Solution crystallization is a common technique to grow advanced, functional crystalline materials. Supersaturation, temperature, and solvent composition are known to influence the growth rates and thereby properties of crystalline materials; however, a satisfactory explanation of how these factors affect the activation barrier for growth rates has not been developed. We report here that these effects can be attributed to a previously unrecognized consequence of solvent fluctuations in the solvation shell of solute molecules attaching to the crystal surface. With increasing supersaturation, the average hydration number of the glutamic acid molecule decreases and can reach an asymptotic limit corresponding to the number of adsorption sites on the molecule. The hydration number of the glutamic acid molecule also fluctuates due to the rapid exchange of solvent in the solvation shell and local variation in the supersaturation. These rapid fluctuations allow quasi-equilibrium between fully solvated and partially desolvated states of molecules, which can be used to construct a double-well potential and thereby to identify the transition state and the required activation barrier. The partially desolvated molecules are not stable and can attach spontaneously to the crystal surface. The activation barrier versus hydration number follows the Evans–Polanyi relation. The predicted absolute growth rates of the α-glutamic acid crystal at lower supersaturations are in reasonable agreement with the experimental observations.
Synthesis of porous, covalent crystals such as zeolites and metal–organic frameworks (MOFs) cannot be described adequately using existing crystallization theories. Even with the development of state-of-the-art experimental and computational tools, the identification of primary mechanisms of nucleation and growth of MOFs remains elusive. Here, using time-resolved in-situ X-ray scattering coupled with a six-parameter microkinetic model consisting of ∼1 billion reactions and up to ∼100 000 metal nodes, we identify autocatalysis and oriented attachment as previously unrecognized mechanisms of nucleation and growth of the MOF UiO-66. The secondary building unit (SBU) formation follows an autocatalytic initiation reaction driven by a self-templating mechanism. The induction time of MOF nucleation is determined by the relative rate of SBU attachment (chain extension) and the initiation reaction, whereas the MOF growth is primarily driven by the oriented attachment of reactive MOF crystals. The average size and polydispersity of MOFs are controlled by surface stabilization. Finally, the microkinetic model developed here is generalizable to different MOFs and other multicomponent systems.
Metal–organic frameworks (MOFs) are the porous, crystalline structures made of metal–ligands and organic linkers that have applications in gas storage, gas separation, and catalysis. Several experimental and computational tools have been developed over the past decade to investigate the performance of MOFs for such applications. However, the experimental synthesis of MOFs is still empirical and requires trial and error to produce desired structures, which is due to a limited understanding of the mechanism and factors affecting the crystallization of MOFs. Here, we show for the first time a comprehensive kinetic model coupled with population balance model to elucidate the mechanism of MOF synthesis and to estimate size distribution of MOFs growing in a solution of metal–ligand and organic linker. The oligomerization reactions involving metal–ligand and organic linker produce secondary building units (SBUs), which then aggregate slowly to yield MOFs. The formation of secondary building units (SBUs) and their evolution into MOFs are modeled using detailed kinetic rate equations and population balance equations, respectively. The effect of rate constants, aggregation frequency, the concentration of organic linkers, and concurrent crystallization of organic linkers are studied on the dynamics of SBU and MOF formation. The results qualitatively explain the longer timescales involved in the synthesis of MOF. The fundamental insights gained from modeling and simulation analysis can be used to optimize the operating conditions for a higher yield of MOF crystals.
Synthesis of crystalline materials involves the two most important methods: antisolvent and cooling crystallization. Despite the extensive use of the antisolvent method in the crystallization of various organic and inorganic crystals, the governing mechanism of the antisolvent in activating this process is not fully understood. Thermodynamically, the antisolvent is known to increase the chemical potential, and thereby supersaturation, of solute in the solution leading to crystal nucleation and growth. It is well-known that, before the solute molecules can self-assemble to form crystals, they must leave their solvation shell. Here, we show a previously unrecognized three-step mechanism of antisolvent-driven desolvation, where the antisolvent first enters the solvation shell due to attractive interactions with solute, followed by its reorganization and then expulsion of an antisolvent−solvent pair from the solvation shell due to repulsive forces. To confirm this mechanism, molecular simulations of histidine (solute) in water (solvent) at various concentrations of ethanol (antisolvent) and supersaturation are performed. The simulations reveal competitive binding of ethanol to hydrated histidine followed by its dewetting to allow significant solute−solute interactions for crystal growth. This threestep mechanism is then used to obtain an activation barrier for desolvation of histidine followed by prediction of crystal growth rates using a computationally inexpensive semiclassical approach. Growth rates obtained from the activation barrier reproduce the experimental growth rates reasonably, thereby validating the governing three-step mechanism for antisolvent crystallization.
G protein-coupled receptor (GPCR) association is an emerging paradigm with far reaching implications in the regulation of signalling pathways and therapeutic interventions. Recent super resolution microscopy studies have revealed that receptor dimer steady state exhibits sub-second dynamics. In particular the GPCRs, muscarinic acetylcholine receptor M (M1MR) and formyl peptide receptor (FPR), have been demonstrated to exhibit a fast association/dissociation kinetics, independent of ligand binding. In this work, we have developed a spatial kinetic Monte Carlo model to investigate receptor homo-dimerisation at a single receptor resolution. Experimentally measured association/dissociation kinetic parameters and diffusion coefficients were used as inputs to the model. To test the effect of membrane spatial heterogeneity on the simulated steady state, simulations were compared to experimental statistics of dimerisation. In the simplest case the receptors are assumed to be diffusing in a spatially homogeneous environment, while spatial heterogeneity is modelled to result from crowding, membrane micro-domains and cytoskeletal compartmentalisation or 'corrals'. We show that a simple association-diffusion model is sufficient to reproduce M1MR association statistics, but fails to reproduce FPR statistics despite comparable kinetic constants. A parameter sensitivity analysis is required to reproduce the association statistics of FPR. The model reveals the complex interplay between cytoskeletal components and their influence on receptor association kinetics within the features of the membrane landscape. These results constitute an important step towards understanding the factors modulating GPCR organisation.
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