Polynuclear crystal growth in electrocrystallization of silver: Determining the nucleus size via the nucleation theorem

We employ the nucleation theorem for a model-independent determination of the size of the two-dimensional (2D) Ag nucleus with the aid of experimental data for nucleation-mediated electrochemical crystal growth. The growth is investigated of a screw dislocation-free Ag(100) single crystal face in aqueous solution of AgNO₃ at 318 K. The data are for the stationary values of the overpotential during galvanostatic pulses with sufficiently high amplitudes to ensure polynuclear growth mechanism. It is found that the Gibbs-Thomson equation of the classical theory of 2D nucleation describes very well the experimentally obtained overpotential dependence of the size of the 2D Ag nucleus. Published in Russian in Elektrokhimiya, 2008, vol. 44, No. 6, pp. 698–703. The text was submitted by the authors in English.     

Determining the nucleation rate from the dimer growth probability

A new method is proposed for the determination of the stationary one-component nucleation rate J with the help of data for the growth probability P2 of a dimer which is the smallest cluster of the nucleating phase. The method is based on an exact formula relating J and P2, and is readily applicable to computer simulations of nucleation. Using the method, the dependence of J on the supersaturation s is determined by kinetic Monte Carlo simulations of two-dimensional (2D) nucleation of monolayers on the (100) face of Kossel crystal. The change of J over nearly 11 orders of magnitude is followed and it is found that the classical nucleation theory overestimates the simulation J values by an s-dependent factor. The 2D nucleus size evaluated via the nucleation theorem is described satisfactorily by the classical Gibbs-Thomson equation and its corrected version accounting for the spinodal limit of 2D nucleation.     

Rate of two-dimensional nucleation: verifying classical and atomistic theories by Monte Carlo simulation

We present kinetic Monte Carlo simulation data for the stationary rate J of two-dimensional nucleation of monolayer-thick crystal clusters in the growth of an atomically smooth (100) face of single-component Kossel crystal. The data are over a wide range of supersaturations s and effective broken-bond energies omega of nearest-neighbor atoms, and the J values span about 15 orders of magnitude. The simulation reveals that, in the s,omega range studied, the ln J vs s curve is smooth but with nearly linear portions connected with rather sharply curved segments when the omega value is sufficiently great. The simulation J(s) data are used for verification of the classical (CNT) and atomistic (ANT) nucleation theories without free parameters. It turns out that whereas J is overestimated by CNT, it is underestimated by ANT. The disagreement between theory and simulation is much greater for CNT than for ANT and, with increasing omega, it increases for the former but almost disappears for the latter. However, the ANT prediction about broken linear ln J vs s dependence is not confirmed by the simulation in the s,omega range studied.     

Accounting for fluctuations in cluster parameters upon the description of nucleation in supersaturated vapor

A theory is proposed for stationary homogeneous nucleation in supersaturated vapor in which a modified expression for the rate of cluster evaporation was used to calculate the equilibrium distribution over the nucleus sizes and the rates of their formation. This rate was determined by the extrapolation to the region of small sizes of the corresponding expression for the macroscopic droplet derived according to thermodynamic notions that take fluctuations into account. Modified dependences of the size of critical nucleus and the rate of nucleation on the supersaturation and the temperature are determined and compared with the data of the classical theory of nucleation and experimental results.     

Experimental study of homogeneous nucleation from the bismuth supersaturated vapor: evaluation of the surface tension of critical nucleus

The homogeneous nucleation of bismuth supersaturated vapor is studied in a laminar flow quartz tube nucleation chamber. The concentration, size, and morphology of outcoming aerosol particles are analyzed by a transmission electron microscope (TEM) and an automatic diffusion battery (ADB). The wall deposit morphology is studied by scanning electron microscopy. The rate of wall deposition is measured by the light absorption technique and direct weighting of the wall deposits. The confines of the nucleation region are determined in the "supersaturation cut-off" measurements inserting a metal grid into the nucleation zone and monitoring the outlet aerosol concentration response. Using the above experimental techniques, the nucleation rate, supersaturation, and nucleation temperature are measured. The surface tension of the critical nucleus and the radius of the surface of tension are determined from the measured nucleation parameters. To this aim an analytical formula for the nucleation rate is used, derived from author's previous papers based on the Gibbs formula for the work of formation of critical nucleus and the translation-rotation correction. A more accurate approach is also applied to determine the surface tension of critical drop from the experimentally measured bismuth mass flow, temperature profiles, ADB, and TEM data solving an inverse problem by numerical simulation. The simulation of the vapor to particles conversion is carried out in the framework of the explicit finite difference scheme accounting the nucleation, vapor to particles and vapor to wall deposition, and particle to wall deposition, coagulation. The nucleation rate is determined from simulations to be in the range of 10(9)-10(11) cm(-3) s(-1) for the supersaturation of Bi(2) dimers being 10(17)-10(7) and the nucleation temperature 330-570 K, respectively. The surface tension σ(S) of the bismuth critical nucleus is found to be in the range of 455-487 mN/m for the radius of the surface of tension from 0.36 to 0.48 nm. The function σ(S) changes weakly with the radius of critical nucleus. The value of σ(S) is from 14% to 24% higher than the surface tension of a flat surface.     

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.     

Crisis of stability of hydration shell of Na<Superscript>+</Superscript> ion in condensing water vapor

The Gibbs energy and equilibrium work of the formation of nuclei of the condensed phase on sodium ions are calculated on the molecular level by a Monte Carlo simulation using a detailed interaction model. The stationary rate of nucleation is estimated based on the data obtained. The presence of ionic impurities only substantially affects the rate of nucleation at strong vapor supersaturation. The nucleus losses its thermodynamic stability with an increase in the size of the nucleus and the barrier is formed depending on the work of formation on the size of the nucleus. An abrupt loss of stability is accompanied by pushing the ion off of the microdroplet surface and the restoration of the network of hydrogen bonds. The effect of pushing an ion to the surface of a cluster greatly depends on many-particle polarization interactions.     

Transition-metal nanocluster size vs formation time and the catalytically effective nucleus number: a mechanism-based treatment

A mechanism-based equation for the size of a forming transition-metal nanocluster vs time has been derived based on the Finke-Watzky two-step mechanism for transition-metal nanocluster nucleation (A --> B, rate constant k1) and autocatalytic growth (A + B --> 2B, rate constant k2), where A is the nanocluster precursor and B is the growing nanocluster. The resultant equation expresses nanocluster diameter as a function of time, D(t), in terms of k1, k2, the initial concentration of the nanocluster precursor complex, [A]0, and the number of catalytically effective nuclei derived from either (i) the final nanocluster size, D(f), or (ii) the number of atoms in the average catalytically effective nucleus, N*, and the induction period time, t ind (N* being by definition the number of atoms present in the average size nucleus at the end of the induction period and when observable catalysis begins). By fitting experimentally determined nanocluster size vs time data using this equation, evidence for the validity of the equation is obtained for Ir(0) nanoclusters formed from the well-studied system of H2 reduction of the precursor [(1,5-COD)Ir x P2W15Nb3O62](8-). The D(t) equation is then used to determine N* for nine prior Ir(0) nanocluster preparations from five different [(1,5-COD)Ir(+)]n [anion(n-)] precursors. Also given is a relationship allowing one to interconvert between nanocluster size data and nanocluster precursor concentration data, again when the two-step nucleation and growth mechanism has been shown to apply. Some of the key experimental factors that are known to affect the kinetics of nanocluster formation, and therefore nanocluster size, are also summarized. A look ahead to needed future work is also provided.     

Graphene nucleation on transition metal surface: structure transformation and role of the metal step edge

The nucleation of graphene on a transition metal surface, either on a terrace or near a step edge, is systematically explored using density functional theory calculations and applying the two-dimensional (2D) crystal nucleation theory. Careful optimization of the supported carbon clusters, C(N) (with size N ranging from 1 to 24), on the Ni(111) surface indicates a ground state structure transformation from a one-dimensional C chain to a 2D sp(2) C network at N ≈ 10-12. Furthermore, the crucial parameters controlling graphene growth on the metal surface, nucleation barrier, nucleus size, and nucleation rate on a terrace or near a step edge are calculated. In agreement with numerous experimental observations, our analysis shows that graphene nucleation near a metal step edge is superior to that on a terrace. On the basis of our analysis, we propose the use of graphene seeds to synthesize high-quality graphene in large area.     

High-pressure acceleration of the growth kinetics of glucose isomerase crystals

The growth and dissolution rates of glucose isomerase crystals ({1 0 1} face) were measured in situ at 0.1 and 100 MPa. From these data, we determined that the solubilities at 25 degrees C were C(e) = 3.1 +/- 0.9 and 2.6 +/- 0.5 mg mL(-1) at 0.1 and 100 MPa, respectively. At the same supersaturation of sigma = 2.5 (sigma identical with ln(C/C(e)), C = the concentration of glucose isomerase, C(e) = the solubility) and temperature (T = 25 degrees C), the growth rate under 100 MPa was 7.6 times larger than that under 0.1 MPa. This result shows, for the first time, a kinetic acceleration of the growth rates of protein crystals with increasing pressure. The growth rates vs sigma data fitted well with a two-dimensional nucleation growth model of a polynucleation type. The fitting results indicate that the acceleration is mainly due to the decrease in the molecular surface energy of the glucose isomerase crystal with pressure.     

纳米二氧化硅对镍电沉积影响及在复合镀层中的化学键合状态

用线性扫描伏安法和电位阶跃法研究了n-SiO2/Ni复合电刷镀体系的电化学响应,探讨了纳米颗粒的影响;用X射线光电子谱研究了复合镀层中n-SiO2/Ni颗粒表面与基质金属间的相互作用．结果表明纳米颗粒使金属沉积过电位显著降低,电流效率、金属成核率及晶体生长速度增加,纳米颗粒对金属镍电结晶有明显的催化效应;n-SiO2/Ni表面氧的不饱和化学键与表面扩散过程中吸附态金属Ni原子键合形成Ni-O键,纳米颗粒与基质镍以化学键方式结合．     

Evaluation of surface tension and Tolman length as a function of droplet radius from experimental nucleation rate and supersaturation ratio: metal vapor homogeneous nucleation

Zinc and silver vapor homogeneous nucleations are studied experimentally at the temperature from 600 to 725 and 870 K, respectively, in a laminar flow diffusion chamber with Ar as a carrier gas at atmospheric pressure. The size, shape, and concentration of aerosol particles outcoming the diffusion chamber are analyzed by a transmission electron microscope and an automatic diffusion battery. The wall deposit is studied by a scanning electron microscope (SEM). Using SEM data the nucleation rate for both Zn and Ag is estimated as 10(10) cm(-3) s(-1). The dependence of critical supersaturation on temperature for Zn and Ag measured in this paper as well as Li, Na, Cs, Ag, Mg, and Hg measured elsewhere is analyzed. To this aim the classical nucleation theory is extended by the dependence of surface tension on the nucleus radius. The preexponent in the formula for the vapor nucleation rate is derived using the formula for the work of formation of noncritical embryo [obtained by Nishioka and Kusaka [J. Chem. Phys. 96, 5370 (1992)] and later by Debenedetti and Reiss [J. Chem. Phys. 108, 5498 (1998)]] and Reiss replacement factor. Using this preexponent and the Gibbs formula for the work of formation of critical nucleus the dependence of surface tension on the radius R(S) of the surface of tension is evaluated from the nucleation data for above-mentioned metals. For the alkali metals and Ag the surface tension was determined to be a strong function of R(S). For the bivalent metals (Zn, Hg, and Mg) the surface tension was independent of radius in the experimental range. A new formula for the Tolman length delta as a function of surface tension and radius R(S) is derived by integration of Gibbs-Tolman-Koenig equation assuming that delta is a monotonic function of radius. The formula derived is more correct than the Tolman formula and convenient for the elaboration of experimental data. Using this formula the values of delta are determined as a function of R(S) from the experimental nucleation data. It is determined that all the metals considered are characterized by strong dependence of delta on radius; for the bivalent metals delta changes sign.     

Modeling shell formation in core-shell nanocrystals in reverse micelle systems

The mechanisms responsible for the formation of the shell in core-shell nanocrystals are ion-displacement and heterogeneous nucleation. In the ion-displacement mechanism, the shell is formed by the displacement reaction at the surface of the core nanoparticle whereas in heterogeneous nucleation the core particle induces the nucleation (or direct deposition) of shell material on its surface. The formation of core-shell nanocrystals via the post-core route has been examined in the current investigation. A purely probabilistic Monte Carlo scheme for the formation of the shell has been developed to predict the experimental results of Hota et al. (Hota, G.; Jain, S.; Khilar, K. C. Colloids Surf., A 2004, 232, 119) for the precipitation of Ag2S-coated CdS (Ag2S@CdS) nanoparticles. The simulation procedure involves two stages. In the first stage, shell formation takes place as a result of the consumption of supersaturation, ion displacement, and reaction between Ag+ and excess sulfide ions. The growth in the second stage is driven by the coagulation of nanoparticles. The results indicate that the fraction of shell deposited by the ion-displacement mechanism increases with increasing ion ratio and decreases with increasing water-to-surfactant molar ratio.     

On the formation mechanism of the "pancake" decahedron gold nanoparticle

We have studied the thermodynamic and kinetic growth mechanisms behind the formation of the "pancake" decahedron (D(h)) gold nanoparticle using computer simulation. Free energy calculations showed that the full pancake morphology is thermodynamically unstable across all the nanoparticle size ranges studied. However, from observations of growth simulations we discovered that a kinetic transport mechanism plays a significant contributing role in the formation process through a transfer of adatoms from the top and bottom (111) D(h) faces to the side (100) faces. More specifically we observed how diffusing adatoms on the (111) face are at times "pulled" off this face and into the (111)-(100) edge of the D(h), forcing a row of (100) side atoms into a (1x5) hexagonal reconstruction. Subsequently, this row of atoms was observed to buckle and then deconstruct forcing adatoms out onto the (100) side face completing the transfer. This transport mechanism is shown to be the main kinetic driving force behind the growth of the thermodynamically unstable pancake D(h) nanoparticle. The observed mechanism has implications for the nonequilibrium morphologies of nanoparticles involving a (100)-(111) surface boundary, especially for systems with surface reconstructions which increase the density of the surface.     

镁铁双羟基复合金属氧化物的可控合成及晶面生长特征研究

采用成核/晶化隔离法合成镁铁双羟基复合金属氧化物MgFe-LDH,考察了Mg ∶ Fe摩尔比对MgFe-LDH晶形的影响,探讨了晶化温度及晶化时间对晶面生长选择性及晶粒尺寸的影响规律.结果表明,随Mg ∶ Fe摩尔比增大,层板阳离子排列更为规整.晶化温度对晶粒尺寸的影响显著大于晶化时间的影响.晶化温度相同,随晶化时间延长, MgFe-LDH的晶体结构趋于完整,晶粒尺寸变化不大;晶化时间相同,随晶化温度升高,晶体结构趋于完整,晶粒尺寸明显增大.所得到的MgFe-LDH沿a轴方向的晶粒尺寸对晶化温度变化的敏感程度远大于对晶化时间变化的敏感程度,但总是沿a轴方向的晶粒尺寸大于沿c轴方向的尺寸,即[110]晶面的生长速率比[002]晶面的生长速率快.     

铋在玻碳电极上电化学结晶初步研究(英文)

应用循环伏安法和计时安培法研究了铋在玻碳电极上的电结晶行为.循环伏安曲线显示了铋在玻碳电极上成核的典型特征,并表明其于玻碳电极上的电结晶是一个扩散控制过程.根据计时安培法响应曲线分析阐明了铋的浓度和过电势对成核生长机理的影响.进一步的定量测试表明该成核速率常数A和活化点密度N0随过电势增加呈现指数增大规律;扩散系数D随过电势增加呈指数衰减.以上实验结果至今未见报道.同时表明:Scharifker公式和Heerman公式均可用于本实验的理论解释.     

Atomistic nature of NaCl nucleation at the solid-liquid interface

The early stage of heterogeneous nucleation of NaCl from supersaturated NaCl aqueous solution at the water-NaCl (001) interface has been investigated by molecular dynamics simulations. The critical size of the nuclei for spontaneous growth was found to be as small as two atoms (a Na(+)-Cl(-) ion pair) at high supersaturation. Due to the presence of a relatively stable water network and the effect of the hydration force at the interface, the stable nuclei formed on the NaCl (001) are found to contain more Na(+) ions than Cl(-) ions. The different deposition characteristics of the Na(+) and Cl(-) solutes lead to a positively charged substrate and thus may introduce another driving force for nucleation besides the level of solution supersaturation. The role of water was further confirmed by comparison with NaCl epitaxy growth in the vacuum.     

Interrelation between cluster formation time, cluster growth probability, and nucleation rate

Approximate expressions are derived for the mean time tau for formation of a cluster of n molecules in nucleation of single-component phases. The derivation elucidates the interrelation between tau, the cluster growth probability P, and the stationary nucleation rate. The extraction of both tau(n) and P(n) data from individual cluster growth curves obtained in experiments or simulations is discussed. It is shown that the analysis of tau(n) data allows a model-independent determination of the nucleus size, the Zeldovich factor, the stationary nucleation rate, the frequency with which molecules are attached to the nucleus, and the difference between the works to form the nucleus and the smallest "cluster" of one molecule.     

Nucleation and growth of copper on glassy carbon: Studies in extended overpotential interval

The nucleation and growth of copper crystals on a glassy carbon electrode are investigated at different constant overpotentials. Current transients are recorded and the number of copper nuclei is microscopically registered. The experimental data for the growth current are interpreted according to the theories of progressive and instantaneous nucleation and information is obtained on the stationary nucleation rate, the saturation nucleus number density and the exchange current density at the crystals–solution interface boundary.     

纳米陶瓷颗粒的电催化效应及其在复合刷镀层中的化学状态

采用循环伏安法和电位阶跃法研究了nano-Al₂O₃ / Ni复合电刷镀体系的电化学响应，探讨了纳米颗粒对复合电沉积的影响；用X射线光电子谱研究了复合镀层中nano-Al₂O₃颗粒与基质金属之间的相互作用。结果表明纳米颗粒能使金属沉积过电位显著降低，电流效率、金属成核率及晶体生长速度增加，从而对金属镍的电结晶表现出明显的催化效应；在金属镍电结晶过程中，部分到达阴极附近的nano-Al₂O₃颗粒被电极表面捕获。金属生长面上的吸附态镍原子到达纳米颗粒与电极表面接触处，与该处纳米颗粒表面的不饱和氧原子形成Ni-O化学键，纳米颗粒与基质镍以化学键形式结合。纳米颗粒与电极表面的结合区域成为新的成核或生长中心，在随后的刷镀过程中纳米颗粒逐渐被电沉积的金属镍包埋，从而形成复合镀层。