Interfacial nematodynamics of heterogeneous curved isotropic-nematic moving fronts

The early stages of liquid crystal phase ordering upon thermal quenches of isotropic phases into unstable and metastable temperature ranges is studied using two-dimensional (2D) computational solutions of the governing Landau-de Gennes (L-dG) equations for low molar mass nematic liquid crystals and analysis based on the corresponding interfacial nematodynamic model. The early phase ordering stage, for both unstable and metastable quenches of the isotropic phase, is shown to lead to highly textured nematic spherulites through a mechanism of interfacial defect nucleation. The underlying mechanisms of interface-driven texturing are elucidated using complementary 2D computational parametric studies of the bulk L-dG equation and analysis of the IN model. It is shown that for highly curved nanodomains and realistic elastic anisotropy, sharp interfacial transitions between uniaxial and biaxial states arise and are resolved by interfacial defect nucleation, which upon subsequent migration into the spherulite's interior leads to strong texturing. This paper shows that texture formation in the early stages of phase ordering is interface driven, and due to low interface tension, elastic anisotropy, and large curvature. Interfacial defect shedding in highly curved, low tension, anisotropic interfaces is a significant defect nucleation mechanism that needs to be taken into account when considering texturing processes.     

Molecular dynamics investigation of the transient regime in the freezing of salt clusters

Molecular dynamics (MD) investigations of the freezing of supercooled liquids can identify nuclei far smaller than can be detected in laboratory experiments, to date, and consequently can provide information about nucleation so far inaccessible to experiment. In a recent MD study of the freezing of clusters of SeF6, a new method of recording nucleation events was introduced. It involved the observation of times of first appearance of nuclei of the size of n. An advantage of the new approach is that it provides information about the size of the critical nucleus. For nuclei smaller than the critical size, it also avoids the overshoots of nucleation rates that precluded the application of the Miloshev-Wu method in the subcritical region. Kinetic information in the transient regime can be characterized by three parameters, the time lag, the reduced moment, and the steady state nucleation rate. To get some idea of how general the new approach is, a very different system was investigated, that of clusters of NaCl. Two different fitting functions were used to analyze the results. The first one adopted the log-normal probability distribution of Wu. The second function was a modification of Shneidman's analytical solution appropriate for large nuclei. The second function gave a rather good account of MD data for all nuclear sizes and temperatures and gave more stable results in the subcritical region. Several inferences of the sizes of critical nuclei were made. Applying the criterion for n* based on the Zeldovich solution of the Becker-D?ring equations, we estimated the critical nucleus sizes to be 14, 18, and 24 ions for quench temperatures of 640, 690, and 740 K, respectively. Even though the interionic interactions initiating nucleation in salt are very different from the van der Waals interactions in clusters of SeF6, the characteristic aspects of the transient regimes of the two systems were quite similar.     

Macrophase and microphase separations for surfactants adsorbed on solid surfaces: a gauge cell monte carlo study in the lattice model

By combining the gauge cell method and lattice model, we study the surface phase transition and adsorption behaviors of surfactants on a solid surface. Two different cases are considered in this work: macrophase transition and adsorption in a single-phase region. For the case of macrophase transition, where two phases coexist, we investigate the shape and size of the critical nuclei and determine the height of the nucleation barrier. It is found that the nucleation depends on the bulk surfactant concentration. Our simulations show that there exist a critical temperature and critical adsorption energy, below which the transition from low-affinity adsorption to the bilayer structure shows the characteristic of a typical first-order phase transition. Such a surface phase transition in the adsorption isotherm is featured by a hysteresis loop. The hysteresis loop becomes narrower at higher temperature and weaker adsorption energy and finally disappears at the critical value. For the case where no macrophase transition occurs, we study the adsorption isotherm and microphase separation in a single-phase region. The simulation results indicate that the adsorption isotherm in adsorption processes is divided into four regions in a log-log plot, being in agreement with experimental observations. In this work, the four regions are called the low-affinity adsorption region, the hemimicelle region, the morphological transition region, and the plateau region. Simulation results reveal that in the second region the adsorbed monomers aggregate and nucleate hemimicelles, while adsorption in the third region is accompanied by morphological transitions.     

Influence of initial conditions on homogeneous nucleation kinetics in a closed system

The formation of nuclei of a new phase from the supersaturated mother phase in a closed system is studied. The depletion of the mother phase due to phase transition is taken into account. Basic kinetic equations describing such process are solved numerically to determine the number density of nuclei of newly forming phase and nucleation rate. It is shown that in contrary to the standard nucleation model, when the depletion of the mother phase is not taken into account, the initial size distribution of the clusters affects considerably the nucleation process at higher supersaturations. Our model starts with the equilibrium size distribution of clusters up to various cluster sizes in the undercritical region. At lower supersaturation the formation of nuclei is similar to the standard model because of the low depletion of the mother phase. At higher supersaturation, the depletion of the mother phase plays an important role and some extremal value appears at the size distribution of nuclei, which is not observed in the standard model. The extremum in the size distribution is not a consequence of the coalescence process itself, but it is caused rather by the depletion of the mother phase during the phase transformation.     

Molecular dynamics study of homogeneous nucleation in supercooled clusters of sodium bromide

Molecular dynamics simulations are carried out on clusters comprised of 108, 256, 500, and 864 Na⁺Br⁻ ion pairs represented by a Born–Mayer–Hugins interaction potential. Clusters with free boundaries are chosen in order to avoid the interference with nucleation caused by periodic boundary conditions. The melting point increases with increasing size of cluster as expected. The nucleation has been found to start near the surface of a NaBr cluster. The rates of nucleation in melted clusters are estimated based on classical nucleation theory. The interfacial free energies of 73.3–76.4 mJ/m² in temperature range of 400–550 K derived from kinetics of freezing are in the same order of magnitude as those predicted by Turnbull's relation and Buckle and Ubbelohde's observation. Sizes of critical nuclei are inferred from classical expressions and Voronoi polyhedra analyses.     

Nucleation of self-associating fluids: free versus activated association

We use the density functional theory of statistical mechanics in a square gradient approximation to analyze the structure, size, and work of formation of critical nuclei in self-associating fluids where association reduces the strength of the interactions between bonded particles. This effect is expected in systems of strongly dipolar particles that associate into chains. In this work we analyze the nucleation behavior of two types of self-associating fluids: a system comprised of particles that can freely associate, and a system in which the association process involves a thermally activated initiation step. For the first case, we explore the properties of critical nuclei in fluids that exhibit a metastable critical point between a vapor phase and a highly associated liquid phase. In fluids where the association dynamics involves an initiation step, we investigate the nucleation behavior in the vicinity of the polymerization transition. In both cases critical nuclei undergo a structural transition that shares many of the features of the coil-globule transition reported in Monte Carlo simulations of strongly dipolar Stockmayer fluids. Our results suggest that the sharp structural transition observed in these simulations is evidence of the existence of a second-order or nearly second-order association transition in these model fluids.     

Thermodynamics of diamond nucleation on the nanoscale

To have a clear insight into the diamond nucleation upon the hydrothermal synthesis and the reduction of carbide (HSRC), we performed the thermodynamic approach on the nanoscale to elucidate the diamond nucleation taking place in HSRC supercritical-fluid systems taking into account the capillary effect of the nanosized curvature of the diamond critical nuclei, based on the carbon thermodynamic equilibrium phase diagram. These theoretical analyses showed that the nanosize-induced interior pressure of diamond nuclei could drive the metastable phase region of the diamond nucleation in HSRC into the new stable phase region of diamond in the carbon phase diagram. Accordingly, the diamond nucleation is preferable to the graphite phase formation in the competing growth between diamond and graphite upon HSRC. Meanwhile, we predicted that 400 MPa should be the threshold pressure for the diamond synthesis by HSRC in the metastable phase region of diamond, based on the proposed thermodynamic nucleation on the nanoscale.     

Calculation of solid-liquid interfacial free energy: a classical nucleation theory based approach

We present a simple approach to calculate the solid-liquid interfacial free energy. This new method is based on the classical nucleation theory. Using the molecular dynamics simulation, we employ spherical crystal nuclei embedded in the supercooled liquids to create an ideal model of a homogeneous nucleation. The interfacial free energy is extracted by fitting the relation between the critical nucleus size and the reciprocal of the critical undercooling temperature. The orientationally averaged interfacial free energy is found to be 0.302+/-0.002 (in standard LJ unit). The temperature dependence of the interfacial free energy is also obtained in this work. We find that the interfacial free energy increases slightly with increasing temperature. The positive temperature coefficient of the interfacial free energy is in qualitative agreement with Spaepen's analysis [Solid State Phys. 47, FS181 (1994)] and Turnbull's empirical estimation [J. Appl. Phys. 21, 1022 (1950)].     

Hit and miss of classical nucleation theory as revealed by a molecular simulation study of crystal nucleation in supercooled sulfur hexafluoride

Classical nucleation theory pictures the homogeneous nucleation of a crystal as the formation of a spherical crystalline embryo, possessing the properties of the macroscopic crystal, inside a parent supercooled liquid. In this work we study crystal nucleation in moderately supercooled sulfur hexafluoride by umbrella sampling simulations. The nucleation free energy evolves from 5.2kBT at T=170 K to 39.1kBT at T=195 K. The corresponding critical nucleus size ranges from 40 molecules at T=170 K to 266 molecules at T=195 K. Both nucleation free energy and critical nucleus size are shown to evolve with temperature according to the equations derived from the classical nucleation theory. Inspecting the obtained nuclei we show, however, that they present quite anisotropic shapes in opposition to the spherical assumption of the theory. Moreover, even though the critical nuclei possess the structure of the stable bcc plastic phase, the only mechanically stable crystal phase for SF6 in the temperature range investigated, they are shown to be less ordered than the corresponding macroscopic crystal. Their crystalline order is nevertheless shown to increase regularly with their size. This is confirmed by a study of a nucleus growth from a critical size to a size of the order of 10(4) molecules. Similarly to the fact that it does not affect the temperature dependence of the nucleation free energy and of the critical nucleus size, the ordering of the nucleus with size does not affect the growth rate of the nucleus.     

Recent developments in the kinetic theory of nucleation

A review of recent progress in the kinetics of nucleation is presented. In the conventional approach to the kinetic theory of nucleation, it is necessary to know the free energy of formation of a new-phase particle as a function of its independent variables at least for near-critical particles. Thus the conventional kinetic theory of nucleation is based on the thermodynamics of the process. The thermodynamics of nucleation can be examined by using various approaches, such as the capillarity approximation, density functional theory, and molecular simulation, each of which has its own advantages and drawbacks. Relatively recently a new approach to the kinetics of nucleation was proposed [Ruckenstein E, Nowakowski B. J Colloid Interface Sci 1990;137:583; Nowakowski B, Ruckenstein E. J Chem Phys 1991;94:8487], which is based on molecular interactions and does not employ the traditional thermodynamics, thus avoiding such a controversial notion as the surface tension of tiny clusters involved in nucleation. In the new kinetic theory the rate of emission of molecules by a new-phase particle is determined with the help of a mean first passage time analysis. This time is calculated by solving the single-molecule master equation for the probability distribution function of a surface layer molecule moving in a potential field created by the rest of the cluster. The new theory was developed for both liquid-to-solid and vapor-to-liquid phase transitions. In the former case the single-molecule master equation is the Fokker-Planck equation in the phase space which can be reduced to the Smoluchowski equation owing to the hierarchy of characteristic time scales. In the latter case, the starting master equation is a Fokker-Planck equation for the probability distribution function of a surface layer molecule with respect to both its energy and phase coordinates. Unlike the case of liquid-to-solid nucleation, this Fokker-Planck equation cannot be reduced to the Smoluchowski equation, but the hierarchy of time scales does allow one to reduce it to the Fokker-Plank equation in the energy space. The new theory provides an equation for the critical radius of a new-phase particle which in the limit of large clusters (low supersaturations) yields the Kelvin equation and hence an expression for the macroscopic surface tension. The theory was illustrated with numerical calculations for a molecular pair interaction potential combining the dispersive attraction with the hard-sphere repulsion. The results for the liquid-to-solid nucleation clearly show that at given supersaturation the nucleation rate depends on the cluster structure (for three cluster structures considered-amorphous, fcc, and icosahedral). For both the liquid-to-solid and vapor-to-liquid nucleation, the predictions of the theory are consistent with the results of classical nucleation theory (CNT) in the limit of large critical clusters (low supersaturations). For small critical clusters the new theory provides higher nucleation rates than CNT. This can be accounted for by the fact that CNT uses the macroscopic interfacial tension which presumably overpredicts the surface tension of small clusters, and hence underpredicts nucleation rates.     

Stresses inside critical nuclei

The usual derivation of classical nucleation theory is inappropriate for crystal nucleation. In particular, it leads to a seriously flawed estimate of the pressure inside a critical nucleus. This has consequences for the prediction of possible metastable phases during the nucleation process. In this paper, we reanalyze the theory for crystal nucleation based on the thermodynamics of small crystals suspended in a liquid, due to Mullins (J. Chem. Phys. 1984, 81, 1436). As an illustration of the difference between the classical picture and the present approach, we consider a numerical study of crystal nucleation in binary mixtures of hard spherical colloids with a size ratio of 1:10. The stable crystal phase of this system can be either dense or expanded. We find that, in the vicinity of the solid-solid critical point where the crystallites are highly compressible, small crystal nuclei are less dense than large nuclei. This phenomenon cannot be accounted for by either classical nucleation theory or by the Gibbsian droplet model.     

Towards understanding the nucleation mechanism for multi-component systems: an atomistic simulation of the ternary nucleation of water/n-nonane/1-butanol

Inspired by the previous finding of some unusual vapour/liquid nucleation results on the ternary water/n-nonane/1-butanol system, atomistic simulations were carried out for a detailed investigation of this mixture. These simulations reproduced the experimentally-reported non-ideal nucleation behaviour for this system, including both onset activities and the average compositions of the critical nuclei. Close examination of the nucleation free energy data and the structure of the critical nuclei reveals two types of phase separation. One occurs internally inside the cluster via formation of a multi-layered structure. The other takes place externally, leading to the coexistence of multiple nucleation channels, characterized by critical clusters of different compositions. Such mechanistic and structural heterogeneity is the microscopic origin of the complex nucleation behaviour observed for this ternary mixture.     

氟化钾团簇的相变、成核和重结晶的分子动力学模拟

我们利用Born-Mayer-Huggins相互作用势函数对(KF)_N(N=108，256，500和864)团簇进行了分子动力学(MD)模拟。为了避免周期性边界条件对相变、成核和重结晶的干扰作用，对体系采用了自由边界。基于MD模拟结果，对团簇的熔化温度、熔化焓、扩散系数、成核速率、固液界面自由能、临界核大小等进行了计算和讨论。在对(KF)₈₆₄双晶团簇的热退火模拟中，观察到了固态的重结晶和晶粒的生长。经典的成核理论成功地解释了(KF)₈₆₄双晶团簇的重结晶MD模拟结果。     

Modeling a solid-phase electrochemical reaction of lithium intercalation in aluminum during a noninstantaneous nucleation of Β-LiAl

The interfacial surface area and the electrode surface coverage by a product during the nucleation and growth of a new phase are modeled numerically and calculated analytically for electrochemical intercalation of lithium in aluminum in the course of which intermetallic compound Β-LiAl forms. As opposed to the theoretical calculation, the model accounts for mutual influence of the new-phase nuclei on their distribution over the cathode surface under conditions of noninstantaneous nucleation. The ordering of such a distribution varies extremally (passes through a maximum) with increasing size of zones where the nucleation probability is low and which surround the nuclei. This makes the dependence of a maximum specific interfacial area on the zone radius extremal as well. The model may be applied for analyzing potentiostatic current transients during cathodic intercalation of lithium in aluminum from a LiClO₄ solution in propylene carbonate.     

高分子在氧化铝纳米孔道中受限结晶的研究进展

高分子材料在微纳米尺度常常表现出不同于本体的物理性质.对结晶性高分子来说,在纳米受限空间的成核机理、结晶结构和动力学特征都与本体材料有所不同.本文总结了近年来基于多孔氧化铝纳米模板(AAO)开展的高分子受限结晶的研究进展,重点介绍了本课题组的工作.研究发现,在AAO模板中,高分子结晶的过冷度大大增加,成核机理从本体的异相成核转变为均相成核或表面成核;高分子结晶结构通常表现为各向异性,动力学因素、热力学因素和界面性质均对取向结构有重要影响;受限情况下高分子结晶速率大大降低,表现出"成核控制"的动力学特征;空间受限使高分子结晶度降低,倾向于形成亚稳态晶型.最后,对该领域尚待解决的问题进行了展望.     

Molecular dynamics simulations of nucleation from vapor to solid composed of Lennard-Jones molecules

We performed molecular dynamics (MD) simulations of nucleation from vapor at temperatures below the triple point for systems consisting of 10(4)-10(5) Lennard-Jones (L-J) type molecules in order to test nucleation theories at relatively low temperatures. Simulations are performed for a wide range of initial supersaturation ratio (S(0) ? 10-10(8)) and temperature (kT = 0.2-0.6ε), where ε and k are the depth of the L-J potential and the Boltzmann constant, respectively. Clusters are nucleated as supercooled liquid droplets because of their small size. Crystallization of the supercooled liquid nuclei is observed after their growth slows. The classical nucleation theory (CNT) significantly underestimates the nucleation rates (or the number density of critical clusters) in the low-T region. The semi-phenomenological (SP) model, which corrects the CNT prediction of the formation energy of clusters using the second virial coefficient of a vapor, reproduces the nucleation rate and the cluster size distributions with good accuracy in the low-T region, as well as in the higher-T cases considered in our previous study. The sticking probability of vapor molecules onto the clusters is also obtained in the present MD simulations. Using the obtained values of sticking probability in the SP model, we can further refine the accuracy of the SP model.     

Universal Asymptotics of the Thermodynamic Characteristics of the Nucleation on Small Macroscopic Nuclei of Soluble Surfactants

Asymptotic behavior of thermodynamic characteristics of nucleation on small macroscopic nuclei of soluble surfactants at their complete dissolution in a nucleating droplet is studied. It is taken into account that, in the region of small sizes of nuclei and corresponding small sizes of critical nuclei of liquid phase, the chemical potential of condensate and the work of droplet formation are affected by the presence of dense surfactant adsorption monolayer on the droplet surface. It is shown that, as the limiting surface area per surfactant molecule in adsorption monolayer increases, the behavior of thermodynamic characteristics of nucleation in the region of small nucleus sizes is characterized by the transition from asymptotics at the adsorption of almost all substance comprising nucleus in a monolayer to the asymptotics at constant adsorption. The study performed is not limited by the selection of specific adsorption isotherms; therefore, the obtained asymptotic dependences of thermodynamic characteristics on the nucleus size can be considered as universal for the heterogeneous nucleation on the nuclei of soluble surfactants.     

Dumbbells and onions in ternary nucleation

Molecular simulations for a ternary nucleation system (water/n-nonane/1-butanol) demonstrate a more complex nucleation mechanism than previously thought, where critical nuclei with different compositions are present even for a given vapour-phase composition; the spatial distribution in these critical nuclei is heterogeneous and dumbbell and onion motifs are found; in the former, water and nonane nano-droplets are connected through a butanol handle, while in the latter a water core is surrounded by a nonane corona with an interfacial butanol shell.     

Interfacial study of cubic boron nitride films deposited on diamond

We have studied the nucleation and growth of cubic boron nitride (cBN) films deposited on silicon and diamond-coated silicon substrates using fluorine-assisted chemical vapor deposition (CVD). These comparative studies substantiate that the incubation amorphous/turbostratic BN layers, essential for the cBN nucleation on silicon, are not vital precursors for cBN nucleation on diamond, and they are inherently eliminated. At vastly reduced critical bias voltage, down to -10 V, cBN growth is still maintained on diamond surfaces, and cBN and underlying diamond crystallites exhibit an epitaxial relationship. However, the epitaxial growth is associated with stress in the cBN-diamond interfacial region. In addition, some twinning of crystallites and small-angle grain boundaries are observed between the cBN and diamond crystallites because of the slight lattice mismatch of 1.36%. The small-angle grain boundaries could be eliminated by imposing a little higher bias voltage during the initial growth stage. The heteroepitaxial growth of cBN films on different substrate materials are discussed in the view of lattice matching, surface-energy compatibility, and stability of the substrate against ion irradiation.