Surface nucleation in the crystallisation of polyethylene droplets

The division of semi-crystalline polymeric material into small domains is an effective tool for studying crystal nucleation. The scaling behavior of the nucleation rate as a function of domain size can reveal important information about the mechanism responsible for the birth of a crystal nucleus. We have investigated the process of crystal nucleation in a system of dewetted polyethylene droplets. Through the use of a correlation sample analysis, we are able to differentiate between heterogeneous and homogeneous nucleation mechanisms in a droplet sample. An analysis of the dependence of the nucleation rate on droplet size reveals that the nucleation probability scales with the surface area of the droplet.     

Role of the prestructured surface cloud in crystal nucleation

For the homogeneous crystal nucleation process in a soft-core colloid model, we identify optimal reaction coordinates from a set of novel order parameters based on the local structure within the nucleus, by employing transition path sampling techniques combined with a likelihood maximization of the committor function. We find that nucleation is governed by solid clusters that consist of an hcp core embedded within a cloud of surface particles that are highly correlated with their nearest neighbors but not ordered in a high-symmetry crystal structure. The results shed new light on the interpretation of the surface and volume terms in classical nucleation theory.     

Homogeneous bulk, surface, and edge nucleation in crystalline nanodroplets

The birth of a crystal is initiated by a nucleus from which the crystal grows--a dust grain in a snowflake is a familiar example. These nuclei can be heterogeneous defects, like the dust grain, or homogeneous nuclei which are intrinsic to the material. Here we study homogeneous nucleation in nanoscale polymer droplets on a substrate which itself can be crystalline or amorphous. We observe a large difference in the nucleating ability of the substrate. Furthermore, the scaling dependence of nucleation on the size of the droplets proves that the birth of the crystalline state can be directed to originate predominantly within the bulk, at the substrate surface, or at the droplets' edge, depending on how we tune the substrate.     

Homogeneous nucleation of dislocations

The mechanism and stochastic properties of the homogeneous nucleation of dislocations have been studied. An approach has been proposed for determining the nucleation rate based on consideration of the lifetimes of a metastable state. Primary data have been obtained using the molecular dynamics method. The dependences of the nucleation rate on the shear stresses have been determined for several temperatures. An approximation of the obtained results in terms of the Arrhenius equation has been proposed. The regions of shear stresses and temperatures in which the mechanism of homogeneous dislocation nucleation can be realized have been estimated.     

Direct visualisation of homogeneous and heterogeneous crystallisation in an ensemble of confined domains of poly(ethylene oxide)

We present a study of homogeneous and heterogeneous nucleation in polymer crystallisation. In bulk samples the crystallization is typically dominated by nucleation from defects (heterogeneous nucleation), and consequently studies must rely on sample preparation to minimize this effect. We present a study of nucleation within discrete droplets of poly(ethylene oxide) that are formed by the dewetting of a thin film on an unfavourable substrate. The samples provide an ensemble of impurity-free droplets, with length scales that can easily be measured. We show that the data for heterogeneous and homogeneous nucleation is qualitatively different, and that the data mirrors the fundamental differences in the underlying mechanisms for the two nucleation processes. The experiments presented here provide a simple method that can be used to study heterogeneous and homogeneous nucleation in great detail.Received: 1 January 2003, Published online: 30 October 2003PACS: 61.41. + e Polymers, elastomers, and plastics - 68.55.-a Thin film structure and morphology - 81.10.-h Methods of crystal growth; physics of crystal growth     

The phase coexistence method to obtain surface free energies and nucleation barriers: a brief review

ABSTRACT

A recently developed method where one analyses the finite size effects associated with liquid–solid phase equilibria including vapour–crystal coexistence is briefly reviewed. It is shown that the estimation of the chemical potential of the vapour surrounding the crystal as function of the crystal volume yields information on the bulk coexistence conditions, when an extrapolation to the thermodynamic limit is performed. Estimating the pressure of the fluid surrounding the crystal nucleus in the finite simulation box and the volume of this nucleus that coexists with the fluid in thermal equilibrium, an estimate for the total surface excess free energy can be obtained, which to a very good approximation is independent of the size of the simulation box. The free energy barrier against homogeneous nucleation of crystals thus can be estimated as a function of the nucleus volume. Monte Carlo simulations for the soft effective Asakura–Oosawa model of colloid-polymer mixtures which form face-centered cubic colloidal crystals are used to exemplify this method, computing the surface excess free energy of these crystals over a wide range of crystal volumes, without the need to characterise the non-spherical crystal shape. A possible extension of these concepts to heterogeneous nucleation is also briefly discussed.     

Thermodynamics of nucleation in an internal oxide getter in silicon

Nucleation of precipitates of silicon dioxide is studied theoretically within the framework of the classical theory of nucleation. Elastic stresses, accompanying nucleation, are taken into account under the assumption that the nucleus and matrix are incoherent and the silicon is elastically isotropic. The results of a numerical calculation of the form and dimensions of the critical nucleus, the free energy of its formation, and the rate of nucleation as a function of the annealing temperature in the range 773–1473 K for oxygen concentrations in the starting single crystal of (0.4–1.4)·10¹⁸ cm^–3 are presented. It is shown that homogeneous nucleation of precipitates is, in principle, possible. The magnitude of the specific free energy of the interphase boundary is estimated based on the data obtained.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 25–29, August, 1988.     

Computer simulation of heterogeneous nucleation on curved surfaces using a simplified string method combined with phase-field simulations

We show how the combination of string method with the phase-field approach can be extended from simulations of homogeneous nucleation to heterogeneous nucleation. From these simulations, it is possible to directly obtain nucleation barriers for heterogeneous nucleation on arbitrary surfaces as well as information about the size and shape of the critical nucleus. We test the method by comparing the dependence of the nucleation barrier for heterogeneous nucleation on concave and convex surfaces on the surface curvature obtained from three-dimensional phase-field simulations with predictions from classical nucleation theory and find good agreement between them.     

Atomistic study of dislocation loop emission from a crack tip

We report the first atomistic calculation of the saddle-point configuration and activation energy for the nucleation of a 3D dislocation loop from a stressed crack tip in single crystal Cu. The transition state is found using reaction pathway sampling schemes, the nudged elastic band, and dimer methods. For the (111)[110] crack, loaded typically at 75% of the athermal critical strain energy release rate for spontaneous dislocation nucleation, the calculated activation energy is 1.1 eV, significantly higher than the continuum estimate. Implications concerning homogeneous dislocation nucleation in the presence of a crack-tip stress field are discussed.     

Attainable superheating of solutions of cryogenic liquids

The kinetics of spontaneous boiling-up of superheated binary solutions of cryogenic liquids is studied. Within the framework of the Kramers-Zeldovich method, an expression is obtained for the steady state rate of homogeneous nucleation in a solution that takes into account free-molecular and diffusion regimes of the substance supply to a growing bubble. Viscous and inertial forces are also taken into account in the study of the nucleus growth dynamics. The work of critical nucleus formation is determined within the framework of the Gibbs and van der Waals capillarity theories. The dependence of the surface tension of critical bubbles in the solution on their size is investigated. The temperature of attainable superheating and nucleation rates in superheated solutions of cryogenic liquids with complete or partial solubility of the components are determined by a method of lifetime measurement. The experiments were conducted in a wide range of pressures and solution concentrations. The measurement results are compared with the theory of homogeneous nucleation taking or not taking into account the size effect in nucleation. It has been found that, by taking into account the size dependence of the surface tension of a nucleus, better agreement between the theory and experiment is obtained. The boundary of essential instability of the solution, that is, the diffusion spinodal, is computed.     

Shear‐Enhanced Nucleation of Isotactic Polypropylene in Limited Space

The nucleation rate was measured by directly counting the number of nuclei, which were developed while an isotactic polypropylene melt was flowing under shear in a thin film. The nucleation rate was enhanced with an increased rate of shear, e.g., by a factor of 10 larger at the rate of shear of 14 s^?1 compared with the quiescent state, at 134°C. The ratio of the shear‐enhanced nucleation rate to the nucleation rate in the quiescent state was larger at a higher temperature of crystallization, i.e., about 10 times at 134°C to 590 times at 140°C. The increase of the nucleation rate under shear flow was explained by a reduction of the lateral and end (fold) surface free energies; the product σ _s ² σ _e decreased to 3.2×10^?7 for the sheared melt, from 6.0×10^?7 (J m^?2)³ for the isotropic state. The free energy reduction was caused by transition of the nucleus formation mode from three‐dimensional folded chain nuclei to two‐dimensional bundle nuclei, in which chains lie down on the glass substrate, aligning parallel to the flow direction.     

Theory of the nucleation of protein macromolecular ions

Protein molecules are amphoteric and exist in aqueous solution as macromolecular ions that carry a charge which depends upon temperature and pH. Despite the repulsive Coulomb forces acting between them, protein macromolecular ions can form crystals in pH buffered solutions of strong electrolytes. It is proposed that the first step in the mechanism of crystallization is the formation of crystal nuclei made from partially discharged macromolecular ions that have exchanged H⁺ with the buffer. We suggest that the strength of the bare Coulomb repulsive force is weakened by the Debye-Hückel plasma screening provided by the inert electrolyte. This screening causes the rate of nucleus formation to increase with increasing ionic strength. Extending classic nucleation theory to account for these various charge effects, the results are applied to the case of lysozyme and a calculation is made of the dependence of the steady state nucleation rate upon temperature, pH, ionic strength, and protein supersaturation. It is found that the nucleation rate increases with increasing temperature and increasing ionic strength. Under condition of fixed temperature, supersaturation, and inionic strength, the nucleation rate has local maxima at low pH, where individual lysozyme macro ions are highly charged, and at pH ? 11, where they have zero average net charge. At both pH values, the nucleus that determines the rate has minimum size. In contrast to standard nucleation theory, which ignores charge, it is found that the size of the nucleus that controls the rate is different from the size of the nucleus that has the lowest concentration. All other conditions being the same, it is predicted that lysozyme crystals should nucleate most rapidly near pH = 2 and near pH = 11.     

Spinodal twinning of a deformed crystal

We propose the possibility of a spinodal mechanism for deformation twinning in addition to the nucleation and growth mechanism assumed in all existing studies of twinning, using the thermodynamic stability analysis of a homogeneously deformed crystal by examining its energy landscape as a function of strain along the twinning direction obtained from first-principles calculations. Twinning occurs continuously owing to thermodynamic instability with respect to twinning at large shear strains, whereas it can only take place through the nucleation and growth mechanism at small shear strains.     

Non-uniformities in polymer/liquid crystal mixtures

We theoretically model the nucleation of nematic droplets during phase ordering in mixtures of a flexible polymer and a low-molecular-weight liquid crystal. By appealing to classical nucleation theory (CNT), we calculate the energy barrier to nucleation and the size of a critical nucleus. We study the influence of a metastable intermediate phase on the nucleation of the nematic. Below a triple point in the phase diagram, there are two distinct mechanisms for the formation of a nematic nucleus: 1) direct nucleation from the isotropic phase and 2) nucleation via a precursor metastable isotropic phase. We calculate the crossover concentration as a function of temperature, delineating the regions of the phase diagram in which each mechanism prevails. In the latter case, the presence of a hidden metastable isotropic-isotropic binodal may either promote or delay the nucleation of a nematic phase. Received 9 August 2002 RID="a" ID="a"e-mail: matuyama@chem.mie-u.ac.jp     

Melting mechanisms at the limit of superheating

The atomic-scale details during melting of a surface-free Lennard-Jones crystal were monitored using molecular dynamics simulations. Melting occurs when the superheated crystal spontaneously generates a sufficiently large number of spatially correlated destabilized particles that simultaneously satisfy the Lindemann and Born instability criteria. The accumulation and coalescence of these internal local lattice instabilities constitute the primary mechanism for homogeneous melt nucleation inside the crystal, in lieu of surface nucleation for equilibrium melting. The vibrational and elastic lattice instability criteria as well as the homogeneous nucleation theory all coincide in determining the superheating limit.     

Shear-induced first-order sponge-to-lamellar transition in a lyotropic surfactant system

We report a shear-induced sponge (L3) to lamellar (L(alpha)) transition in a surfactant system. Under a constant shear rate, after a delay time t(n) we observe random nucleation and subsequent growth of the L(alpha) phase, demonstrating that the shear-induced transition is first order. A simple argument for the energy of a two-dimensional nucleus accounts for the observed delay and its shear-rate dependence.     

On the theory of transient nucleation at the intermediate stage of phase transitions

The evolution of a system of growing aggregates in a macroscopically homogeneous medium with account of both the reduction in metastability and the continuing initiation of new nuclei is studied. The corresponding integro-differential model describing the intermediate stage of phase transitions is solved analytically for arbitrary nucleation kinetics and growth rates of nuclei. An exact solution of the Fokker–Planck equation is found with allowance for the diffusivity along the axis of nucleus radii. In limiting cases of purely kinetic and mixed kinetic-diffusion rates of crystal growth for a special form of diffusivity, the obtained solutions transform to earlier known expressions.     

A composite model of the plastic flow of amorphous covalent materials

A model based on the data available in the literature on the computer simulation of amorphous silicon has been proposed for describing the specific features of the plastic flow of amorphous covalent materials. The mechanism of plastic deformation involves homogeneous nucleation and growth of inclusions of a liquidlike phase under external shear stress. Such inclusions experience plastic shear, which is modeled by glide dislocation loops. The energy changes associated with the nucleation of these inclusions at room and increased temperatures have been calculated. The critical stress has been found, at which the barrierless nucleation of inclusions becomes possible. It has been shown that this stress decreases with an increase in temperature. According to the calculations, the heterogeneous (homogeneous) plastic flow of an amorphous material should be expected at relatively low (high) temperatures. Above the critical stress, the homogeneous flow is gradually replaced by the heterogeneous flow.