Rate of homogeneous crystal nucleation in molten NaCl

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 ("Tosi Fumi") NaCl is approximately 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.     

Crystal nucleation of colloidal hard dumbbells

Using computer simulations, we investigate the homogeneous crystal nucleation in suspensions of colloidal hard dumbbells. The free energy barriers are determined by Monte Carlo simulations using the umbrella sampling technique. We calculate the nucleation rates for the plastic crystal and the aperiodic crystal phase using the kinetic prefactor as determined from event driven molecular dynamics simulations. We find good agreement with the nucleation rates determined from spontaneous nucleation events observed in event driven molecular dynamics simulations within error bars of one order of magnitude. We study the effect of aspect ratio of the dumbbells on the nucleation of plastic and aperiodic crystal phases, and we also determine the structure of the critical nuclei. Moreover, we find that the nucleation of the aligned close-packed crystal structure is strongly suppressed by a high free energy barrier at low supersaturations and slow dynamics at high supersaturations.     

Atomistic simulation of the homogeneous nucleation and of the growth of N2 crystallites

We report on a computer simulation study of the early stages of the crystallization of molecular nitrogen. First, we study how homogeneous nucleation takes place in supercooled liquid N(2) for a moderate degree of supercooling. Using the umbrella sampling technique, we determine the free energy barrier of formation for a critical nucleus of N(2). We show that, in accord with Ostwald's rule of stages, the structure of the critical nucleus is predominantly that of a metastable polymorph (alpha-N(2) for the state point investigated). We then monitor the evolution of several critical nuclei through a series of unbiased molecular dynamics trajectories. The growth of N(2) crystallites is accompanied by a structural evolution toward the stable polymorph beta-N(2). The microscopic mechanism underlying this evolution qualitatively differs from that reported previously. We do not observe any dissolution or reorganization of the alpha-like core of the nucleus. On the contrary, we show that alpha-like and beta-like blocks coexist in postcritical nuclei. We relate the structural evolution to a greater adsorption rate of beta-like molecules on the surface and show that this transition actually starts well within the precritical regime. We also carefully investigate the effect of the system size on the height of the free energy barrier of nucleation and on the structure and size of the critical nucleus.     

Crystal nucleation in binary hard sphere mixtures: a Monte Carlo simulation study

We present calculations of the nucleation barrier during crystallization in binary hard sphere mixtures under moderate degrees of supercooling using Monte Carlo simulations in the isothermal-isobaric semigrand ensemble in conjunction with an umbrella sampling technique. We study both additive and negatively nonadditive binary hard sphere systems. The solid-fluid phase diagrams of such systems show a rich variety of behavior, ranging from simple spindle shapes to the appearance of azeotropes and eutectics to the appearance of substitutionally ordered solid phase compounds. We investigate the effect of these types of phase behavior upon the nucleation barrier and the structure of the critical nucleus. We find that the underlying phase diagram has a significant effect on the mechanism of crystal nucleation. Our calculations indicate that fractionation of the species upon crystallization increases the difficulty of crystallization of fluid mixtures and in the absence of fractionation (azeotropic conditions) the nucleation barrier is comparable to pure fluids. We also calculate the barrier to nucleation of a substitutionally ordered compound solid. In such systems, which also show solid-solid phase separation, we find that the phase that nucleates is the one whose equilibrium composition is closer to the composition of the fluid phase.     

Pore nucleation in mechanically stretched bilayer membranes

We report a computer-simulation study of the free-energy barrier for the nucleation of pores in the bilayer membrane under constant stretching lateral pressure. We find that incipient pores are hydrophobic but as the lateral size of the pore nucleus becomes comparable with the molecular length, the pore becomes hydrophilic. In agreement with previous investigations, we find that the dynamical process of growth and closure of hydrophilic pores is controlled by the competition between the surface tension of the membrane and the line tension associated with the rim of the pore. We estimate the line tension of a hydrophilic pore from the shape of the computed free-energy barriers. The line tension thus computed is in a good agreement with available experimental data. We also estimate the line tension of hydrophobic pores at both macroscopic and microscopic levels. The comparison of line tensions at these two different levels indicates that the "microscopic" line tension should be carefully distinguished from the "macroscopic" effective line tension used in the theoretical analysis of pore nucleation. The overall shape of the free-energy barrier for pore nucleation shows no indication for the existence of a metastable intermediate during pore nucleation.     

Slow dynamics of the high density Gaussian core model

We numerically study crystal nucleation and glassy slow dynamics of the one-component Gaussian core model (GCM) at high densities. The nucleation rate at a fixed supercooling is found to decrease as the density increases. At very high densities, the nucleation is not observed at all in the time window accessed by long molecular dynamics (MD) simulation. Concomitantly, the system exhibits typical slow dynamics of the supercooled fluids near the glass transition point. We compare the simulation results of the supercooled GCM with the predictions of mode-coupling theory (MCT) and find that the agreement between them is better than any other model glassformers studied numerically in the past. Furthermore, we find that a violation of the Stokes-Einstein relation is weaker and the non-Gaussian parameter is smaller than canonical glassformers. Analysis of the probability distribution of the particle displacement clearly reveals that the hopping effect is strongly suppressed in the high density GCM. We conclude from these observations that the GCM is more amenable to the mean-field picture of the glass transition than other models. This is attributed to the long-ranged nature of the interaction potential of the GCM in the high density regime. Finally, the intermediate scattering function at small wavevectors is found to decay much faster than its self part, indicating that dynamics of the large-scale density fluctuations decouples with the shorter-ranged caging motion.     

Free energy landscapes for homogeneous nucleation of ice for a monatomic water model

We simulate the homogeneous nucleation of ice from supercooled liquid water at 220 K in the isobaric-isothermal ensemble using the MW monatomic water potential. Monte Carlo simulations using umbrella sampling are performed in order to determine the nucleation free energy barrier. We find the Gibbs energy profile to be relatively consistent with that predicted by classical nucleation theory; the free energy barrier to nucleation was determined to be ~18 k(B)T and the critical nucleus comprised ~85 ice particles. Growth from the supercooled liquid gives clusters that are predominantly cubic, whilst starting with a pre-formed subcritical nucleus of cubic or hexagonal ice results in the growth of predominantly that phase of ice only.     

On the coupling between slow diffusion transport and barrier crossing in nucleation

We model the coupling between slow diffusion transport and nucleation using the diffusion equation, an Ostwald-Freundlich boundary condition, and a mass balance linking nucleus size to flux across the nucleus-solution interface. The model retains some characteristics of the classical nucleation theory because of the common theoretical foundations behind classical nucleation theory and the Ostwald-Freundlich equation. For example, the classically critical-sized nucleus in the uniform supersaturated concentration field is an unstable equilibrium point. However, the model also shows that certain types of concentration profiles can drive a classically pre-critical nucleus over the nucleation barrier. We identify the separatrix as a function of both nucleus size and characteristics of the local concentration field. Our analysis may be useful for understanding the effects of local concentration fluctuations and especially for understanding the role of dense precursor particles in driving two-step nucleation processes. Our analysis may also provide a starting point for further statistical field theory analyses of local concentration fluctuations and their effects on nucleation rates.     

氩蒸气在球形固体颗粒上异质核化的分子动力学模拟

异质核化在大气中广泛存在, 但是其微观核化机理鲜为人知, 本文应用分子动力学方法模拟过热氩蒸气在纳米球形固体颗粒物上异质核化的动态特性, 讨论不同的冷却率对核化过程中系综温度、团簇分布、团簇大小以及核化速率的影响. 结果显示, 系综内蒸气的核化温度随着冷却率的增加而降低, 预先存在的球形固体颗粒在团簇的形成阶段起着重要的作用, 而且存在一个临界冷却率1.80×10^-9J·s^-1. 在该冷却率下, 在异质核化系综内均质核化出现, 并与异质核化共存, 但是异质核化在整个核化过程中仍然占主导地位.     

Heterogeneous and homogeneous nucleation compared: rapid nucleation on microscopic impurities

We use computer simulation to calculate the rates of both homogeneous nucleation and heterogeneous nucleation on microscopic impurities. We do so in perhaps the simplest model of fluids and magnets: the two-dimensional Ising model. We expect our results to be qualitatively applicable to many simple and complex fluids. We find that heterogeneous nucleation on an impurity that is not only microscopic but also as small as possible, that is, a single fixed spin, is more than four orders of magnitude faster than homogeneous nucleation. The rate of heterogeneous nucleation then increases by a factor of approximately five for each additional fixed spin in the impurity. These results suggest that impurities as small as single molecules can result in homogeneous nucleation being irrelevant due to heterogeneous nucleation on these microscopic impurities being much faster.     

Spinodal for the solution-to-crystal phase transformation

The formation of crystalline nuclei from solution has been shown for many systems to occur in two steps: the formation of quasidroplets of a disordered intermediate, followed by the nucleation of ordered crystalline embryos within these droplets. The rate of each step depends on a respective free-energy barrier and on the growth rate of its near-critical clusters. We address experimentally the relative significance of the free-energy barriers and the kinetic factors for the nucleation of crystals from solution using a model protein system. We show that crystal nucleation is 8-10 orders of magnitude slower than the nucleation of dense liquid droplets, i.e., the second step is rate determining. We show that at supersaturations of three or four k(B)T units, crystal nuclei of five, four, or three molecules transform into single-molecule nuclei, i.e., the significant nucleation barrier vanishes below the thermal energy of the molecules. We show that the main factor, which determines the rate of crystal nucleation, is the slow growth of the near-critical ordered clusters within the quasidroplets of the disordered intermediate. Analogous to the spinodal in supersaturated fluids, we define a solution-to-crystal spinodal from the transition to single-molecule crystalline nuclei. We show that heterogeneous nucleation centers accelerate nucleation not only because of the wettinglike effects that lower the nucleation barrier, as envisioned by classical theory, but by helping the kinetics of growth of the ordered crystalline embryos.     

Enhanced protein crystallization around the metastable critical point

We report on a computer-simulation study of homogeneous crystal nucleation in a model for globular proteins. We find that the presence of a metastable vapour-liquid critical point drastically changes the pathway for the formation of a critical nucleus. But what is more important, the large density fluctuations near the critical point also lowers the free-energy barrier to nucleation and hence increases the nucleation rate. As␣the location of the vapour-liquid critical point can be controlled by changing the solvent conditions, our simulation results suggest a guided approach to protein crystallization. Received: 4 June 1998/Accepted: 3 September 1998 / Published online: 10 December 1998     

Melting dynamics of superheated argon: nucleation and growth

We investigate the microscopic melting process of a superheated argon solid using molecular dynamics simulations. We characterize the melting dynamics by following the temperature and time evolutions of liquid atoms and demonstrate the formation of a critical liquid nucleus via fluctuations and subsequent growth. The critical liquid nucleus size (about 120 atoms) obtained from our direct simulations is in accord with the prediction of the classical nucleation theory. The dynamic nucleation and growth of liquid also agree with the Johnson-Mehl-Avrami law, and the growth exponent n approximately 3 at the early stage followed by a substantial increase in n thereafter.     

Nonclassical nucleation kinetics in the crystallization of a supercooled melt

A molecular dynamics simulation of homogenous nucleation of a crystal in supercooled aluminum melt is performed. Nucleation rates at a temperature of 900 K in the range of pressures from 12 to 15 GPa are calculated. Analysis of the mean first-passage times of crystalline cluster sizes is performed. A stepwise dependence of the mean first-passage time on crystal nucleus size is observed, in contrast to the sigmoidal dependence that follows from classical nucleation theory. Based on the data from atomistic simulations, it is established that the form of the free energy barrier during nucleation differs significantly from the one assumed in classical nucleation theory for a spherically symmetric nucleus. It is supposed that the observed differences are apparently due to the complex structure of the crystalline nucleus.     

Reorganization and growth of metastable alpha-N2 critical nuclei into stable beta-N2 crystals

We report on results on the crystal nucleation and growth of nitrogen. Using molecular dynamics simulations, we show that while nucleation proceeds into the metastable alpha-phase (i.e., the crystalline phase associated with the lowest free energy barrier of formation), growth of the crystallite proceeds through a reorganization of the nucleus into the thermodynamically stable beta-phase.     

Heterogeneous critical nucleation on a completely wettable substrate

Heterogeneous nucleation of a new bulk phase on a flat substrate can be associated with the surface phase transition called wetting transition. When this bulk heterogeneous nucleation occurs on a completely wettable flat substrate with a zero contact angle, the classical nucleation theory predicts that the free-energy barrier of nucleation vanishes. In fact, there always exists a critical nucleus and a free-energy barrier as the first-order prewetting transition will occur even when the contact angle is zero. Furthermore, the critical nucleus changes its character from the critical nucleus of surface phase transition below bulk coexistence (undersaturation) to the critical nucleus of bulk heterogeneous nucleation above the coexistence (oversaturation) when it crosses the coexistence. Recently, Sear [J. Chem. Phys. 129, 164510 (2008)] has shown, by a direct numerical calculation of nucleation rate, that the nucleus does not notice this change when it crosses the coexistence. In our work, the morphology and the work of formation of critical nucleus on a completely wettable substrate are re-examined across the coexistence using the interface-displacement model. Indeed, the morphology and the work of formation changes continuously at the coexistence. Our results support the prediction of Sear and will rekindle the interest on heterogeneous nucleation on a completely wettable substrate.     

A Unified Thermodynamic Model of Flow-induced Crystallization of Polymer

We propose a unified thermodynamic model of flow-induced crystallization of polymer (uFIC),which incorporates not only the conformational entropy reduction but also the contributions of flow-induced chain orientation,the interaction of ordered segments,and the free energy of crystal nucleus and crystal morphology.Specifically,it clarifies the determining parameters of the critical crystal nucleus size,and is able to account for the acceleration of nucleation,the emergence of precursor,different crystal morphologies and structures induced by flow.Based on the nucleation barrier under flow,we analyze at which condition precursor may occur and how flow affects the competition among different crystal forms such as orthorhombic and hexagonal phases of polyethylene.According to the uFIC model,the different crystal morphologies and structures in the flow-temperature space have been clarified,which give a good agreement with experiments of FIC.     

Nucleation rates in a new phenomenological model

In this paper we develop a new theory to evaluate the nucleation rate in the framework of the EMLD-DNT model. Beyond the model, our theory deals with cluster translation and exclusion, effects that have been virtually ignored in classical nucleation theory. We apply the model to the case of 1-pentanol, and compare the predictions with experimental results. We find an excellent agreement between the nucleation rate predicted by our theory and experimental data. The distinguishing feature of the model is its ability to predict successfully the rate of formation of the critical nucleus without the use of an intermolecular potential, employing only macroscopic thermodynamic properties.     

Atomistic theory of amyloid fibril nucleation

We consider the nucleation of amyloid fibrils at the molecular level when the process takes place by a direct polymerization of peptides or protein segments into β-sheets. Employing the atomistic nucleation theory (ANT), we derive a general expression for the work to form a nanosized amyloid fibril (protofilament) composed of successively layered β-sheets. The application of this expression to a recently studied peptide system allows us to determine the size of the fibril nucleus, the fibril nucleation work, and the fibril nucleation rate as functions of the supersaturation of the protein solution. Our analysis illustrates the unique feature of ANT that the size of the fibril nucleus is a constant integer in a given supersaturation range. We obtain the ANT nucleation rate and compare it with the rates determined previously in the scope of the classical nucleation theory (CNT) and the corrected classical nucleation theory (CCNT). We find that while the CNT nucleation rate is orders of magnitude greater than the ANT one, the CCNT and ANT nucleation rates are in very good quantitative agreement. The results obtained are applicable to homogeneous nucleation, which occurs when the protein solution is sufficiently pure and/or strongly supersaturated.     

Sensitivity of nucleation phenomena on range of interaction potential

Theoretical and computational investigations of nucleation have been plagued by the sensitivity of the phase diagram to the range of the interaction potential. As the surface tension depends strongly on the range of interaction potential and as the classical nucleation theory (CNT) predicts the free energy barrier to be directly proportional to the cube of the surface tension, one expects a strong sensitivity of nucleation barrier to the range of the potential; however, CNT leaves many aspects unexplored. We find for gas-liquid nucleation in Lennard-Jones system that on increasing the range of interaction the kinetic spinodal (KS) (where the mechanism of nucleation changes from activated to barrierless) shifts deeper into the metastable region. Therefore the system remains metastable for larger value of supersaturation and this allows one to explore the high metastable region without encountering the KS. On increasing the range of interaction, both the critical cluster size and pre-critical minima in the free energy surface of kth largest cluster, at respective kinetic spinodals, shift towards smaller cluster size. In order to separate surface tension contribution to the increase in the barrier from other non-trivial factors, we introduce a new scaling form for surface tension and use it to capture both the temperature and the interaction range dependence of surface tension. Surprisingly, we find only a weak non-trivial contribution from other factors to the free energy barrier of nucleation.