Number of Nuclei Formed during Electrocrystallization and Overall Time Dependence of Their Growth Current

A model for continuous (progressing) nucleation is developed. The model takes into account (1) the mixed kinetics of growth of every nucleus, (2) different degree of the diffusion influence on the growth rate of nuclei formed at different time instants after switching the current on, and (3) the presence of hemispherical diffusion simultaneously with the developing front of plane diffusion. Equations that are obtained for the time dependence of the current include, in addition to values of concentrations, diffusion coefficients, and individual parameters of metals, the exchange current density and the overvoltage. The nucleation in depleted-by-diffusion zones around the growing nuclei is considered. It is shown that the average nucleation retardation degree in such zones is time-independent. Therefore, at an arbitrary time instant, the entire surface may be represented as comprising areas with an ordinary nucleation rate (whose share diminishes) and areas with a lower (but constant) nucleation rate (whose share rises). At not-too-low overvoltages, the decrease in the nucleation rate is mainly due to the decrease in the surface concentration of ions-reactants. The overall number of clusters, calculated with the proposed model, is usually a few orders of magnitude than found by known models.     

Galvanostatic phase formation

The results of a theoretical study on initial stages of electrodeposition under galvanostatic conditions are presented. The model of three-dimensional nucleation and growth under these conditions is developed. This model is used to calculate the times dependences of the overpotential, number of clusters formed on the electrode, and nucleation rate. The peculiarities of nucleation and growth kinetics are analyzed.     

Nucleation of ordered solid phases of proteins via a disordered high-density state: phenomenological approach

Nucleation of ordered solid phases of proteins triggers numerous phenomena in laboratory, industry, and in healthy and sick organisms. Recent simulations and experiments with protein crystals suggest that the formation of an ordered crystalline nucleus is preceded by a disordered high-density cluster, akin to a droplet of high-density liquid that has been observed with some proteins; this mechanism allowed a qualitative explanation of recorded complex nucleation kinetics curves. Here, we present a simple phenomenological theory that takes into account intermediate high-density metastable states in the nucleation process. Nucleation rate data at varying temperature and protein concentration are reproduced with high fidelity using literature values of the thermodynamic and kinetic parameters of the system. Our calculations show that the growth rate of the near-critical and supercritical ordered clusters within the dense intermediate is a major factor for the overall nucleation rate. This highlights the role of viscosity within the dense intermediate for the formation of the ordered nucleus. The model provides an understanding of the action of additives that delay or accelerate nucleation and presents a framework within which the nucleation of other ordered protein solid phases, e.g., the sickle cell hemoglobin polymers, can be analyzed.     

2，2，3-三甲基丁烷(C7H16)晶体的成核动力学

High temperature solid phase I of 2,2,3-trimethylbutane(C7H16)(TMB) was investigated by X-ray powder diffraction. The electron diffraction technique for observing the kinetics of phase transitions in the condensed matter has been applied to study the freezing of TMB clusters with diameter of~13nm. Cluster beams were generated from the supersonically expanded TMB vapor with mole fraction of 0.01 in neon carrier gas. The freezing evolution was monitored by electron diffraction in interval of 7-9 μs. Clusters with an average size of ~5,500 molecules were observed to freeze into the solid phase I at a nucleation rate of 3.5 × 1028 m-3•s- 1 at the freezing temperature of clusters, ～170K. The estimated growth rate of postcritical nuclei indicates that the observed nucleation in the present experiment corresponds to mononuclear freezing of the clusters into single crystals of solid phase I.     

The formation and kinetics of Ionized Cluster Beams

The formation and kinetics of large vapourized-material cluster beams (large size metal clusters) are discussed. The clusters are formed by injecting the vapour of solid state materials into a high vacuum region through a nozzle of a heated crucible. The conditions under which metal clusters form are analysed using nucleation theory. Computer simulation by combining the nucleation and flow equations has also been made. The results show that the theory can be useful in predicting qualitative dependences of metal cluster formation on operation conditions. Several experimental results are also presented, which support the finding that a large size metal cluster is formed by homogeneous nucleation and growth. The advantageous characteristics of ionized cluster beam for thin film formation are also discussed.     

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.     

Experimental study of shear-induced crystallization of an impact polypropylene copolymer

The crystallization kinetics of polypropylene was observed during shear and after shear experiments under isothermal condition. The crystallizations were performed in a plate-plate and a fiber pull-out device. The nucleation density, the crystalline growth and the overall kinetics were measured and compared with data obtained in a similar way but during static experiments. The morphologies are spherulitic and formed from nuclei which seem to be randomly distributed. -phase spherulites are always observed but with a nucleation density and a growth rate which depend on shearrate. The nucleation density is strongly enhanced by shear and acts as the main factor on the overall kinetics. The overall kinetics can be analyzed with a two-step Avrami model, where an Avrami exponentn ₁ with a very high value is always observed first after shear and a more usual parametern ₂ for the subsequent crystallization period. This high value ofn ₁ seems to be related to the strong enhancement of nucleation density. The growth rate increases with the shear-rate, but the basic growth mechanisms do not seem to be modified. For crystallizations after shear the growth rate decreases with a long-time delay after shear but not down to the static value. The effect is characteristic of a partial relaxation of chain orientation after shear but with a very unusual time constant.     

Kinetics of formation of filamentary crystals at electrodeposition

Initial stages of nucleation and growth of filamentary crystals at the electrodeposition is considered. Time dependences of overpotential and the number and the size of filamentary crystals are simulated. The effect of current and electrolyte concentration on the kinetics of nucleation and growth of crystals is studied.     

Thermodynamics of crystalline nanonucleus formation from liquid phase

The energy of crystal nucleation from liquid phase was considered, with the following two stages taken into account: (1) the formation of metastable supercooled melt (solution), containing pre-nuclei with intermediate amorphous (quasicrystalline) structure, and (2) the transformation of amorphous clusters into solid crystalline nuclei having different structures. With growth of a nucleus the nucleation energy profile manifests 2–3 maxima corresponding to these stages, and the kinetics of the non-stationary nucleation has five characteristic variations.     

Kinetics of ion-induced nucleation in a vapor-gas mixture

A general solution for the steady-state ion-induced nucleation kinetics has been derived, considering the differences between ion-induced nucleation and homogeneous nucleation. This solution includes a new effect for nucleation kinetics, the interaction of charged clusters with vapor molecules. Analytical expressions for the ion-induced nucleation rate have been obtained for the limiting cases of high and low thermodynamic barriers. The physical explanation of the so-called sign effect is proposed based on multipole expansion of an electric field of the cluster ion. This theory gives good agreement with experiments and is used to elucidate experimentally observed phenomena.     

Vapor Nucleation and Droplet Growth: Cluster Distribution Kinetics for Open and Closed Systems

A theory based on cluster distribution kinetics for single-monomer addition and dissociation is presented as a framework for homogeneous and heterogeneous vapor nucleation and growth dynamics. For continuous cluster and monomer distributions in a well-mixed non-steady-state flow system, population (mass) balance equations yield moment equations for the cluster mass moments. Nuclei are either homogeneously generated or heterogeneously seeded, and subsequent cluster growth occurs by reversible condensation of vapor monomers. The zeroth moment is the number (or moles) of clusters, the first moment is cluster mass, and the second moment gives cluster-size variance. Solutions are proposed for steady-state flow (open) and non-steady-state batch (closed) systems. Experimental data are interpreted by recognizing that droplets typically observed in nucleation experiments have grown much larger than their nuclei. This allows resolution of the large temperature-dependent discrepancy between experiment and classical nucleation theory. Copyright 2000 Academic Press.     

Current transient study of the kinetics of nucleation and diffusion-controlled growth of bimetallic phases

A model to describe the kinetics of nucleation and diffusion-controlled growth of bimetallic phases has been developed, and analytical expressions have been obtained for the elucidation of nucleation kinetics through determination of the number density N ₀ of active sites and their nucleation frequency A, from experimental current transients obtained under potentiostatic control. The validity of the model has been demonstrated with the electrodeposition of Ag–Hg phases at two distinct compositions.     

Nonisothermal bulk crystallization studies of high density polyethylene using light depolarizing microscopy

The quiescent nonisothermal bulk crystallization kinetics of two high-density polyethylene resins were investigated by a modified light-depolarizing microscopy (LDM) technique. The technique allows studies at average cooling rates up to 2500°C/min. The polymer was found to crystallize at a pseudo-isothermal temperature even at these very high cooling rates. The overall bulk crystallization rate increased rapidly as the cooling rate and supercooling increased. Crystallization kinetics was analyzed by Avrami analysis. Avrami exponents near 3 suggested spherical growth geometry and instantaneous nucleation at predetermined sites. Observation of spherulites by optical microscopy together with a number density of spherulites that changed little with increase in cooling rate or supercooling supported this model of crystallization behavior. Analysis of the half-time of crystallization based on the Lauritzen and Hoffman secondary nucleation theory indicated that the regime II-III transition was found to occur at a degree of supercooling of approximately 22°C. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 681–692, 1998     

Electrocrystallization: Nucleation and growth of nano-clusters on solid surfaces

Electrocrystallization phenomena are considered and basic thermodynamic and kinetic concepts related to the electrochemical nucleation and growth are defined and discussed in details. Theoretical and experimental findings related to the stationary and non-stationary nucleation kinetics, growth of single two-and three-dimensional crystals as well as underpotential deposition phenomena and spatial distribution of clusters are reviewed and the reader is referred to suitable sources of reliable information on the most important subjects concerned. Published in Russian in Elektrokhimiya, 2008, Vol. 44, No. 6, pp. 669–698. The text was submitted by the author in English.     

The nucleation rate of crystalline ice in amorphous solid water

The kinetics of crystalline ice nucleation and growth in nonporous, molecular beam deposited amorphous solid water (ASW) films are investigated at temperatures near 140 K. We implement an experimental methodology and corresponding model of crystallization kinetics to decouple growth from nucleation and quantify the temperature dependence and absolute rates of both processes. Nucleation rates are found to increase from approximately 3x10(13) m(-3) s(-1) at 134 K to approximately 2x10(17) m(-3) s(-1) at 142 K, corresponding to an Arrhenius activation energy of 168 kJ/mol. Over the same temperature range, the growth velocity increases from approximately 0.4 to approximately 4 A s(-1), also exhibiting Arrhenius behavior with an activation energy of 47 kJ/mol. These nucleation rates are up to ten orders of magnitude larger than in liquid water near 235 K, while growth velocities are approximately 10(9) times smaller. Crystalline ice nucleation kinetics determined in this study differ significantly from those reported previously for porous, background vapor deposited ASW, suggesting the nucleation mechanism is dependent upon film morphology.     

Three-dimensional nucleation and growth under galvanostatic conditions

The nucleation and growth of new phase clusters have been studied under galvanostatic conditions. Time dependences of the overpotential, number, and size of clusters formed on the electrode have been calculated from a model of the electrocrystallization process.     

Non-activated metal cluster growth during nozzle jet expansion

Based on the classical liquid-drop nucleation theory for small clusters, we show quantitatively the existence of a boundary which separates the nucleation and growth and non-activated (physical spinodal) cluster growth regions for supersaturated vapors. We found that for the expansion geometry such as the one used by Yamada and Takagi in their nozzle jet experiments for producing metal clusters, the non-activated growth process may play an important, if not predominant, role in the growth of clusters.     

Polymer crystallization from the melt at large undercoolings

Consideration of crystallization kinetics in high-molecular-weight polymers shows that adjacent reentry is unlikely in melt crystallization and that sections of individual chains will crystallize concurrently at several sites. Hence the characteristic crystallization process will be that of a loop of chain with both ends attached to different sites on the crystal surface. Analysis of this process leads to predictions of crystallinity values for various conditions of chain mobility in the crystal and of entanglements in the amorphous regions. Observations on polymers crystallized at high undercoolings where a crystallinity of about 30% is usually observed suggest that the common case is that of a highly entangled amorphous layer and rapid, local annealing of the chains but with no long-range motion in the crystal. This model of loop crystallization is shown to agree with available small-angle neutron scattering data. The overall crystallization kinetics are in accord with surface nucleation controlled growth which also arises out of the Lauritzen-Hoffman adjacent reentry model and has been shown to fit experimental results on growth rates.