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The morphological evolution of organic crystals during crystallization depends on the face-specific growth rates. Classical growth rate models relate the face-specific growth rates to the crystal lattice, energy of stable facets, growth mechanism, and supersaturation. The complexities of these models have increased over time to account accurately for solution conditions, the structure of growth units, and their attachment rates. Such advanced growth rate models require several layers of computations to obtain attachment energies of facets, nucleation rates, kink density, and attachment rates. Among these, the most intensive and time-consuming computation is for attachment rates, which require molecular dynamic simulations. This substantially increases the overall computation time to predict the absolute growth rate for even one crystallization condition. Since it is nearly impossible to iterate such a growth rate model, optimization schemes cannot be implemented to identify solution conditions that favor specific crystal growth. To reduce the computational time for attachment rate calculations, we implement a group contribution method (GCM) that relates the properties of functional groups in a molecule to their attachment rates to the crystal lattice, thereby rapidly estimating the growth rates of organic crystals. The process of molecular attachment involves partial desolvation of a solvated molecule, referred to as a transition state, followed by total desolvation via spontaneous attachment to a crystal facet. The first step in GCM is to identify the equilibrium states of fully solvated and partially desolvated solute molecules. The degree of supersaturation dictates the extent of this equilibrium and, thereby, the activation barrier for the growth of crystals, according to transition state theory. Identifying this equilibrium phenomenon allows for capturing the functional-group-specific interactions that depend on molecular motion, which could be related to operating conditions such as temperature and pressure. The stochastic optimization technique with Monte-Carlo sampling allows an efficient optimization problem solution to obtain the group interaction parameters. The GCM approach is first validated for the estimation of growth rates of glutamic acid and L-histidine, and then extended to predict growth rates of alanine and glycine rapidly. The optimized parameters and GCM scheme can be used to estimate growth rates in other crystallization systems. 

The induction time for the onset of nucleation is known to decrease with increasing solution supersaturation. A large variation in induction time is experimentally observed for various organic crystals, whose origin is often associated with the stochastic nature of the nucleation process. Although several empirical models for induction time and nucleation rate have been developed, they remained highly unreliable, with model predictions differing by orders of magnitude from experimental measurements. A satisfactory explanation for the induction time variation has not been developed yet. We report here that the variations in induction times can be attributed to a previously unrecognized consequence of the phase separation or emulsification of supersaturated solution, in addition to the effect of stochastic nucleation. A large-scale Brownian dynamics simulation of antisolvent crystallization of histidine in a water–ethanol mixture is performed to demonstrate the mechanism of microphase/emulsion formation in supersaturated solutions and its consequence on induction time variation. Furthermore, we show that the average induction time depends on supersaturation, and the supersaturation-dependent diffusion of histidine molecules governs the stochastic nature of the induction time. Moreover, at varying supersaturations, the likelihood of forming stable and metastable polymorphs of histidine was estimated. This approach provides valuable insights into the crystallization behavior of histidine, and predicted induction time reasonably matches the experimentally observed induction time. 

The chemical pathway for synthesizing covalent organic frameworks (COFs) involves a complex medley of reaction sequences over a rippling energy landscape that cannot be adequately described using existing theories. Even with the development of state-of-the-art experimental and computational tools, identifying primary mechanisms of nucleation and growth of COFs remains elusive. Other than empirically, little is known about how the catalyst composition and water activity affect the kinetics of the reaction pathway. Here, for the first time, we employ time-resolved in situ Fourier transform infrared spectroscopy (FT-IR) coupled with a six-parameter microkinetic model consisting of ∼10 million reactions and over 20 000 species. The integrated approach elucidates previously unrecognized roles of catalyst p K a on COF yield and water on growth rate and size distribution. COF crystalline yield increases with decreasing p K a of the catalysts, whereas the effect of water is to reduce the growth rate of COF and broaden the size distribution. The microkinetic model reproduces the experimental data and quantitatively predicts the role of synthesis conditions such as temperature, catalyst, and precursor concentration on the nucleation and growth rates. Furthermore, the model also validates the second-order reaction mechanism of COF-5 and predicts the activation barriers for classical and non-classical growth of COF-5 crystals. The microkinetic model developed here is generalizable to different COFs and other multicomponent systems. 

The two-step nucleation (TSN) theory and crystal structure prediction (CSP) techniques are two disjointed yet popular methods to predict nucleation rate and crystal structure, respectively. The TSN theory is a well-established mechanism to describe the nucleation of a wide range of crystalline materials in different solvents. However, it has never been expanded to predict the crystal structure or polymorphism. On the contrary, the existing CSP techniques only empirically account for the solvent effects. As a result, the TSN theory and CSP techniques continue to evolve as separate methods to predict two essential attributes of nucleation – rate and structure. Here we bridge this gap and show for the first time how a crystal structure is formed within the framework of TSN theory. A sequential desolvation mechanism is proposed in TSN, where the first step involves partial desolvation to form dense clusters followed by selective desolvation of functional groups directing the formation of crystal structure. We investigate the effect of the specific interaction on the degree of solvation around different functional groups of glutamic acid molecules using molecular simulations. The simulated energy landscape and activation barriers at increasing supersaturations suggest sequential and selective desolvation. We validate computationally and experimentally that the crystal structure formation and polymorph selection are due to a previously unrecognized consequence of supersaturation-driven asymmetric desolvation of molecules. 

Magnetophoresis is an important physical process with application to drug delivery, biomedical imaging, separation, and mixing. Other than empirically, little is known about how the magnetic field and magnetic properties of a solution affect the flux of magnetic particles. A comprehensive explanation of these effects on the transport of magnetic particles has not been developed yet. Here we formulate a consistent, constitutive equation for the magnetophoretic flux of magnetic nanoparticles suspended in a medium exposed to a stationary magnetic field. The constitutive relationship accounts for contributions from magnetic diffusion, magnetic convection, residual magnetization, and electromagnetic drift. We discovered that the key physical properties governing the magnetophoresis are magnetic diffusion coefficient, magnetic velocity, and activity coefficient, which depend on relative magnetic energy and the molar magnetic susceptibility of particles. The constitutive equation also reveals previously unknown ballistic and diffusive limits for magnetophoresis wherein the paramagnetic particles either aggregate near the magnet or diffusive away from the magnet, respectively. In the diffusive limit, the particle concentration is linearly proportional to the relative magnetic energy of the suspension of paramagnetic particles. The region of the localization of paramagnetic particles near the magnet decreases with increasing the strength of the magnet. The dynamic accumulation of nanoparticles, measured as the thickness of the nanoparticle aggregate, near the magnet compares well with the theoretical prediction. The effect of convective mixing on the rate of magnetophoresis is also discussed for the magnetic targeting applications.