andrew H. Nguyen [1]; Valeria Molinero (corresponding author) [1] The freezing of water [...]

Free energies of crystals computed using a center of mass constraint require a finite-size correction, as shown in previous work by Polson et al. [J. Chem. Phys. 112, 5339–5342 (2000)]. Their reference system is an Einstein crystal with equal spring constants. In this paper, we extend the work of Polson et al. [J. Chem. Phys. 112, 5339–5342 (2000)] to the case of differing spring constants. The generalization is convenient for constraining the center of mass in crystals with atoms of differing masses, and it helps to optimize the free energy calculations. To test the theory, we compare the free energies of LiI and NaCl crystals from calculations with differing spring constants to those computed using equal spring constants. Using these center of mass finite size corrections, we compute the true free energies of these crystals for different system sizes to eliminate the intrinsic finite-size effects. These calculations help demonstrate the size of these finite-size corrections relative to other contributions to the absolute free energy of the crystals. [ABSTRACT FROM AUTHOR]

For disordered catalysts such as atomically dispersed "single-atom" metals on amorphous silica, the active sites inherit different properties from their quenched-disordered local environments. The observed kinetics are site-averages, typically dominated by a small fraction of highly active sites. Standard sampling methods require expensive ab initio calculations at an intractable number of sites to converge on the site-averaged kinetics. We present a new method that efficiently estimates the site-averaged turnover frequency (TOF). The new estimator uses the same importance learning algorithm [Vandervelden et al., React. Chem. Eng. 5, 77 (2020)] that we previously used to compute the site-averaged activation energy. We demonstrate the method by computing the site-averaged TOF for a simple disordered lattice model of an amorphous catalyst. The results show that with the importance learning algorithm, the site-averaged TOF and activation energy can now be obtained concurrently with orders of magnitude reduction in required ab initio calculations. [ABSTRACT FROM AUTHOR]

Lattice-switch Monte Carlo and the related diabat methods have emerged as efficient and accurate ways to compute free energy differences between polymorphs. In this work, we introduce a one-to-one mapping from the reference positions and displacements in one molecular crystal to the positions and displacements in another. Two features of the mapping facilitate lattice-switch Monte Carlo and related diabat methods for computing polymorph free energy differences. First, the mapping is unitary so that its Jacobian does not complicate the free energy calculations. Second, the mapping is easily implemented for molecular crystals of arbitrary complexity. We demonstrate the mapping by computing free energy differences between polymorphs of benzene and carbamazepine. Free energy calculations for thermodynamic cycles, each involving three independently computed polymorph free energy differences, all return to the starting free energy with a high degree of precision. The calculations thus provide a force field independent validation of the method and allow us to estimate the precision of the individual free energy differences. [ABSTRACT FROM AUTHOR]

Solid–fluid phase equilibria are difficult to predict in simulations because bound degrees of freedom in the crystal phase must be converted to free translations and rotations in the fluid phase. Here, we avoid the solid-to-fluid transformation step by starting with chemical potentials for two reference systems, one for the fluid phase and one for the solid phase. For the solid, we start from the Einstein crystal and transform to the fully interacting molecular crystal. For the fluid phase, we introduce a new reference system, the "centroid," and then transform to gas phase molecules. We illustrate the new calculations by predicting the sublimation vapor pressure of succinic acid in the temperature range of 300 K–350 K. [ABSTRACT FROM AUTHOR]

In an infrequent metadynamics (iMetaD) simulation, a well-tempered metadynamics bias accumulates in the reactant basin, accelerating escapes to the product state. Like the earlier hyperdynamics strategy, iMetaD enables estimates of the unbiased escape rates. However, iMetaD applies the bias to visited locations in a collective variable (CV) space, not to the more specific visited locations in a full configuration space as done in hyperdynamics. This difference makes rate estimates from iMetaD sensitive to the choice of CVs, to parameters that control the bias deposition rate, and to the preparation of the initial state within the reactant basin. This paper uses an extremely simple discrete state model to illustrate complications that can arise in systems that exhibit fluxional transitions between sub-basins of the reactant state. Specifically, we show how the reactant-to-product escape time and relaxation times within the reactant basin(s) impose bounds on the admissible parameter choices for an iMetaD calculation. Predictions from the discrete state model are validated by iMetaD simulations on a corresponding two-dimensional potential energy surface. [ABSTRACT FROM AUTHOR]

For inertial reaction dynamics, a transition state theory rate constant obtained from an inaccurate reaction coordinate can be a posteriori corrected with reactive flux methods. In contrast, reaction coordinate errors in overdamped mean first passage time calculations cannot be a posteriori corrected. This work develops an overdamped version of the transmission coefficient. The calculation requires information from committor analyses and an estimate of the diffusivity along the committor coordinate. We illustrate the calculation for a simple two-dimensional potential that admits exact solutions. [ABSTRACT FROM AUTHOR]