Supersaturation Dependence Research Articles

Gradient theory of nucleation in polar fluids

Gradient theory (GT), a form of density functional theory (DFT), was applied to water, methanol, and ethanol using the cubic perturbed hard body (CPHB) equation of state (EOS). Compared to the standard form of classical nucleation theory (CNT), the GT results for water showed an improved temperature dependence, but the supersaturation dependence was slightly poorer. GT and several forms of CNT were also found to be in good agreement with a single high T molecular dynamics rate for TIP4P water. The rates predicted by GT for methanol and ethanol were improved by several orders of magnitude compared to CNT, but no improvement in the predicted temperature dependence of the rates was found.

Deliquescence‐controlled activation of organic aerosols

We examine the cloud condensation nucleation behavior expected for dry submicron particles composed of organic species having limited solubility in water and thus exhibiting deliquescence only under water‐supersaturated conditions. If saturated solution water activities aw are approximately 0.97 < aw < 1, then deliquescence is likely to control the supersaturation required to activate submicron particles, leading to high sensitivity of critical supersaturation to dry diameter. Similar behavior may occur for species, including polymeric compounds, that exhibit limited miscibility in water until very dilute conditions. Treating the sparingly‐soluble or limited‐miscibility species as insoluble aerosol components in calculations of their hygroscopic growth does not reproduce the predicted strong dependence of critical supersaturation on dry particle size. Lack of information on the solubility characteristics of organic‐species‐dominated atmospheric particulate matter may thus lead to discrepancies between predicted and measured droplet activation, even when particle composition and size are well‐constrained by measurements.

Supersaturation and Polarization Dependence of Polymorph Control in the Nonphotochemical Laser-Induced Nucleation (NPLIN) of Aqueous Glycine Solutions

The temperature and concentration dependence of nonphotochemical laser-induced nucleation (NPLIN) was studied in aqueous glycine solutions at wavelengths of 532 and 1064 nm, using linearly, circularly, and elliptically polarized light. We observed a narrow supersaturation window (c/c0 = 1.45−1.55, where c is the solution molality, and c0 is the molality of a saturated solution) for “polarization switching”, i.e., different polarizations producing different polymorphs. We also observed that, within this window, a small range of ellipticities near unity could induce the nucleation of the α-polymorph and that this range depended on supersaturation. Similar “polarization switching” behavior was observed at wavelengths of 1064 and 532 nm, although the supersaturation window became narrower at lower laser intensities at both wavelengths. Order-parameter ellipsoids and triangles based on optical Kerr alignment are presented to aid in the interpretation of the experimental results.

Evaluation of surface tension and Tolman length as a function of droplet radius from experimental nucleation rate and supersaturation ratio: Metal vapor homogeneous nucleation

Zinc and silver vapor homogeneous nucleations are studied experimentally at the temperature from 600 to 725 and 870 K, respectively, in a laminar flow diffusion chamber with Ar as a carrier gas at atmospheric pressure. The size, shape, and concentration of aerosol particles outcoming the diffusion chamber are analyzed by a transmission electron microscope and an automatic diffusion battery. The wall deposit is studied by a scanning electron microscope (SEM). Using SEM data the nucleation rate for both Zn and Ag is estimated as 10(10) cm(-3) s(-1). The dependence of critical supersaturation on temperature for Zn and Ag measured in this paper as well as Li, Na, Cs, Ag, Mg, and Hg measured elsewhere is analyzed. To this aim the classical nucleation theory is extended by the dependence of surface tension on the nucleus radius. The preexponent in the formula for the vapor nucleation rate is derived using the formula for the work of formation of noncritical embryo [obtained by Nishioka and Kusaka [J. Chem. Phys. 96, 5370 (1992)] and later by Debenedetti and Reiss [J. Chem. Phys. 108, 5498 (1998)]] and Reiss replacement factor. Using this preexponent and the Gibbs formula for the work of formation of critical nucleus the dependence of surface tension on the radius R(S) of the surface of tension is evaluated from the nucleation data for above-mentioned metals. For the alkali metals and Ag the surface tension was determined to be a strong function of R(S). For the bivalent metals (Zn, Hg, and Mg) the surface tension was independent of radius in the experimental range. A new formula for the Tolman length delta as a function of surface tension and radius R(S) is derived by integration of Gibbs-Tolman-Koenig equation assuming that delta is a monotonic function of radius. The formula derived is more correct than the Tolman formula and convenient for the elaboration of experimental data. Using this formula the values of delta are determined as a function of R(S) from the experimental nucleation data. It is determined that all the metals considered are characterized by strong dependence of delta on radius; for the bivalent metals delta changes sign.

Infrared spectroscopic study of polytypic effects on the crystal-growth mechanism of n-hexatriacontane (n-C36H74)

The solution-crystallization mechanism was investigated for two polytypes in the M011 modification of n-hexatriacontane (n-C36H74), single-layered structure Mon, and double-layered one Orth II. The crystal growth under controlled supersaturation was followed with a micro- Fourier-transform-infrared spectrometer equipped with an optical system for oblique transmission measurements. Supersaturation dependence of growth behavior was significantly different between Mon and Orth II. Although the Mon crystal continued growing at a supersaturation of 0.27, the overgrowth of Orth II on the (001) face of the Mon crystal was confirmed at supersaturations below 0.21. Such a polytypic transformation was not observed for the Orth II crystal at any supersaturation below 0.30. The growth rate of Mon showed a quadratic dependence on supersaturation, while that of Orth II was approximately linear, suggesting spiral growth and two-dimensional-nucleation mechanisms for Mon and Orth II, respectively.

Homogeneous nucleation of water between 200 and 240 K: New wave tube data and estimation of the Tolman length

We have measured homogeneous nucleation rates of water at 200-240 K in the carrier gas helium, in the range of 10(13) - 10(17) m(-3) s(-1) using an expansion wave tube. The rates agree well with the results of Wolk and Strey [J. Phys. Chem. B 105, 11683 (2001)] in the range of overlap (220-240 K), and are summarized by the empirical fit J = S exp[4.6 + 0.244T-(906.8 - 2.914T)(ln S)(2)], with J the nucleation rate in m(-3) s(-1), S the supersaturation, and T the temperature in K. We find that the supersaturation dependence of both our rates and those of Wolk and Strey is lower than classical theory predicts, and that the critical cluster is smaller than the classical critical size. These deviations are explained in the framework of the Tolman theory for surface tension, and the "Tolman length" is estimated from our experimental results. We find a positive Tolman length that increases with decreasing temperature, from about 0.1 Angstrom at 260 K to (0.6 +/- 0.4) Angstroms at 200 K. We present a nucleation rate expression that takes the Tolman length into account and show that both the supersaturation and temperature dependence are improved, compared to the classical theory.

Kinetics of two-step nucleation of crystals

When the nucleation of a stable crystalline phase directly in a supersaturated old phase is greatly retarded, the crystal nuclei might nucleate within faster-forming particles of an intermediate phase. Here we present a theoretical investigation of the kinetics of this two-step nucleation of crystals and derive general expressions for the time dependence of the number of crystals nucleated within the particles of the intermediate phase. The results reveal that crystal nucleation can be strongly delayed by the slow growth of the particles and/or by the slow nucleation of the crystals in them. Furthermore, the linear part of the time dependence of the number of nucleated crystals is determined by the formation rate of the intermediate particles. This is in contrast with the one-step nucleation of crystals when this linear part is determined by the rate of crystal nucleation directly in the old phase. Criteria are proposed for distinction between the one- and two-step nucleation mechanisms, based on the supersaturation dependence of the delay time for nucleation. The application of the theoretical approach to the analysis of experimental data on the nucleation of crystals and other ordered aggregates of protein and other soluble materials is discussed.

Effect of kink contamination on habit of two-dimensional crystal during growth with edge diffusion

The theoretical description of growth morphology diagram (morphodrome) of a two-dimensional crystal growing with impurities that shows possibility of habit change is presented. By taking into account the diffusion of adatoms along the edge of a step and contamination of kink sites with impurity atoms, we analyze the structures and growth rates of steps bounding a two-dimensional island on a (0 0 1) surface of a Kossel crystal. The first and second nearest-neighbor interactions as well as heights of activation barriers for different elementary processes on the crystal structure are taken into consideration. The change in growth habit from the square-like shape to the diamond-like one is predicted as an effect of strong interplay between edge diffusion and kink contamination. In the absence of edge diffusion, addition of impurities into kinks does not cause habit change. When the edge diffusion dominates the kinetics, the habit change is caused by edge diffusion, while kink contamination lowers the threshold supersaturation, at which habit change occurs. In case of moderate edge diffusion that is not strong enough to result in habit change, contamination of kinks with impurity atoms can cause habit change. The constructed morphodrome shows the dependence of the habit change threshold supersaturation on the concentration of impurities that is qualitatively similar to the experimental data.

Infrared spectroscopic study on polytypic transformation of growing single crystal of n-hexatriacontane ( n-C 36H 74)

There are two polytypic structures, single-layered structure Mon and double-layered structure Orth II for the M 011 modification of n-hexatriacontane ( n-C 36H 74). The solution crystal growth of the two polytypes under controlled supersaturation was investigated by the oblique IR transmission method. As to the supersaturation dependence of growth behavior, there was a significant difference between the two polytypes. While the overgrowth of Orth II took place on the (0 0 1) face of the Mon crystal at moderate supersaturations, the overgrowth of Mon on the Orth II crystals was not confirmed at any supersaturations below 0.30. The growth rate of Mon showed about a second-order dependence on supersaturation, whereas that of Orth II showed a first-order dependence. The growth mechanism of the M 011 modification and the cause for the one-way overgrowth were deduced on the basis of the thermodynamical stabilities and the supersaturation dependence of the growth rates.

Nucleus size and Zeldovich factor in two-dimensional nucleation at the Kossel crystal (0 0 1) surface

A Monte Carlo simulation method to determine the growth probability of two-dimensional clusters on the Kossel (0 0 1) surface is described. From this growth probability the nucleus size and the Zeldovich factor for two-dimensional nucleation were obtained. For low supersaturations the Gibbs–Thomson equation describes the supersaturation dependency of the nucleus size very well. At higher supersaturations a deviation from the predicted nucleus sizes is observed. This is mainly due to the size dependence of the apparent specific step free energy and/or the shape factor of the nucleus. A small systematic deviation between the theoretical and actual growth probability is observed and explained.

Sensitivity of Morphology Prediction to the Force Field: Paracetamol as an Example

The growth morphology of paracetamol is known to show a strong supersaturation dependence. Most morphology prediction methods, like the attachment energy method, cannot include this dependence in their prediction. Monte Carlo simulations are able to use the supersaturation as an input parameter and can also include the growth mechanism. This makes the Monte Carlo technique a powerful tool to study the growth of organic crystals. Some studies in the literature show that the attachment energy method is only weakly influenced by the force field used to calculate the attachment energies. The present paper presents the sensitivity of the Monte Carlo simulation results to the force field and charge set using paracetamol as a case study. The force field and atomic point charges are found to influence the results to a large extent. This is due to subtle differences in step energies that determine the growth rates of the crystal faces.

Supersaturation and temperature dependency of gibbsite growth in laminar and turbulent flows

The temperature and supersaturation dependencies of gibbsite crystal growth rates in caustic aluminate solutions were experimentally investigated in both the laminar (Taylor–Couette precipitator) and turbulent (stirred tank) mixing regimes. The gibbsite precipitation experiments were conducted batchwise in a temperature range from 55°C to 90°C, but all with the same initial liquor composition and seed type. At low supersaturation it was found that gibbsite crystal growth could be described satisfactorily by a screw dislocation growth mechanism over the complete temperature range, irrespective of the flow regime. At higher supersaturation and lower temperatures, i.e. 55°C and 60°C, it is proposed that two-dimensional polynuclear growth is the dominant growth mechanism in turbulent flows. Any differences observed in the measured growth rate estimates from the laminar and turbulent systems were explained by error analysis.

In situ study of the kinetics of displacement of growth steps on {010} faces of potassium acid phthalate single crystals grown from aqueous solutions

AbstractExperimental results of an in situ study of displacement rates of growth steps, observed by optical microscopy, of different height on the {010} faces of potassium acid phthalate single crystals from aqueous solutions of predefined supersaturations up to 8.5% at about 30 °C are reported and discussed. It was found that: (1) there is a large spread in the displacement rate of steps even for the same supersaturation but the spread decreases with increasing value of supersaturation, (2) in some cases the step displacement rate decreases while in others it increases with increasing growth duration, (3) the average displacement rate of low‐height steps increases linearly with an increase in supersaturation, and (4) the velocity of steps decreases with an increase in their height. Analysis of the results showed that (1) the linear supersaturation dependence of step velocity occurs in the case of a supersaturation independent activation energy for growth, and (2) the supersaturation dependence of relative decrease in the velocity of steps with their height may be explained by three approaches: (i) net flux of growth units from the surface terrace to the advancing step, (ii) time dependent adsorption of solute molecules to the advancing step, and (iii) anisotropy in solute transport by surface diffusion to a step from the two terraces on its either sides (Schwoebel effect). In approaches (i) and (ii) the decrease in the step velocity is associated with the nucleation of kinks on step edges.

Review: Nucleation in solutions revisited

AbstractExisting and new results in nucleation in solutions are outlined from a unified point of view. The thermodynamics of the process is considered and expressions are given for the supersaturation, the nucleation work and the size of the nucleus in homogeneous or heterogeneous nucleation. It is shown how the nucleation theorem can be used for a model‐independent determination of the nucleus size from experimental data. The mechanism and kinetics of nucleation are also considered and formulae are presented for the supersaturation dependence of the monomer attachment frequency and the stationary rate of homogeneous or heterogeneous nucleation. General expressions for the induction time and the critical supersaturation ratio for crystallization are given. An approximate formula is derived for estimating the width of the metastable zone with the help of data for the solubility of the substance crystallized. Existing experimental data are used for verification of the validity of some of the presented theoretical dependences.

Effects of high pressure on the growth kinetics of orthorhombic lysozyme crystals

Growth processes of the (0 1 1) and (0 1 ̄ 1) faces of an orthorhombic lysozyme crystal were observed in situ under 0.1 and 100 MPa. The growth rates of the (0 1 1) and (0 1 ̄ 1) faces were equal within an experimental error. From the comparison between the growth rates under 0.1 and 100 MPa at the same supersaturation level, we found that the growth kinetics of the orthorhombic lysozyme crystals significantly decreases with an increase in pressure. Supersaturation dependencies of the growth rates under 0.1 and 100 MPa were well fitted with a two-dimensional (2D) nucleation growth model of a birth-and-spread type. The fitting results show that the decrease in the growth kinetics with pressure can be explained by the increase activation energies in the incorporation processes of solute molecules.

On the kinetics of xanthine adsorption at the mercury ∣ electrolyte interface

The short-term and long-term capacity–time dependence of xanthine in 0.2 M NaCl at 35 °C inside the potential region of the capacity pit was measured at the mercury ∣ electrolyte interface. The short-term capacity–time dependence can be described well theoretically by 2D instantaneous nucleation with a constant growth rate and, for potentials near the more negative pit edge, with 2D nucleation according to an exponential law with a constant growth rate. The long-term capacity–time dependence corresponding to secondary adsorption can be modelled well by 1D instantaneous nucleation with a diffusion controlled growth rate. This mechanism refers to the formation of linear surface molecular stacks. The potential dependence of the overall nucleation and growth rate constant for the short-term and long-term capacity–time dependences will be discussed on the basis of the potential dependence of the interfacial supersaturation.

Induction time in crystallization of gas hydrates

The kinetics of the initial stage of crystallization of one-component gas hydrates in aqueous solutions are analyzed. The temporal evolution of the volume of hydrate crystallized and the moles of gas consumed are determined. Expressions are derived for the supersaturation dependence of the hydrate crystallite growth rate and the induction time in hydrate crystallization. These expressions are used for revealing how additives in the solution that act as kinetic inhibitors of hydrate crystallization can affect the induction time of the process. The results obtained are applied to crystallization of methane, ethane and cyclopropane hydrates.

Condensation of Supersaturated Water Vapor on Charged/Neutral Nanoparticles of Glucose and Monosodium Glutamate

The effects of size, charge, dissolution, and dissociation on the condensation of supersaturated water vapor on monodisperse nanoparticles of glucose and monosodium glutamate (MSG) were investigated in a flow cloud chamber (FCC). The dependence of the critical supersaturation, S cr, on particle size in the range of 30 to 90 nm and on temperature in the range of 10 to 50°C were determined experimentally. The results show that the experimental S cr decreases with increasing particle size at a rate in reasonable agreement with the predictions of the Kohler and Volmer theories of nucleation for soluble particles, but decreases with increasing temperature at a rate higher than the prediction of the Volmer theory. The dissociation of MSG into ions lowers the experimental S cr to a value smaller than that for the more soluble glucose, agreeing with predictions. The experimental S cr is smaller than the predictions of both theories, and the discrepancy cannot be fully explained by the reductions in surface tension due to the dissolution of particles and curvature dependence. The condensation of supersaturated vapor on singly positively charged particles with diameters of 30, 60, and 90 nm was also examined, and no obvious charge effect on S cr was observed.

Explanation for the Supersaturation-Dependent Morphology of Monoclinic Paracetamol

The growth morphology of monoclinic paracetamol as a function of the supersaturation is determined using Monte Carlo simulations based on the crystal structure. The results are compared with experimental results reported recently on both the morphology and the relevant growth mechanisms. The change of an elongated to a more bulky habit with increasing supersaturation is reproduced well by the simulations. The method used opens ways to predict the crystal morphology for real crystal structures in dependence of supersaturation once information on the relevant growth mechanism for the various faces is known.

On the nature of supersaturation barriers observed during the growth of crystals from aqueous solutions containing impurities

The nature of supersaturation barriers observed during the growth of single crystals from aqueous solutions containing impurities is investigated using theoretical and empirical expressions relating the face growth rate and step velocity with supersaturation. For the analysis, the experimental data of the supersaturation dependence of growth rate of the (1 0 0) face of ammonium oxalate monohydrate (AO) crystals and step velocity of the (1 0 0) face of potassium dihydrogen phosphate (KDP) crystals growing from aqueous solutions containing trivalent metal chloride impurities at a constant temperature and predefined supersaturations were used. It was found that: (1) at relatively low supersaturations the model involving a complex source of cooperating screw dislocations and the power-law approach predict the same values of supersaturation barrier while an empirical parabolic relation predicts somewhat lower values of supersaturation barrier than the other models, (2) the origin of two supersaturation barriers for the step velocity during the growth of KDP crystals is associated with instantaneous and time-dependent adsorption of the impurity on the growing surface, (3) the dependence of supersaturation barriers on impurity concentration follows Freundlich and Langmuir adsorption isotherms during the growth of AO and KDP crystals, respectively, and (4) Kubota–Mullin's mechanism of adsorption of impurities at kinks in the ledges holds in the case of growth of AO and KDP crystals in the presence of trivalent cations.