Supersaturation Dependence Research Articles

Rapid, low-cost exploration of nucleation rates in l-glutamic acid crystallization in pure media and the presence of polymers through novel parallel experimentation

Crystal nucleation is crucial in various fields of science and technology, ranging from materials synthesis to pharmaceutical production. Our research aims to determine the nucleation rates from parallel induction time measurement experiments followed by low-cost external bulk video imaging. Stirred conditions are applied, making our results industry-relevant where the crystallizers are also mixed. The L-Glutamic Acid-water system (L-GA/water) is used as a surrogate. The study is conducted through a series of parallel, small-scale stirred experiments that explore the effects of supersaturation, temperature, and polymer additives on nucleation rates. The methodology involves careful data collection through controlled experimental setup and analysis of induction time distributions that the stochastic nature of nucleation explains the induction time distribution. The discussion section interprets the findings within the context of the research question, highlighting the implications of varying temperature and supersaturation levels as two experimental parameters and polymers on crystal nucleation rates. The specific parameters of supersaturation and temperature dependencies are in the range of those reported in the literature, which validated the developed rapid nucleation rate measurement platform. Stepping outside of these established measurements, analyzing the influence of polymers with high potential in controlling particle size, shape, and polymorphism was touched as well. As an unexpected result, the nucleation rates appeared to depend not only on the chemical structure and amount of the polymer but also on the polymer solution preparation method. The remarkable influence of polymers on nucleation rates was shown that cannot be explained with the solubility altering effect of the polymers alone.

Influence of magnetic field on growth kinetics of sodium chlorate crystals from aqueous solution

The results of the study of the influence of a static magnetic field of 55 ± 3 mT on the face growth kinetics of sodium chlorate crystals in the supersaturation range of (0.89–1.78) % are presented. The supersaturation dependence of growth rate was analyzed using different theoretical models and the kinetic parameters of crystal growth in zero and in the applied magnetic field were estimated. It is shown that in both types of experiments the observed crystals grew by a complex dislocation source. Analysis of the growth rate distribution by using the Weibull distribution function was performed to obtain the maximum growth rate Rmax depending on their corresponding initial length lmax. The linear relationship between these quantities is derived from the model of growth by a group of cooperating screw dislocations. It was observed that both the initial size threshold l*max and the slope dRmax/dlmax exhibit higher values in the presence of a magnetic field.

Homogeneous Organic Crystal Nucleation Rates in Solution from the Perspective of Chemical Reaction Kinetics

It is demonstrated for 11 different combinations of organic solutes and solvents that the supersaturation dependence of homogeneous organic crystal nucleation rates from solution can be predicted from the solubility, bar a single empirical rate constant, when it is assumed that nucleation takes place in reversible aggregates of solvated solutes formed in supersaturated solutions. Reversible solute aggregation represents natural solute density fluctuations that take place in any solute/solvent system. For thermodynamically ideal solutions, the steady state size distribution, and thus the population of reversible aggregates in supersaturated solution, can be predicted quantitatively from the overall solute concentration by a simple mathematical expression. Supersaturation creates an excess of reversible aggregates with sizes exceeding that of the largest aggregate in saturated solution. It is shown that the number of these excess aggregates is proportional to experimental homogeneous nucleation rates, suggesting a rate equation for homogeneous nucleation that has only one empirical parameter, namely, a rate constant specific to the solute/solvent combination. This rate constant can be determined from standard nucleation rate data. The system-specificity of homogeneous nucleation rates thus appears to be encoded solely in a rate constant for the transformation of the large excess aggregates into crystal nuclei. The driving force for triggering nucleation events in these aggregates is likely the extremely high local supersaturation, which provides the conditions for spatiotemporally aligned bond-breaking (e.g., de-solvation) and bond-forming (e.g., solute–solute bonding) events that create stable crystal nuclei. The possible influence of heterogeneous nucleation by solid impurities is considered.

Sequential Amplification of Amino Acid Enantiomeric Excess by Conglomerate and Racemic Compound: Plausible Prebiotic Route Towards Homochirality.

Some amino acids can crystallize from aqueous solution both as conglomerates and racemic compounds: under high supersaturation following rapid evaporation, dissolved amino acids draining over porous sand-bars behave like conglomerates whereas in the resulting deeper pool of water, amino acid solution switches to the more common racemic-compound system. We show how the two forms might have sequentially combined under prebiotic conditions to form the basis of homochirality. The paper is a quantitative analysis of enantiomeric excess (EE) this dual behavior of amino acids is capable of producing in tandem: Initial amplification by preferential crystallization (PC) in conglomerate system (CS) followed by further amplification in the racemic compound system (RCS). Using aspartic acid as a model system, ternary phase diagram shows that a minimum supersaturation of 1.65 is required in the CS for the solution-EE to reach its maximum value of 50% at the RCS eutectic point. A relationship is derived for the dependence of this threshold supersaturation on the eutectic solubilities of CS and RCS. For given supersaturation in CS, a relation is also derived for minimum solution-EE that must be produced by PC before CS switches to RCS. Required PC-induced threshold solution-EE of 0.194, 0.070, 0.033 is calculated for supersaturation of 2, 5, 10 respectively in aspartic acid. Switching from CS to RCS further amplifies solution-EE, resulting in an overall growth of aspartic acid solution EE from near-zero in CS to around 50% in RCS.

Homogeneous Freezing Events Sampled in the Tropical Tropopause Layer

AbstractHigh‐frequency (20 Hz) aircraft measurements of tropical tropopause layer (TTL) cirrus and humidity are used to examine recent homogeneous freezing ice nucleation events. Several localized regions with peak ice concentrations greater than 10 cm−3 are documented. These high ice concentrations are almost certainly generated by homogeneous freezing of aqueous aerosols. The high‐frequency data reveals considerable structure in the cloud properties and humidity at along‐track scales as short as 8.5 m. Simulations of vapor depletion by growing ice crystals are used to assess the time since nucleation in these high ice concentration patches. Comparisons between observed and simulated dependence of supersaturation on ice concentration indicate the nucleation events occurred within minutes (sometimes only a few minutes) of the aircraft sampling. The infrequency and short ages of the events suggest that the high ice concentrations do not persist for long times, but they may still be important for TTL cirrus microphysical properties by providing a source of ice crystals that can lead to extensive, persistent clouds with lower ice concentrations. We have also used the extensive TTL measurements provided by the high‐altitude aircraft campaigns to evaluate the threshold supersaturation for homogeneous freezing. Peak supersaturations observed are consistent with recent laboratory experiments indicating that ice saturation ratios of about 1.75–1.95 are required for homogeneous freezing of aqueous aerosols at temperatures of 185–200 K.

Understanding the pH Dependence of Supersaturation State—A Case Study of Telmisartan

Creating supersaturating drug delivery systems to overcome the poor aqueous solubility of active ingredients became a frequent choice for formulation scientists. Supersaturation as a solution phenomenon is, however, still challenging to understand, and therefore many recent publications focus on this topic. This work aimed to investigate and better understand the pH dependence of supersaturation of telmisartan (TEL) at a molecular level and find a connection between the physicochemical properties of the active pharmaceutical ingredient (API) and the ability to form supersaturated solutions of the API. Therefore, the main focus of the work was the pH-dependent thermodynamic and kinetic solubility of the model API, TEL. Based on kinetic solubility results, TEL was observed to form a supersaturated solution only in the pH range 3–8. The experimental thermodynamic solubility-pH profile shows a slight deviation from the theoretical Henderson–Hasselbalch curve, which indicates the presence of zwitterionic aggregates in the solution. Based on pKa values and the refined solubility constants and distribution of macrospecies, the pH range where high supersaturation-capacity is observed is the same where the zwitterionic form of TEL is present. The existence of zwitterionic aggregation was confirmed experimentally in the pH range of 3 to 8 by mass spectrometry.

Simple Accurate Nonequilibrium Step Velocity Model for Crystal Growth of Symmetric Organic Molecules

Crystal growth models depend on the density of kink sites along step edges, which are primary sites for surface integration of growth units. Since the kink density is a fundamental quantity in these growth models, disregarding its supersaturation dependence results in the loss of effects that get magnified at higher supersaturation. In this work, a simplified steady-state framework is developed for estimating the nonequilibrium kink density as a function of supersaturation. It involves balancing the rates of the dominant surface events that produce kinks with those that destroy kinks. The master equations obtained are solved simultaneously to yield closed-form expressions for the nonequilibrium kink density. Predicted step velocities are in excellent agreement with kinetic Monte Carlo simulations.

Coupled Population Balance and Species Balance Models of Crystallization: Analytic Solutions and Data Fits

Obtaining kinetic constants in rate laws for nucleation and growth is challenging and essential to the design of the crystallization processes. Starting from the coupled species and population balance equations, we linearize the equations by expanding around the steady state. We then develop analytic solutions that describe the response to a step change in the feed flow rate. We use the analytic solution to extract parameters in the rate laws for nucleation and growth from experimental crystal size distribution data. Specifically, the response of the crystal size distribution to a step change in the feed flow rate, as fitted to the analytic solution, reveals the rate constants and supersaturation dependence in rate laws for growth and secondary nucleation.

Crystal Growth of the Acentric Organic Nonlinear Optical Material Methyl-p-hydroxybenzoate: Morphological Variations in Crystals Grown by Physical Vapor Transport

Single crystals of the acentric compound methyl-p-hydroxybenzoate were grown by self-nucleation and seeded growth from the vapor phase by the physical vapor transport (PVT) process. In the temperature range of 80–95 °C (nucleation supersaturation 0.97 to 0.88), all crystals were of the polymorphic form as produced by room-temperature solution growth. Self-nucleated crystals varied in macromorphology from columnar to octahedral to skewed octahedral and finally to skewed columnar but retained the same crystal forms indicated by theoretical calculations. Micromorphological studies of growth faces indicated that these variations result from changes in growth mechanisms that influence both the defect structure and perfection of the growing crystal. X-ray topographic studies confirmed that growth under the most ideal conditions, when the dominant faces of the crystals were growing by a dislocation induced Burton, Cabrera, and Frank mechanism, yielded the structurally most perfect crystals. Preliminary studies of seeded growth were performed as a prelude to using PVT for the growth of larger crystals. The seeded growth followed a different pattern of supersaturation dependence. All crystals showed the same asymmetric growth along the polar axis that has come to be regarded as characteristic of these highly polar acentric materials when grown from solution.

Cloud droplet activation properties and scavenged fraction of black carbon in liquid-phase clouds at the high-alpine research station Jungfraujoch (3580 m a.s.l.)

Abstract. Liquid clouds form by condensation of water vapour on aerosol particles in the atmosphere. Even black carbon (BC) particles, which are known to be slightly hygroscopic, have been shown to readily form cloud droplets once they have acquired water-soluble coatings by atmospheric aging processes. Accurately simulating the life cycle of BC in the atmosphere, which strongly depends on the wet removal following droplet activation, has recently been identified as a key element for accurate prediction of the climate forcing of BC. Here, to assess BC activation in detail, we performed in situ measurements during cloud events at the Jungfraujoch high-altitude station in Switzerland in summer 2010 and 2016. Cloud droplet residual and interstitial (unactivated) particles as well as the total aerosol were selectively sampled using different inlets, followed by their physical characterization using scanning mobility particle sizers (SMPSs), multi-angle absorption photometers (MAAPs) and a single-particle soot photometer (SP2). By calculating cloud droplet activated fractions with these measurements, we determined the roles of various parameters on the droplet activation of BC. The half-rise threshold diameter for droplet activation (Dhalfcloud), i.e. the size above which aerosol particles formed cloud droplets, was inferred from the aerosol size distributions measured behind the different inlets. The effective peak supersaturation (SSpeak) of a cloud was derived from Dhalfcloud by comparing it to the supersaturation dependence of the threshold diameter for cloud condensation nuclei (CCN) activation measured by a CCN counter (CCNC). In this way, we showed that the mass-based scavenged fraction of BC strongly correlates with that of the entire aerosol population because SSpeak modulates the critical size for activation of either particle type. A total of 50 % of the BC-containing particles with a BC mass equivalent core diameter of 90 nm was activated in clouds with SSpeak≈0.21 %, increasing up to ∼80 % activated fraction at SSpeak≈0.50 %. On a single-particle basis, BC activation at a certain SSpeak is controlled by the BC core size and internally mixed coating, which increases overall particle size and hygroscopicity. However, the resulting effect on the population averaged and on the size-integrated BC scavenged fraction by mass is small for two reasons: first, acquisition of coatings only matters for small cores in clouds with low SSpeak; and, second, variations in BC core size distribution and mean coating thickness are limited in the lower free troposphere in summer. Finally, we tested the ability of a simplified theoretical model, which combines the κ-Köhler theory with the Zdanovskii–Stokes–Robinson (ZSR) mixing rule under the assumptions of spherical core–shell particle geometry and surface tension of pure water, to predict the droplet activation behaviour of BC-containing particles in real clouds. Predictions of BC activation constrained with SSpeak and measured BC-containing particle size and mixing state were compared with direct cloud observations. These predictions achieved closure with the measurements for the particle size ranges accessible to our instrumentation, that is, BC core diameters and total particle diameters of approximately 50 and 180 nm, respectively. This clearly indicates that such simplified theoretical models provide a sufficient description of BC activation in clouds, as previously shown for activation occurring in fog at lower supersaturation and also shown in laboratory experiments under controlled conditions. This further justifies application of such simplified theoretical approaches in regional and global simulations of BC activation in clouds, which include aerosol modules that explicitly simulate BC-containing particle size and mixing state.

Recent Insights into Protein Crystal Nucleation

Homogeneous nucleation of protein crystals in solution is tackled from both thermodynamic and energetic perspectives. The entropic contribution to the destructive action of water molecules which tend to tear up the crystals and to their bond energy is considered. It is argued that, in contrast to the crystals’ bond energy, the magnitude of destructive energy depends on the imposed supersaturation. The rationale behind the consideration presented is that the critical nucleus size is determined by the balance between destructive and bond energies. By summing up all intra-crystal bonds, the breaking of which is needed to disintegrate a crystal into its constituting molecules, and using a crystallographic computer program, the bond energy of the closest-packed crystals is calculated (hexagonal closest-packed crystals are given as an example). This approach is compared to the classical mean work of separation (MWS) method of Stranski and Kaischew. While the latter is applied merely for the so-called Kossel-crystal and vapor grown crystals, the approach presented can be used to establish the supersaturation dependence of the protein crystal nucleus size of arbitrary lattice structures.

On some aspects of crystallization process energetics, logistic new phase nucleation kinetics, crystal size distribution and Ostwald ripening

Nucleation, nucleus number densities, and the respective supersaturation dependence, crystal growth and Ostwald ripening are reconsidered from the energetics perspective. Supersaturation-dependent critical nucleus sizes are calculated accordingly. It is argued that the logistic time-dependent nucleation resembles one period of a harmonic oscillation. The general conclusion is that a crystallizing system adapts to the distorting influence of the supersaturation imposed, and during crystal nucleation and growth, the system gradually consumes this supersaturation to reach a new equilibrium state at the end of Ostwald ripening (completely exhausted supersaturation). This is an indication that the system responds to the change in its energetic status according to the well known Le Châtelier–Braun principle. The extent to which the nucleation process affects the crystal size distribution (CSD) is also discussed. Slightly altered by the crystal growth, the CSD also preserves some trace of the nucleation stage shape during Ostwald ripening.

Role of stationary and transient waves in CO2 supersaturation during northern winter in the Martian atmosphere revealed by MGS radio occultation measurements

AbstractThe Martian atmosphere, which mainly consists of carbon dioxide (CO2), is characterized by extremely low temperatures that cause CO2 gas to freeze and dry ice to form. To date, temperatures below the CO2 saturation temperature, which can be attributed to the effects of atmospheric waves, have been observed in the polar winter and in the mesosphere. Using data from Mars Global Surveyor (MGS) radio occultation measurements, we investigated the role of large‐scale atmospheric waves including stationary and transient waves at northern high latitudes in winter on CO2 supersaturation. A distinct longitudinal dependence of CO2 supersaturation was observed at altitudes higher than the pressure level of 200–400 Pa, where a stationary wave with a wave number of 2, whose temperature amplitude had minima at 30–100 Pa, lowered the background temperature to a level close to the CO2 saturation temperature. However, the stationary wave alone was not sufficient to cause CO2 supersaturation. Additional temperature disturbances caused by transient waves, namely, superposition of both waves, had a significant role in CO2 supersaturation. The longitudinal dependence of the occurrence of CO2 supersaturation revealed by our study might affect the longitudinal distribution of CO2 snowfall and the formation of the seasonal polar ice cap.

Supersaturation dependence of glycine polymorphism using laser-induced nucleation, sonocrystallization and nucleation by mechanical shock.

The nucleation of glycine from aqueous supersaturated solution has been studied using non-photochemical laser-induced nucleation (NPLIN), ultrasound (sonocrystallization), and mechanical shock of sample vials. It was found that at higher supersaturation, samples were more susceptible to nucleation and produced more of the γ-glycine polymorph. The results are described in terms of a mechanism common to all three nucleation methods, involving the induction of cavitation events and pressure shockwaves. The switch in preference from α- to γ-glycine was observed to occur over a narrower range of supersaturation values for NPLIN. We attribute this to induction of cavitation events with higher energies, which result in higher localized pressures and supersaturations. Experiments on NPLIN using circularly versus linearly polarized light showed no evidence for binary polarization switching control of glycine polymorphism.

Investigation of Growth Mechanisms of Sodium Chlorate Crystals from Aqueous Solutions

Difficulties in determining the crystal growth mechanism from growth rate versus solution supersaturation dependence are discussed. Obtained results indicate that in the supersaturation range of 0.66–1.56%, sodium chlorate crystals grow in accordance with the spiral growth model. It is shown that in the supersaturation range of 0.44–1.32%, the growth mechanism depends on crystal growth history. Namely, the exponent n in the power law R = Kσn depends on the manner of supersaturation changes (varied from 1.3 to 1.9%). This indicates that the overlapping of diffusion fields of neighboring steps depends on growth history.

Pinning Down the Reasons for the Size, Shape, and Stability of Nanobubbles.

A thermodynamic analysis of the size, shape, and stability of nanobubbles is carried out by modifying classical nucleation theory to include the supersaturation dependence of the surface tension. It is shown that the free energy of a nanobubble is a minimum at the critical radius when the contact line is pinned, that the size of the nanobubble is determined by the decrease in the surface tension caused by the degree of supersaturation, and that together these explain the increased exterior contact angle of a nanobubble compared with the corresponding angle of a macroscopic bubble or droplet on the same surface.

Black carbon simulations using a size‐ and mixing‐state‐resolved three‐dimensional model: 2. Aging timescale and its impact over East Asia

AbstractThis study evaluates the aging timescale and the cloud condensation nuclei (CCN) activity of black carbon (BC) over East Asia and its outflow region using a size‐ and mixing‐state‐resolved three‐dimensional model, the Weather Research and Forecasting model with chemistry (WRF‐chem) with the Aerosol Two‐dimensional bin module for foRmation and Aging Simulation (ATRAS) and the Model for Simulating Aerosol Interactions and Chemistry (MOSAIC). The WRF‐chem/ATRAS‐MOSAIC model explicitly calculates BC aging (condensation and coagulation) and removal processes, with 12 size and 10 BC mixing state bins (128 bins in total). The model reveals large spatial and temporal variability of the BC aging timescale and the CCN activity of BC‐containing particles over East Asia (spring 2009) with their strong size and supersaturation dependence. The BC aging timescale differs from 0.19 to 3.1 days (period and domain average at an altitude of 1 km), depending on the choice of size (mass or number) and supersaturation (1.0% or 0.1%). As a result, almost 100% of BC‐containing particles are CCN‐active at a supersaturation of 1.0%, whereas 20–50% of BC‐containing particles are CCN‐inactive at a supersaturation of 0.1%, with a strong size dependence. These results show the importance of resolving BC aging processes and their dependence on size and supersaturation in models for more accurate simulations of BC concentrations and their distribution and lifetime. A sensitivity simulation without resolving BC mixing state shows the underestimation of total BC mass concentrations by 5–10% and the BC mass concentrations in the CCN‐inactive particles (at a supersaturation of 0.1%) by 40–60% over the outflow region (at 150°E), compared with the simulation resolving BC mixing state. Because BC aging speed is very slow at 150°E and eastward, the change in BC mass and its CCN activity by resolving BC mixing state will continue over long distances and may have a large impact on BC transport from East Asia to remote regions such as North America and the Arctic.

Nucleation phenomena in electrochemical systems: thermodynamic concepts

Basic thermodynamic concepts related to the initial stages of first-order phase transitions are defined in terms of electrochemical quantities. Theoretical expressions are derived for the nucleation work and for the size of the critical nucleus revealing the supersaturation dependence of these most important physical quantities.

Time dependent driving forces and the kinetics of tricalcium silicate hydration

Simulations of tricalcium silicate (C3S) hydration using a kinetic cellular automaton program, HydratiCA, indicate that the net rate depends both on C3S dissolution and on hydration product growth. Neither process can be considered the sole rate-controlling step because the solution remains significantly undersaturated with respect to C3S yet significantly supersaturated with respect to calcium silicate hydrate (C–S–H). The reaction rate peak is attributed to increasing coverage of C3S by C–S–H, which reduces both the dissolution rate and the supersaturation of C–S–H. This supersaturation dependence is included in a generalized boundary nucleation and growth model to describe the kinetics without requiring significant impingement of products on separate cement grains. The latter point explains the observation that paste hydration rates are insensitive to water/cement ratio. The simulations indicate that the product layer on C3S remains permeable; no transition to diffusion control is indicated, even long after the rate peak.

Supersaturation of aqueous species and hydrothermal crystal growth of ZnO

Synthesis of ZnO crystals prepared with zinc acetate or chloride, disodium dihydrogen ethylenediaminetetraacetate (EDTA), potassium hydroxide and sodium triflate at 200°C and variable pH 8–12 is reported. Crystals were imaged and size-analyzed with optical microscopy. Using aqueous speciation modeling software, supersaturation dependence on pH was calculated for five zinc species—Zn2+, Zn(OH)+, Zn(OH)2, Zn(OH)3–and Zn(OH)42–—to investigate connections between predominate crystal habits at different pH and dominant aqueous species. For zinc acetate and chloride systems, the zinc species with highest supersaturation was Zn(OH)42– throughout the pH 8–12 range, and the second highest was Zn2+ or Zn(OH)3–, with a crossover pH of 10.2–10.4 depending on counterion. The prominence of the tetrahydroxyl zinc species in ZnO crystal growth is supported by these calculations, and total supersaturation is inversely proportional to average crystal sizes, as expected. Optical microscopy and size analysis on products revealed crystals with a needle or prismatic habit throughout the studied pH range, and the change in aspect ratio correlates with supersaturation changes for the Zn2+ in this pH range, thus suggesting that growth rates along the [001] crystallographic direction are affected by small concentration changes of this ion.