Polymorph formation studied by 3D nucleation simulations. Application to a yellow isoxazolone dye, paracetamol, and L-glutamic acid

Knowledge of the nucleation and growth behavior of polymorphs is vital in a variety of industrial applications. With the aid of the growth probability method the nucleus size is obtained as a function of the driving force for crystallization by simulating the growth probability of clusters of various sizes. From these values the cluster interfacial energy can be computed, allowing for the determination of the nucleation rate. The simulations show that nucleation of the metastable form of a yellow isoxazolone dye dominates at higher driving forces while below a certain driving force the stable form nucleates. Two other compounds show dominant nucleation of their stable form, even at extreme driving forces. This is in accordance with experimental findings for all these compounds. The growth probability method is therefore a promising indicator for polymorph nucleation behavior.     

Monte Carlo simulations of critical cluster sizes and nucleation rates of water

We have calculated the critical cluster sizes and homogeneous nucleation rates of water at temperatures and vapor densities corresponding to experiments by Wolk and Strey [J. Phys. Chem B 105, 11683 (2001)]. The calculations have been done with an expanded version of a Monte Carlo method originally developed by Vehkamaki and Ford [J. Chem. Phys. 112, 4193 (2000)]. Their method calculates the statistical growth and decay probabilities of molecular clusters. We have derived a connection between these probabilities and kinetic condensation and evaporation rates, and introduce a new way for the calculation of the work of formation of clusters. Three different interaction potential models of water have been used in the simulations. These include the unpolarizable SPC/E [J. Phys. Chem. 91, 6269 (1987)] and TIP4P [J. Chem. Phys. 79, 926 (1983)] models and a polarizable model by Guillot and Guissani [J. Chem. Phys. 114, 6720 (2001)]. We show that TIP4P produces critical cluster sizes and a temperature and vapor density dependence for the nucleation rate that agree well with the experimental data, although the magnitude of nucleation rate is constantly overestimated by a factor of 2 x 10(4). Guissani and Guillot's model is somewhat less successful, but both the TIP4P and Guillot and Guissani models are able to reproduce a much better experimental temperature dependency of the nucleation rate than the classical nucleation theory. Using SPC/E results in dramatically too small critical clusters and high nucleation rates. The water models give different average binding energies for clusters. We show that stronger binding between cluster molecules suppresses the decay probability of a cluster, while the growth probability is not affected. This explains the differences in results from different water models.     

Heterogeneous multicomponent nucleation theorems for the analysis of nanoclusters

In this paper we present a new form of the nucleation theorems applicable to heterogeneous nucleation. These heterogeneous nucleation theorems allow, for the first time, direct determination of properties of nanoclusters formed on pre-existing particles from measured heterogeneous nucleation probabilities. The theorems can be used to analyze the size (first theorem) and the energetics (second theorem) of heterogeneous clusters independent of any specific nucleation model. We apply the first theorem to the study of small water and n-propanol clusters formed at the surface of 8 nm silver particles. According to the experiments the size of the two-component critical clusters is found to be below 90 molecules, and only less than 20 molecules for pure water, less than 300 molecules for pure n-propanol. These values are drastically smaller than the ones predicted by the classical nucleation theory, which clearly indicates that the nucleating clusters are too small to be quantitatively described using a macroscopic theory.     

Key thermodynamic characteristics of nucleation on charged and neutral cores of molecular sizes in terms of the gradient density functional theory

The gradient density functional theory and the Carnahan–Starling model formulated for describing the contribution of hard spheres have been used to calculate the profiles of condensate density in small critical droplets formed via homogeneous nucleation, as well as in stable and critical droplets formed via heterogeneous nucleation on solid charged and neutral condensation cores of molecular sizes. The calculations performed for water and argon at different values of condensate chemical potential have yielded the heights of the activation barriers for homoand heterogeneous nucleation as functions of vapor supersaturation at preset system temperatures. The interaction of condensate molecules with a solid core has been described by the resultant potential of molecular attractive forces. In the case of a charged core, the long-range Coulomb potential of electric forces has additionally been taken into account. Dielectric permittivities have been calculated as known functions of the local density of the fluid and temperature. The radius of the equimolecular droplet surface has been chosen as a variable describing the droplet size. Dependences of the chemical potential of condensate molecules in a droplet on its size have been plotted for water and argon with allowance for the action of capillary, electrostatic, and molecular forces. It has been shown that the role of the molecular force potential in heterogeneous nucleation increases with the size of condensation cores.     

Comparison between the classical theory predictions and molecular simulation results for heterogeneous nucleation of argon

We have performed Monte Carlo simulations of homogeneous and heterogeneous nucleations of Lennard-Jones argon clusters. The simulation results were interpreted using the major concept posing a difference between the homogeneous and heterogeneous classical nucleation theories-the contact parameter. Our results show that the multiplication concept of the classical heterogeneous nucleation theory describes the cluster-substrate interaction surprisingly well even for small molecular clusters. However, in the case of argon nucleating on a rigid monolayer of fcc(111) substrate at T=60 K, the argon-substrate atom interaction being approximately one-third as strong as the argon-argon interaction, the use of the classical theory concept results in an underestimation of the heterogeneous nucleation rate by two to three orders of magnitude even for large clusters. The main contribution to this discrepancy is induced by the failure of the classical theory of homogeneous nucleation to predict the energy involved in bringing one molecule from the vapor to the cluster for clusters containing less than approximately 15 molecules.     

Evolution of photoionization spectra of metal clusters as a function of size

Electronic structure effect in small metallic clusters up ton=15 are investigated through three series of experiments performed on one-valence-electron-atom clusters and two-valence-electron ones. In these experiments the cluster molecular beam is probed by photoionization mass spectroscopy, either by using a tunable laser source for alkali clusters or by synchrotron radiation for mercury ones. With alkali clusters the results are related to fragmentation effects, ionization potential measurements and photoionization efficiency curve profile analysis in the threshold region. The similar behavior of the homogeneous and heterogeneous clusters and the comparison with theoretical models suggest that forn≧3 the valence electrons are partially delocalized. This similarity against the electronic structure is not found in the nucleation process which generates homogeneous and heterogeneous clusters with a strong difference in their respective abundances. For mercury clusters the evolution with size for excitation spectra of two autoionizing lines is obtained up ton=8. Results show that they do not have a metallic character. This is also supported by the observation of small doubly charged mercury clusters forn≧5 which are stable against the Coulomb explosion.     

Direct measurement of critical nucleus size in confined volumes

In crystallization, the critical nucleus size is of pivotal importance. Above this size, it is favorable for the new crystalline phase to form; below this size, the clusters will tend to dissolve rather than grow. To date, there has been no direct method for measuring the critical nucleus size. Instead, the size is typically calculated from the variation of crystallization rates with temperature. This involves using bulk values of the interfacial tension and enthalpy of fusion, which are inappropriate for small critical nucleus sizes. Here, we present a direct method for measuring the size of the critical nucleus, based on observing crystallization temperatures of materials within microemulsions. Using this approach, the number of molecules in the critical nucleus can be found simply by measuring the droplet size. Data on the freezing of water in water-in-oil microemulsions with and without the nucleating agent, heptacosanol, are presented to support our hypothesis. The results show that the critical nucleus contains 90-350 ice molecules for water pool radii of approximately 1.2-1.8 nm for the heptacosanol-doped microemulsions in which heterogeneous nucleation is initiated at the droplet interface. For the microemulsions without heptacosanol, the critical nucleus contains 70-210 ice molecules for water pool radii of approximately 1.2-1.8 nm. The smaller values arise because homogeneous nucleation occurs and therefore the crystallization temperatures are lower. We can also determine how bulk properties are perturbed at the nanoscale, and we find that the ratio of the ice-water interfacial tension to the enthalpy of fusion decreases significantly for water pool radii that are <2 nm.     

Patterning inorganic (CaCO3) thin films via a polymer-induced liquid-precursor process

The biomimetic synthesis of patterned mineral thin films, based on a combination of the microcontact printing technique and a novel crystallization process called the polymer-induced liquid-precursor (PILP) process, is demonstrated. The PILP process enables the deposition of smooth and continuous calcitic mineral films (up to 1500 nm in thickness) under low-temperature and aqueous-based processing conditions. The films are formed by deposition of colloidal droplets composed of a liquid-phase mineral precursor that is induced by a polymeric process-directing agent (polyaspartate or polyacrylate salts). The droplets can be preferentially deposited onto patterned substrates templated with self-assembled monolayers (SAMs) of alkanethiolate on gold. The droplets coalesce to form an amorphous mineral film, which then transforms (solidifies and crystallizes) while retaining the shape of the patterned template, providing a means for patterning the location and morphology of two-dimensional calcite crystals. A vertical substrate experiment supports the premise that the calcite films are created by adsorption of colloidal droplets from solution, rather than heterogeneous nucleation and growth of an amorphous phase on the SAMs. Large single-crystalline domains, on the order of 50-100 microm, can be "molded" into nonequilibrium morphologies by constraining the mineral precursor to a chemically defined "compartment". Biominerals are well recognized for their elaborate nonequilibrium molded crystal morphologies, and increasing evidence suggests that many biominerals are formed from an amorphous precursor that is stabilized by polyanionic proteins. The biomimetic system examined here, which consists of a polyanionic process-directing agent in combination with a functionalized organic template, offers a practical tool for generating complex inorganic structures such as those found in biominerals.     

Mean-field kinetic nucleation theory

A new semiphenomenological model of homogeneous vapor-liquid nucleation is proposed in which the cluster kinetics follows the "kinetic approach to nucleation" and the thermodynamic part is based on the revised Fisher droplet model with the mean-field argument for the cluster configuration integral. The theory is nonperturbative in a cluster size and as such is valid for all clusters down to monomers. It contains two surface tensions: macroscopic (planar) and microscopic. The latter is a temperature dependent quantity related to the vapor compressibility factor at saturation. For Lennard-Jones fluids the microscopic surface tension possesses a universal behavior with the parameters found from the mean-field density functional calculations. The theory is verified against nucleation experiments for argon, nitrogen, water, and mercury, demonstrating very good agreement with experimental data. Classical nucleation theory fails to predict experimental results when a critical cluster becomes small.     

Quasi-unary homogeneous nucleation of H2SO4-H2O

We show that the binary homogeneous nucleation (BHN) of H2SO4-H2O can be treated as quasi-unary nucleation of H2SO4 in equilibrium with H2O vapor. A scheme to calculate the evaporation coefficient of H2SO4 molecules from H2SO4-H2O clusters is presented and a kinetic model to simulate the quasi-unary nucleation of H2SO4-H2O is developed. In the kinetic model, the growth and evaporation of sulfuric acid clusters of various sizes are explicitly simulated. The kinetic quasi-unary nucleation model does not have two well-recognized problems associated with the classical BHN theory (violation of the mass action law and mismatch of the cluster distribution for monomers) and is appropriate for the situations where the assumption of equilibrium cluster distribution is invalid. The nucleation rates predicted with our quasi-unary kinetic model are consistent with recent experimental nucleation experiments in all the cases studied, while the most recent version of the classical BHN model systematically overpredicts the nucleation rates. The hydration of sulfuric acid clusters, which is not considered in the classical model but is accounted for implicitly in our kinetic quasi-unary model, is likely to be one of physical mechanisms that lead to lower nucleation rates. Further investigation is needed to understand exactly what cause the difference between the kinetic quasi-unary model and the classical BHN model.     

Effect of magnesium ions on oriented growth of calcite on carboxylic acid functionalized self-assembled monolayer

The combined effect of templating and solution additives on calcite crystallization was studied. Self-assembled monolayers of mercaptoundecanoic acid supported on silver, as templates, induced the uniform, oriented nucleation of calcite from the (012) plane. The presence of Mg2+ in the crystallizing solution affected the crystal growth dramatically, due to the selective Mg binding to the calcite planes roughly parallel to the c-axis. Highly homogeneous arrays of oriented crystals with characteristic sizes, shapes, and morphology, depending on the relative concentration of Mg and Ca ions, were synthesized.     

自由表面的Ni原子团簇的熔化

采用分子动力学模拟技术研究了不同尺寸的Ni原子团簇的熔化过程.团簇的最初构型为FCC结构.研究结果表明,原子团簇的熔化温度与原子团簇中原子的个数有关,团簇的熔化首先从表面开始,当外层原子成为液态后,整个团簇的熔化从液态层开始,直至核心区域.该熔化过程可以被称为非均质熔化,自由表面充当非均质形核位置.作为对比,对无自由表面的大块固态Ni的熔化过程也进行了模拟,其熔化温度高于实验温度约400 K.表明对无自由表面的大块固态的熔化过程,液相形成无非均质形核位置,熔化的本质过程受均质形核机理控制.     

Modelling of nano-alloying and structural evolution of bimetallic core-shell nanoparticles obtained via the microemulsion route

A Monte Carlo model has been developed to describe the formation of bimetallic nanoparticles via the microemulsion route. The motivation stems from the need to understand the kinetics of nanoparticle formation in microemulsion droplets in order to determine the best experimental conditions to synthesize a nanoparticle with a given structure. We focus our study on the influence of the homogeneous and heterogeneous critical nucleus sizes of both metals on nanoparticle structure, as well as the role played by the surfactant film flexibility. The study reveals that the final structure is sensitive to changes in the critical nucleus numbers, because these parameters determine the rate of nucleation. An increase in the difference between nucleation rates of both metals gives rise to a better segregation of metals in the final nanoparticle. Likewise, as long as the formation of heterogeneous seeds is faster, the degree of alloying is greater. Finally, a fast material intermicellar exchange leads to a better mixture of metals, so the influence of the critical nucleus sizes on nanoparticle structure becomes less pronounced as the flexibility of surfactant film is increased.     

Heterogeneous condensation of the Lennard-Jones vapor onto a nanoscale seed particle

The heterogeneous condensation of a Lennard-Jones vapor onto a nanoscale seed particle is studied using molecular dynamics simulations. Measuring the nucleation rate and the height of the free energy barrier using the mean first passage time method shows that the presence of a weakly interacting seed has little effect on the work of forming very small cluster embryos but accelerates the rate by lowering the barrier for larger clusters. We suggest that this results from a competition between the energetic and entropic features of cluster formation in the bulk and at the heterogeneity. As the interaction is increased, the free energy of formation is reduced for all cluster sizes. We also develop a simple phenomenological model of film formation on a small seed that captures the general features of the nucleation process for small heterogeneities. A comparison of our simulation results with the model shows that heterogeneous classical nucleation theory provides a good estimate of the critical size of the film but significantly overestimates the size of the barrier.     

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.     

Nucleation of NaCl nanoparticles in supercritical water: molecular dynamics simulations

Formation of NaCl nanoparticles in supercritical water is studied using molecular dynamics simulation method. We have simulated particle nucleation and growth in NaCl-H2O fluids, with salt concentration of 5.1 wt %, in the temperature and density range of 673-1073 K and 0.17-0.34 g/cm(3), respectively. The cluster size distributions, the size of critical nuclei and cluster lifetimes are reported. The size distribution of emerging clusters shows a very strong dependence on the system's density, with larger clusters forming at lower densities. Clusters consisting of approximately 14-24 ions appear critical for the thermodynamic states examined. The local structures of critical clusters are found to be amorphous. The lifetime values for clusters containing more than 20 ions are in the range of 10-50 ps. We have calculated the NaCl nucleation rates, which appear to be on the order of 10(28) cm(-3) s(-1).     

Bismuth sulfide thin films with low resistivity on self-assembled monolayers

Using self-assembled monolayers (SAMs), highly crystalline bismuth sulfide thin films with low electrical resistivity have been prepared from aqueous solution at low temperature (40-70 degrees C). The nucleation and growth process of Bi2S3 thin films was investigated in detail by XPS, AES, SEM, XRD, SAED, and HRTEM. Solution conditions have marked effects on the microstructure, growth rate, and mechanism of Bi2S3 films. Increased solution temperature resulted in a higher growth rate and a shorter induction time due to a higher supersaturation degree. In the solution of pH 1.12, homogeneous nucleation and the attachment process dominated the formation of Bi2S3 films. In contrast, at pH 0.47 Bi2S3 thin films were formed via heterogeneous nucleation and growth. The c-axial orientation of bismuthinite films was enhanced with the increase of reaction time. By controlling the solution supersaturation and reaction duration, highly crystalline Bi2S3 films composed of closely packed and coalescent crystallites could be realized, whose dark electrical resistivity could reach as low as 0.014 Omega cm without any post-treatment.     

Role of surface heterogeneity and molecular interactions in the charge-transfer process through self-assembled thiolate monolayers on Au(111)

A comparative study of charge-transfer processes from/to methyl-terminated and carboxylate-terminated thiolate-covered Au(111) surfaces to/from immobilized methylene blue (MB) molecules is presented. Scanning tunneling microscopy images with molecular resolution reveal the presence of molecular-sized defects, missing rows, and crystalline domains with different tilts that turn the thickness of the alkanethiolate SAM (the spacer) uncertain. The degree of surface heterogeneity at the SAMs increases as the number of C units (n) in the hydrocarbon chain decreases from n = 6. Defective regions act as preferred paths for MB incorporation into the methyl-terminated SAMs, driven by hydrophobic forces. The presence of negative-charged terminal groups at the SAMs reduces the number of molecules that can be incorporated, immobilizing them at the outer plane of the monolayer. Only MB molecules incorporated into the SAMs close to the Au(111) surface (at a distance < 0.5 nm) are electrochemically active. MB molecules trapped in different defects explain the broad shape and humps observed in the voltammogram of the redox couple. The heterogeneous charge-transfer rate constants for MB immobilized into methyl-terminated thiolate SAMs are higher than those estimated for carboxylate- terminated SAMs, suggesting a different orientation of the immobilized molecule in the thiolate environment.