Latent-to-sensible heat conversion kinetics during nanoparticle coalescence.

Coagulational growth in an aerosol is a multistep process; first particles collide, and then they coalesce with one another. Coalescence kinetics have been investigated in numerous prior studies, largely through atomistic simulations of nanoclusters (102-104 atoms). However, with a few exceptions, they have either assumed the process is completely isothermal or is a constant energy process. During coalescence, there is the formation of new bonds, decreasing potential energy, and correspondingly increasing internal kinetic (thermal) energy. Internal kinetic energy evolution is dependent not only on coalescence kinetics but also on heat transfer to the surrounding gas. Here, we develop and test a model of internal kinetic energy evolution in collisionally formed nanoclusters in the presence of a background gas. We find that internal kinetic energy dynamics hinge upon a power law relationship describing latent-to-sensible heat release as well as a modified thermal accommodation coefficient. The model is tested against atomistic models of 1.5-3.0 nm embedded-atom gold nanocluster sintering in argon and helium environments. The model results are in excellent agreement with the simulation results for all tested conditions. Results show that nanocluster effective temperatures can increase by hundreds of Kelvin due to coalescence, but that the rise and re-equilibration of the internal kinetic energy is strongly dependent on the background gas environment. Interestingly, internal kinetic energy change kinetics are also found to be distinct from surface area change kinetics, suggesting that modeling coalescence heat release solely due to surface area change is inaccurate.

Investigation of Zero-/High-Field Ion Mobility Orthogonal Separation Using a Hyphenated DMA-FAIMS System and Validation of the Two-Temperature Theory at Arbitrary Field for Tetraalkylammonium Salts in Nitrogen.

Toward greater separation techniques for ions, a differential mobility analyzer (DMA) has been coupled with field asymmetric waveform ion mobility spectrometry (FAIMS) to take advantage of two mobility-related but different methods of separation. The filtering effect of the DMA allows ions to be selected individually based on low-field mobility and studied in FAIMS at variable electric field, yielding mobility separations in two dimensions. Because spectra fully describe ion mobility at variable field strength, results are then compared with a two-temperature theory-predicted mobility up to the fourth-order approximation. The comparison yields excellent results up to at least 100 Td, beyond which the theory deviates from experiments. This is attributed to two effects, the enlargement of the structure due to ion heating and the inelasticity of the collisions with the nitrogen bath gas. The corrected mobility can then be used to predict the dispersion plot through a newly developed implicit equation that circumvents the possible issues related to the more elaborate Buryakov equation. Our results simultaneously show that the DMA-FAIMS coupling yields complete information on ion mobility versus the field-strength to gas-density ratio and works toward predicting such spectra from ion structures and gas properties.

Ion-neutral clustering alters gas-phase hydrogen-deuterium exchange rates.

The rates and mechanisms of chemical reactions that occur at a phase boundary often differ considerably from chemical behavior in bulk solution, but remain difficult to quantify. Ion-neutral interactions are one such class of chemical reactions whose behavior during the nascent stages of solvation differs from bulk solution while occupying critical roles in aerosol formation, atmospheric chemistry, and gas-phase ion separations. Through a gas-phase ion separation technique utilizing a counter-current flow of deuterated vapor, we quantify the degree of hydrogen-deuterium exchange (HDX) and ion-neutral clustering on a series of model chemical systems (i.e. amino acids). By simultaneously quantifying the degree of vapor association and HDX, the effects of cluster formation on reaction kinetics are realized. These results imply that cluster formation cannot be ignored when modeling complex nucleation processes and biopolymer structural dynamics.

Evaluation of Hydrogen-Deuterium Exchange during Transient Vapor Binding of MeOD with Model Peptide Systems Angiotensin II and Bradykinin.

The advancement of hybrid mass spectrometric tools as an indirect probe of molecular structure and dynamics relies heavily upon a clear understanding between gas-phase ion reactivity and ion structural characteristics. This work provides new insights into gas-phase ion-neutral reactions of the model peptides (i.e., angiotensin II and bradykinin) on a per-residue basis by integrating hydrogen/deuterium exchange, ion mobility, tandem mass spectrometry, selective vapor binding, and molecular dynamics simulations. By comparing fragmentation patterns with simulated probabilities of vapor uptake, a clear link between gas-phase hydrogen/deuterium exchange and the probabilities of localized vapor association is established. The observed molecular dynamics trends related to the sites and duration of vapor binding track closely with experimental observation. Additionally, the influence of additional charges and structural characteristics on exchange kinetics and ion-neutral cluster formation is examined. These data provide a foundation for the analysis of solvation dynamics of larger, native-like conformations of proteins in the gas phase.

A neural network parametrized coagulation rate model for <3 nm titanium dioxide nanoclusters.

Coagulation is a key factor governing the size distribution of nanoclusters during the high temperature synthesis of metal oxide nanomaterials. Population balance models are strongly influenced by the coagulation rate coefficient utilized. Although simplified coagulation models are often invoked, the coagulation process, particularly for nanoscale particles, is complex, affected by the coagulating nanocluster sizes, the surrounding temperature, and potential interactions. Toward developing improved models of nanocluster and nanoparticle growth, we have developed a neural network (NN) model to describe titanium dioxide (TiO2) nanocluster coagulation rate coefficients, trained with molecular dynamics (MD) trajectory calculations. Specifically, we first calculated TiO2 nanocluster coagulation probabilities via MD trajectory calculations varying the nanocluster diameters from 0.6 to 3.0 nm, initial relative velocity from 20 to 700 m s-1, and impact parameter from 0.0 to 8.0 nm. Calculations consider dipole-dipole interactions, dispersion interactions, and short-range repulsive interactions. We trained a NN model to predict whether a given set of nanocluster diameters, impact parameter, and initial velocity would lead to the outcome of coagulation. The accuracy between the predicted outcomes from the NN model and the MD trajectory calculation results is >95%. We subsequently utilized both the NN model and MD trajectory calculations to examine coagulation rate coefficients at 300 and 1000 K. The NN model predictions are largely within the range 0.65-1.54 of MD predictions, and importantly NN predictions capture the local minimum coagulation rate coefficients observed in MD trajectory calculations. The NN model can be directly implemented in population balances of TiO2 formation.

Condensable Vapor Sorption by Low Charge State Protein Ions.

Measurement of the gas-phase ion mobility of proteins provides a means to quantitatively assess the relative sizes of charged proteins. However, protein ion mobility measurements are typically singular values. Here, we apply tandem mobility analysis to low charge state protein ions (+1 and +2 ions) introduced into the gas phase by nanodroplet nebulization. We first determine protein ion mobilities in dry air and subsequently examine shifts in mobilities brought about by the clustering of vapor molecules. Tandem mobility analysis yields mobility-vapor concentration curves for each protein ion, expanding the information obtained from mobility analysis. This experimental procedure and analysis is extended to bovine serum albumin, transferrin, immunoglobulin G, and apoferritin with water, 1-butanol, and nonane. All protein ions appear to adsorb vapor molecules, with mobility "diameter" shifts of up to 6-7% at conditions just below vapor saturation. We parametrize results using κ-Köhler theory, where the term κ quantifies the extent of uptake beyond Köhler model expectations. For 1-butanol and nonane, κ decreases with increasing protein ion size, while it increases with increasing protein ion size for water. For the systems probed, the extent of mobility shift for the organic vapors is unaffected by the nebulized solution pH, while shifts with water are sensitive to pH.

Greater than 3-Log Reduction in Viable Coronavirus Aerosol Concentration in Ducted Ultraviolet-C (UV-C) Systems.

Control technologies to inactivate airborne viruses effectively are needed during the ongoing SARS-CoV-2 pandemic, and to guard against airborne transmitted diseases. We demonstrate that sealed UV-C flow reactors operating with fluences near 253 ± 1 nm of 13.9-49.6 mJ cm-2 efficiently inactivate coronaviruses in an aerosol. For measurements, porcine respiratory coronavirus (PRCV) was nebulized in a custom-built, 3.86 m wind tunnel housed in a biosafety level class II facility. The single pass log10 reduction of active coronavirus was in excess of 2.2 at a flow rate of 2439 L min-1 (13.9 mJ cm-2) and in excess of 3.7 (99.98% removal efficiency) at 684 L min-1 (49.6 mJ cm-2). Because virus titers resulting from sampling downstream of the UV-C reactor were below the limit of detection, the true log reduction is likely even higher than measured. Comparison of virus titration results to reverse transcriptase quantitative PCR and measurement of fluorescein concentrations (doped into the nebulized aerosol) reveals that the reduction in viable PRCV is primarily due to UV-C based inactivation, as opposed to physical collection of virus. The results confirm that UV-C flow reactors can efficiently inactivate coronaviruses through incorporation into HVAC ducts or recirculating air purifiers.

Kinetics of nonisothermal phase change with arbitrary temperature-time history and initial transformed phase distributions.

This paper describes the extension of the classic Avrami equation to nonisothermal systems with arbitrary temperature-time history and arbitrary initial distributions of transformed phase. We start by showing that through examination of phase change in Fourier space, we can decouple the nucleation rate, growth rate, and transformed fraction, leading to the derivation of a nonlinear differential equation relating these three properties. We then consider a population balance partial differential equation (PDE) on the phase size distribution and solve it analytically. Then, by relating this PDE solution to the transformed fraction of phase, we are able to derive initial conditions to the differential equation relating nucleation rate, growth rate, and transformed fraction.

Wind tunnel-based testing of a photoelectrochemical oxidative filter-based air purification unit in coronavirus and influenza aerosol removal and inactivation.

Recirculating air purification technologies are employed as potential means of reducing exposure to aerosol particles and airborne viruses. Toward improved testing of recirculating air purification units, we developed and applied a medium-scale single-pass wind tunnel test to examine the size-dependent collection of particles and the collection and inactivation of viable bovine coronavirus (BCoV, a betacoronavirus), porcine respiratory coronavirus (PRCV, an alphacoronavirus), and influenza A virus (IAV), by a commercial air purification unit. The tested unit, the Molekule Air Mini, incorporates a MERV 16 filter as well as a photoelectrochemical oxidating layer. It was found to have a collection efficiency above 95.8% for all tested particle diameters and flow rates, with collection efficiencies above 99% for supermicrometer particles with the minimum collection efficiency for particles smaller than 100 nm. For all three tested viruses, the physical tracer-based log reduction was near 2.0 (99% removal). Conversely, the viable virus log reductions were found to be near 4.0 for IAV, 3.0 for BCoV, and 2.5 for PRCV, suggesting additional inactivation in a virus family- and genus-specific manner. In total, this work describes a suite of test methods which can be used to rigorously evaluate the efficacy of recirculating air purification technologies.

Aerosol Generation from the Respiratory Tract with Various Modes of Oxygen Delivery.

Rationale: Aerosol generation with modes of oxygen therapy such as high-flow nasal cannula and noninvasive positive-pressure ventilation is a concern for healthcare workers during the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) pandemic. The amount of aerosol generation from the respiratory tract with these various oxygen modalities is unknown.Objectives: To measure the size and number concentration of particles and droplets generated from the respiratory tract of humans exposed to various oxygen delivery modalities.Methods: Ten healthy participants with no active pulmonary disease were enrolled. Oxygen modalities tested included nonhumidified nasal cannula, face mask, heated and humidified high-flow nasal cannula, and noninvasive positive-pressure ventilation. Aerosol generation was measured with each oxygen mode while participants performed maneuvers of normal breathing, talking, deep breathing, and coughing. Testing was conducted in a negative-pressure room. Particles with a diameter between 0.37 and 20 µm were measured using an aerodynamic particle spectrometer.Measurements and Main Results: Median particle concentration ranged from 0.041 to 0.168 particles/cm3. Median diameter ranged from 1.01 to 1.53 µm. Cough significantly increased the number of particles measured. Measured aerosol concentration did not significantly increase with the use of either humidified high-flow nasal cannula or noninvasive positive-pressure ventilation. This was the case during normal breathing, talking, deep breathing, and coughing.Conclusions: Oxygen delivery modalities of humidified high-flow nasal cannula and noninvasive positive-pressure ventilation do not increase aerosol generation from the respiratory tract in healthy human participants with no active pulmonary disease measured in a negative-pressure room.

Multidimensional Nanoparticle Characterization through Ion Mobility-Mass Spectrometry.

Multidimensional techniques that combine fully or partially orthogonal characterization methods in a single setup often provide a more comprehensive description of analytes. When applied to nanoparticles, they have the potential to reveal particle properties not accessible to more conventional 1D techniques. Herein, we apply recently developed 2D characterization techniques to nanoparticles using atmospheric-pressure ion mobility-mass spectrometry (IM-MS), and we demonstrate the analytical capability of this approach using ultraporous mesostructured silica nanoparticles (UMNs). We show that IM-MS yields a 2D particle size-mass distribution function, which in turn can be used to calculate not only important 1D distributions, i.e. particle size distributions, but also nanoparticle structural property distributions not accessible by other methods, including size-dependent particle porosity and the specific pore volume distribution function. IM-MS measurement accuracy was confirmed by measurement of NIST-certified polystyrene latex particle standards. For UMNs, comparison of IM-MS results with TEM and N2 physisorption yields quantitative agreement in particle size and qualitative agreement in average specific pore volume. IM-MS uniquely shows how within a single UMN population, porosity increases with increasing particle size, consistent with the proposed UMN growth mechanism. In total, we demonstrate the potential of IM-MS as a standard approach for the characterization of structurally complex nanoparticle populations, as it yields size-specific structural distribution functions.

Recommendations for reporting ion mobility Mass Spectrometry measurements.

Here we present a guide to ion mobility mass spectrometry experiments, which covers both linear and nonlinear methods: what is measured, how the measurements are done, and how to report the results, including the uncertainties of mobility and collision cross section values. The guide aims to clarify some possibly confusing concepts, and the reporting recommendations should help researchers, authors and reviewers to contribute comprehensive reports, so that the ion mobility data can be reused more confidently. Starting from the concept of the definition of the measurand, we emphasize that (i) mobility values (K0 ) depend intrinsically on ion structure, the nature of the bath gas, temperature, and E/N; (ii) ion mobility does not measure molecular surfaces directly, but collision cross section (CCS) values are derived from mobility values using a physical model; (iii) methods relying on calibration are empirical (and thus may provide method-dependent results) only if the gas nature, temperature or E/N cannot match those of the primary method. Our analysis highlights the urgency of a community effort toward establishing primary standards and reference materials for ion mobility, and provides recommendations to do so. © 2019 The Authors. Mass Spectrometry Reviews Published by Wiley Periodicals, Inc.

The charge reduction rate for multiply charged polymer ions via ion-ion recombination at atmospheric pressure.

The charge reduction of multiply charged macromolecular ions via recombination with small ions in the gas phase is commonly employed to modulate the charge on macromolecules prior to mass spectrometric and mobility analyses. We employ a recently developed continuum-Molecular Dynamics (MD) calculation approach to determine the recombination rate coefficient of multiply charged (1 to 7 excess positive charged) polyethylene glycol ions (mass of 4600 Da) with smaller singly charged anions, modeled as NO2- ions. The continuum-MD approach accounts explicitly for the influence of the background gas on the recombination process, accounts explicitly for ion translational, vibrational, and rotational motion, and enables recombination rate coefficient calculation in nitrogen near atmospheric pressure, wherein neither low pressure nor high pressure recombination theories are strictly applicable. Continuum-MD simulations yield recombination rate coefficients near 3.9 × 10-14 m3 s-1 for singly charged ions, increasing to 3.0 × 10-11 m3 s-1 for the +7 ion. Pre-existing collision rate coefficient expressions for rigid ions are found to be within a factor of 2-5 of calculations for all charge states, but their use requires knowledge of an appropriate collision distance, which is not well-defined for flexible polymer ions. Continuum-MD-inferred rate coefficients are incorporated into a model of charge reduction, and the charge state distribution versus anion concentration determined with it is compared to charge reduction measurements made via atmospheric pressure differential mobility analysis. Good agreement is observed between simulations and experiments; although results are extremely sensitive to the recombination rate coefficients, experimental results are bound by models utilizing rates within a factor of 2 (0.5-2.0×) of the continuum-MD rates.

Calculation of the ion-ion recombination rate coefficient via a hybrid continuum-molecular dynamics approach.

Accurate calculation of the ion-ion recombination rate coefficient has been of long-standing interest as it controls the ion concentration in gas phase systems and in aerosols. We describe the development of a hybrid continuum-molecular dynamics (MD) approach to determine the ion-ion recombination rate coefficient. This approach is based on the limiting sphere method classically used for transition regime collision phenomena in aerosols. When ions are sufficiently far from one another, the ion-ion relative motion is described by diffusion equations, while within a critical distance, MD simulations are used to model ion-ion motion. MD simulations are parameterized using the Assisted Model Building with Energy Refinement force-field as well as by considering partial charges on atoms. Ion-neutral gas collisions are modeled in two mutually exclusive cubic domains composed of 103 gas atoms each, which remain centered on the recombining ions throughout calculations. Example calculations are reported for NH4 + recombination with NO2 - in He, across a pressure range from 10 kPa to 10 000 kPa. Excellent agreement is found in comparison with calculations to literature values for the 100 kPa recombination rate coefficient (1.0 × 10-12 m3 s-1) in He. We also recover the experimentally observed increase in the recombination rate coefficient with pressure at sub-atmospheric pressures, and the observed decrease in the recombination rate coefficient in the high pressure continuum limit. We additionally find that non-dimensionalized forms of rate coefficients are consistent with recently developed equations for the dimensionless charged particle-ion collision rate coefficient based on Langevin dynamics simulations.

Perceived influence of power distance, psychological safety, and team cohesion on team effectiveness.

Interprofessional education needs a stronger theoretical basis informed by the challenges facing collaboration across professions. This study explores the impact of power distance (perception of role hierarchy), on team effectiveness as mediated by team cohesion and psychological safety (believe one can speak up without the fear of negative consequences). Furthermore, it tests for differences between medical and nursing students in these concepts. Final-year medical and nursing students completed a paper survey on study constructs at the end of a three-session, 6-h interprofessional critical care simulation activity. Two hundred and forty-three (76% response rate) retrospective surveys found the relationship between power distance and perceived team effectiveness was mediated by perceptions of team cohesion and psychological safety, suggesting these concepts influence desired interprofessional collaboration. There were no differences between medical and nursing students on study variables. While interprofessional training typically focuses on general attitudes toward interprofessional collaboration and on the acquisition and demonstration of knowledge and skills, these findings suggest important team concepts underlying effective collaboration may include perceptions of psychological safety and power distance. These concepts can be key drivers of cohesion and effectiveness during interprofessional simulation exercises and may be targets for future interventions.

Direct observation of C60- nano-ion gas phase ozonation via ion mobility-mass spectrometry.

Improved methods to probe the reactivity of nano-ions, such as C60-, would find utility in nanochemistry, combustion chemistry, and in generally understanding the behavior of matter at the nanometer scale. We demonstrate that ion mobility-mass spectrometry (IM-MS) with a low-field differential mobility analyzer can be used to probe nano-ion reaction kinetics. We used the developed IM-MS approach to examine the gas phase reactivity of C60- ions with ozone at atmospheric pressure. Experimental results show that ozonation of C60- mainly leads to the formation of C60On-. The controlled reaction time within the ion mobility instrument enables calculation of ozonation reaction rates and assuming oxygen atoms are added sequentially, we find that the reaction rate between C60- and O3 is near the collision controlled limit. We propose an exponentially decaying reaction rate coefficient expression to describe ozonation leading to the addition of >20 oxygen atoms. At high ozone concentrations, CO or CO2 loss from C60On- is additionally observed.

Deducing Proton-Bound Heterodimer Association Energies from Shifts in Ion Mobility Arrival Time Distributions.

Through vapor modification of the counter-current drift gas in an atmospheric pressure drift tube ion mobility spectrometer (IMS), we demonstrate measurement of gas-phase association enthalpies and entropies for select proton-bound heterodimers formed from a phosphonic acid with 2-propanol. Previous efforts to determine gas-phase association thermodynamic properties have relied largely upon lower pressure systems and inference of the relative concentrations of m/ z isolated species. In contrast, the drift tube IMS based approach developed and applied in this study leverages the explicit gas-phase equilibrium that is established within an ion mobility drift cell. The inferred enthalpies and entropies of association are based solely upon monitoring a shift in the arrival time of an ion at different temperatures (and not on the signal intensity or on external instrument drift time calibration). We specifically report the gas-phase Gibbs free energy, enthalpy, and entropy changes for the association of 2-propanol with protonated methyl, ethyl, and propyl phosphonic acid ions (MPA, EPA, PPA) across the 100-175 °C temperature range. For all of these proton-bound heterodimers, the standard enthalpies and entropies of 2-propanol association were negative and positive, respectively. These data indicate that proton-bound heterodimer formation is both enthalpically and entropically favorable, though we find that the magnitude of the standard enthalpy change for vapor association is small (near 1 kcal/mol for all examined heterodimers). Though many prior results (largely obtained with high pressure mass-spectrometry) for other proton-bound organic heterodimer complexes show larger enthalpic favorability and an entropic barrier, our results qualitatively conform to the bulk Kelvin-Thomson-Raoult (KTR) model, which is commonly utilized in describing ion-induced nucleation of a vapor onto a soluble, nanometer scale ion. The KTR model suggests that heterodimer formation due to vapor binding to an ion should be slightly enthalpically favored (due to a larger Thomson effect than the Kelvin effect) and entropically favored because of ion solvation (Raoult's effect). The method presented in this study can be applied to any static-field ion mobility spectrometer and to a wide variety of heterodimers. Due to the ease of implementation and broad applicability, this approach may find consistent use in determining the thermodynamic properties of weakly bound gas-phase heterodimer complexes which are difficult to probe via alternative techniques. Moreover, this renewed implementation of the IMS experiment is directly compatible with soft ionization sources which will enable the characterization of vapor modifier-induced mobility shift experiments for larger molecular complexes.

Excess thermal energy and latent heat in nanocluster collisional growth.

Nanoclusters can form and grow by nanocluster-monomer collisions (condensation) and nanocluster-nanocluster collisions (coagulation). During growth, product nanoclusters have elevated thermal energies due to potential and thermal energy exchange following a collision. Even though nanocluster collisional heating may be significant and strongly size dependent, no prior theory describes this phenomenon for collisions of finite-size clusters. We derive a model to describe the excess thermal energy of collisional growth, defined as the kinetic energy increase in the product cluster, and latent heat of collisional growth, defined as the heat released to the background upon thermalization of the nonequilibrium cluster. Both quantities are composed of a temperature-independent term related to potential energy minimum differences and a size- and temperature-dependent term, which hinges upon heat capacity and energy partitioning. Example calculations using gold nanoclusters demonstrate that collisional heating can be important and strongly size dependent, particularly for reactive collisions involving nanoclusters composed of 14-20 atoms. Excessive latent heat release may have considerable implications in cluster formation and growth.

Heterogeneous Nucleation onto Monoatomic Ions: Support for the Kelvin-Thomson Theory.

In this study, the process of heterogeneous nucleation is investigated by coupling a high-resolution differential mobility analyser (DMA) to an expansion-type condensation particle counter, the size-analyzing nuclei counter (SANC). More specifically, we measured the activation probabilities of monoatomic ions of both polarities by using n-butanol as condensing liquid. All seed ions were activated to grow into macroscopic sizes at saturation ratios well below the onset of homogeneous nucleation, showing for the first time that the SANC is capable of detecting sub-nanometer sized, atomic seed ions. The measured onset saturation ratios for each ion were compared to the Kelvin-Thomson (KT) theory. Despite the fact that certain dependencies of activation behaviour on seed ion properties cannot be predicted by the KT theory, it was found that with a simple adjustment of the n-butanol molecular volume (9-15 % lower compared to bulk properties) good agreement with experimental results is achievable. The corresponding density increase may result from the dipole-charge interaction. This study thus offers support for the application of the KT model for heterogeneous, ion-induced nucleation studies at the sub-nanometer level.

Condensation and dissociation rates for gas phase metal clusters from molecular dynamics trajectory calculations.

In gas phase synthesis systems, clusters form and grow via condensation, in which a monomer binds to an existing cluster. While a hard-sphere equation is frequently used to predict the condensation rate coefficient, this equation neglects the influences of potential interactions and cluster internal energy on the condensation process. Here, we present a collision rate theory-molecular dynamics simulation approach to calculate condensation probabilities and condensation rate coefficients. We use this approach to examine atomic condensation onto 6-56-atom Au and Mg clusters. The probability of condensation depends upon the initial relative velocity (v) between atom and cluster and the initial impact parameter (b). In all cases, there is a well-defined region of b-v space where condensation is highly probable, and outside of which the condensation probability drops to zero. For Au clusters with more than 10 atoms, we find that at gas temperatures in the 300-1200 K range, the condensation rate coefficient exceeds the hard-sphere rate coefficient by a factor of 1.5-2.0. Conversely, for Au clusters with 10 or fewer atoms and for 14- and 28-atom Mg clusters, as cluster equilibration temperature increases, the condensation rate coefficient drops to values below the hard-sphere rate coefficient. Calculations also yield the self-dissociation rate coefficient, which is found to vary considerably with gas temperature. Finally, calculations results reveal that grazing (high b) atom-cluster collisions at elevated velocity (>1000 m s-1) can result in the colliding atom rebounding (bounce) from the cluster surface or binding while another atom dissociates (replacement). The presented method can be applied in developing rate equations to predict material formation and growth rates in vapor phase systems.