Dynamic structure of methane/n-nonane clusters during nucleation and growth

We report results on nucleation, growth, and structure formation of methane/n-nonane clusters in an expanding system investigated by molecular dynamics simulation. From bulk phase equilibria data, it is expected that the concentration of the less volatile substance n-nonane in the clusters is very high. However, analyses of experimental data in the literature suggest somewhat higher methane content at onset of nucleation. Our simulations show that the methane mole fraction is actually very high and increases even further at the beginning of the cluster growth. On the other hand, in this transient state after nucleation the methane mole fraction in the cluster core decreases, leaving a n-nonane rich core, i.e., we observe the phase separation inside the growing cluster. Methane is squeezed out from the core to the surface and then evaporates from the surface shell during expansion of the system.     

Homogeneous nucleation of n-nonane and n-propanol mixtures: a comparison of classical nucleation theory and experiments

The homogeneous nucleation rates for n-nonane-n-propanol vapor mixtures have been calculated as a function of vapor-phase activities at 230 K using the classical nucleation theory (CNT) with both rigorous and approximate kinetic prefactors and compared to previously reported experimental data. The predicted nucleation rates resemble qualitatively the experimental results for low n-nonane gas phase activity. On the high nonane activity side the theoretical nucleation rates are about three orders of magnitude lower than the experimental data when using the CNT with the approximate kinetics. The accurate kinetics improves the situation by reducing the difference between theory and experiments to two orders of magnitude. Besides the nucleation rate comparison and the experimental and predicted onset activities, the critical cluster composition is presented. The total number of molecules is approximated by CNT with reasonable accuracy. Overall, the classical nucleation theory with rigorous kinetic prefactor seems to perform better. The thermodynamic parameters needed to calculate the nucleation rates are revised extensively. Up-to-date estimates of liquid phase activities using universal functional activity coefficient Dortmund method are presented together with the experimental values of surface tensions obtained in the present study.     

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.     

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.     

Energy dependent decay rates of Lennard-Jones clusters for use in nucleation theory

Decay rates of small clusters (containing between 10 and 40 Lennard-Jones atoms) are determined by molecular dynamics simulations. The cluster is defined by the condition that the atoms must lie within a specified distance of their center of mass, and initial isothermal states are generated using a Metropolis Monte Carlo method. Plots of the logarithm of the survival fraction against time are found to be nonlinear, indicating that the decay of constant temperature clusters is non-Markovian and depends on the collision rate with a thermalizing gas. However, when the clusters are banded according to their energies, exponential decay is seen. The energy dependent decay rates from simulations agree to within a factor of 2 with those estimated from equilibrium considerations (using free energies from thermodynamic integration and assuming a Gaussian energy distribution), indicating that clusters defined in this way can be used in Markovian rate equations. During nucleation, the cluster energy distribution is shifted from its equilibrium value, leading to a reduction in the nucleation rate by a temperature dependent factor of 100 or more, in the absence of a thermalizing carrier gas.     

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.     

Probing the nucleation mechanism for the binary n-nonane/1-alcohol series with atomistic simulations

The AVUS-HR approach, which combines histogram reweighting with aggregation-volume-bias Monte Carlo nucleation simulations using self-adaptive umbrella sampling, was extended to multicomponent nucleation systems. It was applied to investigate the homogeneous vapor-liquid nucleation for the binary n-nonane/1-alcohol series, including the n-nonane/methanol, n-nonane/ethanol, n-nonane/1-propanol, n-nonane/1-butanol, n-nonane/1-hexanol, and n-nonane/1-decanol systems. The simple transferable potentials for phase equilibria-united atom force field was used in this investigation. It was found that the nucleation free energy (NFE) contour plots obtained for these binary n-nonane/1-alcohol nucleation systems exhibit rather interesting mechanistic features, some of which are distinct from other binary systems previously studied (such as water/ethanol and water/n-nonane). In addition, the NFE profiles show a subtle evolution with the increase in alcohol chain length, from a somewhat two-pathway type of shape as observed for the n-nonane/methanol system to a more normal single-pathway one for systems involving longer alcohols (1-hexanol and 1-decanol). In contrast, the NFE maps obtained for the other three binary systems involving those medium-length alcohols display the most striking feature with the saddle point stretched almost all the way from the n-nonane-enriched to the alcohol-enriched domain, implying that multiple pathways coexist on the nucleation map. These free energy profiles were shown to be consistent with the non-ideal nucleation behavior observed experimentally for this binary series, namely, a rather reluctant conucleation of the alcohols with n-nonane. In particular, this non-ideal behavior becomes more severe with a decrease in the alcohol chain length. Also, analysis of the compositions of the critical nuclei indicates a reluctant mixing behavior between these two species, i.e., depletion of the alcohol at low alcohol activity or depletion of n-nonane at low n-nonane activity, in agreement with the experimental interpretations. Furthermore, a microscopic inhomogeneity is present inside these critical nuclei, that is, alcohols aggregate via hydrogen bonds forming alcohol-enriched domains.     

On surface tension theory of salt melts

Density functional theory was developed to take into account the effect of charge density gradient on the surface tension of asymmetric ionic melts. The predicted values are compared with the experimental data on the surface tension of the majority of alkali metal halides.     

Connecting theory with experiment to understand the initial nucleation steps of heteropolyoxometalate clusters

A complimentary combination of Density Functional Theory (DFT) methodology and Electrospray Ionization-Mass Spectrometry (ESI-MS) has been utilized to increase our limited understanding of the first nucleation steps in the formation of the [XM(12)O(40)](n-) Keggin polyoxometalates (POMs) (where addenda metal atom M = W or Mo, and the heteroatom X = P or As). We postulate that the first key steps of nucleation into discrete, high nuclearity heteropolyanions proceed via the formation of isodinuclear species (e.g. [M(2)O(7)](2-)), which undergo successive steps of protonation and water condensation to form a heterotrinuclear fragment, which acts as a template for the constituent parts required for subsequent aggregation and formation of the plenary Keggin heteropolyanion. The stability of calculated structures of the numerous postulated intermediates has been analysed and discussed in detail, and these results complemented using experimental mass spectrometry, using an assembly (reaction solution analysis) and disassembly (fragmentation of single crystals) approach. Overall, no significant differences between the Keggin POMs were found when changing the addenda metal atom (W or Mo) or the heteroatom (P or As); although small differences among the lowest-energy structures were detected.     

Towards understanding the nucleation mechanism for multi-component systems: an atomistic simulation of the ternary nucleation of water/n-nonane/1-butanol

Inspired by the previous finding of some unusual vapour/liquid nucleation results on the ternary water/n-nonane/1-butanol system, atomistic simulations were carried out for a detailed investigation of this mixture. These simulations reproduced the experimentally-reported non-ideal nucleation behaviour for this system, including both onset activities and the average compositions of the critical nuclei. Close examination of the nucleation free energy data and the structure of the critical nuclei reveals two types of phase separation. One occurs internally inside the cluster via formation of a multi-layered structure. The other takes place externally, leading to the coexistence of multiple nucleation channels, characterized by critical clusters of different compositions. Such mechanistic and structural heterogeneity is the microscopic origin of the complex nucleation behaviour observed for this ternary mixture.     

Monte Carlo simulation methodology of the ghost interface theory for the planar surface tension

A novel "ghost interface" expression for the surface tension of a planar liquid-vapor interface is derived in detail from consideration of the free energy of the system, and a methodology for utilization of this new technique is given. An augmented Monte Carlo computer simulation procedure is developed specifically for the ghost interface, including derivation of long-range corrections resulting from potential truncation and a modified Gibbs ensemble technique for the simulation of adjacent coexisting phases. Results generated from the ghost interface theory for the surface tension are presented and found to be in good quantitative agreement with those resulting from the Kirkwood-Buff equation. Applications of this new approach to curved and to supersaturated systems are also discussed.     

Simulating the nucleation of water/ethanol and water/n-nonane mixtures: mutual enhancement and two-pathway mechanism

A combination of the aggregation-volume-bias and configurational-bias Monte Carlo algorithms and the umbrella sampling technique was applied to investigate two different binary vapor-liquid nucleation systems: water/ethanol and water/n-nonane. The simulations are able to reproduce the different nonideal nucleation behavior observed experimentally for these two systems, i.e., the mutual enhancement of nucleation rates for water/ethanol mixtures and the two-pathway nucleation for water/n-nonane mixtures. Structural analysis provides microscopic explanations for the observed nucleation behavior. In particular, the simulations show a large and size-dependent surface enrichment of ethanol in the water/ethanol droplets, which confirms the previous experimental interpretation for this system. The immiscibility observed even for small water/n-nonane clusters causes the two-pathway nucleation mechanism.     

Some observations on the scaled-particle theory of solutions and the surface tension of solvents

The energy necessary to form a cavity of appropriate size for a solute can be calculated by use of the scaled-particle theory if the effective hard-sphere diameter σ₁ of the solvent is known. A method is presented for obtaining σ₁ for solvents for which gas-solubility data are not available. The method is based on an empirical correlation between the surface tension of the solvent and the function $$\frac{1}{{\sigma _1^2 }}\left[ {\frac{{3y}}{{1 - y}} + \frac{1}{2}{\text{ }}\left( {\frac{{3y}}{{1 - y}}} \right)^2 } \right]$$ a function which appears in expressions for the surface tension and the cavity energy in the scaled-particle theory. Some general observations about the cavity energies for large solutes (≥6 Å diameter) are also made.     

Flow rate analysis of a surface tension driven passive micropump

A microfluidic passive pumping method relying on surface tension properties is investigated and a physical model is developed. When a small inlet drop is placed on the entrance of a microfluidic channel it creates more pressure than a large output drop at the channel exit, causing fluid flow. The behavior of the input drop occurs in two characteristic phases. An analytical solution is proposed and verified by experimental results. We find that during the first phase the flow rate is stable and that this phase can be prolonged by refilling the inlet drop to produce continuous flow in the microchannel.     

Testing the Gouy-Chapman theory by means of surface tension measurements for SDS-NaCl-H2O mixtures

Surface tension isotherms were measured for sodium dodecyl sulfate (SDS) at different concentrations of added salt (NaCl). The free energy of the surfactant monolayer was assessed by invoking the Gouy-Chapman theory for the charged head groups, the hydrophobic (Tanford) free energy of transfer of the hydrocarbon chain, and the hydrocarbon chain configurational free energy according to Gruen's calculations and finally macroscopic contact terms. In particular, the effect of an increased salt concentration in bulk was examined. Theoretical predictions compare well with the experimental findings, and good agreement was found with respect to both the variation of free energy of the monolayer and the surface pressure behavior. Thus, at least for a liquid-expanded monolayer of SDS, the Gouy-Chapman model yields a satisfactory account of the electrostatic contribution to the thermodynamic properties at different salt concentrations of NaCl.     

Some estimates of the surface tension of curved surfaces using density functional theory

Density functional theory is used to calculate the surface tension of planar and slightly curved surfaces, which can be written as gamma(R)=gamma(infinity)(1-2delta(infinity)R), where R is the radius of curvature of the surface. Calculations are performed for a Lennard-Jones fluid, split into a hard-sphere repulsive potential and an attractive part. The repulsive part is treated using the local density approximation. The attractive part is treated using a high temperature approximation (HTA) in which the pair correlation function is approximated by the Percus-Yevick pair correlation function of a uniform hard-sphere fluid evaluated at a position-dependent average density. An expression relating the Tolman length delta(infinity) to the density profile of the planar surface is derived. Numerical results are presented for the planar surface tension gamma(infinity) and for delta(infinity) and are compared with those using mean field theory (MFT) and with those using the square-gradient approximation. Values for gamma(infinity) using the HTA are 30%-40% higher than those using MFT. Values for delta(infinity) using the HTA are around -0.1 (in units of the Lennard-Jones parameter sigma) and only weakly dependent on temperature. These values are less negative than the values from MFT. The square-gradient approximation gives reasonable estimates of the more accurate nonlocal results for both the MFT and the HTA.     

A dynamical theory of nucleation for colloids and macromolecules

A general theory of nucleation for colloids and macromolecules in solution is formulated within the context of fluctuating hydrodynamics. A formalism for the determination of nucleation pathways is developed and stochastic differential equations for the evolution of order parameters are given. The conditions under which the elements of classical nucleation theory are recovered are determined. The theory provides a justification and extension of more heuristic equilibrium approaches based solely on the free energy. It is illustrated by application to the low-concentration/high-concentration transition in globular proteins, where a novel two-step mechanism is identified, where the first step involves the formation of long-wavelength density fluctuations, and the second step is the actual nucleation event occurring within the fluctuation.     

Quasihomogeneous nucleation of amyloid beta yields numerical bounds for the critical radius, the surface tension, and the free energy barrier for nucleus formation

Amyloid aggregates are believed to grow through a nucleation mediated pathway, but important aggregation parameters, such as the nucleation radius, the surface tension of the aggregate, and the free energy barrier toward aggregation, have remained difficult to measure. Homogeneous nucleation theory, if applicable, can directly relate these parameters to measurable quantities. We employ fluorescence correlation spectroscopy to measure the particle size distribution in an aggregating solution of Alzheimer's amyloid beta molecule (Abeta(1-40)) and analyze the data from a homogeneous nucleation theory perspective. We observe a reproducible saturation concentration and a critical dependence of various aspects of the aggregation process on this saturation concentration, which supports the applicability of the nucleation theory to Abeta aggregation. The measured size distributions show a valley between two peaks ranging from 5 to 50 nm, which defines a boundary for the value of the nucleation radius. By carefully controlling the conditions to inhibit heterogeneous nucleation, we can hold off nucleation in a 25 times supersaturated solution for at least up to 3 h at room temperature. This quasi-homogeneous kinetics implies that at room temperature, the surface energy of the Abeta/water interface is > or =4.8 mJ/m(2), the free energy barrier to nucleation (at 25 times supersaturation) is > or =1.93x10(-19) J, and the number of monomers in the nucleus is > or =29.     

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.