Electrolytic nucleation of silver on a glassy carbon electrode: Part II. Steady-state nucleation rate

The dependence of the number of nuclei on time is investigated in a wide overvoltage interval using different glassy carbon electrodes. The data for the steady-state nucleation rate are interpreted on the basis of both classical and atomistic theoretical concepts. Conclusions are drawn for the applicability of the two models of nucleation.     

Determination of flux from a saddle field fast-atom bombardment gun

The flux or beam density (equivalent current/area) of xenon atoms striking the sample target from a saddle field fast-atom bombardment (FAB) gun has been compared with that from a cesium ion gun mounted on the same instrument. A shielded Faraday cup mounted on the end of a solids probe was used to measure directly the flux of the Cs⁺ beam. Samples of methylene blue in glycerol solution were then exposed to the ion beam at different fluxes and the extents of reduction were measured. The extent of reduction varied linearly with flux up to a value of about 1.16 × 10¹³ particles s^?1 cm^?2 (1.85 μ cm^?2); above this level, the reduction effect appeared to saturate. FAB spectra were obtained from the same dye solution by using varying settings of the FAB gun. By comparing the extents of reduction of the dye from the two guns, the flux from the atom gun could be estimated. Observation of luminescence from a CsI-coated target allowed estimation of the area of the atom beam. The atom beam “equivalent current” could then be calculated by multiplying the flux times the area. It was noted that for given settings, the flux from the atom gun depended on the physical condition of the gun electrodes. With new electrodes, a flux ≥ 1.16 × 10¹³ particles s^?1 cm^?2 was obtained with nominal gun emission currents of 0.60–1.0 mA. Electrodes used extensively, but freshly cleaned, provided a flux of ～ 8 × 10¹² particles s^?1 cm^?2 at nominal emission currents of 0.40–1.0 mA. With dirty electrodes this flux could only be achieved at the highest (1.0 mA) emission current. This decline in performance occurs over a matter of months as a result of contamination and erosion of the electrodes during use. Such behavior can adversely affect spectral reproducibility even when nominal FAB gun voltage and emission current are carefully reproduced.     

Electrochemical nucleation and the classical theory: Overpotential and temperature dependence of the nucleation rate

A comparison between the activation energies for critical nuclei formation obtained from both the classical nucleation theory and Arrhenius kinetic analysis has been proposed. Results obtained indicate that such comparison is hampered by temperature-induced changes of the surface energies, modifying the contact angles and correspondingly the activation energies for nucleation. Published in Russian in Elektrokhimiya, 2008, Vol. 44, No. 6, pp. 704–711. The text was submitted by the authors in English.     

Influence of vapor depletion on nucleation rate

During condensation in finite systems part of molecules is transformed from supersaturated mother phase to a new one and depletion of the mother phase occurs. Kinetic equations describing homogeneous nucleation process including decrease of supersaturation are solved numerically. It is shown that dependency of nucleation rate on nucleus size reaches some maximum, which decreases with time and moves to higher nucleus sizes. Nucleation rate is negative for undercritical size of nuclei.     

The vaporization rate of ice at temperatures near its melting point

The first study of free vaporization kinetics of ice at temperatures near its melting point is reported. The experimental approach employed is based on a unique combination of thermal desorption spectroscopy, microcalorimetry, and time-of-flight mass spectrometry, making it possible to overcome challenges associated with the introduction of volatile solids into a high vacuum environment. Measurements of the vaporization rate of polycrystalline ice demonstrate that the vaporization kinetics deviate dramatically from those predicted by a simple mobile precursor mechanism. The vaporization rate follows Arrhenius behavior from -40 to 0 degrees C with an effective activation energy of 50+/-4 kJ/mol, which is significantly higher than the value predicted by the simple mobile precursor mechanism. Extrapolation of earlier measurements conducted below -40 degrees C yields a value of approximately 0.02 at 0 degrees C for the vaporization coefficient alphav. In contrast, experimentally determined vaporization coefficient is found to be 0.7+/-0.3 and shows a weak dependence on temperature up to the bulk melting point. The role of possible surface phase transitions in the mechanisms of release and uptake of H2O and other chemical species by ice surfaces is discussed.     

On the rate of nucleation in binary systems

The technique used by many authors for finding a saddle point on the free energy surface in a binary system has been criticized recently. It is shown that the new approach proposed in two recent articles does not lead to any better agreement between theory and experiment than the previous method, especially for mixtures presenting strong surface enrichment effects.     

Direct observation of nucleus structure and nucleation pathways in apoferritin crystallization.

Using atomic force microscopy (AFM) in situ during the crystallization of the protein apoferritin from its solution, we imaged the arrangement of the molecules in near-critical clusters, larger or smaller than the crystal nucleus, that are representative of the nucleus structure. At supersaturations Delta mu/k(B)T of 1.1 -- 1.6 -- 2.3, the nuclei contain about 50 -- 20 -- 10 molecules. The molecular arrangement within the nuclei is similar to that in the crystal bulk. Contrary to the general belief, the observed nuclei are not compact molecular clusters, but are planar arrays of several rods of 4--7 molecules set in one or two monomolecular layers. Similarly unexpected nuclei structures might be common, especially for anisotropic molecules. Hence, the nucleus structure should be considered as a variable by advanced theoretical treatments.     

An algorithm for semi-empirical design of nucleation rate surface

During the last half of century, Classical Nucleation Theory (CNT) has been developed and there have been advances in the molecular theory of nucleation. Most of these efforts have been directed towards small molecule system modeling using intermolecular potentials. Summarizing the nucleation theory, it can be concluded that the current theory is far from complete. Agreement is generally not obtained between experimental and theoretical results. In practical applications, parametric theories can be used for the systems of interest. However, experimental measurements are still the best source of information on nucleation. Experiments are labor intensive and costly, and thus, it is useful to extend the value of limited experimental measurements to a broader range of nucleation conditions. The available nucleation parameters represent only small regions of possible nucleation conditions over the range from the critical temperature to absolute zero. Thus, it is useful to develop better tools to use the data to estimate semi-empirical nucleation rate surfaces. Following our published approach, the nucleation rate surface for any system can be constructed over its phase diagram. This concept involves using the phase equilibrium diagram to establish lines of zero nucleation rates. Nucleation rate surfaces arise from equilibrium lines and their extensions that are representing unstable equilibria. Only limited experimental data is available for use in normalizing the slopes of the linearized nucleation rate surfaces. The nucleation rate surface is described in terms of steady-state nucleation rates. To design the surfaces of nucleation rates, several assumptions are presented. In the present study, an algorithm for the semi-empirical design of nucleation rate surfaces is introduced. The topology of the nucleation rate surface for a unary system using the example of water vapor nucleation is created semi-empirically. The nucleation of two concurrent (stable and unstable) phase states of critical embryos is considered in the context of multi-surface nucleation rates. Only one phase transition (melting) in the condensed state of water is considered for simplicity. The nucleation rate surface is constructed numerically using the available experimental results for vapor nucleation and phase diagram for water. The nucleation rate for water vapor is developed for the full temperature interval, i.e. from critical point to absolute zero. The results help to suggest a new direction for experimental nucleation research.     

Dependence on strain rate of the nucleation of cracks in polystyrene at 293°K

The processes associated with the deformation and fracture of polystyrene tested in uniaxial tension have been studied over a range of strain rates from 1.4 × 10^?2 to 4.3 × 10^?7 sec^?1 and at constant stresses between 4.1 and 2.9 kg/mm². The effect of strain rate on the surface craze distribution prior to fracture, the fracture stress, the mechanism of nucleation of cracks, and the nature of fracture surfaces associated with slow and fast crack propagation have been determined. The changes in fracture surface appearance have been studied using optical and stereoscan microscopy. The observations are consistent with the model presented in a previous paper. Fracture is preceded by craze formation, cavitation in the craze, coalescence of cavities to form large planar cavities which propagate slowly until a critical stage is reached at which fast crack propagation occurs. The effect of changes of strain rate and material variables on these processes is discussed.     

Relation between homogeneous nucleation rate and supersaturation in pyrolysis of methane

Conclusions The existence of a maximum for the function: homogeneous nucleation rate of carbon vs methane pressure, was established on the basis of the theory of homogeneous nucleation from the vapors.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 10, pp. 2416–2417, October, 1978.     

Formation mechanism of critical nucleus during nucleation process of liquid metal sodium

To deeply understand the formation mechanism of a critical nucleus during the nucleation process of liquid metal sodium, a system consisting of 10 000 Na atoms has been simulated by using molecular dynamics method. The evolutions of nuclei are traced directly, adopting the cluster-type index method. It is found that the energies of clusters and their geometrical constraints interplay to form the favorable microstructures during the nucleation process. The nucleus can be formed through many different pathways, and the critical size of the nucleus would be different for each pathway. It is also found that the critical nucleus is nonspherical and may include some metastable structures. Furthermore, the size of the cluster and its internal structure both play a crucial role in determining whether it is a critical nucleus, and this is in agreement with the simulations by computing the free energy of the Lennard-Jones system [D. Moroni, P. R. ten Wolde, and P. G. Bolhuis, Phys. Rev. Lett. 94, 235703 (2005)].     

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.     

Power law of nucleation rate of folded-chain single crystals of polyethylene

The number-average molecular weight (M _n) dependence of the primary nucleation rate (I) of polyethylene (PE) folded-chain single crystals was studied in the ordered phase. We observed that the M _n dependence of I is mainly controlled by the diffusion process of polymer chains within the interface between a nucleus and the melt and/or within the nucleus. The results show that I decreases with increasing M _n and follows a power law I∝M _n ^−2.3 for the ordered phase. It is named the power law of the nucleation rate. In a previous article we showed that for the disordered phase I∝M _n ⁻¹. In this article, we concluded that I decreases with increasing M _n and follows a universal power law, I∝M _n ^−H for both ordered and disordered phases. The power H depends on the degree of order of the crystalline phase, which is related to the morphology. Received: 13 September 2000 Accepted: 15 November 2000     

Analysis of experimental data for the nucleation rate of water droplets

A formula for the stationary nucleation rate J is proposed and used for analysis of experimental data for the dependence of J on the supersaturation ratio S in isothermal homogeneous nucleation of water droplets in vapors. It is found that the experimental data are described quite successfully by the proposed formula which is based on (i) the Gibbs presentation of the nucleation work in terms of overpressure, (ii) the Girshick-Chiu [J. Chem. Phys. 93, 1273 (1990); 94, 826 (1991)] self-consistency correction to the equilibrium cluster size distribution, and (iii) the Reguera-Rubi [J. Chem. Phys. 115, 7100 (2001)] kinetic accounting of the nucleus translational-rotational motion. The formula, like that of Wolk and Strey [J. Phys. Chem. B 105, 11683 (2001)], could be used as a semiempirical relation describing the J(S) dependence for nucleation in vapors of single-component droplets or crystals of substances with insufficiently well known equations of state.     

The i-E Equations of Steady-state Voltammograms at Microdisk Electrodes

Based on the theories of conventional electrodes, as well as the properties of microdisk electrode, the i-E equations for chronoamperometry at disk microelectrode for reversible, quasi-reversible and irreversible systems are derived. Steady-state voltammograms for the oxidation of [Fe(CN)6]4- , Fe2+ and ascorbic acid were measured at a series of microdisk electrodes with different radii. The conventional log-plot shows that oxidations of [Fe(CN)6]4- and ascorbic acid are reversible and totally irreversible, respectively, but the oxidation of Fe2+ is reversible at larger radius microdisk electrodes and quasi-reversible at smaller radius microdisk electrodes. The application of the log-plot to the voltammograms yielded a straight line, its slope allows us to evaluate the charge transfer coefficient and the intercept gives values of the electron transfer rate constant.     

Enhanced nucleation, growth rate, and dopant incorporation in ZnO nanowires

Pure and Co-doped ZnO nanowire arrays were grown on polished silicon substrates with high rates via an electrochemical technique. A negative potential applied to the substrate not only enhances the nucleation density on polished substrates more than 4 orders of magnitude but also increases the growth rate by 35 times over that obtained in the absence of the potential. Furthermore, incorporation of metallic dopants in ZnO nanowires was demonstrated in the low-temperature process. This fast growth technique provides a route to fabrication of low-cost highly oriented ZnO nanowires on polished substrate for industrial applications.     

Thermal dependence of nucleation and growth rate in polypropylene by non isothermal calorimetry

Crystallization of polypropylene at a constant cooling rate is studied by differential scanning calorimetry. The results are interpreted using Ozawas theory, which allows the determination of the type of nucleation. In the studied polypropylene, a transition between a sporadic in time and an instantaneous nucleation is found at about 122 °C. Furthermore, an extension of Ozawa's theory is proposed to predict the thermal dependence of the spherulite growth rate. The results are consistent with those obtained by direct microscopic observation.