Homogeneous nucleation of droplets from supersaturated vapor in a closed system

Kinetic equations describing homogeneous nucleation kinetics within standard model are solved numerically under the condition of a constant number of molecules in the considered system. It has consequences to decrease the supersaturation of the supersaturated vapor during the process of the formation of small droplets of a new phase. The decrease of supersaturation occurs in a short time and reaches some value which remains unchanged for a relatively long time (quasistationary regime), especially at lower initial supersaturations. This time interval decreases with increasing value of the initial supersaturation. In the quasistationary regime the nucleation rate reaches its stationary value. At higher initial supersaturation, the rate of formation of nuclei goes to some maximum value corresponding to the stationary nucleation rate and then decreases with time due to the decrease of supersaturation.     

Kinetics of supersaturated vapor nucleation on molecular condensation nuclei

The kinetics of nucleation is calculated for a supersaturated vapor containing molecular condensation nuclei, that is, foreign molecules able to induce the formation of viable nuclei of a condensed phase by themselves. In contrast to the previous calculation, the possibility of the escape of molecular condensation nuclei from very small clusters containing a few condensed vapor molecules is taken into account. More exact equations are derived for the rate of steady-state nucleation and the concentration of aerosol particles in a quasisteady-state regime of nucleation. The calculation demonstrates that, at a high probability of the escape of a molecular condensation nucleus, the predominating mechanism of cluster formation is the attachment of a molecular condensation nucleus to a cluster formed from vapor molecules rather than their condensation on the nucleus. At the same time, allowances for the possible escape of molecular condensation nuclei from clusters slightly affect the rate of nucleation and the concentration of aerosol particles being formed.     

Homogeneous nucleation in supersaturated vapors of methane, ethane, and carbon dioxide predicted by brute force molecular dynamics

Molecular dynamics (MD) simulation is applied to the condensation process of supersaturated vapors of methane, ethane, and carbon dioxide. Simulations of systems with up to a 10(6) particles were conducted with a massively parallel MD program. This leads to reliable statistics and makes nucleation rates down to the order of 10(30) m(-3) s(-1) accessible to the direct simulation approach. Simulation results are compared to the classical nucleation theory (CNT) as well as the modification of Laaksonen, Ford, and Kulmala (LFK) which introduces a size dependence of the specific surface energy. CNT describes the nucleation of ethane and carbon dioxide excellently over the entire studied temperature range, whereas LFK provides a better approach to methane at low temperatures.     

Molecular-dynamics simulation of argon nucleation from supersaturated vapor in the NVE ensemble

The possibility to conduct simulations of homogeneous nucleation of argon from a supersaturated vapor phase using a microcanonical or NVE ensemble is evaluated (NVE: number of particles N, volume V, and energy E are constant). In order to initiate a phase separation kinetic energy is removed from the system in one step which transfers the system into a supersaturated state. After this temperature jump the simulation is continued in a NVE ensemble. The simulations are performed for different initial-state points and different temperature jumps. The cluster formation and growth over the course of the adiabatic simulations are analyzed. The progression of the temperature being related to the cluster size in NVE systems is traced. Also the influence of the size of the simulation system is investigated. For a certain range of low supersaturation a dynamic coexistence between two states has been found. Furthermore, the obtained nucleation rates are correlated with two simple functions. By applying the nucleation theorems to these functions the size and excess energy of the critical cluster are estimated. The results are consistent with other theoretical data and experimental data available in the literature.     

Kinetics of NaCl nucleation in supercritical water investigated by molecular dynamics simulations

At system pressures between 17 MPa and 25 MPa the nucleation and growth of NaCl nanoparticles in water at supercritical conditions was investigated by molecular dynamics simulations at different system temperatures and system densities. Our results show that particle formation takes place within a few hundred picoseconds after the jump from ambient to supercritical conditions. After nucleation a phase of growth by adding monomers is followed by growth via cluster-cluster collisions. We present results on the time development of distributions of cluster sizes, cluster compositions, and cluster temperatures as well as radial distribution functions and nucleation rates.     

Uncovering molecular processes in crystal nucleation and growth by using molecular simulation

Exploring nucleation processes by molecular simulation provides a mechanistic understanding at the atomic level and also enables kinetic and thermodynamic quantities to be estimated. However, whilst the potential for modeling crystal nucleation and growth processes is immense, there are specific technical challenges to modeling. In general, rare events, such as nucleation cannot be simulated using a direct "brute force" molecular dynamics approach. The limited time and length scales that are accessible by conventional molecular dynamics simulations have inspired a number of advances to tackle problems that were considered outside the scope of molecular simulation. While general insights and features could be explored from efficient generic models, new methods paved the way to realistic crystal nucleation scenarios. The association of single ions in solvent environments, the mechanisms of motif formation, ripening reactions, and the self-organization of nanocrystals can now be investigated at the molecular level. The analysis of interactions with growth-controlling additives gives a new understanding of functionalized nanocrystals and the precipitation of composite materials.     

Collective solvent flows around a protein investigated by molecular dynamics simulation

Translational motions of water molecules in various systems equilibrated at room temperature are thought to be diffusive and nondirectional. We performed molecular dynamics simulations of a protein system and showed that the water molecules collectively move around the protein. The motions of two water molecules, which were about 12 A away from each other, are correlated to each other. Such collective motions of water can be regarded as flows around the protein, and the flows exhibited various coherent patterns: fair currents, vortices, and divergent flows. The patterns were highly fluctuating: a set of patterns changed to a different set of patterns within a time scale of 10 ps. Thus, the water motions observed in a scale of length smaller than 12 A and a time scale shorter than 10 ps were nondiffusive, and the motions above these scales were diffusive, where the flows disappeared. The flows near the protein surface had an orientational propensity to be highly parallel to the protein surface, and this propensity gradually vanished with an increment of distance from the protein surface. The divergent patterns of flows, which frequently emerge during the fluctuations of flows, may temporarily cause solvent drying in the vicinity of solutes. The current simulation is supportive of a molecular interaction mechanism that the fluctuations of hydration structure induce attractive interactions between solutes.     

Supramolecular self-assembly of water-soluble cavitands: investigated by molecular dynamics simulation

In this study, we have examined supramolecular self-assembly process of a hydrophobic guest with a water-soluble host known by the trivial name octa acid (OA). Two octa acids form a capsular assembly only in presence of a nonpolar guest(s). Size and shape of the guest control the stoichiometry of the capsular complex. Here, all atom molecular dynamics simulation has been utilized to investigate complex formation mechanisms of a nonpolar guest (nonylbenzene) with two OA cavitands. Nonylbenzene was encapsulated into the nonpolar cavity of OA capsule owing to solvophobic interactions. Upon encapsulation it was twisted and bent due to lack of free space within the capsule. These unusual forms obtained from the simulation study were in accord with experimental findings. The post-complexation attributes of the guest were regulated by the available free space within the OA and favorable non-covalent interactions between the guest and the walls of the OA capsule. In the identical simulation condition two OA cavitands did not form a capsule without a guest, thus indicating requirement of a guest during the self-assembly of OA cavitands.     

Scenarios of heterogeneous nucleation and growth studied by cell dynamics simulation

The dynamics of phase transformation due to homogeneous nucleation has long been analyzed using the classic Kolmogorov-Johnson-Mehl-Avrami (KJMA) theory. However, the dynamics of phase transformation due to heterogeneous nucleation has not been studied systematically even though it is vitally important technologically. In this report, the author studies the dynamics of heterogeneous nucleation theoretically and systematically using the phenomenological time-dependent Ginzburg-Landau (TDGL)-type model combined with the cell dynamics method. In this study the author focuses on the dynamics of phase transformation when the material is sandwiched by two supporting substrates. This model is supposed to simulate phase change storage media. Since both homogeneous and heterogeneous nucleations can occur simultaneously, the author predicts a few scenarios of phase transformation including homogeneous nucleation regime, heterogeneous nucleation regime, and the homogeneous-heterogeneous coexistence regime. These predictions are directly confirmed by numerical simulation using the TDGL model. The outcome of the study was that the KJMA formula has limited use when heterogeneous nucleation exists, but it could still give some information about the microscopic mechanism of phase transformation at various stages during phase transformation.     

Comparative study on methodology in molecular dynamics simulation of nucleation

Gas-liquid nucleation of 1000 Lennard-Jones atoms is simulated to evaluate temperature regulation methods and methods to obtain nucleation rate. The Berendsen and the Andersen thermostats are compared. The Berendsen thermostat is unable to control the temperature of clusters larger than the critical size. Independent of the thermostating method the velocities of individual atoms and the translational velocities of clusters up to at least six atoms are accurately described by the Maxwell velocity distribution. Simulations with the Andersen thermostat yield about two times higher nucleation rates than those with the Berendsen thermostat. Nucleation rate is extracted from the simulations by direct observation of times of nucleation onset and by the method of Yasuoka and Matsumoto [J. Chem. Phys. 109, 8451 (1998)]. Compared to the direct observation, the nucleation rates obtained from the method of Yasuoka and Matsumoto are higher by a factor of 3.     

Homogeneous nucleation and growth of melt in copper

Molecular dynamics simulations are conducted to investigate homogeneous nucleation and growth of melt in copper described by an embedded-atom method (EAM) potential. The accuracy of this EAM potential for melting is validated by the equilibrium melting point obtained with the solid-liquid coexistence method and the superheating-supercooling hysteresis method. We characterize the atomistic melting process by following the temperature and time evolution of liquid atoms. The nucleation behavior at the extreme superheating is analyzed with the mean-first-passage-time (MFPT) method, which yields the critical size, steady-state nucleation rate, and the Zeldovich factor. The value of the steady-state nucleation rate obtained from the MFPT method is consistent with the result from direct simulations. The size distribution of subcritical nuclei appears to follow a power law similar to three-dimensional percolation. The diffuse solid-liquid interface has a sigmoidal profile with a 10%-90% width of about 12 A near the critical nucleation. The critical size obtained from our simulations is in reasonable agreement with the prediction of classical nucleation theory if the finite interface width is considered. The growth of melt is coupled with nucleation and can be described qualitatively with the Johnson-Meh-Avrami law. System sizes of 10(3)-10(6) atoms are explored, and negligible size dependence is found for bulk properties and for the critical nucleation.     

A study of nucleation in supersaturated ibuprofen vapor in a flow diffusion chamber

Isothermal nucleation of supersaturated ibuprofen racemate vapor has been experimentally studied in a flow diffusion chamber at 293.3 and 301.2 K. Nucleation rates have been measured in the range of 10⁴?10⁴ cm^?3 s^?1 as functions of supersaturation. According to the first nucleation theorem, the numbers of molecules in critical nuclei have been found and used to determine the nucleation rate and supersaturation values as depending on the sizes of critical nuclei. The comparison of the experimental data with theoretical predictions has shown that the nucleation rates measured as functions of the numbers of molecules in critical nuclei are higher than the rates predicted by the classical theory by six to seven decimal orders of magnitude but, within one order of magnitude, coincide with the rates predicted by a theory previously proposed in a work by one of the authors, in which nucleation clusters were considered to be microscopic objects.     

Formation of FeCl(2)/NaCl-nanoparticles in supercritical water investigated by molecular dynamics simulations: nucleation rates

Nucleation and growth of FeCl(2) in supercritical water containing NaCl at different state points between temperatures of 798 and 873 K and system densities between 0.24 and 0.14 g cm(-3) have been studied by molecular dynamics simulations. The number of NaCl ion pairs was chosen to simulate particle formation in seawater and brine of higher salinity. Rigid SPC/E water was used to model the water molecules while a combination of Coulomb and Lennard-Jones potentials was used for the ions. Two different methods for determination of nucleation rates are applied and their results compared. We find decreasing nucleation rates with both increasing temperature and decreasing system density. Our results are also compared to those we recently obtained in an investigation of pure FeCl(2) from supercritical water. We find both increasing nucleation rates and a decreasing size of the critical cluster with increasing amount of NaCl.     

Role of nearest-neighbor drops in the kinetics of homogeneous nucleation in a supersaturated vapor

A theory of simultaneous nucleation and drop growth in a supersaturated vapor is developed. The theory makes use of the concept of "nearest-neighbor" drops. The effect of vapor heterogeneity caused by vapor diffusion to a growing drop, formed previously, is accounted for by considering the nucleation of the nearest-neighbor drop. The diffusional boundary value problem is solved through the application of a recent theory that maintains material balance between the vapor and the drop, even though the drop boundary is a moving one. This is fundamental to the use of the proper time and space dependent vapor supersaturation in the application of nucleation theory. The conditions are formulated under which the mean distance to the nearest-neighbor drop and the mean time to its appearance can be determined reliably. Under these conditions, the mean time provides an estimate of the duration of the nucleation stage, while the mean distance provides an estimate of the number of drops formed per unit volume during the nucleation stage. It turns out, surprisingly, that these estimates agree fairly well with the predictions of the simpler and more standard approach based on the approximation that the density of the vapor phase remains uniform during the nucleation stage. Thus, as a practical matter, in many situations, the use of the simpler and less rigorous method is justified by the predictions of the more rigorous, but more complicated theory.     

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.     

Duocarmycins binding to DNA investigated by molecular simulation

Duocarmycins are a potent class of antitumor agents, whose activity arises through their covalent binding to adenine nucleobases of DNA.(1-3) Here, we perform molecular dynamics (MD) and hybrid Car-Parinello QM/MM simulations to investigate aspects of duocarmycin binding to the d(pGpApCpTpApApTpTpGpApC) oligonucleotide. We focus on the derivatives (+)-duocarmycin SA (DSA) and (+)-duocarmycin SI (DSI), for which structural information of the covalent complex with the oligonucleotide is available, as well as on the related, but less reactive, NBOC-duocarmycin SA (NBOC-DSA), interacting with the same oligonucleotide. Comparison is made with adenine alkylation reaction in water performed by the smallest of these compounds (NBOC-DSA). The MD calculations suggest that, in noncovalent complexes, (i) drug binding causes a partial dehydration of the minor groove, without inducing a significant conformational changes, and (ii) DSA and DSI occupy a more favorable position for nucleophilic attack than NBOC-DSA, consistently with the lower reactivity of the latter. The QM/MM calculations, which are used to investigate the first step of the alkylation reaction, turn out to provide strongly underestimated free energy barriers. Within these approximations, our calculations suggest that an important ingredient for the experimentally observed DNA catalytic power is the polarization of the drug by the biomolecular scaffold.     

Homogeneous nucleation of particles from the vapor phase in thermal plasma synthesis

Particle nucleation and growth are simulated for iron vapor in a thermal plasma reactor with an assumed one-dimensional flow field and decoupled chemistry and aerosol dynamics. Including both evaporation and coagulation terms in the set of cluster-balance rate equations, a sharply defined homogeneous nucleation event is calculated. Following nucleation the vapor phase is rapidly depleted by condensation, and thereafter particle growth occurs purely by Browntan coagulation. The size and number of nucleated particles are found to be affected strongly by the cooling rate and by the initial monomer concentration. An explanation is presented in terms of the response time of the aerosol to changing thermodynamic conditions.This work appears in abbreviated from in the proceedings of the International Symposium on Combustion and Plasma Synthesis of High Temperature Materials, San Francisco, Oct. 24–26, 1988, to be published asCombustion and Plasma Synthesis of Hig Temperature Materials, Z. A. Munir and J. B. Holt (eds.), VCH, New York (in press).     

Postnucleation droplet growth in supersaturated gas with arbitrary vapor concentration

This work concerns the reexamination and extension of the current theory of phase transition dynamics for liquid droplets growing on soluble aerosols from a supersaturated gas mixture for the general case of arbitrary value of vapor concentration. We found that the inconsistency in the common treatment of the vapor diffusion, due to an implicit assumption of the constancy of gas density in the vicinity of a droplet by neglecting its dependency on temperature and vapor concentration, leads to the obvious discrepancy in the Maxwell expression for the growth rate regarding droplets of near critical size. Restoring the correct treatment of the vapor diffusion in terms of the mass concentration of water vapor and taking into the consideration variations of gas density in the vicinity of a droplet in compliance with the equation of state of moist air, we have obtained a new expression for the droplet growth rate valid for an arbitrary value of vapor concentration. The limitations imposed by the molecular kinetic fluxes to postnucleation diffusional growth of small droplets with a large Knudsen number are also reevaluated to include previously neglected physical effects. In particular, the essential contribution of the vapor molecular energy flux into the total kinetic molecular heat flux as well as the temperature variations of mean thermal velocities of air and vapor molecules in the vicinity of the droplet interface have been taken into consideration. Surprisingly significant differences have been found in new expressions derived for the droplet growth rate and droplet temperature, even in the limit of small vapor concentration, if comparing with commonly used results. These findings could help with better interpretation of experimental measurements to infer more reliable data for the mass and thermal accommodations coefficients.