Effects of diffusion-controlled association in kinetic model of crystal nucleation in external orienting field

Translational and rotational diffusion equation of orientable single elements in external orienting potential field is used to discuss effective rate of association and dissociation during cluster growth. First and second harmonic terms of orientation-dependent potential energy of single elements are taken into consideration. Tolerance angle accounting for orientational limitations for association is introduced.Effective rate of association of single elements is derived with first-order correction for the effects of orienting potential. Net rate of cluster growth depends on orientation in the field, and it is controlled by longrange diffusion (rotational and translational) of single elements. Influence of diffusion is higher, the narrower the tolerance angle and the faster the association.At slow association, long-range diffusion does not influence the process, the growth of a cluster is controlled by thermodynamic, orientation-dependent potential of the species involved in the process.Effective rate constants of association and dissociation, as well as effective concentration of single elements are derived as functions of orientation angle in the field.The Fokker-Planck equation is proposed for the distribution of cluster size in external orienting potential, with the effects of finite translational and rotational diffusion of single elements, for the case of non-polar clusters.     

Effects of translational and rotational diffusion on the association in kinetic model of nucleation

Kinetics of an association and dissociation of single elements with the effects of translational and rotational diffusion and angular limitations is discussed. Separated clusters embedded in a solution of orientable single elements are considered.Steady-state positional and angular distribution of single elements is calculated from the equation of translational-rotational diffusion and the boundary conditions proposed for orientation-limited association. Although spherical orientable elements are assumed, the model can be used for non-spherical particles with aspect ratios close to unity.Diffusion-limited rate constants of association and dissociation are proposed which depend on translational and rotational diffusion constants of single elements, the tolerance angle of the association, and the cluster size.Effective concentration of single elements and effective rate constants are expressed by the equilibrium and diffusion-limited rate constants. Effects of finite diffusion rates and finite tolerance angle are discussed.The equations of the kinetic model of nucleation are modified due to the diffusion-limited rate of the association.     

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.     

Theory of shear-induced crystallization of polymer melts

In the presented model elements of polymer melt rheology and polymer crystallization kinetics are combined. In particular, the proneness of the melt to the special type of crystallization which is characteristic for shear treatment is supposed to emerge only gradually during shear flow. Following Avrami's early ideas on crystal growth, an induction time is introduced. In principle, the model can be applied to any flow and temperature history. The special case of isothermal flow at constant shear rate is covered in greater detail: A favorable comparison is made with experimental results, as published by Lagasse and Maxwell [10].Dedicated to Prof. J. Meissner on the occasion for his 60th birthday.     

Crystallization kinetics of isotactic polypropylene blended with atactic polystyrene

Crystallization kinetic parameters, such as spherulitic growth rates, nucleation densities, and Avrami-exponents, have been determined by optical microscopy for isotactic polypropylene blended with atactic polystyrene. It is found that the crystallization of iPP is strongly influenced by the presence of polystyrene. With increasing PS concentration in the blend, the nucleation densities decrease, while the spherulitic growth rates as well as the positions of thermal peaks, measured by DSC, remain independent of sample composition. Due to the formation of interfaces as a consequence of increasing dispersion of polystyrene the nucleation changes from preferentially thermal to athermal.     

Identifiability of models for intramolecular two-state excited-state processes with added quencher and coupled species-dependent rotational diffusion

The parameters describing the kinetics of excited-state processes can possibly be recovered by analysis of the fluorescence decay surface measured as a function of the experimental variables. The identifiability analysis of a photophysical model assuming errorless time-resolved fluorescence data can verify whether the model parameters can be determined and may lead to the minimal experimental conditions under which this is possible. In this work, we used the method of similarity transformation to investigate the identifiability of three kinetic models utilized to describe the time-resolved fluorescence of reversible intramolecular two-state excited-state processes in isotropic environments: (1) model without added quencher, (2) model with added quencher, (3) model with added quencher coupled with species-dependent rotational diffusion described by Brownian reorientation. Without a priori information, model 1 is not identifiable. For model 2, two sets of quenching rate constants and combinations of excited-state deactivation/exchange rate constants are possible, but they cannot be allocated to a specific excited-state species. For both sets, upper and lower limits on the excited-state deactivation/exchange rate constants can be obtained. For model 3, both spherically and cylindrically symmetric rotors, with no change in the principal axes of rotation in the latter, are considered. The fluorescence delta-response functions I(parallel)(t) and I(perpendicular)(t), for fluorescence polarized parallel and perpendicular, respectively, to the electric vector of linearly polarized excitation, are used to define the sum S(t) identically equal to I(parallel)(t) + 2 I(perpendicular)(t) and the difference D(t) identically equal to I(parallel)(t) - I(perpendicular)(t). The identifiability analysis is performed using the S(t) and D(t) functions. Also for model 3, two sets of kinetic parameters (i.e., quenching rate constants, combinations of deactivation/exchange rate constants, and rotational diffusion coefficients) exist, but these parameters cannot be assigned unequivocally to a specific species. For the three models, an infinite number of alternative spectroscopic parameters associated with excitation and emission are found.     

Kinetics of adsorption and desorption of sodium alkyl sulfates to and from nylon particles

The desorption rate of surfactant ions from nylon particles was investigated at the concentrations below the critical micelle concentration by applying the stopped-flow method. A mixing cell of stopped-flow spectrophotometer was modified with platinum electrodes for electric conductivity detection. The change in electric conductivity with time in the desorption process was monitored by a memory-recorder system. The surfactants used were sodium decyl, sodium dodecyl, sodium tetradecyl, and sodium hexadecyl sulfates. The desorption rate was independent of the surfactant concentration and the rate constants were obtained by applying the first-order reaction scheme. The adsorption rate constants were estimated from the experimental desorption rate constants and equilibrium constants assuming the second-order kinetics. The desorption rate constants were determined to be 1–6 sec^–1 and the adsorption rate constants to be 2–8×10⁴ mol^–1 dm³ sec^–1; the former decreased and the latter increased with increasing number of carbon atoms in alkyl chain of the surfactants.     

Thermotropic rigid chain copolymers I. crystallization kinetics and thermodynamic properties

The kinetics of structure formation and the thermal properties of the ordered phase were analyzed calorimetrically for a rigid polymer, characterized by an irregular chemical structure. The transition from the nematic melt to a partially ordered state was found to involve two different processes, a fast and a slow one. The fast one corresponds apparently to a thermally activated nucleation and growth mechanism, whereas the slow one is strongly self delaying. Its transition rate is only weakly dependent on the temperature. The thermal properties of the ordered phase, resulting from this process, vary strongly with the annealing temperature and annealing time. The enthalpy and entropy of fusion, characteristic for the pure ordered phase, are lower by a factor of about 10 in comparison to the corresponding values of flexible chain molecules.     

A distribution kinetics approach for crystallization of polymer blends

The cluster distribution approach is extended to investigate the crystallization kinetics of miscible polymer blends. Mixture effects of polymer-polymer interactions are incorporated into the diffusion coefficient. The melting temperature, activation energy of diffusion, and phase transition enthalpy also depend on the blending fraction and lead to characteristic kinetic behavior of crystallization. The influence of different blending fractions is presented through the time dependence of polymer concentration, number and size of crystals, and crystallinity (in Avrami plots). Computational results indicate how overall crystallization kinetics can be expressed approximately by the Avrami equation. The nucleation rate decreases as the blending fraction of the second polymer component increases. The investigation suggests that blending influences crystal growth rate mainly through the deposition-rate driving force and growth-rate coefficient. The model is further validated by simulating the experimental data for the crystallization of a blend of poly(vinylidenefluoride)[PVDF] and poly(vinyl acetate)[PVAc] at various blending fractions.     

Kinetics of condensation of adenine at the mercury electrolyte interface

The kinetics of phase transitions of adenine adsorbed on mercury are studied by chronocoulometry and chronoamperometry from aqueous 0.1 M KClO₄ and 0.5 M NaF solutions. Experimental conditions have been selected to minimise, in the overall kinetic response, the contribution of the initial current decay, due to double-layer charging and the adsorption step. The transients corrected for these fast initial contributions present a peaked shape and can be described by the classical theory for nucleation and growth. The potential dependences of the rate constants of nucleation and growth have been obtained from double potential step experiments. The analysis of the condensation kinetics according to the classical nucleation theory leads to the evaluation of the line tension, and the Gibbs energy of formation of a critical cluster and its size.     

Behavior of pure and mixed DPPC liposomes spread or adsorbed at the air-water interface

Liposomes from pure dipalmitoylphosphatidylcholine (DPPC) and mixed DPPC: distearoylphosphatidylcholine (DSPC): soybean lecithin (SL) prepared by the Bangham method with sonication were dispersed into solution or spread at the interface and the kinetics of the surface film formation was studied by measuring and recording the evolution of superficial tension, surface potential, and superficial (¹⁴C labeled) DPPC density.A simple theoretical approach can describe these kinetics by two processes: irreversible diffusion of closed vesicles into or from the bulk phase, and irrevers ible transformation of closed spherical vesicles into destroyed ones which form the surface film. Diffusion controls the phenomenon for small initial amounts of liposomes.Transformation controls the phenomenon for important initial amounts of liposomes. The kinetic constant of the transformation,K, does not depend on the technique used to form the surface film (spreading or adsorption).The equilibrium and rheological properties of surface films formed after liposome spreading are compared to those of monolayers     

Some novel efforts to describe the nucleation and growth at electrodeposition

Some alternative ways are developed of looking at the model concepts on electrochemical nucleation. The article consists in several parts concerning several stages of the overall process of nucleation and growth: the statistical approach to nucleation kinetics, the kinetics of the initial stage of the nuclei growth, the growth of an individual cluster under combined charge transfer and diffusion control, nucleation rate and the overall number of clusters, the growth of an increasing number of clusters at overlapping of diffusionally depleted zones, and galvanostatic nucleation.     

Multicomponent dynamical nucleation theory and sensitivity analysis

Vapor to liquid multicomponent nucleation is a dynamical process governed by a delicate interplay between condensation and evaporation. Since the population of the vapor phase is dominated by monomers at reasonable supersaturations, the formation of clusters is governed by monomer association and dissociation reactions. Although there is no intrinsic barrier in the interaction potential along the minimum energy path for the association process, the formation of a cluster is impeded by a free energy barrier. Dynamical nucleation theory provides a framework in which equilibrium evaporation rate constants can be calculated and the corresponding condensation rate constants determined from detailed balance. The nucleation rate can then be obtained by solving the kinetic equations. The rate constants governing the multistep kinetics of multicomponent nucleation including sensitivity analysis and the potential influence of contaminants will be presented and discussed.     

A new methodology for the simulation of solid state phase transition kinetics by combination of nucleation and nuclei growth processes

A new methodology for the simulation of solid state phase transition kinetics has been developed by combining the influence of nucleation rate, nuclei growth rate and the power p characterizing the contact area between the growing particles. The equations used in this methodology were well known, and have been used previously for creating some of the most popular solid-state kinetic equations. The developed methodology made possible calculations of separate rate constants for two processes affecting the rate of phase transition—nucleation (described with K ₁) and nuclei growth (described with K ₂). Similar phase transitions were also approximated with the well-known single constant Avrami–Erofeev equation, but we successfully calculated both constants according to the new methodology, which allowed a separate evaluation of these two processes and explained the different induction periods. The effects of empirically adjusted constants on theoretically calculated kinetic curves were thus determined.     

Simulation of secondary nucleation of polymer crystallization via a model of microscopic kinetics

We present simulations of the mechanism of secondary nucleation of polymer crystallization, based on a new model accounting for the microscopic kinetics of attaching and detaching. As the key feature of the model, we introduced multibody-interaction parameters that establish correlations between the attaching and detaching rate constants and the resulting thickness and width of the crystalline lamella. Using MATLAB and Monte Carlomethod, we followed the evolution of the secondary nuclei as a function of various multibody-interaction parameters. We identified three different growth progressions of the crystal:(i) Widening, (ii) thickening and (iii) simultaneously thickening and widening of lamellar crystals, controlled by the corresponding kinetic parameters.     

Nucleation parameters for polymer crystallization from non-isothermal thermal analysis

Differential scanning calorimetry (DSC) has been used to obtain kinetic and nucleation parameters for polymer crystallization under a non-isothermal mode of operation. The available isothermal nucleation growth-rate equation has been modified for non-isothermal kinetic analysis. The values of the nucleation constant (K _g ) and surface free energies (, _e ) have been obtained for i-polybutene-1, i-polypropylene, poly(L-lactic acid), and polyoxymethylene and are compared with those obtained from isothermal kinetic analysis; a good agreement in both is seen.     

Monte Carlo simulations of single crystals from polymer solutions

A novel "anisotropic aggregation" model is proposed to simulate nucleation and growth of polymer single crystals as functions of temperature and polymer concentration in dilute solutions. Prefolded chains in a dilute solution are assumed to aggregate at a seed nucleus with an anisotropic interaction by a reversible adsorption/desorption mechanism, with temperature, concentration, and seed size being the control variables. The Monte Carlo results of this model resolve the long-standing dilemma regarding the kinetic and thermal roughenings, by producing a rough-flat-rough transition in the crystal morphology with increasing temperature. It is found that the crystal growth rate varies nonlinearly with temperature and concentration without any marked transitions among any regimes of polymer crystallization kinetics. The induction time increases with decreasing the seed nucleus size, increasing temperature, or decreasing concentration. The apparent critical nucleus size is found to increase exponentially with increasing temperature or decreasing concentration, leading to a critical nucleus diagram composed in the temperature-concentration plane with three regions of different nucleation barriers: no growth, nucleation and growth, and spontaneous growth. Melting temperatures as functions of the crystal size, heating rate, and concentration are also reported. The present model, falling in the same category of small molecular crystallization with anisotropic interactions, captures most of the phenomenology of polymer crystallization in dilute solutions.     

Dynamics of hydrogen bond complexes in polymer melts

The dynamics of hydrogen bond complex formation between functional groups which are attached to a polymer chain, is studied in the molten state. The concentration of complexes in the thermodynamic equilibrium is distorted by the application of a large oscillatory strain in the nonlinear viscoelastic regime. The relaxation back to the thermodynamic equilibrium is studied as a function of the temperature in the linear viscoelastic regime. From the mechanical response the kinetic analysis can be performed using a modified Doi-Edwards theory. Using the equilibrium constants obtained from IR-spectroscopy, the rate constants for complex formation and decomplexation are obtained. The temperature dependence is equivalent to the temperature dependence of the zero shear viscosity which implies that complex formation is a diffusion-controlled process.     

Modelling the precipitation of copper oxalate aggregates

The precipitation of copper oxalate has been studied in a batch reactor. Like many other systems, the morphology of these particles suggests that they were formed by an aggregation mechanism. A mathematical model has been developed to predict particle-size distributions grown in a batch reactor, which accounts for growth by two competing mechanisms, i.e., atomistic growth and particle aggregation. The results of this model are in good agreement with experimental observations for the precipitation of copper oxalate aggregates and other spherical aggregation systems cited in the literature.