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Daan Frenkel - One of the best experts on this subject based on the ideXlab platform.
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Numerical Simulation of Crystal Nucleation in Colloids
Advances in Polymer Science, 2020Co-Authors: Stefan Auer, Daan FrenkelAbstract:This article reviews the recent progress that has been made in the application of computer simulations to study Crystal Nucleation in colloidal systems. We discuss the concept and the numerical methods that allow for a quantitative prediction of Crystal Nucleation rates. The computed Nucleation rates are predicted from first principles and can be directly compared to experiments. These techniques have been applied to study Crystal Nucleation in hard-sphere colloids, polydisperse hard-sphere colloids, weakly charged or slightly soft colloids and hard- sphere colloids that are confined between two plane hard walls.
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Mechanism of two-step vapour–Crystal Nucleation in a pore
Molecular Physics, 2015Co-Authors: J. A. Van Meel, Daan FrenkelAbstract:We present a numerical study of the effect of hemispherical pores on the Nucleation of Lennard–Jones Crystals from the vapour phase. As predicted by Page and Sear, there is a narrow range of pore radii, where vapour–liquid Nucleation can become a two-step process. A similar observation was made for different pore geometries by Giacomello et al. We find that the maximum Nucleation rate depends on both the size and the adsorption strength of the pore. Moreover, a poe can be more effective than a planar wall with the same strength of attraction. Pore-induced vapour–liquid Nucleation turns out to be the rate-limiting step for Crystal Nucleation. This implies that Crystal Nucleation can be enhanced by a judicious choice of the wetting properties of a microporous nucleating agent.
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rate of homogeneous Crystal Nucleation in molten nacl
Journal of Chemical Physics, 2005Co-Authors: Chantal Valeriani, Eduardo Sanz, Daan FrenkelAbstract:We report a numerical simulation of the rate of Crystal Nucleation of sodium chloride from its melt at moderate supercooling. In this regime Nucleation is too slow to be studied with “brute force” molecular-dynamics simulations. The melting temperature of s“Tosi Fumi” d NaCl is ,1060 K. We studied Crystal Nucleation at T= 800 and 825 K. We observe that the critical nucleus formed during the Nucleation process has the Crystal structure of bulk NaCl. Interestingly, the critical nucleus is clearly faceted, the nuclei have a cubical shape. We have computed the Crystal-Nucleation rate using two completely different approaches, one based on an estimate of the rate of diffusive crossing of the Nucleation barrier, the other based on the forward flux sampling and transition interface sampling methods. We find that the two methods yield the same result within an order of magnitude. However, when we compare the extrapolated simulation data with the only available experimental results for NaCl Nucleation, we observe a discrepancy of nearly five orders of magnitude. We discuss the possible causes for this discrepancy. © 2005 American Institute of Physics . fDOI: 10.1063/1.1896348g
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Crystal Nucleation of colloidal suspensions under shear
Physical Review Letters, 2004Co-Authors: Ronald Blaak, Daan Frenkel, Stefan Auer, Hartmut LöwenAbstract:The formation of Crystals in a supercooled melt is a fascinating yet complex process. It is initiated by a microscopic Nucleation event. The resulting embryonic Crystal then grows to macroscopic size. Understanding the principles of Nucleation and growth is essential for many applications ranging from tailored protein Crystallization to metallurgy [1–3]. At present, the most detailed experimental information on Crystal Nucleation comes from hard-sphere colloids [4 –7]. Such suspensions are ideal to study Crystal formation, as the equilibrium and transport properties of hard-sphere colloids are well understood [8]. Moreover, recent progress in computer simulations has made it possible to predict the absolute rate of Crystal Nucleation in colloidal suspensions [9,10] and thus to compare with experiment. In the present Letter we explore the influence of shear flow on colloidal Crystal Nucleation. Note that applying shear is qualitatively different from the effect of pressure, temperature, or additives as the latter affect the thermodynamic driving force for Crystallization or the rate of Crystal growth. In contrast, a system under shear ends up in a nonequilibrium steady state. Several experimental studies of the effect of shear on Crystallization have been reported in the literature. Some of these report a shearinduced ordering of the liquid which enhances the Nucleation rate [11–14], while others [15,16] report the observation of shear-induced suppression of Crystallization. Both phenomena can be qualitatively understood: on the one hand, shear may induce layering in the metastable fluid, thus facilitating Crystal Nucleation. On the other hand, shear can remove matter from small Crystallites and thus works against the birth of Crystals. At present, it is not clear which mechanism is dominant, and under what conditions. In this Letter we combine the umbrella sampling technique from equilibrium Monte Carlo simulations with Brownian dynamics simulations to study this nonequilibrium problem. We confirm that shear suppresses Crystal Nucleation, at least for small shear rates, as found by Butler and Harrowell [17], and in addition characterize the associated critical nucleus. Below, we consider homogeneous Crystal Nucleation in a simple model for charge-stabilized colloidal suspensions subjected to linear shear flow. The charged colloidal particles interact via a repulsive Yukawa potential [8]
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quantitative prediction of Crystal Nucleation rates for spherical colloids a computational approach
Annual Review of Physical Chemistry, 2004Co-Authors: Stefan Auer, Daan FrenkelAbstract:This review discusses the recent progress that has been made in the application of computer simulations to study Crystal Nucleation in colloidal systems. We discuss the concept and the numerical methods that allow for a quantitative prediction of Crystal-Nucleation rates. The computed Nucleation rates are predicted from first principles and can be directly compared with experiments. These techniques have been applied to study Crystal Nucleation in hard-sphere colloids, polydisperse hard-sphere colloids, weakly charged or slightly soft colloids, and hard-sphere colloids that are confined between two-plane hard walls.
Ilya V. Karpov - One of the best experts on this subject based on the ideXlab platform.
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Field Induced Crystal Nucleation in Chalcogenide Phase Change Memory
Materials and Physics for Nonvolatile Memories, 2009Co-Authors: Marco Nardone, Mira Mitra, V G Karpov, Ilya V. KarpovAbstract:A summary is presented of our theoretical and experimental work over more than two years related to switching in chalcogenide glass phase change memory. As a significant addition to the well known experiments, we have studied switching under considerably lower voltages and elevated temperatures, as well as the statistics of switching events and relaxation oscillations. Our analytical theory, based on field induced Crystal Nucleation, predicts all of our observed features and their dependencies on material parameters.
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Crystal Nucleation in glasses of phase change memory
Journal of Applied Physics, 2008Co-Authors: V G Karpov, Mira Mitra, Yu. A. Kryukov, Ilya V. KarpovAbstract:We propose a theory of field induced Crystal Nucleation in disordered glass structure applicable to chalcogenide phase change memory. In the region of symmetry breaking strong electric fields, the Nucleation is dominated by cylinder shaped particles with bias dependent Nucleation barriers. Statistical fluctuations in microscopic structure of a glass translate into probabilistic distributions of induction times and threshold voltages having respectively log-normal and normal shape. These distributions are exponentially sensitive to the applied voltage, temperature, and material parameters.
Stefan Auer - One of the best experts on this subject based on the ideXlab platform.
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Numerical Simulation of Crystal Nucleation in Colloids
Advances in Polymer Science, 2020Co-Authors: Stefan Auer, Daan FrenkelAbstract:This article reviews the recent progress that has been made in the application of computer simulations to study Crystal Nucleation in colloidal systems. We discuss the concept and the numerical methods that allow for a quantitative prediction of Crystal Nucleation rates. The computed Nucleation rates are predicted from first principles and can be directly compared to experiments. These techniques have been applied to study Crystal Nucleation in hard-sphere colloids, polydisperse hard-sphere colloids, weakly charged or slightly soft colloids and hard- sphere colloids that are confined between two plane hard walls.
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Crystal Nucleation of colloidal suspensions under shear
Physical Review Letters, 2004Co-Authors: Ronald Blaak, Daan Frenkel, Stefan Auer, Hartmut LöwenAbstract:The formation of Crystals in a supercooled melt is a fascinating yet complex process. It is initiated by a microscopic Nucleation event. The resulting embryonic Crystal then grows to macroscopic size. Understanding the principles of Nucleation and growth is essential for many applications ranging from tailored protein Crystallization to metallurgy [1–3]. At present, the most detailed experimental information on Crystal Nucleation comes from hard-sphere colloids [4 –7]. Such suspensions are ideal to study Crystal formation, as the equilibrium and transport properties of hard-sphere colloids are well understood [8]. Moreover, recent progress in computer simulations has made it possible to predict the absolute rate of Crystal Nucleation in colloidal suspensions [9,10] and thus to compare with experiment. In the present Letter we explore the influence of shear flow on colloidal Crystal Nucleation. Note that applying shear is qualitatively different from the effect of pressure, temperature, or additives as the latter affect the thermodynamic driving force for Crystallization or the rate of Crystal growth. In contrast, a system under shear ends up in a nonequilibrium steady state. Several experimental studies of the effect of shear on Crystallization have been reported in the literature. Some of these report a shearinduced ordering of the liquid which enhances the Nucleation rate [11–14], while others [15,16] report the observation of shear-induced suppression of Crystallization. Both phenomena can be qualitatively understood: on the one hand, shear may induce layering in the metastable fluid, thus facilitating Crystal Nucleation. On the other hand, shear can remove matter from small Crystallites and thus works against the birth of Crystals. At present, it is not clear which mechanism is dominant, and under what conditions. In this Letter we combine the umbrella sampling technique from equilibrium Monte Carlo simulations with Brownian dynamics simulations to study this nonequilibrium problem. We confirm that shear suppresses Crystal Nucleation, at least for small shear rates, as found by Butler and Harrowell [17], and in addition characterize the associated critical nucleus. Below, we consider homogeneous Crystal Nucleation in a simple model for charge-stabilized colloidal suspensions subjected to linear shear flow. The charged colloidal particles interact via a repulsive Yukawa potential [8]
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quantitative prediction of Crystal Nucleation rates for spherical colloids a computational approach
Annual Review of Physical Chemistry, 2004Co-Authors: Stefan Auer, Daan FrenkelAbstract:This review discusses the recent progress that has been made in the application of computer simulations to study Crystal Nucleation in colloidal systems. We discuss the concept and the numerical methods that allow for a quantitative prediction of Crystal-Nucleation rates. The computed Nucleation rates are predicted from first principles and can be directly compared with experiments. These techniques have been applied to study Crystal Nucleation in hard-sphere colloids, polydisperse hard-sphere colloids, weakly charged or slightly soft colloids, and hard-sphere colloids that are confined between two-plane hard walls.
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line tension controls wall induced Crystal Nucleation in hard sphere colloids
Physical Review Letters, 2003Co-Authors: Stefan Auer, Daan FrenkelAbstract:We report on a numerical study of the effect of a smooth, hard wall on the Crystallization of hard-sphere colloids. We find that the presence of the wall drastically lowers the barrier for Crystal Nucleation, but it does not eliminate it. Crystal Nucleation becomes noticeable at pressures that are some 5% above the coexistence value. The first particles to Crystallize on the wall form a (111) plane. Initially, this Crystallite grows laterally, rather than in the third dimension. The free energy of the critical Crystal nucleus on the wall is about 2 orders of magnitudes lower than in the bulk. Analysis of the numerical data indicates that, at coexistence, the (111) plane is at the threshold of wetting the wall. The Nucleation barrier is dominated by line tension.
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prediction of absolute Crystal Nucleation rate in hard sphere colloids
Nature, 2001Co-Authors: Stefan Auer, Daan FrenkelAbstract:Crystal Nucleation is a much-studied phenomenon, yet the rate at which it occurs remains difficult to predict. Small Crystal nuclei form spontaneously in supersaturated solutions, but unless their size exceeds a critical value—the so-called critical nucleus—they will re-dissolve rather than grow. It is this rate-limiting step that has proved difficult to probe experimentally. The Crystal Nucleation rate depends on Pcrit, the (very small) probability that a critical nucleus forms spontaneously, and on a kinetic factor (κ) that measures the rate at which critical nuclei subsequently grow. Given the absence of a priori knowledge of either quantity, classical Nucleation theory1 is commonly used to analyse Crystal Nucleation experiments, with the unconstrained parameters adjusted to fit the observations. This approach yields no ‘first principles’ prediction of absolute Nucleation rates. Here we approach the problem from a different angle, simulating the Nucleation process in a suspension of hard colloidal spheres, to obtain quantitative numerical predictions of the Crystal Nucleation rate. We find large discrepancies between the computed Nucleation rates and those deduced from experiments2,3,4: the best experimental estimates of Pcrit seem to be too large by several orders of magnitude.
Wenbing Hu - One of the best experts on this subject based on the ideXlab platform.
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Chain-Folding via Intramolecular Crystal Nucleation: Theory and Simulations
2020Co-Authors: Wenbing HuAbstract:Chain folding reflects a natural wisdom of a single macromolecule seeking for its native state to optimize the parallel packing of regular sequences and their contacts with surroundings at low temperatures. The beta-sheet formation upon protein folding is a typical example. Chain folding has also been widely observed in lamellar Crystallites grown from bulk polymer systems. Can we associate these two cases together, i.e. supposing that the folding process of single chain dominates the Crystal growth of bulk polymers? For a positive answer, we discuss the intramolecular Crystal Nucleation model, by applying the classical Nucleation theory to the single-chain system.[1] For the primary Crystal Nucleation in a single chain, assuming the single extended chain buried inside the fully ordered bulk phase as its ground state, the free energy of the single chain is F=nf+s(N-n)^(2/3), where n is the number of molten units, f is the free energy of each molten unit, N is the chain length, and s the surface free energy absorbing all prefactors. The free energy barrier for primary Crystal Nucleation is thus F_c=4s^3/(27f^2). Since f can be approximated as proportional to the supercooling, this barrier shows a proper supercooling dependence for the primary Crystal Nucleation in bulk polymers, in addition to the chain-length independence. Quantitative evidences of the results have been obtained from the molecular simulations.[2] The similar situation exists for the secondary (two-dimensional) Crystal Nucleation of the single chain on a smooth Crystal growth front, where the free energy F=nf+s(N-n)^(1/2). Here values of F, f and s are variable from the case of primary Crystal Nucleation. Then, the free energy barrier for the secondary Crystal Nucleation becomes F_c=c^2/(4f), which shows again the chain-length independence and a proper supercooling dependence for Crystal growth from bulk polymers. Quantitative evidences of the results can be found in experimental observations. [2] Corresponding to a Crystallization temperature for the intramolecular Nucleation as the dominant mode of secondary Crystal Nucleation from bulk polymers, there exists an equilibrium melting point of two-dimensional (2D) single-chain single Crystal, which defines a critical chain length N_c=(s/f)^2 increasing with the Crystallization temperature.[3] For a polydisperse polymer sample at high Crystallization temperatures, those polymer fractions shorter than N_c will be spontaneously excluded from the Crystal growth front, giving rise to the molecular segregation phenomenon. This 2D melting point is much lower than the equilibrium melting points of bulk extended-chain Crystals and extended-infinitely-long-chain Crystals, indicating a large prerequisite supercooling to initiate the Crystal growth of the criticallength polymers. On the other hand, at low temperatures, polymer fractions with their chain lengths multifold larger than N_c will exhibit multiple Nucleation along the chain either in the same Crystals or in the separate Crystals, producing the variable-cluster conformation typical in the semiCrystalline texture of polymers.[4] As a preliminary test, we apply the intramolecular Nucleation model to interpret the intrinsic regime transitions of the Crystal growth rate upon the temperature changes, following the framework constructed by the thankworthy Hoffman's theory.[5] To this end, we assume that at the growth front, the intramolecular Nucleation is instantly initiated by a local slack chain with the part of chain length S. After the usually clumsy Nucleation, an instant reorganization process followed with the lateral spreading of the surface Crystal has to provide an enough large and perfect growth front to host the subsequent surface Nucleation. The instant reorganization includes a fast perfection process together with quick thickening and spreading fed by the local slack chain. The following spreading will pull the polymer chain from the amorphous surroundings, which is relatively slow due to a long-distance diffusion of the chain. In regime I, the instant reorganization and the subsequent spreading can provide the growth front on time to the next slow Nucleation event at high temperatures. So the advancing of the growth front is dominated by the intramolecular secondary Nucleation, with a rate 1/t =iL, where t is the incubation period of Nucleation, i is the Nucleation rate per area, and L is the area of the growth front which can be instantly reached by the local slack chain. L∼lbS^(1/2), where l is the front thickness, b is the linear size of the chain unit, bS^(1/2) is thus the linear size of the slack coil. L has its temperature dependence much weaker than the Nucleation rate. We assume L>b^2S, i.e. l>bS^(1/2). In regime II, the lateral spreading rate becomes less fast compared to the fast surface Nucleation at lower temperatures (L_s=2gt lbN_c^(1/2)) of the growth front to the subsequent surface Nucleation. Again, the advancing of the growth front is dominated by the intramolecular secondary Nucleation, with a rate 1/t=ib^2S. It should be mentioned that for polymers with ultra-high molecular weight or in lightly cross-linked, the pulling will be prohibited by the entanglements rich between Crystallites, by multiple nuclei along the chain, or by the cross-links. At high temperatures, the length of the local slack chain can be expanded with an up-limit by repeated trying of Crystal Nucleation to reach the critical chain length, so the Crystal growth is forced to stay only in regime III with a low growth rate and a low Crystallinity.[7] In summary, the origin of the adjacent chain folding in polymer Crystallites can be described as the intramolecular Crystal Nucleation. The eventual degree of adjacent chain folding is related with the extent of lateral spreading allowed in each regime of Crystal growth. In a broad sense, the intramolecular Nucleation model does not reject the intermolecular Nucleation process that may be essential in the initiation of Crystallization from very short chains, from very rigid chains, from stretched chains, or from the polymerization process, etc. In fact, it only provides an explanation to the free energy barrier in the rate equations of the primary and secondary Crystal Nucleation processes. The other terms in the rate equations (such as the molecular-weight effect in the prefactor[6]) and the other processes before or after the ratedetermining step (such as the saturated metastable Crystal thickness) will also be considered, as can be found from the literatures, to figure out a comprehensive description to polymer Crystallization behaviors.
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Effect of comonomer sizes on the strain-induced Crystal Nucleation of random copolymers
European Polymer Journal, 2016Co-Authors: Yixian Wu, Wenbing HuAbstract:Abstract We performed dynamic Monte Carlo simulations of random copolymers containing variable sliding mobility of non-Crystallizable comonomer sequences (reflecting their relative sizes) in the Crystalline monomer regions. Upon raising strains, we observed that the comononer sliding mobility does not affect the strain evolution curves of Crystallinity. However, in the middle temperature region, the low mobility causes a delay of switching from the intra-molecular to the inter-molecular modes of Crystal Nucleation in the copolymers holding low fractions of comonomers. We attributed the effect to the difficulty of comonomers to be excluded from the nucleating domains that are limited by sequence segregation in the oriented amorphous segments. The implication of this effect to the efficiency of Crystal Nucleation upon cyclic loading has been discussed.
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Intramolecular Crystal Nucleation Favored by Polymer Crystallization: Monte Carlo Simulation Evidence
Journal of Physical Chemistry B, 2016Co-Authors: Rong Zhang, Wenbing HuAbstract:We performed dynamic Monte Carlo simulations of half–half binary blends of symmetric (double and mutual) Crystallizable polymers. We separately enhanced the driving forces for polymer-uniform and polymer-staggered Crystals. Under parallel enhancements, polymer-uniform Crystals exhibit faster Nucleation and growth, with more chain folding and less lamellar thickening, than those in polymer-staggered Crystals. We attributed the results to intramolecular Crystal Nucleation, ruined by enhanced polymer-staggered Crystallization. Our observations provide direct molecular-level evidence to support the fact that intramolecular Crystal Nucleation is favored by polymer Crystallization in quiescent solutions and melt, which yields chain folding for the characteristic β-sheet or lamellar morphology of macromolecular Crystals.
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How Polydispersity of Network Polymers Influences Strain-induced Crystal Nucleation in a Rubber
Chinese Journal of Polymer Science, 2014Co-Authors: Miao-miao Zhang, Wenbing HuAbstract:Network polymers in a rubber or a gel often contain non-uniform chain lengths. By means of dynamic Monte Carlo simulations of polymer mixtures with various compositions of two chain lengths, we investigated how the factor of polydispersity influences their strain-induced Crystal Nucleation. Under a high temperature and a high strain rate, the stretching of both polymers revealed that Crystal Nucleation is mainly accelerated by the presence of short-chain polymers; nevertheless, both polymers join together in the Nucleation process. Further analysis proved that Crystal Nucleation is initiated from those highly stretched short segments, which are rich on the short-chain polymers.
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Understanding Crystal Nucleation in solution-segregated polymers
Polymer, 2009Co-Authors: Wenbing HuAbstract:We report dynamic Monte Carlo simulations of Crystal Nucleation in polymer bulk phase segregated from solutions. We found that poorer solvent enhances Crystal Nucleation in the concentrated phase of polymers. In addition, when the solvent becomes poor enough, Crystal Nucleation prefers to occur at the diffuse interfaces. The results are consistent with the predictions from theoretical phase diagrams, but something different from immiscible polymer blends. The surface-enhanced Crystallization may explain the bowl-shaped Crystal aggregates observed experimentally in poor solvent.
V G Karpov - One of the best experts on this subject based on the ideXlab platform.
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Field Induced Crystal Nucleation in Chalcogenide Phase Change Memory
Materials and Physics for Nonvolatile Memories, 2009Co-Authors: Marco Nardone, Mira Mitra, V G Karpov, Ilya V. KarpovAbstract:A summary is presented of our theoretical and experimental work over more than two years related to switching in chalcogenide glass phase change memory. As a significant addition to the well known experiments, we have studied switching under considerably lower voltages and elevated temperatures, as well as the statistics of switching events and relaxation oscillations. Our analytical theory, based on field induced Crystal Nucleation, predicts all of our observed features and their dependencies on material parameters.
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Crystal Nucleation in glasses of phase change memory
Journal of Applied Physics, 2008Co-Authors: V G Karpov, Mira Mitra, Yu. A. Kryukov, Ilya V. KarpovAbstract:We propose a theory of field induced Crystal Nucleation in disordered glass structure applicable to chalcogenide phase change memory. In the region of symmetry breaking strong electric fields, the Nucleation is dominated by cylinder shaped particles with bias dependent Nucleation barriers. Statistical fluctuations in microscopic structure of a glass translate into probabilistic distributions of induction times and threshold voltages having respectively log-normal and normal shape. These distributions are exponentially sensitive to the applied voltage, temperature, and material parameters.