Emulsion polymerization. VII. Effects of instantaneous chain termination during the interval of particle nucleation

In the Smith-Ewart treatment of particle nucleation all particles were assumed to grow as if they contained exactly one radical. Modification of particle growth rate by chain termination in growing particles and reinitiation of nongrowing particles by radicals entering them was neglected in this interval although such effects were taken into account after the particle number became constant. The present theory eliminates this inconsistency for the case where chain termination is instantaneous. This refinement does not change previous predictions for the final number of particles, the steady state rate or the particle radius. Unlike the old theory, the present theory predicts continuous decay of the average number of radicals per particle from the initial value of unity to the steady-state value of one half. It also provides new theoretical predictions for the shape of the conversion-time curve at the initial stages of the reaction. Experimental data are reviewed in the context of the theory. Experimental particle sizes, steady-state conversion rates, and conversions at completion of particle nucleation were often in good quantitative agreement with the theoretical predictions. The predicted maximum in the conversion rate at the time when particle nucleation became completed was observed in a few instances. The theoretically predicted initial shape of the conversion-time curve may not be always observable due to experimental difficulties mainly associated with induction effects.     

On the behaviour of molecules of the quinoline group at the water—Mercury interface: Part III. The kinetics of the isoquinoline transition in the presence of an “inert” electrolyte

The reorientation transition, which involves two distinct monolayers of isoquinoline molecules, has been investigated by using the single-potential step and the double-potential step methods under various experimental conditions.The cathodic transients correspond to a liquid → solid transition. Their morphology and half-times have been measured at various initial and final potentials, and for several isoquinoline concentrations close to the saturation value. At small overvoltages, the reorientation process is determined by heterogeneous (“instantaneous”) nucleation, while progressive nucleation and growth prevail at higher potentials. Recourse to the double-potential step method affords an efficient way of assessing separately the influence of the overvoltage on the rate constants for nucleation and growth. Determination of the critical nucleus size and the activation energy for each of the two processes has been based on an adaptation of the Brandes theory developed for two-dimensional crystallization from a supersaturated vapour phase. The kinetics are markedly dependent on the initial state, which can be easily controlled by the potential and the bulk concentration. When the potential is stepped from the region where there is superadsorption, progressive nucleation is particularly fast, while starting from a partially depleted layer gives much slower transients with extensive tailing due to diffusional hindrance.The anodic transients show consonant characteristics which indicate that the initial film can be considered as a two-dimensional solid, and that boundary defects are acting as nucleation centres, during the solid → liquid transition triggered by the potential step.     

Nucleation of silica nanoparticles measured in situ during controlled supersaturation increase. Restructuring toward a monodisperse nonspherical shape

The first stages of the nucleation and growth of silica nanoparticles are followed in situ using both SAXS and Raman spectroscopy. Coupling these two techniques allows the determination of the fractions of soluble and solid silica as a function of the reaction time. SAXS also enables demonstrating that major modifications of the structure occur after the initial precipitation period, inducing an increase of the precipitate density. These structural modifications have important implications in the initial nucleation growth stages, which have never been introduced either in classical models or in more recent kinetic nucleation theories. Such restructuration stages could contribute to explain the monodispersity of the obtained silica nanoparticles that is not predicted by classical models.     

Multivariable kinetic theory of the first order phase transitions

The problem of calculation of the steady state homogeneous nucleation rate in the multidimensional space of the variables describing a nucleus is considered. Within the framework of the theory proposed, expressions for the nucleation rate and the steady state distribution function of nuclei are derived. The expression for the nucleation rate is invariant with respect to the space dimensionality and, in particular, involves the result of the one-dimensional theory. The distribution function is obtained in the initial, physical variables. In connection with the analysis of restrictions on the current direction, the question of symmetry of the matrix of diffusivities is considered; on the basis of the detailed balance principle it is shown that this matrix is symmetric. The question of normalizing the equilibrium distribution functions is investigated and the physical picture of the equilibrium state is described. The procedure of reducing the multidimensional theory to the one-dimensional one is described.     

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 water vapor in microcracks on the surface of β-AgI aerosol particles: 2. Thermodynamics of nucleation

Free energy, entropy, and the work of formation of condensation nuclei at 260 K in microcracks of β-AgI crystal structure at the initial stage of nucleation preceding crystallization are calculated by the Monte Carlo method. Unlike ideal crystal surface, nuclei in microcracks are thermodynamically stable and the barrier of free energy of nucleation is absent. Conditions of microcrack are favorable for the crystallization that qualitatively changes the regime and rate of nucleation. Stable size of nuclei at the humidity corresponding to natural atmosphere is sufficient for the filling of nanoscopic microcracks and the attainment of substrate surface. The probability of nucleus formation in microcracks by the fluctuation mechanism is incomparably higher than the probability of their formation on the defect-free surface. High crystallization ability of the particles of βAgI aerosol is ensured by multiple surface microcracks acting as active sites in combination with its complementary crystal structure. The efficiency of aerosols as stimulants of the nucleation of water vapor at negative Celsius temperatures is determined by the surface density and geometry of nanoscopic cracks and fissures on the particle surface.     

On the importance of surface structure in electrochemistry: the well-defined Au (111) single crystal electrode surface

The electrochemical nucleation of cadmium onto vitreous carbon and onto tin oxide electrodes in studied using potentiostatic methods. The influence of supporting electrolyte is investigated and in every case new and interesting features arise. The deposition of cadmium on tin oxide is of particular interest and evidently occurs via an initial process of 2D nucleation followed, at higher overpotentials, by 3D nucleation.     

Isothermal crystallization of poly(vinylidene fluoride) in the presence of high static electric fields. I. Primary nucleation phenomenon

Primary nucleation of poly(vinylidene fluoride) (PVF₂) γ-phase crystals from the melt is affected by the presence of an electric field. Crystallization under the electric field is studied by polarized optical microscopy, thermal analysis, and wide-angle x-ray diffraction. Preliminary results indicate that the γ-phase crystal nucleation rate and content are enhanced by the electric field. A modification of the classical theory of homogeneous nucleation of a crystalline phase is proposed to account for the experimental observations. Electrostatic interaction between the nucleus total polarization and the electric field contributes to the free energy of nucleation to a very large extent at low undercooling. Theoretical predictions indicate that a static electric field will increase the nucleation rate of a polar phase and will decrease the nucleation rate of a nonpolar phase. Confirmation of the former fact is observed experimentally.     

A multigrid method for N-component nucleation

A multigrid algorithm has been developed enabling more efficient solution of the cluster size distribution for N-component nucleation from the Becker-D?ring equations. The theoretical derivation is valid for an arbitrary number of condensing components, making the simulation of many-component nucleating systems feasible. A steady state ternary nucleation problem is defined to demonstrate its efficiency. The results are used as a validation for existing nucleation theories. The non-steady state ternary problem provides useful insight into the initial stages of the nucleation process. We observe that for the ideal mixture the main nucleation flux bypasses the saddle point.     

非均匀成核法表面包覆氧化铝的尖晶石LiMn2O4研究

采用高温固相法合成尖晶石LiMn2O4,以非均匀成核方式对其进行包覆氧化铝的表面处理.通过XRD、SEM、粒度分析等技术对表面处理前后的LiMn2O4进行表征,分析了表面处理前后LiMn2O4物理特性的变化,并结合电化学性能测试,研究了表面处理工艺对LiMn2O4电化学容量与循环性能的影响.未经表面处理的LiMn2O4在1 C倍率下初期放电容量为86.5 mA•h•g－1,50次循环充放电后容量衰减26.3％.表面包覆0.5％、1％(w)氧化铝的LiMn2O4在1 C倍率下的初期放电容量分别为96.0、80.1 mA•h•g－1,经过50次循环后,容量分别降低7.0％、5.6％.实验结果表明,表面处理后的LiMn2O4循环性能显著提高,而且随着氧化物含量的增加,循环性能增强,但放电容量降低.     

Electrolytic nucleation of silver on a glassy carbon electrode: Part I. Mechanism of critical nucleus formation

The initial stage of electrodeposition of silver on a glassy carbon electrode is investigated using a double-pulse potentiostatic method. Data are obtained for the concentration dependence of the steady-state nucleation rate I and conclusions are drawn for the probable mechanism of critical nucleus formation.     

超临界水中碳酸钠团簇成核与生长分子动力学模拟

应用分子动力学方法研究了碳酸钠颗粒在超临界水中的成核与生长过程. 计算了温度为700-1100 K、压力在23-30 MPa下碳酸钠的团聚过程, 计算时间为1 ns. 对体系结合能与径向分布函数的分析表明, 碳酸钠成核过程主要受静电作用的影响. 在超临界态下, 水分子与Na⁺和CO₃^2- 之间的静电作用降低, Na⁺与CO₃^2- 能够很容易碰撞形成Na₂CO₃小团簇. 在Na₂CO₃整个成核过程中, 单个离子的碰撞在前50 ps 内完成, 同时离子碰撞速率达到10³⁰ cm^-3·s^-1. 另外, 在成核阶段温度的影响比压力更加明显, 温度越高, 离子碰撞速率越快, 形成的初始团簇越多. 而压力对Na₂CO₃团簇的进一步生长影响较大.     

Bubble nucleation in polymeric liquids. II. theoretical considerations

A theory based on classical nucleation theory is developed for bubble nucleation in polymer solutions. The theory requires information on solubility, diffusivity, concentration, surface tension, temperature, and degree of supersaturation. The effects of supersaturation and of the presence of large molecules in a liquid mixture on the free energy of bubble formation are included in the theoretical development. A semiempirical equation for the determination of bubble nucleation rate is developed, with the aid of experimental results reported in part I of this series. Using the experimental data, computer simulations of bubble nucleation in polymer solutions are performed. The consumptions of the volatile component in a liquid mixture, due to bubble nucleation and subsequent growth, and the variation of bubble nucleation rate during the expansion process are included in the simulation of the bubble nucleation process.     

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.     

Na_5P_3O_(10)-Ca(OH)_2-CO_2-H_2O体系纳米CaCO_3的成核与生长

通过化学分析、SEM显微分析技术结合RosinRamiler概率统计理论从介观层次研究Na5P3O10CaOH2CO2H2O体系纳米CaCO3的合成反应及其成核和生长过程。结果表明Na5P3O10对CaOH2的碳化反应具有抑制作用。随着Na5P3O10的增加体系中CaCO3的成核速率B0逐渐增大。在Na5P3O10=0ppm时CaCO3结晶的生长由长程扩散和凝聚生长控制Na5P3O10=380.4760.9ppm时前期受短程扩散和界面反应控制、后期受长程扩散控制。Na5P3O10的存在抑制了纳米CaCO3的晶体生长。     

Water vapor nucleation on an infinite substrate with complementary structure: 1. The mechanism of nucleation

The nucleation of water vapor on the infinite surface of a silver iodide crystal at 260 K is simulated. Long-range electrostatic and polarization interactions are taken into account by the Ewald method. The free energy and work of equilibrium formation of nuclei are calculated at the molecular level by the method of bicanonical statistical ensemble. It is shown that, at the initial stage, the substrate is completely covered with a water monolayer. The substrate tends to decrease by two orders of magnitude the vapor pressure required to form the critical nucleus of a monomolecular film with a size of 10² molecules, the nucleation rate being increased by tens of orders of magnitude as compared to homogeneous nucleation. The saturation pressure above the adsorbed monomolecular film is 12 times lower than that above the flat ice surface. The free energy at the edges of “spots” per unit length is 1.4 × 10^?11 J/m. The critical size of the spot increases with a decrease in vapor pressure as the inverse second power of the logarithm of pressure.     

Complete thermodynamically consistent kinetic model of particle nucleation and growth: numerical study of the applicability of the classical theory of homogeneous nucleation

A complete thermodynamically consistent elementary reaction kinetic model of particle nucleation and growth from supersaturated vapor was developed and numerically evaluated to determine the conditions for the steady-state regime. The model treats all processes recognized in the aerosol science (such as nucleation, condensation, evaporation, agglomerationcoagulation, etc.) as reversible elementary reactions. It includes all possible forward reactions (i.e., of monomers, dimers, trimers, etc.) together with the thermodynamically consistent reverse processes. The model is built based on the Kelvin approximation, and has two dimensionless parameters: S0-the initial supersaturation and Theta-the dimensionless surface tension. The time evolution of the size distribution function was obtained over the ranges of parameters S0 and Theta. At low initial supersaturations, S0, the steady state is established after a delay, and the steady-state distribution function corresponds to the predictions of the classical nucleation theory. At high initial supersaturations, the depletion of monomers due to condensation on large clusters starts before the establishing of the steady state. The steady state is never reached, and the classical nucleation theory is not applicable. The boundary that separates these two regimes in the two dimensionless parameter space, S0 and Theta, was determined. The model was applied to several experiments on water nucleation in an expansion chamber [J. Wolk and R. Strey, J. Phys. Chem. B 105, 11683 (2001)] and in Laval nozzle [Y. J. Kim et al., J. Phys. Chem. A 108, 4365 (2004)]. The conditions of the experiments performed using Laval nozzle (S0=40-120) were found to be close to the boundary of the non-steady-state regime. Additional calculations have shown that in the non-steady-state regime the nucleation rate is sensitive to the rate constants of the initial steps of the nucleation process, such as the monomer-monomer, monomer-dimer, etc., reactions. This conclusion is particularly important for nucleation from supersaturated water vapor, since these processes for water molecules at and below the atmospheric pressure are in the low pressure limit, and the rate constants can be several orders of magnitude lower than the gas kinetic. In addition, the impact of the thermodynamic inconsistency of the previously developed partially reversible kinetic numerical models was assessed. At typical experimental conditions for water nucleation, S0=10 and Theta=10 (T=250 K), the error in the particle nucleation rate introduced by the thermodynamic inconsistency exceeds one order of magnitude.     

Electrochemical nucleation: Part II. The electrodeposition of silver on vitreous carbon.

A study has been made of the electrochemical nucleation of silver on vitreous carbon from aqueous solutions of silver nitrate.The nucleation is shown to be progressive and mass transferred controlled. The rate of nucleation is somewhat better described bythe atomistic theory than by classical theories. The addition of EDTA reduces the rate of nucleation as the result, it is suggested,of the adsorption of EDTA by the graphite surface. The sensitivity of the rate of the nucleation to the condition of the graphitesurface is also shown by the effects of changing the salvation acidity.