Constant Supersaturation Research Articles

Tailoring Crystallization Kinetics in Thin Sucrose Films during Convective Drying: Impact of Temperature and Humidity on Onset, Growth, and Nucleation Rate.

Drying experiments with varying air temperature and humidity were conducted to investigate the influence of the drying process on the crystallization of thin sucrose films. For the first time, the effects of the nucleation onset, nucleation rate, and growth rate were investigated in situ and their differentiated influence on product crystallinity could be assessed. The growth rate was not influenced by air humidity but showed a strong dependence on temperature. It increased with drying temperature; however, at high temperatures, growth was inhibited when the water content falls below a critical level. Noticeable differences in nucleation behavior could be observed with regard to air humidity. Dry air led to crystallization onsets at lower levels of supersaturation, while moderately humid air retarded it. At higher temperatures, nucleation onset commenced at lower water contents but at a constant supersaturation level. The nucleation rate doubled in experiments with moderately humid air (15% RH), while an elevated drying temperature showed generally lower nucleation rates. The observed differences in the nucleation onset and rate could be explained by the film-internal concentration profile, which is strongly influenced by drying parameters. The insights therefore provide a differentiated understanding of the formation of the physical state and how it can be influenced during convective drying.

Novel strategy for improved sylvite flotation through controlled crystallization

By understanding minerals as crystals, a crystallization-controlled methodology was performed to enhance the floatability of soluble minerals. Here, aimed strategies were applied to modulate the crystallization of KCl salt to grow crystals with various shapes as cubic-, hopper- and needle-like structure. Stereoscope and scanning electronic microscopy (SEM) helped to unveil the morphologies where X ray diffraction (XRD) characterized their high crystallinities. Afterwards, Atomic Force Microscope (AFM) was performed to research the crystallizing behaviors that cubic-like structure was obtained by turbid fast growth, while hopper-like structure formation was due to the constant high supersaturation and needle-like crystal occurred under still fast crystallization. Flotation tests with octadecylamine hydrochloride (ODA) as collector demonstrated the floatability of samples obeyed the order as needle-like (96.19 %) > hopper-like (81.59 %) > cubic-like (80.08 %) KCl samples. The mechanism was studied by surface area and related interaction tests. BET result demonstrated the highest surface area of needle-like structure than that of hopper-like and cubic-like structure. Besides, induction time combined with adhesion & desorption force tests further explained the better interaction of needle-like sample with bubble than cubic-like sample. While the special structure of hopper-like structure with lower weight but inner filled solution resulted in its near equivalent floatability with cubic-like sample. In conclusion, a new strategy for promoting flotation behavior by designing the crystallization of soluble KCl was proposed, shedding some light on further application on other soluble or semi-soluble minerals.

Explicit Habit‐Prediction in the Lagrangian Super‐Particle Ice Microphysics Model McSnow

AbstractThe Monte‐Carlo ice microphysics model McSnow is extended by an explicit habit prediction scheme, combined with the hydrodynamic theory of Böhm. Böhm's original cylindrical shape assumption for prolates is compared against recent lab results, showing that interpolation between cylinder and prolate yields the best agreement. For constant temperature and supersaturation, the predicted mass, size, and density of the ice crystals agree well with the laboratory results, and a comparison with real clouds using the polarizability ratio shows regimes capable of improvement. An updated form of the inherent growth function to describe the primary habit growth tendencies is proposed and combined with a habit‐dependent ventilation coefficient. The modifications contrast the results from general mass size relations and significantly impact the main ice microphysical processes. Depending on the thermodynamic regime, ice habits significantly alter depositional growth and affect aggregation and riming. The influence of primary ice behavior on precipitation formation needs to be considered in future development of microphysical parameterizations, but the consideration of secondary habits and the geometry of aggregates should be further improved in future work.

Two-step nucleation and crystal growth in a metastable solution

This study is concerned with a theory of two-step nucleation and growth of crystals in a metastable liquid. This mechanism is that crystalline nuclei formation occurs in dense liquid clusters suspended in the solution. These clusters contain higher solution concentration and viscosity, leading to a lower surface free energy barrier and faster phase transition route. The theory is based on growth laws of crystals during the two-step bulk phase transformation. At the initial stage, the crystals evolve in a diffusion-limited environment with almost unchanged supersaturation. At the second stage, they become larger, move beyond these clusters, and evolve in accordance with a hyperbolic tangent law. A generalized particle growth law joining the first and second stages is obtained by stitching the diffusion limited and hyperbolic tangent laws. On this basis, an integrodifferential model of the evolution of a polydisperse ensemble of crystals was formulated and solved. The crystal-size distribution function increases and the solution supersaturation remains practically unchanged until the particle size corresponds to a transition in the particle growth rate from a diffusion-limited branch to a hyperbolic tangent branch. This is followed by an increase in the crystal growth rate, a decrease in the distribution function and solution supersaturation. Then the distribution function increases up to the maximum size of crystals grown in the solution. A sufficiently long time interval of almost constant supersaturation and the N-shaped behavior of the distribution function are the consequences of a two-step nucleation and growth mechanisms.

Inhibition of calcium carbonate scale under severe conditions

Despite extensive works have been devoted to study the scale inhibition behavior, the performance of inhibitors is still not fully understood. In this paper, we present a laboratory study to elucidate the impact of water composition on the performance of some commonly used phosphonate and polymeric calcium carbonate scale inhibitors, in highly supersaturated brines at high temperature. Calcium tolerance inhibitor chemicals with various molecular structures are studied using dynamic scale loop test method at 150 °C. Brine composition is varied by changing the non-stoichiometry of scaling lattice ions, e.g., ( Ca 2 + ) / ( CO 3 2 − ) ratio, over a wide range. Test results indicate that the effectiveness of inhibitors can be significantly changed by the scaling ion ratio. In general, the efficacy of inhibitors decreases significantly with calcium concentration in the test brine even at constant supersaturation state and temperature, and also the performance ranking of the different inhibitor chemistries can be changed with brine composition. This could be caused by the alternations of interactions between inhibitor molecules and the surface of calcium carbonate scale crystals. Findings from this study suggest that the effect of scaling ion ratio must be considered in scaling risk assessment and for the optimization of inhibitor treatment programs.

Ligancy effects on nucleation kinetics.

Nucleation of particles into crystalline structures can be observed in a wide range of systems from metallic and metal-organic compounds to colloidal and polymeric patch particles. Here, we perform kinetic Monte Carlo simulations to study the nucleation kinetics of particles with different ligancies z at constant supersaturation s. This approach allows one to determine several physico-chemical quantities as a function of s, including the growth probability P(n), the critical nucleus size n*, and the stationary nucleation rate Js. Our numerical results are rationalized in terms of a self-consistent nucleation theory where both n* and Js present a non-trivial dependence on s, but which can be determined from the values of effective z-dependent parameters.

Biological Mineralization of Hydrophilic Intraocular Lenses

Biomaterials calcify upon implantation in contact with biological fluids, which are supersaturated with respect to more than one crystalline phase of calcium phosphate. The implantation of intraocular lenses (IOLs) for cataract treatment has been hailed as a major advance. Hydrophilic acrylic IOLs, made of Poly(2-hydroxyethyl methacrylate) (PHEMA), upon contact with aqueous humor, exhibit significant incidence of opacification, due to the formation of calcium phosphate crystals, mainly hydroxyapatite (Ca5(PO4)3OH, HAP) on the surface or in their interior. The aqueous humor is supersaturated with respect to HAP. Clinical findings were duplicated by laboratory experiments through the development of appropriate experimental models which included batch reactors, well stirred operating at constant supersaturation (CCR) and reactors simulating anterior eye chamber (ECSR). In both CCR and ECSR, simulated aqueous humor was used. In ECSR the flow rate was the same as in the eye chamber (2.5 mL per 24 h). HAP formed both on the surface and inside the IOLs tested. Induction times preceding the crystallization of HAP on the surface of the IOLs and crystal growth rates were measured. Surface hydroxyl ionized groups favored the development of locally high supersaturation by surface complexation. In the interior of the IOLs, HAP formed by the diffusion of the calcium and phosphate ions inside the polymeric matrix.

Two-step crystal nucleation kinetics: Solution of the master equation

The master equation of two-step nucleation is numerically solved with parameters characterizing isothermal homogeneous nucleation of ice crystals and water droplets in steam below the water freezing temperature. The time dependences of the crystal and droplet size distributions and nucleation rates as well as of the nucleation rate of ice crystals in the droplets are determined at different constant supersaturations. The stationary values of these nucleation rates are obtained in a wide supersaturation range. It is found that when the crystallization of the water droplets is slower than their growth, the stationary rate of two-step crystal nucleation is orders of magnitude lower than the corresponding stationary rate of one-step crystal nucleation. As to the stationary nucleation rate of the water droplets, it is practically unaffected by the ice crystals nucleating and growing in both the droplets and the steam. Finally, the delay times of the different nucleation processes are determined and it is found that at both low and high supersaturations the delay time of the two-step crystal nucleation is negative because of the presence of high initial peak in the nonstationary rate of this process. The results obtained provide unprecedented mechanistic insight into the kinetics of two-step crystal nucleation.

Influence of Monovalent Salts on α-Glycine Crystal Growth from Aqueous Solution: Molecular Dynamics Simulations at Constant Supersaturation Conditions.

The growth of α-glycine crystals from aqueous solution is investigated at constant supersaturations by utilizing the constant chemical potential molecular dynamics method. The study considers two faces (010) and (011) that predominantly determine the α-glycine crystal morphology. The general Amber force field (GAFF) with two different charge sets derived from semi-empirical calculations using the complete neglect of differential overlap method (CNDO) and from density functional calculations using the double-numerical plus d- and p-polarization basis set (DNP) is applied to describe α-glycine. The extended simple point charge model is used to simulate water. It is observed that the GAFF/DNP set leads to a much slower integration of glycine molecules into the crystal structure than the GAFF/CNDO set. The GAFF/CNDO set, however, causes the growth even at concentrations well below the experimental solubility. For the GAFF/DNP set, the influence of potassium chloride (KCl) and sodium chloride (NaCl) on the face growth rates is investigated. The parameters recently proposed by Yagasaki et al. [J. Chem. Theory Comput. 2020, 16, 2460-2473] are used to describe salt ions, as standard GAFF parameters lead to the unexpected formation of salt clusters at a concentration lower than the experimental solubility value. According to our simulation results, both salts suppress the growth of the (011) and (010) faces. The inhibiting effect of NaCl is much stronger than that of KCl for the (011) face, while both salts have a similar inhibiting effect on the (010) face. The results are in line with the experimental observations of the impact of salt ions on the α-glycine growth rates for the (011) face reported in literature.

Importance of Supersaturation in Arctic Black Carbon Simulations

AbstractBlack carbon (BC) aerosol particles in the Arctic heat the atmosphere and snow/ice surfaces and may strengthen the snow-albedo feedback that amplifies Arctic warming. Model simulations of BC concentrations in the Arctic depend strongly on the representation of microphysical processes such as aging, activation, and wet removal. Most BC modeling studies have classified BC particles into hydrophobic BC, which cannot form cloud droplets, and hydrophilic BC, which can form cloud droplets, by assuming a globally constant critical supersaturation threshold value (Sthre), without considering its consistency with cloud maximum supersaturation (Smax). Here we show that it is essential to consider the consistency of Sthre with Smax in global model simulations to reduce uncertainties in near-surface ambient BC concentrations in the Arctic. Previous studies often obtained good agreement between simulated and observed near-surface Arctic BC mass concentrations when a low Sthre (~0.1%) was assumed in their models. However, this Sthre may be too low (activation and wet removal of BC may be underestimated) for the Arctic, because some recent observations and our model simulations suggest that Smax may actually be higher (~0.3%) there. We also demonstrate that spatially varying Sthre values and their consistency with Smax, which previous studies did not consider, must be represented in models for more accurate estimation of BC budget in the Arctic. Because both Smax and BC-aging speed depend on climatic conditions, our findings are an important step toward better simulations of BC impacts on past, present, and future Arctic climates.

Evaluation of the contribution of new particle formation to cloud droplet number concentration in the urban atmosphere

Abstract. The effect of new particle formation (NPF) on cloud condensation nuclei (CCN) varies widely in diverse environments. CCN or cloud droplets from NPF sources remain highly uncertain in the urban atmosphere; they are greatly affected by the high background aerosols and frequent local emissions. In this study, we quantified the effect of NPF on cloud droplet number concentration (CDNC, or Nd) at typical updraft velocities (V) in clouds based on field observations on 25 May–18 June 2017 in urban Beijing. We show that NPF increases the Nd by 32 %–40 % at V=0.3–3 m s−1 during the studied period. The Nd is reduced by 11.8 ± 5.0 % at V=3 m s−1 and 19.0 ± 4.5 % at V=0.3 m s−1 compared to that calculated from constant supersaturations due to the water vapor competition effect, which suppresses the cloud droplet formation by decreasing the environmental maximum supersaturation (Smax). The effect of water vapor competition becomes smaller at larger V that can provide more sufficient water vapor. However, under extremely high aerosol particle number concentrations, the effect of water vapor competition becomes more pronounced. As a result, although a larger increase of CCN-sized particles by NPF events is derived on clean NPF days when the number concentration of preexisting background aerosol particles is very low, no large discrepancy is presented in the enhancement of Nd by NPF between clean and polluted NPF days. We finally reveal a considerable impact of the primary sources on the evaluation of the contribution of NPF to CCN number concentration (NCCN) and Nd based on a case study. Our study highlights the importance of full consideration of both the environmental meteorological conditions and multiple sources (i.e., secondary and primary) to evaluate the effect of NPF on clouds and the associated climate effects in polluted regions.

Insights into the selection mechanism of Widmanstätten growth by phase-field calculations

We investigate the growth of Widmanstätten structures in metallic alloys with phase field calculations. We show that elastic energy anisotropy associated with shear dominated transformations is alone sufficient to give rise to plate or needle like precipitates with constant lengthening rates at constant supersaturations. We show that Ivantsov analytical solutions still provide good estimates of the diffusion flux around tips even when elasticity is accounted for. A careful analysis demonstrates that, for shear dominated transformations, (i) the lengthening direction lies in the habit plane determined by one of the minima of the elastic kernel; (ii) the tip shape and size are equilibrium features, driven by elastic forces, rather than dynamically determined as usually assumed; (iii) the tip size of acicular precipitates can be rationalized by the value of the elastic kernel in the lengthening direction.

Heterogeneous Nucleation of Butanol on NaCl: A Computational Study of Temperature, Humidity, Seed Charge, and Seed Size Effects.

Using a combination of quantum chemistry and cluster size distribution dynamics, we study the heterogeneous nucleation of n-butanol and water onto sodium chloride (NaCl)10 seeds at different butanol saturation ratios and relative humidities. We also investigate how the heterogeneous nucleation of butanol is affected by the seed size through comparing (NaCl)5, (NaCl)10, and (NaCl)25 seeds and by seed electrical charge through comparing (Na10Cl9)+, (NaCl)10, and (Na9Cl10)− seeds. Butanol is a common working fluid for condensation particle counters used in atmospheric aerosol studies, and NaCl seeds are frequently used for calibration purposes and as model systems, for example, sea spray aerosol. In general, our simulations reproduce the experimentally observed trends for the NaCl–BuOH–H2O system, such as the increase of nucleation rate with relative humidity and with temperature (at constant supersaturation of butanol). Our results also provide molecular-level insights into the vapor–seed interactions driving the first steps of the heterogeneous nucleation process. The main purpose of this work is to show that theoretical studies can provide molecular understanding of initial steps of heterogeneous nucleation and that it is possible to find cost-effective yet accurate-enough combinations of methods for configurational sampling and energy evaluation to successfully model heterogeneous nucleation of multicomponent systems. In the future, we anticipate that such simulations can also be extended to chemically more complex seeds.

On the complete similitude of technical precipitation. Part I: Impinging mixers

The particle size distribution (PSD) of precipitated products, for example, pharmaceutical or catalyst materials, is often affected by the intensity of mixing the educts. Until now, scientists have always seen the Reynolds number, Re, as the most significant Π group for technical precipitation. Consequently, previous authors have commonly presented the PSD or its descriptive statistical parameters as a function of only Re. However, it has not yet been understood why products from reactors with the same value of Re do not show the same PSD. We take a new look at this issue within this work by conducting a comprehensive dimensional analysis of sparingly soluble salt precipitation. It is shown that Re is not the only relevant Π group for reaching complete similitude. The solids formation Damköhler number, Dasf, is revealed to be of equal importance. We find that the relationship between PSD and Re can only be investigated correctly if Dasf is kept constant by adjusting the supersaturation for each process point. Therefore, previous studies presumably misinterpreted the impact of Re on precipitation since constant supersaturation levels were applied here. We successfully validate our hypotheses by barium sulfate precipitation experiments in confined impinging jet mixers (CIJMs). Since our study solves how Re impacts the PSD, we anticipate that it will be the starting point for future applications of complete similitude to scale-up technical precipitation reactors.

How to Manage a Crystallization Process Aimed at Obtaining a Desired Combination of Number of Crystals and Their Distribution by Size: Learn Here

AbstractManaging a crystallization process adequately, it is possible to obtain a crystalline product having the desired crystal size distribution. Recommendations for selecting crystallization parameters that are needed to achieve this goal are given basing of a theoretical analysis in which special attention is paid to the growth of crystals from solutions with a preset concentration. Mathematical equations which enable calculation of the theoretical yield for the crystallization process have been elaborated. New formula giving the crystal nuclei number per unit volume as a function of both supersaturation and nucleation time has been devised based on the logistic kinetics of crystal nucleation proceeding under constant supersaturation. The quantitative relation between number density and mean size of crystals growing in batch crystallization is calculated. The calculation shows that the mean size of crystals reached at any time of their growth is inversely proportional to root third of the crystal number density.

Kinetic broadening of size distribution in terms of natural versus invariant variables.

We study theoretically the size distributions of nanoparticles (islands, droplets, nanowires) whose time evolution obeys the kinetic rate equations with size-dependent condensation and evaporation rates. Different effects are studied which contribute to the size distribution broadening, including kinetic fluctuations, evaporation, nucleation delay, and size-dependent growth rates. Under rather general assumptions, an analytic form of the size distribution is obtained in terms of the natural variable s which equals the number of monomers in the nanoparticle. Green's function of the continuum rate equation is shown to be Gaussian, with the size-dependent variance. We consider particular examples of the size distributions in either linear growth systems (at a constant supersaturation) or classical nucleation theory with pumping (at a time-dependent supersaturation) and compare the spectrum broadening in terms of s versus the invariant variable ρ for which the regular growth rate is size independent. For the growth rate scaling with s as s^{α} (with the growth index α between 0 and 1), the size distribution broadens for larger α in terms of s, while it narrows with α if presented in terms of ρ. We establish the conditions for obtaining a time-invariant size distribution over a given variable for different growth laws. This result applies for a wide range of systems and shows how the growth method can be optimized to narrow the size distribution over a required variable, for example, the volume, surface area, radius or length of a nanoparticle. An analysis of some concrete growth systems is presented from the viewpoint of the obtained results.

In vitro calcification studies on bioprosthetic and decellularized heart valves under quasi-physiological flow conditions

The lifespan of biological heart valve prostheses available in the market is limited due to structural alterations caused by calcium phosphate deposits formed from blood plasma in contact with the tissues. The objective of this work is to present a comparative methodology for the investigation of the formation of calcium phosphate deposits on bioprosthetic and tissue-engineered scaffolds in vitro and the influence of mechanical forces on tissue mineralization. Based on earlier investigations on biological mineralization at constant supersaturation, a circulatory loop simulating dynamic blood flow and physiological pressure conditions was developed. The system was appropriately adapted to evaluate the calcification potential of decellularized (DCV) and glutaraldehyde-fixed (GAV) porcine aortic valves. Results indicated that DCV calcified at higher, statistically nonsignificant, rates in comparison with GAV. This difference was attributed to the tissue surface modifications and cell debris leftovers from the decellularization process. Morphological analysis of the solids deposited after 20 h by scanning electron microscopy in combination with chemical microanalysis electron-dispersive spectroscopy identified the solid formed as octacalcium phosphate (Ca8(PO4)6H2·5H2O, OCP). OCP crystallites were preferentially deposited in high mechanical stress areas of the test tissues. Moreover, GAV tissues developed a significant transvalvular pressure gradient increase past 36 h with a calcium deposition distribution similar to the one found in explanted prostheses. In conclusion, the presented in vitro circulatory model serves as a valuable prescreening methodology for the investigation of the calcification process of bioprosthetic and tissue-engineered valves under physiological mechanical load.

Kinetic factors may reshape the dependence of crystal nucleation rate on temperature in protein bulk solution.

Here we provide an analysis of primary results obtained from a study of apoferritin crystal nucleation in compositionally invariant bulk solution at constant supersaturation ratio of the protein. The temperature dependence of the stationary crystal nucleation rate in the protein bulk solution is obtained with the help of experimentally determined probability for detection of at least one crystal per solution volume until a given time. The stationary crystal nucleation rate demonstrates unusual behavior with temperature. We emphasize that this is caused by kinetic factors that are often disregarded in the frame of the classical nucleation theory but can certainly affect the nucleation kinetics.

Model for the Nucleation and Diffusion-Controlled Growth of Binary Alloy Nuclei under Potentiostatic Conditions

An approach is proposed to perform a mathematical description of the electrochemical formation and growth of binary alloy nuclei on the surface of an indifferent electrode under constant supersaturation (overpotential). This approach considers the total flux of two species of deposited ions in the electrolyte bulk to the surface of hemispherical new-phase nuclei. The concentration profile is averaged with allowance for the mole fraction ratio of the components. The cases of instantaneous and progressive nucleation with diffusion-controlled growth are studied. The overlap of the diffusion zones of the nuclei is analyzed in terms of the Scharifker–Hills model. Equations are derived to calculate the apparent diffusion coefficient of deposited ions, the number of nuclei per unit electrode surface, and the steady-state nucleation rate.

Continuous production of magnetic iron oxide nanocrystals by oxidative precipitation

Abstract Continuous processes are always preferred over batch ones when reproducible and scalable industrial procedures are needed. This work illustrates the production of magnetite nanoparticles by oxidative precipitation in aqueous media, following a continuous approach that offers additional advantages. Particularly, the developed reaction setup succeeds (i) the complete separation of the green rust’s precipitation from Fe3O4 nucleation, (ii) the achievement of constant concentrations in all ionic and solid forms throughout the production line when steady-state is reached, what means constant supersaturation from both the formation of green rust and Fe3O4, and (iii) the possibility to control critical parameters, such as OH− excess over the initial stoichiometric Fe(OH)2 precipitation, through on-line regulation of synthesis parameters such as the reactor’s pH and redox potential. Importantly, continuous flow synthesis of Fe3O4 nanoparticles enables high production capacities, low energy consumption and proportional scale-up at any volume. As a proof of concept, obtained nanoparticles were evaluated according to their magnetic response as potential magnetic hyperthermia agents indicating significant improvement of heating efficiency that goes up to 1.5–2 kW/gFe3O4 for both smaller (~40 nm) and larger (~200 nm) particles.