Nonisothermal nucleation and formation of SiO2 clusters

Heat and mass transfers are coupled processes, also in nucleation. In principle, a nucleating cluster would have a different temperature compared to the surrounding supersaturated old phase because of the heat release involved with attaching molecules to the cluster. In turn a difference in temperature across the cluster surface is a driving force for the mass transfer to and from the cluster. This coupling of forces in nonisothermal nucleation is described using mesoscopic nonequilibrium thermodynamics, emphasizing measurable heat effects. An expression was obtained for the nonisothermal nucleation rate in a one-component system, in the case where a temperature difference exists between a cluster distribution and the condensed phase. The temperature is chosen as a function of the cluster size only, while the temperature of the condensed phase is held constant by a bath. The generally accepted expression for isothermal stationary nucleation is contained as a limiting case of the nonisothermal stationary nucleation rate. The equations for heat and mass transport were solved for stationary nucleation with the given cluster distribution and with the temperature controlled at the boundaries. A factor was defined for these conditions, determined by the heat conductivity of the surrounding phase and the phase transition enthalpy, to predict the deviation between isothermal and nonisothermal nucleation. For the stationary state described, the factor appears to give small deviations, even for primary nucleation of droplets in vapor, making the nonisothermal rate smaller than the isothermal one. The set of equations may lead to larger and different thermal effects under different boundary conditions, however.

Nucleation of clusters from the gas phase is a widely encountered phenomenon, e.g. regional air quality and global climate are both directly impacted by particle formation from atmospheric trace gases [1]. Still, the underlying out-of-equilibrium dynamics of this process are not well understood. The classical view of nucleation assumes isothermal conditions where the nucleating clusters are in thermal equilibrium with their surroundings. However, as in all first-order phase transitions, latent heat is released, potentially heating the clusters and suppressing the nucleation. The question of how the released energy affects cluster temperatures during nucleation as well as the growth rate remains controversial.To investigate the nonisothermal dynamics and energetics of homogeneous nucleation, we have performed molecular dynamics (MD) simulations of a supersaturated Lennard-Jones (LJ) vapor in the presence of thermalizing carrier gas. In addition, a previous study of homogeneous nucleation of carbon dioxide in argon carrier gas [2] was revisited for temperature analysis of the growing CO2  clusters. The results obtained from these simulations are compared against kinetic modeling of isothermal nucleation and the classical nonisothermal theory by Feder et al. [3], which also predicts the existence of cool subcritical clusters, and has been quite controversial.For the studied systems, we find that nucleation rates are suppressed by two orders of magnitude at most, despite substantial release of latent heat. Our analyses further reveal that while the temperatures of the entire cluster size populations are indeed elevated, the temperatures of the specific clusters driving the nucleation flux evolve from cold to hot when growing from subcritical to supercritical sizes. This resolves the apparent contradiction between elevated cluster temperatures and minor nonisothermal corrections to the nucleation rate, both often reported in literature, and is in excellent agreement with the theory of Feder et al. Our findings provide unprecedented insight into realistic nucleation events and allow us to directly assess earlier theoretical considerations of nonisothermal nucleation. References[1] M. Kulmala et al., Direct observations of atmospheric aerosol nucleation. Science 339, 943–946 (2013).[2] R. Halonen et al., Homogeneous nucleation of carbon dioxide in supersonic nozzles II: Molecular dynamics simulations and properties of nucleating clusters. Phys. Chem. Chem. Phys. 23, 4517–4529 (2021).[3] J. Feder, K. C. Russell, J. Lothe, G. M. Pound, Homogeneous nucleation and growth of droplets in vapours. Adv. Phys. 15, 111–178 (1966).

Nucleation of clusters from the gas phase is a widely encountered phenomenon, yet rather little is understood about the underlying out-of-equilibrium dynamics of this process. The classical view of nucleation assumes isothermal conditions where the nucleating clusters are in thermal equilibrium with their surroundings. However, in all first-order phase transitions, latent heat is released, potentially heating the clusters and suppressing the nucleation. The question of how the released energy affects cluster temperatures during nucleation as well as the growth rate remains controversial. To investigate the nonisothermal dynamics and energetics of homogeneous nucleation, we have performed molecular dynamics simulations of a supersaturated vapor in the presence of thermalizing carrier gas. The results obtained from these simulations are compared against kinetic modeling of isothermal nucleation and classical nonisothermal theory. For the studied systems, we find that nucleation rates are suppressed by two orders of magnitude at most, despite substantial release of latent heat. Our analyses further reveal that while the temperatures of the entire cluster size populations are elevated, the temperatures of the specific clusters driving the nucleation flux evolve from cold to hot when growing from subcritical to supercritical sizes and resolve the apparent contradictions regarding cluster temperatures. Our findings provide unprecedented insight into realistic nucleation events and allow us to directly assess earlier theoretical considerations of nonisothermal nucleation.

Heterogeneous nucleation often occurs in the atmosphere, but its microscopic mechanism is mostly unknown. In our work, molecular dynamics simulations were performed to explore the dynamic characteristics of the heterogeneous nucleation of supersaturated argon vapor onto a spherical solid nanoparticle. We discuss the effect of the cooling rate on the evolution of the system temperature, the cluster distribution, the cluster size, and the nucleation rate during the nucleation process. Our results show that the pre-existing nucleus plays an important role in the cluster formation stage. Furthermore, in the system with a pre-existing heterogeneous nucleus, a critical cooling rate (1.8×10 J·s-1) exists at which homogeneous nucleation emerges and coexists with heterogeneous nucleation but heterogeneous nucleation still dominates the entire nucleation process.

Non-isothermal nucleation and growth of embryoes on a substrate from the vapor phase

Condensation phenomenon has been studied actively for decades because of its extensive and significant applications in various fields of technology and engineering. The condensation phenomenon of condensable component in supersonic flows is still not understood very well as a result of the complex nucleation and droplet growth process, especially the condensation characteristic of gas mixture. In this paper, the Laval nozzle was designed based on the bi-cubic curve, state equation of real gas, arc plus straight line and viscous correction of boundary layer. The physical and mathematical models were developed to predict the condensation process in the supersonic air flows based on the nucleation and droplet growth theories, surface tension model and gas-liquid governing equations. The condensation processes of gaseous water/air binary (single condensable) gas and water/ethanol/air ternary (double condensable) gas mixture in the designed nozzle were simulated, and the reliability of the established models was verified by the experimental data. By comparing the condensation process of water/air binary gas with water/ethanol ternary gas, the influence of the second condensable component on the condensation process was analyzed. The results show that in the condensation process of gaseous water, as the pressure and temperature of water vapor decrease in the nozzle, spontaneous condensation occurs further downstream the nozzle throat. The nucleation rate grows rapidly from 0 to peak in a very short distance. With the consumption of water vapor, due to the decrease of the degree of supercooling, the nucleation environment is destroyed, and the nucleation rate quickly decreases to 0. The nucleation process is rapid in time and space, while the droplet growth process could maintain longer. The droplet number and mass fraction increase continuously till the nozzle outlet. There is a weak condensation in the nozzle due to the release of latent heat, but it is not obvious because the air acts as a heat container and absorbs the latent heat released by condensation. In the water/ethanol/air ternary system, the ethanol nucleates prior to water vapor. With the increase of supercooling, water vapor also begins to nucleate. In essence, there are two kinds of condensation nuclei (water nuclei and ethanol nuclei), and both the water and ethanol vapor can aggregate on these two kinds of condensation nuclei. Compared with the condensation process of water, the Wilson point of condensation is closer to the throat and the outlet mass fraction of liquid phase is greater in the condensation process of water/ethanol mixture, which shows that the water and ethanol can affect and promote each other. The maximum nucleation rate, droplet growth rate, droplet radius and outlet mass fraction of liquid phase of water/air binary and water/ethanol/air ternary mixture are about 9.46 × 1026 m−3s−1 and 2.57 × 1027 m−3s−1, 1.65 × 10−5 m/s and 1.02 × 10−5m/s, 1.32 × 10−7m and 1.63 × 10−7m, 0.19% and 1.34%, respectively.

The formation of aerosols, and subsequent cloud condensation nuclei, remains one of the least understood atmospheric processes upon which global climate change critically depends. Under atmospheric conditions, the process of homogeneous nucleation (formation of stable clusters ∼ 1 nm in size), and their subsequent growth into new particles (>3 nm), determines the aerosol and cloud nuclei population, yet, hitherto, no theory has elucidated the new particle formation phenomenon in detail. In this study, we present a new theory which provides a mechanistic explanation for new particle formation via activation of stable inorganic clusters by organic vapors. The new nano‐particle activation theory is analogous to Köhler theory which describes cloud formation in a supersaturated water vapor field but differs in that it describes the activation of inorganic stable nano‐clusters into aerosol particles in a supersaturated organic vapor which initiates spontaneous and rapid growth of clusters. Inclusion of the new theory into aerosol formation models predicts that increases in organic vapor densities lead to even greater increases in particle production, which, in turn, will influence the global radiative cooling effect of atmospheric aerosols.

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

A method is developed for calculating the rate of homogeneous nucleation in a supersaturated vapor in which the molecular dynamics method and the nucleation theorem are combined. This approach allows us to predict the experimental data with good accuracy.

Homogeneous nucleation and growth of zinc from supersaturated vapor are investigated by nonequilibrium molecular dynamics simulations in the temperature range from 400 to 800 K and for a supersaturation ranging from log S=2 to 11. Argon is added to the vapor phase as carrier gas to remove the latent heat from the forming zinc clusters. A new parametrization of the embedded atom method for zinc is employed for the interaction potential model. The simulation data are analyzed with respect to the nucleation rates and the critical cluster sizes by two different methods, namely, the threshold method of Yasuoka and Matsumoto [J. Chem. Phys. 109, 8451 (1998)] and the mean first passage time method for nucleation by Wedekind et al. [J. Chem. Phys. 126, 134103 (2007)]. The nucleation rates obtained by these methods differ approximately by one order of magnitude. Classical nucleation theory fails to describe the simulation data as well as the experimental data. The size of the critical cluster obtained by the mean first passage time method is significantly larger than that obtained from the nucleation theorem.

A New technique for ion nucleation using resonance ionization within supersaturated vapors

This work reports the direct observation and separation of size-selected aluminum nanoparticles acting as heterogeneous nuclei for the condensation of supersaturated vapors of both polar and nonpolar molecules. In the experiment, we study the condensation of supersaturated acetonitrile and n-hexane vapors on charged and neutral Al nanoparticles by activation of the metal nanoparticles to act as heterogeneous nuclei for the condensation of the organic vapor. Aluminum seed nanoparticles with diameters of 1 and 2 nm are capable of acting as heterogeneous nuclei for the condensation of supersaturated acetonitrile and hexane vapors. The comparison between the Kelvin and Fletcher diameters indicates that for the heterogeneous nucleation of both acetonitrile and hexane vapors, particles are activated at significantly smaller sizes than predicted by the Kelvin equation. The activation of the Al nanoparticles occurs at nearly 40% and 65% of the onset of homogeneous nucleation of acetonitrile and hexane supersaturated vapors, respectively. The lower activation of the charged Al nanoparticles in acetonitrile vapor is due to the charge-dipole interaction which results in rapid condensation of the highly polar acetonitrile molecules on the charged Al nanoparticles. The charge-dipole interaction decreases with increasing the size of the Al nanoparticles and therefore at low supersaturations, most of the heterogeneous nucleation events are occurring on neutral nanoparticles. No sign effect has been observed for the condensation of the organic vapors on the positively and negatively charged Al nanoparticles. The present approach of generating metal nanoparticles by pulsed laser vaporization within a supersaturated organic vapor allows for efficient separation between nucleation and growth of the metal nanoparticles and, consequently controls the average particle size, particle density, and particle size distribution within the liquid droplets of the condensing vapor. Strong correlation is found between the seed nanoparticle's size and the degree of the supersaturation of the condensing vapor. This result and the agreement among the calculated Kelvin diameters and the size of the nucleating Al nanoparticles determined by transmission electron microscopy provide strong proof for the development of a new approach for the separation and characterization of heterogeneous nuclei formed in organic vapors. These processes can take place in the atmosphere by a combination of several organic species including polar compounds which could be very efficient in activating charged nanoparticles and cluster ions of atmospheric relevance.

A model has been developed to investigate the growth of droplets in a supersaturated cold vapor taking into account their possible solid-liquid phase transition. It is shown that the solid-liquid phase transition is nontrivially coupled, through the energy released in attachment, to the nucleation process. The model is based on the one developed by J. Feder, K. C. Russell, J. Lothe, and G. M. Pound [Adv. Phys. 15, 111 (1966)], where the nucleation process is described as a thermal diffusion motion in a two-dimensional field of force given by the derivatives of a free-energy surface. The additional dimension accounts for droplets internal energy. The solid-liquid phase transition is introduced through a bimodal internal energy distribution in a Gaussian approximation derived from small clusters physics. The coupling between nucleation and melting results in specific nonequilibrium thermodynamical properties, exemplified in the case of water droplets. Analyzing the free-energy landscapes gives an insight into the nucleation dynamics. This landscape can be complex but generally exhibits two paths: the first one can generally be ascribed to the solid state, while the other to the liquid state. Especially at high supersaturation, the growth in the liquid state is often favored, which is not unexpected since in a supersaturated vapor the droplets can stand higher internal energy than at equilibrium. From a given critical temperature that is noticeably lower than the bulk melting temperature, nucleation may end in very large liquid droplets. These features can be qualitatively generalized to systems other than water.

The width ( δ ) of a laminar flame is often characterized as a basic property of the flame and is sometimes used in turbulent combustion models to categorize the turbulence scale of the mixture. From computed flame speeds and temperature profiles of C3H8/Oa/Ns (ø=1) flames we have determined widths, using definitions based on ( dT*sol;dx)max, Q (the heat release rate) and r (the characteristic chemical time) and characteristic distances have been determined from the transport properties of the burned (δ b) and unburned (δ u) gases. The flame widths are compared via the transport properties, (A/Cp), of the gas mixtures in the flame where A is the thermal conductivity and Cp is the heat capacity. A derived or approximate transport property for the flame widths is defined by the product of the mass flow rate (Mƒ) and the flame width. The functional dependence of these flame widths is compared by varying the Na fraction and initial mixture temperature. Both the set of Na fractions and mixture temperatures show the same range of flame speeds (40–350 cm/sec), but exhibit very different flame width values and dependence. The values of the derived transport properties from the ( dT/dx) max definition approximate the transport properties of the burned gas mixture (ST∼2*SI,) while those from the characteristic chemical time approximate the transport properties of the unburned gas mixture (δt;∼$). However, the values of the derived transport property based on the half-width of the heat release rate gives physically unreasonable transport properties in excess of either the burned or the unburned gases. These calculated flame widths differ significantly in absolute value and show a non-linear dependence on dilution. Although flame speeds for increasing mixture temperature and for differing dilutions are similar, the flame widths calculated for increasing mixture temperatures decrease only slightly compared to those for decreasing dilutions. These definitions of flame width, although given the same name, do not describe similar flame properties. The flame width definition based on the temperature gradient is proposed to be the proper specification of a laminar length scale because it is based on the physically measurable temperature profile and because it incorporates the effects of both heat release and transport which determine the temperature profile.

Homogeneous and heterogeneous nucleation of water vapor: A comparison using molecular dynamics simulation