Dependence Of Nucleation Rate Research Articles

Discovery of Molecular Intermediates and Nonclassical Nanoparticle Formation Mechanisms by Liquid Phase Electron Microscopy and Reaction Throughput Analysis

Formation kinetics of metal nanoparticles are generally described via mass transport and thermodynamics‐based models, such as diffusion‐limited growth and classical nucleation theory (CNT). However, metal monomers are commonly assumed as precursors, leaving the identity of molecular intermediates and their contribution to nanoparticle formation unclear. Herein, liquid phase transmission electron microscopy (LPTEM) and reaction kinetic modeling are utilized to establish the nucleation and growth mechanisms and discover molecular intermediates during silver nanoparticle formation. Quantitative LPTEM measurements show that their nucleation rate decreases while growth rate is nearly invariant with electron dose rate. Reaction kinetic simulations show that Ag4 and Ag− follow a statistically similar dose rate dependence as the experimentally determined growth rate. We show that experimental growth rates are consistent with diffusion‐limited growth via the attachment of these species to nanoparticles. The dose rate dependence of nucleation rate is inconsistent with CNT. A reaction‐limited nucleation mechanism is proposed and it is demonstrated that experimental nucleation kinetics are consistent with Ag42+ aggregation rates at millisecond time scales. Reaction throughput analysis of the kinetic simulations uncovered formation and decay pathways mediating intermediate concentrations. We demonstrate the power of quantitative LPTEM combined with kinetic modeling for establishing nanoparticle formation mechanisms and principal intermediates.

Measurement of nucleation kinetics for ibuprofen crystals from ethanol and water-ethanol mixtures

Ibuprofen is a popular analgesic and is mostly marketed as tablet dosage form. It is helpful in tablet production to have feed crystals of regular shape and narrow size distribution. Controlled crystallization techniques can provide such a desired size and shape of ibuprofen crystal/powder. To design a controlled crystallizer for ibuprofen [((RS)-2-(4-(2-methylpropyl) phenyl) propanoic acid)] from ethanol and water - ethanol mixtures it is necessary to know the nucleation rate kinetics of its solutions. Secondary nucleation rates for the crystallization of racemic ibuprofen from aqueous ethanol have been measured by adding seeds to an ibuprofen solution supersaturated above the secondary nucleation threshold (SNT). After the onset of nucleation, crystal samples were taken over short time intervals and the numbers of crystals in the vessel determined. The rate of change in the number of crystals gave the nucleation rate B. It is assumed that the order of the nucleation rate dependence on supersaturation s and the order of dependence on the crystal content Mc are both first order, giving equation B = kBMcs, where s is the supersaturation in ΔI/E (mass ratio ibuprofen to ethanol) units. For aqueous ethanolic solutions and for the nucleation rate B in number/min/(kg crystal/L slurry) units, kB = 2.4 × 109/T1.4(independent of XW, the solution water content), where T is the solution temperature in oC. The estimated 95% probable uncertainty in the constant is ±6%, while that of the temperature exponent is ±30%. The correlation fits 95% of the experimental data within a factor of 6.

Analysis of methane hydrate nucleation in water-in-oil emulsions: Isothermal vs constant cooling ramp method and new method for data treatment

Temperature dependence of methane hydrate nucleation rate in 50 wt% water in oil emulsion was studied within the temperature range from +2 to −6 °C (supercooling values: 13–21 °C). It turned out that the temperature dependence of nucleation rate in this temperature interval cannot be described by the equations of the classical nucleation theory. This point is discussed with use of available literature data. An approach to the analysis of isothermal survival curves is suggested. Using the approach allows us to establish the amount of nucleation centers in the system and their relative activity. A probable number of nucleation centers and the effect of temperature on the manifestation activity of these centers were determined for the obtained experimental data.

Crystallization kinetics of gehlenite glass microspheres

The glass of gehlenite composition was prepared by flame synthesis in the form of microspheres. The powder precursor was synthesised by standard solid-state reaction method using SiO2, Al2O3 and CaCO3. The prepared glasses were characterized from the point of view of surface morphology, phase composition and thermal properties by optical microscopy, scanning electron microscopy (SEM), X-ray diffraction (XRD) and differential scanning calorimetry (DSC), respectively. The prepared samples contained only completely re-melted spherical particles. SEM did not reveal any features indicating the presence of crystalline phases. However, traces of crystalline gehlenite were detected by XRD. The high-temperature XRD measurements (HT XRD) were carried out to identify the phase evolution during glass crystallization. In the studied temperature range, gehlenite phase was identified as the main crystalline phase. Non-isothermal DSC analysis of prepared glass microspheres was carried out from room temperature up to 1200 °C at five different heating rates: 2, 4, 6, 8 and 10 °C/min to determine the thermal properties of microspheres. In order to study the crystallization kinetics, the DSC curves were transformed into dependence of fractional extent of crystallization (α) on temperature. The Johnson–Mehl–Avrami–Kolmogorov model was found to be suitable for description of crystallization kinetics. Frequency factor A = 5.56 × 1029 ± 1.73 × 1029 min−1, apparent activation energy Eapp = 722 ± 3 kJ mol−1 and the Avrami coefficient m = 2 were determined. In the studied system, the linear temperature dependence of nucleation rate, diffusion controlled crystal growth interface and a 2D crystal growth were confirmed.

Heterogeneous Ice Nucleation in the Tropical Tropopause Layer

AbstractRecent laboratoryexperiments have advanced our understanding of heterogeneous ice nucleation at low temperatures. We use these laboratory results, along with field measurements of aerosol composition, to constrain a parameterization of heterogeneous nucleation rate dependence on temperature and supersaturation. We apply this nucleation parameterization in detailed simulations of transport and cloud formation in the Tropical Tropopause Layer (TTL, ≃14–18 km) constrained by high‐altitude aircraft measurements of TTL cirrus microphysical properties and supersaturation. The model results indicate that if the abundant TTL organic‐containing aerosols were effective glassy ice nuclei (IN), as indicated by laboratory experiments with simple sugars/acids, then heterogeneous nucleation would prevent the occurrences of large ice concentrations and large ice supersaturations, both of which are clearly indicated by the in situ observations. If glassy organic aerosols are relatively poor IN, as indicated by laboratory experiments with more atmospherically relevant secondary organic aerosol‐like composition, then the simulated ice concentrations and supersaturations are in reasonable agreement with the observations. Concentrations of effective mineral dust or ammonium sulfate IN larger than about 50/L can drive significant changes in cirrus microphysical properties and occurrence frequency. The cloud occurrence frequency can either increase or decrease, depending on the efficacy and abundance of IN added to the TTL. Relatively low TTL concentrations of mineral dust particles (≤10 L−1 indicated by the limited available field measurements) have negligible impact on cirrus frequencies or microphysical properties. Given the assortment of uncertainties, meaningful estimates of TTL aerosol‐cirrus indirect effects on radiative forcing are likely not possible at this time.

Microstructure evolution under isothermal and continuous cooling conditions via a combined multiphase field and nucleation approach

We demonstrate the microstructure evolution involving the nucleation and grain growth of a binary alloy during the continuous cooling process via a combined multiphase field model and stochastic nucleation computational model. The nuclei are initiated by adding into the total free energy a term of the nucleation energy related to the variables that represents grains of different orientation. Moelans’ interpolation functions are implemented to construct the chemical bulk free energy from coexisting phases/grains for increased stability of multiphase/grain junctions. It was found that the temperature dependent nucleation rate and interface mobility are the main materials properties controlling the features of the resultant microstructures. More even-sized and fine grains can be formed under a high cooling rate given the specified temperature dependent nucleation rate. Solute trapping is the most prominent and solute segregation is the slightest at the highest cooling rate. Equipped with a grain-tracking method, this computational framework provides a viable and computationally efficiently pathway to investigate the large-scale microstructure evolution under various temperature histories that could occur in manufacturing processes.

Nucleation rates of droplets in supersaturated steam and water vapour–carrier gas mixtures between 200 and 450 K

We compare experimental nucleation rates for water vapour in various carrier gases, estimated nucleation rates for steam, and nucleation rates obtained from molecular simulations. The data for steam are deduced from empirical adjustments of the classical nucleation theory developed by various authors to reproduce pressure and optical data for condensing steam flows in converging-diverging nozzles and turbine stages. By combining the data for nucleation in carrier gases and the data for steam nucleation, an unprecedented temperature range of 250 K is available to study the temperature dependence of nucleation rate. Original results of molecular dynamic simulations for TIP4P/2005 force field in the NVE (system constrained by number of particles, volume and energy) conditions are provided. Correction of classical nucleation theory for non-isothermal nucleation conditions is applied to experimental and simulated data. The nucleation rate data for steam follow a similar temperature trend as the nucleation rate data for water vapour in carrier gases at lower temperatures. The ratio of observed nucleation rates to classical nucleation theory predictions decreases more steeply with temperature than the empirical correlation by Wölk et al. ( J Chem Phys 2002; 117: 4954–4960). On the contrary to experimental data, the ratios of nucleation rates computed from molecular simulations to classical nucleation theory predictions do not show a significant temperature trend.

Critical Nuclei Size, Rate, and Activation Energy of H2 Gas Nucleation.

Electrochemical measurements of the nucleation rate of individual H2 bubbles at the surface of Pt nanoelectrodes (radius = 7-41 nm) are used to determine the critical size and geometry of H2 nuclei leading to stable bubbles. Precise knowledge of the H2 concentration at the electrode surface, CH2surf, is obtained by controlled current reduction of H+ in a H2SO4 solution. Induction times of single-bubble nucleation events are measured by stepping the current, to control CH2surf, while monitoring the voltage. We find that gas nucleation follows a first-order rate process; a bubble spontaneously nucleates after a stochastic time delay, as indicated by a sudden voltage spike that results from impeded transport of H+ to the electrode. Hundreds of individual induction times, at different applied currents and using different Pt nanoelectrodes, are used to characterize the kinetics of phase nucleation. The rate of bubble nucleation increases by four orders of magnitude (0.3-2000 s-1) over a very small relative change in CH2surf (0.21-0.26 M, corresponding to a ∼0.025 V increase in driving force). Classical nucleation theory yields thermodynamic radii of curvature for critical nuclei of 4.4 to 5.3 nm, corresponding to internal pressures of 330 to 270 atm, and activation energies for nuclei formation of 14 to 26 kT, respectively. The dependence of nucleation rate on H2 concentration indicates that nucleation occurs by a heterogeneous mechanism, where the nuclei have a contact angle of ∼150° with the electrode surface and contain between 35 and 55 H2 molecules.

Gravitational waves from first-order phase transitions: towards model separation by bubble nucleation rate

We study gravitational-wave production from bubble collisions in a cosmic first-order phase transition, focusing on the possibility of model separation by the bubble nucleation rate dependence of the resulting gravitational-wave spectrum. By using the method of relating the spectrum with the two-point correlator of the energy-momentum tensor < T(x)T(y) >, we first write down analytic expressions for the spectrum with a Gaussian correction to the commonly used nucleation rate, Γ ∝ eβ tarrow eβ t−γ2t2, under the thin-wall and envelope approximations. Then we quantitatively investigate how the spectrum changes with the size of the Gaussian correction. It is found that the spectral shape shows \U0001d4aa(10)% deviation from Γ ∝ eβ t case for some physically motivated scenarios. We also briefly discuss detector sensitivities required to distinguish different spectral shapes.

Controlling the crystal polymorph by exploiting the time dependence of nucleation rates.

Most substances can crystallise into two or more different crystal lattices called polymorphs. Despite this, there are no systems in which we can quantitatively predict the probability of one competing polymorph forming instead of the other. We address this problem using large scale (hundreds of events) studies of the competing nucleation of the alpha and gamma polymorphs of glycine. In situ Raman spectroscopy is used to identify the polymorph of each crystal. We find that the nucleation kinetics of the two polymorphs is very different. Nucleation of the alpha polymorph starts off slowly but accelerates, while nucleation of the gamma polymorph starts off fast but then slows. We exploit this difference to increase the purity with which we obtain the gamma polymorph by a factor of ten. The statistics of the nucleation of crystals is analogous to that of human mortality, and using a result from medical statistics, we show that conventional nucleation data can say nothing about what, if any, are the correlations between competing nucleation processes. Thus we can show that with data of our form it is impossible to disentangle the competing nucleation processes. We also find that the growth rate and the shape of a crystal depend on it when nucleated. This is new evidence that nucleation and growth are linked.

Crystallization kinetics of glass microspheres with yttrium aluminium garnet (YAG) composition

A combination of sol–gel Pechini method and flame synthesis was used to prepare yttrium aluminate glass microspheres with the garnet composition (YAG, 62.5 mol% aluminium oxide, 37.5 mol% yttrium oxide). Prepared glass microbeads were studied by optical microscopy, SEM, X-ray diffraction (XRD), differential scanning calorimetry (DSC) and high-temperature (HT) XRD analysis. Formation of YAG as the only crystalline phase was observed during HT XRD experiment in the temperature interval (750–1200 °C), with the onset of YAG phase crystallization in the temperature interval 860–870 °C and most prominent increase in the YAG phase content between 905 and 910 °C. The experimental data obtained by DSC analysis and the Johnson–Mehl–Avrami–Kolmogorov model were used for determination of crystallization behaviour of the studied system. The frequency factor A = 5.2 × 1048 ± 9.6 × 1048 min−1, apparent activation energy E app = 1100 ± 10 kJ mol−1 and the Avrami coefficient m = 4 were determined. The linear temperature dependence of nucleation rate, reaction-controlled crystal growth interface and a 3-D crystal growth were confirmed in the studied system.

Nucleation and the spall strength of liquid metals

This article presents calculation of the nucleation rate for liquid metals (Al, Fe, Mo) based on molecular dynamic simulation for embedded atom method (EAM) potentials. The dependence of nucleation rate on pressure and temperature could be approximated accurately in the form of classical nucleation theory taking into account surface tension dependency on pore radius σ = σ0/(1 + 2δ/r), where σ—surface tension, δ—the Tolman length. Basing on the results of the calculations, we have developed a model allowing calculating the spall strength of liquid metals under tension using such parameters as surface tension, viscosity, which could be measured experimentally. The obtained results for Mo and Al are consistent with experimental data and direct MD calculations at strain rates approx. 1010-1011 s-1.

Bulk Crystallization of Supercooled Metal Films

The overwhelming majority of modern materials are knowingly produced by crystallization from melts. Leaving apart powder metallurgy and some other technologies, the mainstream is melting and homogenizing a charge followed by its transition to a solid state. In this case, technologies based on a method of ultrafast hardening from a liquid state, the key point of which is putting a substance into a deep metastable state with a further intense phase transition, are of particular importance. This allows producing amorphous, nanocrystalline, bioactive, and other promising materials widely used in modern industry and technologies, microelectronics, medicine, etc. In particular, they can be used as durable anti-corrosion coatings. Since the quality and physicochemical properties of these materials depend directly on their morphology, the skill in controlling this morphology is an effective way of producing materials with specified functional characteristics. This requires the ability to describe in detail the kinetics of phase transitions at all stages of the process. Like any other first-order phase transitions, crystallization occurs via fluctuation-induced nucleation and growth of centers of a new phase. Hence, the overall kinetics of such a process is determined by nucleation and the growth rate of nuclei. These quantities are related to a set of various thermodynamic and kinetic parameters that are important under specific conditions and primarily to a degree of metastability of the parent phase. The main problem here is finding the time dependence of the fraction of the crystalline phase and the size distribution of the nuclei. The kinetic theory of fluctuation-induced nucleation and crystal growth is elaborated pretty well, whereas the thermophysical aspects of this problem are poorly investigated. In particular, the effect of heat release at the phase transition on the rate of the process is insufficiently studied. Theoretical analysis of phase transition shows that for the most cases the process can be divided into two particular stages. The first one is the nucleation stage. The majority of new phase nuclei form during this particular stage. Nonlinear nature of nucleation expressed in strong dependence of nucleation rate from the degree of metastability. At the beginning of this stage the process is conditioned by the factors producing metastability, though the stage ends due to reduction in the degree of metastability. This reduction results from the transition of a portion of material from metastable phase to stable phase accompanied by release of latent heat of phase transition. Typically the portion of the new phase is relatively small at the moment of the end of nucleation stage. This is due to the fact that formation of even small portion of a new phase is enough for significant reduction in nucleation rate. The main part of initial phase transits to stable state during the subsequent growth of crystals already formed during nucleation stage. In studying the phase transition the nucleation stage attracts great interest, but it is a problem of great complexity. It involves thermodynamics of small systems, nucleation kinetics, knowing the growth mechanism in a wide range of parameters, correct accounting for effect that assembly of crystals has on metastability, etc. Combined with account for the factors producing metastability it all leads to challenging, nonlinear mathematical problem described by the system of integro-differential equations. At this time the complete solution of this problem is yet to be found. In current work nonequilibrium theory of bulk crystallization of melts rapidly quenched to deeply supercooled state is developed. This theory correctly takes into account the heat release due to phase transition. It is achieved by using the real temperature fields formed around crystals in kinetic equations. Limits of validity of theories using heat release obtained from global heat balance are estimated. Proposed theory allows to describe accurately the kinetics of crystal nucleation and growth in metastable liquid and to determine the microstructure of solidified material. Particular attention was paid to the mechanism of crystal growth in highly nonequilibrium conditions and with account taken of the shrinkage during solidification. The problem of solidification of a thin layer of metal melt brought into contact with a massive cold substrate is developed. Based on the amorphization conditions formulated, the thickness of the amorphous sublayer formed near substrate is determined. The suggested model of bulk crystallization of melt makes it possible to find the morphology of the solidified layer. The work is supported by RFBR (grant #15-08-04474).

Exact solutions of population balance equation

Population balance equations have been used to model a wide range of processes including polymerization, crystallization, cloud formation, and cell dynamics, but the lack of analytical solutions necessitates the use of numerical techniques. The one-dimensional homogeneous population balance equation with time dependent but size independent growth rate and time dependent nucleation rate is investigated. The corresponding system of equations is solved analytically in this paper.

Heterogeneous nucleation on complex networks with mobile impurities

We study the heterogeneous nucleation of Ising model on complex networks under a nonequilibrium situation where the impurities perform degree-biased motion controlled by a parameter α. Through the forward flux sampling and detailed analysis on the nucleating clusters, we find that the nucleation rate shows a nonmonotonic dependence on α for small number of impurities, in which a maximal nucleation rate occurs at corresponding to the degree-uncorrelated random motion. Furthermore, we demonstrate the distinct features of the nucleating clusters along the pathway for different preference of impurities motion, which may be used to understand the resonance-like dependence of nucleation rate on the motion bias of impurities. Our theoretical analysis shows that the nonequilibrium diffusion of impurities can always induce a positive energy flux that can facilitate the barrier-crossing nucleation process. The nonmonotonic feature of the average value of the energy flux with α may be the origin of our simulation results.

The dependence of homogeneous nucleation rate on supersaturation.

The claim that classical nucleation theory (CNT) correctly predicts the dependence on supersaturation of the steady-state rate of homogeneous nucleation is reexamined in light of recent experimental studies of nucleation of a range of substances, including water, argon, nitrogen, and several 1-alcohols. Based on these studies (which include, for water, a compilation of nine different studies), it is concluded that the dependence of nucleation rate on supersaturation is not correctly predicted by CNT. It is shown that CNT's incorrect prediction of the supersaturation dependence of nucleation rate is due to its incorrect prediction of the Gibbs free energy change associated with formation of small clusters from the monomer vapor, evaluated at the substance's equilibrium vapor pressure, even though that free energy change is itself a function only of temperature.

Homogenous nucleation rates of n-propanol measured in the Laminar Flow Diffusion Chamber at different total pressures.

Nucleation rates of n-propanol were investigated in the Laminar Flow Diffusion Chamber. Nucleation temperatures between 270 and 300 K and rates between 10(0) and 10(6) cm(-3) s(-1) were achieved. Since earlier measurements of n-butanol and n‑pentanol suggest a dependence of nucleation rates on carrier gas pressure, similar conditions were adjusted for these measurements. The obtained data fit well to results available from literature. A small positive pressure effect was found which strengthen the assumption that this effect is attributed to the carbon chain length of the n-alcohol [D. Brus, A. P. Hyvärinen, J. Wedekind, Y. Viisanen, M. Kulmala, V. Ždímal, J. Smolík, and H. Lihavainen, J. Chem. Phys. 128, 134312 (2008)] and might be less intensive for substances in the homologous series with higher equilibrium vapor pressure. A comparison with the theoretical approach by Wedekind et al. [Phys. Rev. Lett. 101, 12 (2008)] shows that the effect goes in the same direction but that the intensity is much stronger in experiments than in theory.

Parameter identification in non-isothermal nucleation and growth processes

We study non-isothermal nucleation and growth phase transformations, which are described by a generalized Avrami model for the phase transition coupled with an energy balance to account for recalescence effects. The main novelty of our work is the identification of temperature dependent nucleation rates. We prove that such rates can be uniquely identified from measurements in a subdomain and apply an optimal control approach to develop a numerical strategy for its computation.

Microstructure evolution at the onset of discontinuous dynamic recrystallization: A physics-based model of subgrain critical size

• Evolution of subgrains to recrystallization nuclei is possible at very low strains. • Dynamic recrystallization nuclei increases on a sigmoidal curve with strain. • Nucleation rate increases up to a maximum and decreases to zero at peak strain. • Growth of recrystallized nuclei diminishes to zero at or over the peak. • Site saturation is the mechanism of dynamic recrystallization up to the peak. A physical model based on the evolution of subgrains size is proposed to describe the nucleation and growth processes during discontinuous dynamic recrystallization. The evolution of subgrains to viable recrystallization nuclei was found possible at very low strains. Afterwards, the number of stable nuclei considerably increased on a sigmoidal trend with strain and reached a saturated state at about 0.6 times the peak strain. The dependence of nucleation rate on strain was modeled using an Avrami-type equation and the driving force for the growth of recrystallized nuclei was similarly modeled in terms of strain. It is also shown that “site saturation” is the governing mechanism for the initiation of the discontinues dynamic recrystallization at the grain boundaries. The flow stress of the material was calculated using the law of mixture of recrystallized and unrecrystallized regions with fractional softening as the stress-partitioning factor. Satisfactory agreement between predicted and experimental results was obtained, thereby confirming the validity of the proposed model.

Description of fluid dynamics and coupled transports in models of a laminar flow diffusion chamber

The aim of this study is to assess how much the results of nucleation experiments in a laminar flow diffusion chamber (LFDC) are influenced by the complexity of the model of the transport properties. The effects of the type of fluid dynamic model (the steady state compressible Navier-Stokes system for an ideal gas/parabolic profile approximation) and the contributions of the coupled terms describing the Dufour effects and thermodiffusion on the predicted magnitude of the nucleation maxima and its location were investigated. This study was performed on the model of the homogeneous nucleation of an n-butanol-He vapor mixture in a LFDC. The isothermal dependencies of the nucleation rate on supersaturation were determined at three nucleation temperatures: 265 K, 270 K, and 280 K. For this purpose, the experimental LFDC data measured by A. P. Hyvärinen et al. [J. Chem. Phys. 124, 224304 (2006)] were reevaluated using transport models at different levels of complexity. Our results indicate that the type of fluid dynamical model affects both the position of the nucleation maxima in the LFDC and the maximum value of the nucleation rate. On the other hand, the Dufour effects and thermodiffusion perceptibly influence only the value of the maximal nucleation rate. Its position changes only marginally. The dependence of the maximum experimental nucleation rate on the saturation ratio and nucleation temperature was acquired for each case. Based on this dependence, we presented a method for the comparison and evaluation of the uncertainties of simpler models' solutions for the results, where we assumed that the model with Navier-Stokes equations and both coupled effects taken into account was the basis. From this comparison, it follows that an inappropriate choice of mathematical models could lead to relative errors of the order of several hundred percent in the maximum experimental nucleation rate. In the conclusion of this study, we also provide some general recommendations concerning the proper choice and setting of the mathematical model of transport processes in the LFDC.