Homogeneous Nucleation Rates Research Articles

Optimizing the activation efficiency of sub-3 nm particles in a laminar flow condensation particle counter: Model simulation

The measurement of airborne particles with sizes below 3 nm is critical, as it helps the understanding of atmospheric nucleation and elucidates important particle synthesis mechanisms in the gas phase. Condensation particle counters (CPCs) have been widely used to measure the concentration of aerosols. However, it is challenging for the CPCs to measure particles below 3 nm due to the insufficient activation of these particles via vapor condensation. Methods have been proposed to increase the saturation ratio of the condensing vapor to promote the detection efficiency of sub-3 nm particles in the CPCs. Different working fluids also make a considerable impact on particle detection. Given the various types of parameters and the wide range of values these parameters can take, modeling studies are needed in searching for the optimal operating conditions of a CPC.In this work, we simulated the sub-3 nm particle activation and growth in a laminar flow CPC using COMSOL Multiphysics®, which has the advantages of simulating complex flow conditions and interfacing with post-processing software such as MATLAB. Our simulation incorporates the influence of temperature-dependent air and working fluid properties on particle activation and the impact of latent heat and non-continuum effects on droplet growth. Following the method introduced by Iida, Stolzenburg and McMurry (2009), particle activation is optimized for a given working fluid and condenser temperature by adjusting the saturator temperature to achieve a homogeneous nucleation rate of 1 s−1. The results, characterized by Dkel,0 (largest particle size that cannot be activated) and Dkel,50 (particle size activated with 50% efficiency), were compared against the analytical Graetz model used in Stolzenburg (1988). Our COMSOL simulations show that glycerine, diethylene glycol, ethylene glycol, 2-aminoethanol, and dimethyl phthalate are the best five working fluids achieving the smallest Dkel,50 among 45 commonly used solvents. The Dkel,50 values simulated by COMSOL under a condenser temperature of 10 °C for the five working fluids are 1.56, 1.88, 1.92, 1.98, and 2.10 nm, respectively, while the values simulated by the analytical Graetz solution differ slightly from 0.4% to 0.7%. The results demonstrate excellent agreement between these two simulation methods. For the five best working fluids activating the same 2.1 nm particles, the droplets can grow to sizes detectable by a second-stage CPC. The sensitivity of the COMSOL solution to the inlet condition and the form of convective diffusion equations is investigated. We also discussed the effect of CPC operating conditions, such as the condenser geometry and flow conditions, on particle activation for optimizing the performance of the CPC in detecting sub-3 nm particles.

Homogenous nucleation rate of CO2 hydrates using transition interface sampling.

Carbon dioxide and water can form solid clathrate structures in which water cages encapsulate the gas molecules. Such hydrates have sparked much interest due to their possible application in CO2 sequestration. How the solid structure forms exactly from the liquid phase via a homogenous nucleation process is still poorly understood. This nucleation event is rare on the molecular timescale even under moderate undercooling or supersaturation conditions because of the large free energy barrier toward crystallization, rendering a brute force simulation of hydrate nucleation unfeasible for moderate undercooling or supersaturation. Here, we perform transition interface sampling simulations to quantify the homogenous nucleation rate for CO2 hydrate formation using accurate atomistic force fields at 500 bars for three different temperatures between 260 and 273 K. Collecting more than 100 000 pathways comprising roughly two milliseconds of simulation time, we computed a nucleation rate in the amorphous phase of ∼1021 nuclei s-1 cm-3 for a temperature of 260 K and a rate of ∼1012 nuclei s-1 cm-3 for a temperature of 265 K. For a temperature of 273 K, we find that the hydrate forms an sI crystalline phase with a rate of order of ∼101 nuclei s-1 cm-3. We compare these rates to classical nucleation theory estimates as well as experiments, and to nucleation rate estimates for methane hydrates and discuss possible causes of the observed differences. Our findings shed light on the kinetics of this important clathrate and should assist in future hydrate formation investigation.

Identification of critical nuclei in the rapid solidification via configuration heredity

The identification and characterization of critical nuclei is a long-standing issue in the rapid solidification of metals and alloys. An ambiguous description for their sizes and shapes used to lead to an overestimation or underestimation of homogeneous nucleation rates in the framework of classical nucleation theory (CNT). In this paper, a unique method able to distinguish the critical nucleus from numerous embryos is put forward on the basis of configuration heredities of clusters during rapid solidifications. As this technique is applied to analyze the formation and evolution of various fcc-Al single crystal clusters in a large-scale molecular dynamics simulation system, it is found that the size n c and geometrical configuration of critical nuclei as well as their liquid–solid interfacial structure can be determined directly. For the present deep super-cooled system with an undercooling of , the average size of critical nuclei is demonstrated to be , but most of which are non-spherical lamellae. Also, their liquid–solid interfaces are revealed to be not an fcc-liquid duplex-phase interface but an fcc/hcp-liquid multi-phase structure. These findings shed some lights on the CNT, and a good agreement with previous simulations and experiments in indicates this technique can be used to explore the early-stage of nucleation from atomistic levels.

A theoretical model for predicting homogeneous ice nucleation rate based on molecular kinetic energy distribution

An accurate description of homogeneous ice nucleation (HIN) rate strongly relies on the availability of data of ice-water interface energy and activation energy when water molecules cross the ice-water interface. However, it proves extremely challenging to experimentally measure the values of these two quantities for the supercooled water. In this study, a theoretical model based on the molecular kinetic energy distribution is presented, thus avoiding the need to specifying the above two parameters. The predicted HIN temperatures under different pressures agree with the experimental data with deviations less than 3%. Nonlinear variations of ice germ size and concentration were found, which suggests it might be erroneous to utilise the data obtained under high temperatures to linearly extrapolate water characteristics in low-temperature regions. Significant improvements in model prediction accuracy were achieved after the inclusions of temperature fluctuation and droplet internal high pressure. The presentmodel proves capable of accurately predicting the HIN rate over temperatures down to 190 K.

Molecular dynamics simulations of homogeneous nucleation of liquid phase in highly supersaturated propylene glycol vapors

The homogeneous nucleation rate of the liquid phase from a supersaturated propylene glycol vapor is a key factor in aerosol formation from condensation aerosol generators. The droplet nucleation rate is difficult to measure experimentally at high supersaturations. This paper demonstrates the feasibility of using classical Molecular Dynamics (MD) simulations to describe the nucleation of propylene glycol from the vapor phase in air at 320 and 343 K. After an initial induction period, nucleation was observed in many of the scenarios studied here. The classical nucleation theory underestimates the nucleation rate compared to the MD simulation results at high supersaturations. However, a kinetic model that assumed no free energy barrier to nucleation had better agreement with the MD predictions at extremely high supersaturations. For systems where a quasi-steady state was reached during the simulation, it is possible to determine the nucleation free energy as a function of cluster size. From this analysis it is found that the MD simulations predict over a factor of two larger critical clusters and about 50% higher free energy barriers than the classical nucleation theory.

Molecular dynamics simulations of spontaneous and seeded nucleation and theoretical calculations for zinc selenide

Understanding and controlling the liquid to crystal transformation is a central topic for numerous natural phenomena and technological applications. However, the microscopic mechanism of crystal nucleation is still elusive, which leads to strong controversies regarding the ability of the most used model, the Classical Nucleation Theory (CNT), to describe nucleation rates in supercooled liquids. In this work, we were able to deeply supercool Zinc Selenide (ZnSe), and determine spontaneous homogeneous steady-state nucleation rates, JMD, by MD simulations using the mean lifetime method. At moderate supercoolings, where the nucleation rates are much smaller, we used the seeding method to compute the nucleation rates by the CNT formalism, JCNT, without any fitting parameter, using the physical properties obtained by MD simulations: the melting temperature, Tm, density, melting enthalpy, diffusion coefficient, D+, and the critical nucleus size, N∗, combined with two expressions for the thermodynamic driving force, Δμ. The values of interfacial free energy, γ, calculated by the CNT expression using the MD simulation data, via both the seeding method and the mean lifetime method at moderate and deep supercoolings show a weak temperature dependence, which is in line with the Diffuse Interface Theory. The extrapolated values of γ, from the spontaneous nucleation regime to the seeding nucleation region cover the range of values of γ calculated via the seeding method and the CNT formalism. Finally, the JCNT extrapolated from moderate supercoolings to deep supercoolings are in good agreement with the JMD. These results confirm the validity of the CNT.

Predicting the Rate of Homogeneous Intermetallic Nucleation within Steep Composition Gradients

Simulations of isothermal homogeneous nucleation from deeply undercooled amorphous melts exhibit systematic variations in nucleation behavior depending upon the strength of an imposed composition g...

Seeding method for ice nucleation under shear

Hydrodynamic flow can have complex and far-reaching consequences on the rate of homogeneous nucleation. We present a general formalism for calculating the nucleation rates of simply sheared systems. We have derived an extension to the conventional Classical Nucleation Theory, explicitly embodying the shear rate. Seeded molecular dynamics simulations form the backbone of our approach. The framework can be used for moderate supercooling, at which temperatures brute-force methods are practically infeasible. The competing energetic and kinetic effects of shear arise naturally from the equations. We show how the theory can be used to identify shear regimes of ice nucleation behavior for the mW water model, unifying disparate trends reported in the literature. At each temperature, we define a crossover shear rate in the limit of 1000 s-1-10 000 s-1, beyond which the nucleation rate increases steadily up to a maximum, at the optimal shear rate. For 235 K, 240 K, 255 K, and 260 K, the optimal shear rates are in the range of ≈106 s-1-107 s-1. For very high shear rates beyond 108 s-1, nucleation is strongly inhibited. Our results indicate that the optimal shear rates have a non-monotonic dependence on temperature.

Critical assessment of the alleged failure of the Classical Nucleation Theory at low temperatures

The Classical Nucleation Theory allegedly fails to describe the temperature dependence of the homogeneous crystal nucleation rates below the temperature of maximum nucleation, Tmax. Possible explanations for this suspected breakdown have been advanced in the literature. However, the simplest hypothesis has never been tested, that it is a byproduct of nucleation datasets that have not reached the steady-state regime. In this work, we tested this possibility by analyzing published nucleation data for oxide supercooled liquids, using only nucleation and viscosity data measured in samples of the same glass batch that also have satisfied a steady-state regime test. Furthermore, all the uncertainty and regression confidence bands were computed and considered. Having this rigorous protocol, among the 6 datasets analyzed, we only found weak evidence supporting the existence of the nucleation break in 2 datasets. Our collective results thus indicate that the break at Tmax is not a common feature of all glass-formers.

Homogeneous Ice Nucleation Under Shear.

Homogeneous ice nucleation involving a water flow is subject to shear, which may greatly affect the ice nucleation rate. In this work, we investigate the homogeneous ice nucleation rate under shear through molecular dynamics simulations. It is found that the ice nucleation rate changes nonlinearly with varying shear rates and reaches a maximum at an intermediate shear rate. Such a behavior is determined by two distinct effects of shear rates. On the one hand, shear increases the free energy barrier for the nucleation, which hinders the ice nucleation. On the other hand, shear enhances the diffusion of water molecules, assists the adsorption of water molecules on the ice nucleus, and consequently promotes the growth of ice nucleus. The latter effect dominates at low shear rates, while the former effect becomes significant at high shear rates. The competition between these two effects leads to a non-monotonic dependence of the ice nucleation rate on the shear rate.

Dominant Effect of Heterogeneous Dynamics on Homogenous Crystal Nucleation in Supercooled Liquids

Understanding the microscopic (molecular) mechanism of crystal nucleation remains intangible. For instance, it is still impossible to predict in which regions of a supercooled liquid nucleation will occur. Moreover, allegedly the Classical Nucleation Theory fails to describe the homogeneous crystal nucleation rates below the glass transition temperature. In this mini-review article, we revisit, critically comment, and link some highly selected recent studies using examples of an oxide glass-former, water, and a metallic alloy on the largely neglected effect of dynamic heterogeneities on crystal nucleation.

Inclusion of Viscosity Into Classical Homogeneous Nucleation Theory for Water Bubbles in Silicate Melts: Reexamination of Bubble Number Density in Ascending Magmas

AbstractTo evaluate the effect of melt viscosity on bubble nucleation, we formulated the homogeneous nucleation rate of water bubbles to explicitly include melt viscosity. The viscosity coefficient appears in the preexponential factor of the nucleation rate in terms of the Péclet number: the ratio of the bubble growth timescale by molecular diffusion and the viscous relaxation timescale. The preexponential factor is almost constant when viscosity is low (or a high Péclet number), whereas it linearly decreases with increasing viscosity (or a decreasing Péclet number) exceeding the crossover value of viscosity, under a given supersaturation. The crossover point depends on whether homogeneous or heterogeneous nucleation takes place. We numerically solved the evolution of bubble nucleation and growth processes in ascending magmas by using the new nucleation rate formula and a precise approximation of moment equations of the bubble size distribution function. The resultant bubble number density has two regimes, similar to the previous study, but the transition point between the diffusion‐controlled regime and the viscosity‐controlled regime moves to higher viscosity or higher decompression rates by 0.6 log units at the maximum. In the viscosity‐controlled regime, the effect of the better approximation of bubble size distribution moment equations reduces bubble number density by a few orders of magnitude compared with the previous study. As a result of compiling the past laboratory experimental data, it turned out that all the experiments are conducted under the conditions equivalent to the diffusion‐controlled regime. We propose an experimental condition to confirm the presence of the viscosity‐controlled regime.

Homogeneous ice nucleation rates and crystallization kinetics in transiently-heated, supercooled water films from 188 K to 230 K.

The crystallization kinetics of transiently heated, nanoscale water films were investigated for 188 K < Tpulse < 230 K, where Tpulse is the maximum temperature obtained during a heat pulse. The water films, which had thicknesses ranging from approximately 15-30 nm, were adsorbed on a Pt(111) single crystal and heated with ∼10 ns laser pulses, which produced heating and cooling rates of ∼109-1010 K/s in the adsorbed water films. Because the ice growth rates have been measured independently, the ice nucleation rates could be determined by modeling the observed crystallization kinetics. The experiments show that the nucleation rate goes through a maximum at T = 216 K ± 4 K, and the rate at the maximum is 1029±1 m-3 s-1. The maximum nucleation rate reported here for flat, thin water films is consistent with recent measurements of the nucleation rate in nanometer-sized water drops at comparable temperatures. However, the nucleation rate drops rapidly at lower temperatures, which is different from the nearly temperature-independent rates observed for the nanometer-sized drops. At T ∼ 189 K, the nucleation rate for the current experiments is a factor of ∼104-5 smaller than the rate at the maximum. The nucleation rate also decreases for Tpulse > 220 K, but the transiently heated water films are not very sensitive to the smaller nucleation rates at higher temperatures. The crystallization kinetics are consistent with a "classical" nucleation and growth mechanism indicating that there is an energetic barrier for deeply supercooled water to convert to ice.

Subsecond measurements on aerosols: From hygroscopic growth factors to efflorescence kinetics

The hygroscopicity and phase state of atmospheric aerosols, depending on relative humidity (RH), dominate their impacts on global climate and heterogeneous atmospheric chemistry. It is challenging to achieve full course measurements on hygroscopic mass growth factors (MGFs), deliquescence relative humidity (DRH), efflorescence relative humidity (ERH) and efflorescence kinetics of aerosols at different ambient RH, which concerns the gas, liquid and solid phases. The combination of a rapid scan vacuum FTIR and a RH pulsed controlling system allowed us to directly and synchronously determine ambient RH and MGFs of aerosols, as well as nucleation rates in the efflorescence process with a subsecond time resolution. With an excellent signal-to-noise ratio and high time resolution spectra, the vacuum FTIR method allowed for real-time in situ measurements of water partitioning between gas and particle phases as it changed with RH, as well as the ratio between the number of crystallized aerosol droplets and the total number of particles during the efflorescence of aerosols. The hygroscopicity and efflorescence kinetics of NaCl and (NH4)2SO4 aerosols were studied in linear RH change mode and in pulsed RH change mode. The measured MGF values, DRH and ERH agreed well with theoretical data from the Extended Aerosol Inorganic Model (EAIM) and literature for both the linear and pulsed RH change modes. In addition, the pulsed RH mode also provided both heterogeneous and homogeneous nucleation rates for NaCl and (NH4)2SO4 aerosols. There were significant advantages of the vacuum FTIR method combined with the pulsed RH controlling technique. First, the RH was continuously changed and was determined in real-time with a time resolution of 0.12 s in the pulsed mode. During the RH change process, the water content in the aerosols was measured synchronously with the same time resolution, allowing for high-efficiency measurements of MGFs, ERH and DRH. The deviations of measured MGFs from the EAIM predictions in the RH range of 75–55% were less than ±3.3%. Second, FTIR spectroscopy was sensitive to phase transitions, which provided quantitative information on the ratio of the number of aerosols transformed from droplets to solid particles at ERH, allowing for the measurement of nucleation kinetics during the efflorescence of aerosols.

Heterogeneous versus homogeneous crystal nucleation of hard spheres.

Hard-sphere model systems are well-suited in both experiment and simulations to investigate fundamental aspects of the crystallization of fluids. In experiments on colloidal models of hard-sphere fluids, the fluid is unavoidably in contact with the walls of the sample cell, where heterogeneous crystallization may take place. In this work we use simulations to investigate the competition between homogeneous and heterogeneous crystallization. We report simulations of wall-induced nucleation for different confining walls. Combining the results of these simulations with earlier studies of homogeneous crystallization allows us to assess the competition between homogeneous and heterogeneous nucleation as a function of the wall type, fluid density and the system size. On flat walls, heterogeneous nucleation will typically overwhelm homogeneous nucleation. Even for surfaces randomly coated with spheres with a diameter that was some three times larger than that of the fluid spheres - as has been used in some experiments - heterogeneous nucleation is likely to be dominant for volume fractions smaller than ∼0.535. Only for a disordered coating that has the same structure as the liquid did we find that nucleation was likely to occur in the bulk. Hence, such coatings might be used to suppress heterogeneous nucleation in experiments. Finally, we report the apparent homogeneous nucleation rate taking into account the formation of crystallites both in the bulk and at the walls. We find that the apparent overall nucleation rates coincide with those reported in "homogeneous nucleation" experiments. This suggests that heterogeneous nucleation at the walls could partly explain the large discrepancies found between experimental measurements and simulation estimates of the homogeneous nucleation rate.

Crystallization kinetics of the Fe40Ni40P14B6 metallic glass in an extended range of heating rates

The effect of heating rate (in the range of 0.083–3.333 K s−1) on the parameters of thermal stability and crystallization kinetics of the Fe40Ni40P14B6 metallic glass has been investigated by differential scanning calorimetry and X-ray diffraction. An analytical model of glass crystallization describing the homogeneous nucleation rate, the velocity of interface-limited growth, the number of crystal volume density in crystallized samples as well as the crystallization kinetics at constant rate heating is presented. A modified procedure of estimation of thermodynamic and kinetic parameters governing the rate of crystal nucleation and growth based on the use of the measured heating rate-dependent variations of the volume fraction crystallized and the average grain size is proposed. The values of the effective diffusivity have been estimated by the Kissinger-like isoconversional method accounting the contribution of both the free energy difference and the specific interfacial nucleus-melt energy changes estimated from the structural data. It has been shown for the first time that the shapes of the non-isothermal experimental kinetic crystallization curves measured at the heating rates ≤ 1.333 K s−1 are well described by the approximate analytical equation and the values of the Avrami exponent lowering from 5.5 to 2.3 with the heating rates increasing have been estimated. The evaluated ranges of the nucleation rate (1.4 × 1016–2.5 × 1017 m−3 s−1) and growth velocity of crystals (2.05 × 10−9–3.0 × 10−7 m s−1) in Fe40Ni40P14B6 glass at temperatures from 653 to 714 K are in reasonable agreement with the experimental data. Possible variations of the established eutectic crystallization mechanism revealed by changes of the Avrami exponent with the heating rate increasing are discussed.

Communication: Nucleation rates of supersaturated aqueous NaCl using a polarizable force field.

In this work, we use molecular dynamics simulations with a polarizable force field, namely, the modified AH/BK3 model [J. Kolafa, J. Chem. Phys. 145, 204509 (2016)], in combination with the forward flux sampling technique, to calculate the rates of homogeneous nucleation of NaCl from supersaturated aqueous solutions at 298 K and 1 bar. A non-polarizable model that reproduces the experimental equilibrium solubility {AH/TIP4P-2005 of Benavides et al. [J. Chem. Phys. 147, 104501 (2017)]} is also used for comparison. Nucleation rates calculated from the polarizable force field are found to be in good agreement with experimental measurements, while the non-polarizable model severely underestimates the nucleation rates. These results, in combination with our earlier study of a different non-polarizable force field [H. Jiang et al., J. Chem. Phys. 148, 044505 (2018)], lead to the conclusion that nucleation rates are sensitive to the details of force fields, and a good representation of nucleation rates may not be feasible using available non-polarizable force fields, even if these reproduce the equilibrium salt solubility. Inclusion of polarization could be important for an accurate prediction of nucleation rates in salt solutions.

Homogeneous Ice Nucleation Rate in Water Droplets

To predict the radiative forcing of clouds it is necessary to know the rate with which ice homogeneously nucleates in supercooled water. Such rate is often measured in drops to avoid the presence of impurities. At large supercooling small (nanoscopic) drops must be used to prevent simultaneous nucleation events. The pressure inside such drops is larger than the atmospheric one by virtue of the Laplace equation. In this work, we take into account such pressure raise in order to predict the nucleation rate in droplets using the TIP4P/Ice water model. We start from a recent estimate of the maximum drop size that can be used at each supercooling avoiding simultaneous nucleation events [Espinosa et al. J. Chem. Phys., 2016]. We then evaluate the pressure inside the drops with the Laplace equation. Finally, we obtain the rate as a function of the supercooling by interpolating our previous results for 1 and 2000 bar [Espinosa et al. Phys. Rev. Lett. 2016] using the Classical Nucleation Theory expression for the rate. This requires, in turn, interpolating the ice-water interfacial free energy and chemical potential difference. The TIP4P/Ice rate curve thus obtained is in good agreement with most droplet-based experiments. In particular, we find a good agreement with measurements performed using nanoscopic drops, that are currently under debate. The successful comparison between model and experiments suggests that TIP4P/Ice is a reliable model to study the water-to-ice transition and that Classical Nucleation Theory is a good framework to understand it.

Predicting homogeneous nucleation rates in silicate glass-formers

We employed the Classical Nucleation Theory using a characteristic value of the pre-exponential constant and an average (temperature dependent) interfacial energy and derived an expression to estimate the maximum nucleation rates, Imax, as a function of the reduced glass transition temperatures, Tgr ≡ Tg/Tm (Tg is the laboratory glass transition temperature and Tm is the melting point or liquidus temperature). The theoretical predictions were surprisingly good for 51 out of 54 silicate glass-formers tested and describe well the experimental trend that Imax strongly decreases with increasing Tgr. This trend, in turn, explains the well-known fact that only silicate glasses having a relatively low Tgr, Tgr < 0.6, show internal homogeneous nucleation in laboratory time/sample-size scales.

Forward-flux sampling with jumpy order parameters.

Forward-flux sampling (FFS) is a path sampling technique that has gained increased popularity in recent years and has been used to compute rates of rare event phenomena such as crystallization, condensation, hydrophobic evaporation, DNA hybridization, and protein folding. The popularity of FFS is not only due to its ease of implementation but also because it is not very sensitive to the particular choice of an order parameter. The order parameter utilized in conventional FFS, however, still needs to satisfy a stringent smoothness criterion in order to assure sequential crossing of FFS milestones. This condition is usually violated for order parameters utilized for describing aggregation phenomena such as crystallization. Here, we present a generalized FFS algorithm for which this smoothness criterion is no longer necessary and apply it to compute homogeneous crystal nucleation rates in several systems. Our numerical tests reveal that conventional FFS can sometimes underestimate the nucleation rate by several orders of magnitude.