Surface Topology of the Ion-Induced Vapor Nucleation Rate

ABSTRACT

Ion-induced nucleation involves additional electrostatic interactions between vapor molecules (atoms) and ions. The electrostatic force helps to form the ion stabilized prenucleation embryos and lowers the free energy barrier for nucleation. The free energy for ion-induced critical embryos formation has been calculated using the Thomson's term in the framework of the classical theory of nucleation. Nucleation theory has made obvious progress, but the understanding of the nucleation phenomenon is far from complete. Some ideas for the identification of possible new directions to improve both homogeneous and heterogeneous nucleation theories can be found by analyzing the topology of nucleation rate surfaces. The creation of the ion-induced nucleation rate surfaces is based on the knowledge of phase state diagrams, experimental results on ion-induced nucleation, and a few plausible assumptions. In this article the surfaces of the ion-induced nucleation rates for metastable vapor nucleation will be constructed. Semiempirical rules are formulated for the ion-induced vapor nucleation based on both known experimental and theoretical results. By using surface topology analysis, problems in heterogeneous nucleation theory can be formulated more clearly, and future directions for improvements can be discussed. A point on the spinodal line was found by extrapolation of the logarithm of the actual vapor pressure for ion-induced and homogeneous nucleation at a constant nucleation rate as a function of inverse temperature. Nucleation rate scaling of the surface should yield a quantitative scale for the ion-induced nucleation rates. Phase diagrams need to be incorporated into the interpretation of experimental and theoretical results on ion-induced nucleation.     

Mineral admixtures in mortars: Quantification of the physical effects of inert materials on short-term hydration

This work is the second part of an overall project, the aim of which is the development of general mix design rules for concrete containing different kinds of mineral admixtures. The first part presented the separation of the different physical effects responsible for changes in cement hydration when chemically inert quartz powders are used in mortars. This second part describes the development of an empirical model, based on semiadiabatic calorimetry measurements, which leads to the quantification of the enhancement of cement hydration due to the heterogeneous nucleation effect at short hydration times. Experimental results show that not all the admixture particles participate in the heterogeneous nucleation process. Consequently, the concept of efficient surface S_eff is introduced in the model. S_eff is the total admixture surface S (m² of mineral admixture/kg of cement) weighted by a function ξ(p). The efficiency function ξ(p) depends only on the replacement rate p and is independent of time, fineness and type of mineral admixture used. It decreases from 1 to 0: Low replacement rates give an efficiency value near 1, which means that all admixture particles enhance the hydration process. An efficiency value near 0 is obtained for high replacement rates, which indicates that, from the hydration point of view, an excess of inert powder does not lead to an increase in the amount of hydrates compared with the reference mortar without mineral admixture. The empirical model, which is mainly related to the specific surface area of the admixtures, quantifies the variation of the degree of hydration induced by the use of inert mineral admixtures. One application of the model, coupled with Powers' law, is the prediction of the short-term compressive strength of mortars.     

Ternary nucleation applied to gas to particle conversion

Atmospheric aerosol formation involving three gaseous components is considered with an emphasis on systems in which one component is water. Analytic methods discussed qualitatively are physical equilibrium phase diagram analysis and heteromolecular nucleation. The possibility of chemical reactions before or after nucleation is considered. Atmospheric applications are discussed.

Additional experimental measurements of thermodynamic parameters, such as the equilibrium vapor pressure of low volatile products and the surface tension of ternary systems are strongly recommended for further studies of ternary aerosols.     

Simulation of nano-particle formation in a wall-heated aerosol reactor including coalescence

The initial stage of particle formation during gas phase synthesis is characterized by a high concentration of particles that undergo rapid coagulation. The surface area of the agglomerates is reduced by coalescence. In this study a model is presented that accounts, in addition to nucleation and coagulation, for the shape of the particles by tracing both the particle volume and the total surface area density of the agglomerates. A moment model, based on a unimodal lognormal size distribution gives the concentration, polydispersity, and average volume of the particles as a function of space and time. The total surface area density of the particles is determined by solving an additional transport equation, incorporating a linear decay law to describe the decrease in surface area of a coalescing structure. The aerosol dynamics are calculated in combination with the convective and diffusive particle transport in a spatially inhomogeneous aerosol reactor.     

A Transition from Heterogeneous to Homogeneous Nucleation in the Turbulent Mixing CNC

A new method for changing the supersaturation in the Turbulent Mixing CNC has been developed and used to examine the transition from heterogeneous nucleation of test particles to homogenous nucleation of working fluid: dibutylphthlate (DBP). Supersaturation was controlled by changing the DBP vapor pressure in the nozzle flow by saturating only a predetermined part of the flow, while the total flow and temperature remain constant. This approach allows for the changing of the initial DBP vapor pressure, while keeping the flow structure and temperature field unchanged. The DBP concentration in the outlet of the vapor generator was measured experimentally for different ratios of saturated and bypass flows and found to be close to estimated values. Experimental results for transitions from heterogeneous nucleation to homogeneous nucleation are presented for NaCl and WO_x particles at various DBP vapor pressures. With an increasing of the DBP vapor pressure, the concentration of enlarged particles increases until it reaches a plateau. At higher initial values of DBP pressure, homogeneous nucleation prevails, and the number concentration of particles follows a curve typical for homogeneous nucleation recorded in the absence of nuclei. Nuclei with different mobility diameters were activated at different values of vapor pressure. There are significant differences in the slopes of particle activation curves for NaCl and WO_x particles. The reasons for such differences are a subject for continuing research.     

Aerosol formation in gas-liquid contact devices—nucleation, growth and particle dynamics

In gas-liquid contact devices like absorbers, scrubbers, quench coolers or condensers, aerosols can be formed by spontaneous phase transitions, initiated by homogeneous or heterogeneous nucleation, if special process operation conditions lead to a metastable, i.e. a supersaturated state in the gas phase. Aerosol formation can impact severely the mass separation efficiency of gas-liquid contactors. This is demonstrated by experiments performed in semi-technical plants.The paper is aimed to identify strategies for understanding and describing the complex aerosol behaviour in gas-liquid contact devices.Operation conditions are identified under which supersaturation can arise, and the fundamentals of modelling aerosol formation and growth in gas-liquid contactors are discussed.The SENECA code developed by the authors allows to simulate aerosol formation and behaviour in contact devices as well as in multistage gas cleaning processes. Experimental results show that most of all important features of aerosol behaviour in flue gas cleaning and in condensation processes can be predicted with good accuracy by SENECA.     

An analysis of various nucleation mechanisms for sulfate particles in the stratosphere

A theoretical analysis of particle formation mechanisms under stratospheric conditions was carried out using a fully interactive one-dimensional model of aerosol formation and evolution. The formation mechanisms considered are homogeneous, ion and heterogeneous heteromolecular nucleation of H₂SO₄---H₂O systems, the clustering of sulfate radicals, and heterogeneous nucleation onto stable neutral ion—ion recombination complexes. We develop theoretical expressions for the nucleation rates, describe the manner in which the nucleation mechanisms are incorporated into the model, and present the results of model calculations. We find that although the different nucleation processes lead to greatly different rates of particle formation, the observed characteristics of the aerosol are hardly affected by the assumed particle formation mechanism. Consequently, it will be difficult to devise measurements to evaluate the relative importance of the various formation mechanisms. Our results show that the homogeneous and ion nucleation rates in the stratosphere are negligible. Heterogeneous nucleation onto stable ion—ion recombination products and the clustering of sulfate radicals are two processes which could lead to the generation of large numbers of particles in the stratosphere. Using presently available experimental techniques it is not possible to determine unambiguously which formation mechanism is responsible for the production of the stratospheric particles.     

FORMATION OF HYDROBROMIC AND HYDROCHLORIC ACID AEROSOLS IN WET FLUE GAS CLEANING PROCESSES

The formation and behavior of hydrobromic and hydrochloric acid aerosols in a wet flue gas cleaning pilot plant were investigated. The optical three-wavelength extinction (3-WE) method was used to determine mean aerosol droplet diameters and droplet number concentrations. The experimental data are compared with theoretical results of the simulation tool AerCoDe (aerosol formation in contact devices). Results are presented for a raw gas temperature of 200°C and raw gas concentrations up to 260 mg/m³(STP) for HBr, and 2500 mg/m³ (STP) for HCl. Under these conditions aerosol formation for both species is initiated by heterogeneous nucleation. It is shown that during absorption processes HBr is forming essentially higher supersaturated gas phases in comparison to HCl, resulting in higher droplet number concentrations and smaller droplet sizes. For both species the number concentration is a strong function of the maximum degree of saturation, which corresponds to the classical theory of heterogeneous nucleation. HBr aerosol droplets cannot be detected by the 3-WE method directly after the first stage of the flue gas cleaning plant (quench column) because they are smaller than the detection limit ( ≈ 500 nm) of the 3-WE method for nonabsorbing particles. In this case the droplets are enlarged in a second step, and the number concentration is determined after enlargement. Using the actual number concentration as an input parameter, the mean diameter after the first stage can be calculated with the simulation tool AerCoDe.     

A simulation tool for aerosol formation during sulphuric acid absorption in a gas cleaning process

A simulation tool has been developed to predict sulphuric acid aerosol formation in typical industrial absorption processes for gas cleaning. The underlying model comprises homogeneous nucleation and the growth of a polydisperse droplet collective under the special circumstances of a gas–liquid contact device where heat and mass transfer processes between the bulk phases take place simultaneously. The model is applied to a hot flue gas (200 °C) with sulphuric acid concentrations between 5 and 100 mg m⁻³ (STP) (STP: standard temperature and pressure). The simulation yields high droplet number concentrations up to 10¹⁶ m⁻³ especially for low gas inlet concentrations of sulphuric acid (5 mg m⁻³ (STP)), and very small droplet sizes in the range 20–100 nm. The droplet number concentrations decrease and the droplet sizes increase with increasing sulphuric acid inlet concentrations. It is shown that small droplets (<20 nm) need relatively high supersaturation for growing. If the saturation in the absorption equipment is not high enough the droplets partially re-evaporate but do not vanish due to the extremely low vapor pressure of concentrated sulphuric acid. The resulting size distributions of the aerosol droplets are not very sensitive with respect to the nucleation model used. This is demonstrated by comparing nucleation models with and without hydrate formation. The new simulation tool allows an estimate of the true sulphuric acid removal efficiency of absorption processes which is often not more than 50% due to aerosol formation. In general, the simulation results enable a deeper insight in the mechanisms of aerosol formation and behavior in absorption processes.     

Large aerosol particles as freezing nuclei

Aerosol particles ingested by cloud supply nuclei which initiate formation of ice. These particles may either condense water or collide with cloud droplets thus becoming hydrosol particles. Ice nucleation through freezing was found to be time-dependent; nucleation sites are being formed or exposed continuously on the surfaces of hydrosol particles. In severe storms large soil particles (dia. > 40 μm) accrete cloud droplets; they freeze the accreted supercooled water at temperatures warmer than the ice nucleation temperature of their submicron- and micron-sized shed particles. Solid phase (ice) formation in clouds cannot be reconstructed by determining freezing temperature spectra of hydrosol present in precipitatation samples where surfaces of hydrosolized aerosol particles have already undergone physical and chemical changes.     

Nucleation truncation by time-dependent supersaturation: a unified model for homogeneous and heterogeneous nucleation

In this paper, a unified model for heterogeneous, as well as for homogeneous two-dimensional nucleation and growth processes for electrochemical phase transitions is derived. It accounts for three different mechanisms of the termination of nucleation and growth: the geometric mechanism by surface exhausting, the stoichiometric mechanism by the consumption of active surface sites and the systemic mechanism by the time dependence of the supersaturation of the initial phase as the thermodynamic driving force of the phase transition. The special role of time-dependent supersaturation in truncating the nucleation process is discussed by means of numerical simulations of the model equations. It could be shown that some—until now—poorly understood experimental findings concerning phase transition kinetics at electrodes, as for example, the occurrence of instantaneous homogeneous nucleation at the mercury electrode or of non-integer Avrami slopes for heterogeneous nucleation at single crystal electrodes, can be explained easily in the frame of the presented model.     

Studies of hydrate nucleation with high pressure differential scanning calorimetry

Current models for hydrate formation in subsea pipelines require an arbitrary assignment of a subcooling criterion for nucleation. In reality hydrate nucleation times depend on both the degree of subcooling and the amount of time the fluid has been subcooled. In this work, differential scanning calorimetry was applied to study hydrate nucleation for gas phase hydrate formers. Temperature ramping and isothermal approaches were combined to explore the probability of hydrate nucleation for both methane and xenon. A system-dependent subcooling of around 30 K was necessary for hydrate nucleation from both guest molecules. In both systems, hydrate nucleation occurred over a narrow temperature range (2-3 K). The system pressure had a large effect on the hydrate nucleation temperature but the ice nucleation temperature was not affected over the range of pressures investigated (3-20 MPa). Cooling rates in the range of (0.5-3 K/min) did not have any statistically significant effect on the nucleation temperature for each pressure investigated. In the isothermal experiments, the time required for nucleation decreased with increased subcooling.     

Methane Hydrate Formation and Dissociation in the presence of Bentonite Clay Suspension

The present work reports the effect of bentonite clay on methane hydrate formation and dissociation in synthetic seawater of salinity 3.55 % of total dissolved salts. Extensive observations of pressure‐temperature equilibrium during formation and decomposition of methane hydrate under different conditions have been made. It is observed that phase equilibrium conditions of hydrate are affected on changing the concentration of bentonite clay in synthetic seawater. Induction time for hydrate nucleation has been measured under different concentrations of clay and subcooling conditions. The presence of bentonite clay in synthetic seawater reduces the induction time of hydrate formation. Enthalpy of hydrate dissociation is calculated by Clausius‐Clapeyron equation using measured phase equilibrium data. The amount of gas consumed during hydrate formation has been calculated using real gas equation. It is found that a larger amount of gas is consumed upon addition of bentonite clay in synthetic seawater.     

Influence of the presence of bubbles on the parameters of crystal nucleation in the 26Li<Subscript>2</Subscript>O · 74SiO<Subscript>2</Subscript> glass

The crystal nucleation in the glass of composition (mol %) 26Li₂O · 74SiO₂ has been investigated in the cases of homogeneous and heterogeneous nucleation. Parameters of homogeneous nucleation, such as the stationary nucleation rate I _st, the time of nonstationary nucleation τ, and the crystal growth rate U, have been determined. The temperature dependences of these parameters have been constructed. The surface energy σ at the nucleus-glass melt interface has been determined, and its temperature dependence has been obtained. The surface energy σ has been evaluated using the graphical method for solving the transcendental equation derived by transforming the relationships for the stationary crystal nucleation rate and the time of nonstationary crystal nucleation. The critical nucleus sizes r* and the free energy of formation of the critical nucleus Φ* have been determined. The heterogeneous nucleation on bubbles specially produced in the glass has been studied. It has been demonstrated that the presence of bubbles in the initial glass does not affect the crystal growth rate and substantially changes the nonstationary nucleation rate. The largest contribution to the change in the nucleation rate is made by “active” bubbles (filled by water vapor) formed in the glasses synthesized with the use of hydrated silicon dioxide.     

Ash Vaporization and Condensation During Combustion of a Suspended Coal Particle

The results of a theoretical study of the formation and growth of the submicron flyash aerosol around a single burning coal particle are presented. The vaporization of ash and subsequent aerosol formation near the coal particle are studied because the local combustion environment influences these processes strongly. A mathematical model is developed that describes the transport of ash vapor and and the growth of the aerosol. The ash aerosol calculation is superimposed on an existing solution to the combustion problem. Included in the model are the effects of convective transport and of both homogeneous and heterogeneous condensation of the ash vapor. The results of the calculations show that refractory compounds with low surface tension, like silica, nucleate very near the coal particle's surface and produce a substantial mass loading of aerosol. The presence of the aerosol does not greatly affect the ash vaporization rate, which is primarily a function of combustion conditions. The size and amount of the submicron ash aerosol are determined by both the local combustion conditions and the ash's physical properties.     

Dynamics of catalyst particle formation and multi-walled carbon nanotube growth in aerosol-assisted catalytic chemical vapor deposition

In aerosol-assisted catalytic chemical vapor deposition (CCVD), the catalyst and carbon precursors are introduced simultaneously in the reactor. Catalyst particles are formed in situ and aligned multi-walled CNTs grow at a high rate. To scale-up the process, it is crucial to understand the chemical transformation of the precursors along the thermal gradient of the reactor, and to correlate nanotube growth with catalyst nanoparticle formation. The products synthesized along a cylindrical CVD reactor from an aerosol composed of ferrocene and toluene, as catalyst and carbon precursor, respectively, were studied. The product surface density and iron content are determined as a function of the location and the iron vapor pressure in the reactor. Samples are analyzed by electron microscopy, X-ray diffraction and Raman spectroscopy. We show the strong influence of the thermal gradient on location and rate of formation of both iron particles and CNTs, and demonstrate that catalyst particles are formed by gas phase homogeneous nucleation with a size which correlates with iron vapor pressure. They are gradually deposited on the reactor walls where nanotubes grow with an efficiency which is varying linearly with catalyst particle density. CNT crystallinity appears very high for a large range of temperature and iron content.     

SIMULATION OF AEROSOL FORMATION IN GAS-LIQUID CONTACT DEVICES

In gas-liquid contact devices like absorbers, quench coolers, or condensers, aerosols can be formed by spontaneous phase transitions, initiated by homogeneous or heterogeneous nucleation, if a supersaturated gas phase emerges due to simultaneous heat and mass transfer processes or chemical reactions. Typical examples are the absorption of acid gases, like HCl or SO₃, the condensation of solvents in the presence of inert gases, and the humidification of cold gases by hot liquids.

In this article the basic principles of aerosol formation in contact devices are briefly described. A strategy for modeling and simulation of aerosol formation and particle dynamics is discussed. Simulation results generated with the process tool AerCoDe for the countercurrent absorption of HCl and the humidification of air are presented.     

Aerosol synthesis of silicon nanoparticles with narrow size distribution—Part 2: Theoretical analysis of the formation mechanism

This work investigates the mechanisms which lead to the formation of silicon nanoparticles with narrow size distributions by means of population balance modeling. The model accounts for the full aerosol process, including chemical reaction, nucleation from supersaturated vapor, growth and agglomeration. The results are in good agreement with experimental data. The effects of the process parameters temperature, silane concentration and reactor total pressure are systematically investigated. The simulation allows an in-depth insight into the particle formation mechanism and reveals the key requirements which are necessary for the generation of narrow particle size distributions. In this mechanism, only a short nucleation burst occurs, while surface growth plays the dominant role in silane precursor consumption. A key role is attributed to condensation, because the numerical calculations can only reflect the experimental observations, if the condensation mechanism is included in the model.     

Computational Modeling of Silicon Nanoparticle Synthesis: II. A Two-Dimensional Bivariate Model for Silicon Nanoparticle Synthesis in a Laser-Driven Reactor Including Finite-Rate Coalescence

In this work, a two-dimensional model was developed for silicon nanoparticle synthesis by silane thermal decomposition in a six-way cross laser-driven aerosol reactor. This two-dimensional model incorporates fluid dynamics, laser heating, gas phase and surface phase chemical reactions, and aerosol dynamics, with particle transport and evolution by convection, diffusion, thermophoresis, nucleation, surface growth, coagulation, and coalescence processes. Because of the complexity of the problem at hand, the simulation was carried out via several sub-models. First, the chemically reacting flow inside the reactor was simulated in three dimensions in full geometric detail, but with no aerosol dynamics and with highly simplified chemistry. Second, the reaction zone was simulated using an axisymmetric two-dimensional CFD model, whose boundary conditions were obtained from the first step. Last, a two-dimensional aerosol dynamics model was used to study the silicon nanoparticle formation using more complete silane decomposition chemistry, together with the temperature and velocities extracted from the reaction zone CFD simulation. A bivariate model was used to describe the evolution of particle size and morphology. The aggregates were modeled by a moment method, assuming a lognormal distribution in particle volume. This was augmented by a single balance equation for primary particles that assumed locally equal number of primary particles per aggregate and fractal dimension. The model predicted the position and size at which the primary particle size is frozen in, and showed that increasing the peak temperature was a more effective means of improving particle yield than increasing silane concentration or flowrate.     

Early Stages of Diamond-Film Formation on Cobalt-Cemented Tungsten Carbide

The surface composition of cemented tungsten carbide (WC-5.8 wt% Co) was studied by X-ray photoelectron spectroscopy (XPS), during the early stages of diamond-film deposition, by hot-filament chemical vapor deposition (HFCVD). The nucleated diamond films were analyzed by scanning electron microscopy (SEM), energy-dispersive spectroscopy (EDS), and automatic image analysis (AIA). The evolution of the surface composition of cemented tungsten carbide during the early stages of diamond-film deposition was strongly dependent on the substrate temperature. At relatively low temperature (750°C), cobalt-rich particles started to segregate at the substrate surface after a few minutes of diamond deposition. The conspicuous segregation of the binder partly inhibited the formation of stable diamond nuclei, through intense carbon dissolution or carbon segregation at the binder surface, but did not affect nucleic growth. At higher temperatures (940°C), no cobalt-rich particles formed at the substrate surface, even after 2 h of deposition. However, XPS results demonstrated the presence of cobalt in a surface layer, although in a lower amount than at 750°C. Nevertheless, the nucleation density of diamond at 940°C was much lower than at 750°C. Gaps between WC grains formed within 10 mins. Therefore, intergranular cobalt was removed at 940°C, a finding attributed to the etching performed by monohydrogen, rather than to binder evaporation. The time evolution of the substrate area fraction covered by diamond islands, S ( t ), was well described by Avrami kinetics for two-dimensional phase transformations, suggesting that diamond formation took place via a heterogeneous nucleation process. The S ( t ) functions exhibited a similar trend at 750° and 940°C, because the higher growth rate of diamond crystallites at higher temperature counteracted the slower nucleation rate at the higher temperature.