Critical Supersaturation Ratio Research Articles

On the particle formation of leucine in spray drying of inhalable microparticles

The particle formation of L-leucine, a dispersibility-enhancing amino acid used in the spray drying of inhalable pharmaceutical aerosols, was extensively studied using three experimental methods, and the results were interpreted with the aid of theory. A comparative-kinetics electrodynamic balance was used to study the shell formation behavior in single evaporating microdroplets containing leucine and trehalose. Different concentration thresholds of solidification and shell formation were determined for trehalose and leucine, which were then used in the particle formation model to predict the properties of spray-dried particles. Furthermore, a droplet chain instrument was used to study the particle morphologies and particle densities that were not accessible in the single particle experiments. Lab-scale spray drying was also used to produce powders typical for actual pharmaceutical applications. Raman spectroscopy confirmed that a glass former, such as trehalose, can inhibit the crystallization of leucine. The surface compositions of these spray-dried powders were analyzed via time-of-flight secondary ion mass spectrometry. The leucine surface coverage in a polydisperse powder was determined to be a function of the particle size or the initial droplet diameter of each respective particle. This observation confirms the important role of leucine crystallization kinetics in its shell-forming capabilities. A critical supersaturation ratio of 3.5 was also calculated for leucine, at which it is assumed to instantaneously nucleate out of solution. This ratio was used as the threshold for the initiation of crystallization. Crystallinity predictions for the leucine-trehalose particles based on this supersaturation ratio were in good agreement with the solid-state characterizations obtained by Raman spectroscopy. This study improves the fundamental understanding of the particle formation process of leucine-containing formulations, which can apply to other crystallizing systems and potentially facilitate the rational design of such formulations with reduced experimental effort.

In Silico Modeling Approach for the Evaluation of Gastrointestinal Dissolution, Supersaturation, and Precipitation of Posaconazole.

The aim of this study was to evaluate gastrointestinal (GI) dissolution, supersaturation, and precipitation of posaconazole, formulated as an acidified (pH 1.6) and neutral (pH 7.1) suspension. A physiologically based pharmacokinetic (PBPK) modeling and simulation tool was applied to simulate GI and systemic concentration-time profiles of posaconazole, which were directly compared with intraluminal and systemic data measured in humans. The Advanced Dissolution Absorption and Metabolism (ADAM) model of the Simcyp Simulator correctly simulated incomplete gastric dissolution and saturated duodenal concentrations of posaconazole in the duodenal fluids following administration of the neutral suspension. In contrast, gastric dissolution was approximately 2-fold higher after administration of the acidified suspension, which resulted in supersaturated concentrations of posaconazole upon transfer to the upper small intestine. The precipitation kinetics of posaconazole were described by two precipitation rate constants, extracted by semimechanistic modeling of a two-stage medium change in vitro dissolution test. The 2-fold difference in exposure in the duodenal compartment for the two formulations corresponded with a 2-fold difference in systemic exposure. This study demonstrated for the first time predictive in silico simulations of GI dissolution, supersaturation, and precipitation for a weakly basic compound in part informed by modeling of in vitro dissolution experiments and validated via clinical measurements in both GI fluids and plasma. Sensitivity analysis with the PBPK model indicated that the critical supersaturation ratio (CSR) and second precipitation rate constant (sPRC) are important parameters of the model. Due to the limitations of the two-stage medium change experiment the CSR was extracted directly from the clinical data. However, in vitro experiments with the BioGIT transfer system performed after completion of the in silico modeling provided an almost identical CSR to the clinical study value; this had no significant impact on the PBPK model predictions.

Evaluation of the difficulty of crystallization of organic compounds using the critical supersaturation ratio (Sc)

In the case of solvent selection, supersolubility is an index for improving crystallization behavior. However, supersolubility is affected by kinetic factors such as the cooling rate. An index for suitable solvent selection is needed. The supersaturation ratio (S) is one of the operation design indices of controlling crystallization behavior such as supersolubility. The S at 298K (S298) of the pharmaceutical compounds theophylline, noscapine, clotrimazole, indomethacin, carbamazepine, naproxene and tolbutamide were measured in ethanol using a polythermal method. If the compound had a large lnS298, the cooling rate strongly affected the temperature of the cloud point in the cooling crystallization method. In order to estimate the crystallization behavior without the cooling rate effect, the critical supersaturation ratio (Sc) was proposed. Sc at 298K (Sc298) was calculated from dissolution/cloud points at 0K/min extrapolated from that of several heating/cooling rates to remove the kinetic effects on S. The lnSc298 values of theophylline, noscapine and clotrimazole were estimated in acetonitrile, methyl ethyl ketone, tetrahydrofuran, ethyl acetate, methanol, ethanol and isopropanol. The lnSc298 value of clotrimazole was the largest in all solvents. The results showed that lnSc298 was a simple index which could be used to evaluate the crystallization behavior resulting from the interaction between the solvent and the compound. In conclusion, the proposed lnSc298 should be useful for comparing the difficulty of crystallization which indicates how we should obtain desired crystals within a certain finite time period for development API in the manufacturing field without considering the effect of the heating/cooling rate.

EXTENSION OF MODIFIED CLASSICAL THEORY TO NUCLEATION OF LKAP FROM AQUEOUS SOLUTION

The dependence of the induction period of crystallization on super cooling was determined for the system lithium chloride—potassium acid phthalate (KAP) over the composition of 1mole % LiCl2. This dependence can be described by 1/ ( lnS) 2 against ln τ curve. In order to reduce the effect of heterogeneous nucleation on the nucleation parameters, the interfacial energy was calculated from the slopes determined in the linear region of the line plots. Nucleation parameters like free energy change, rate of nucleation and critical radius were determined using the value of interfacial energy. Correction was made to the interfacial energy based on the thermodynamically approach. An attempt has been made to calculate the nucleation parameters corresponding to the critical super saturation ratio using the modified classical nucleation theory

Formation of Alumina Inclusions during Counter Diffusion of Aluminum and Oxygen Dissolved in Molten Iron

The formation of alumina (Al2O3) inclusions was experimentally investigated with the capillary-reservoir method. The inclusions were observed with a SEM (scanning electron microscope). The compositions of iron matrix and inclusion were measured with an EDX (energy dispersive X-ray analysis). The content profile of aluminum was discussed by the counter-diffusion model of aluminum and oxygen with an instantaneous irreversible reaction for alumina formation. The inclusions of spherical and polygonal alumina and spherical hercynite (FeOAl2O3) were observed in the vicinity of the diffusion front of aluminum. The hercynite was detected when the initial oxygen content was 0.075 mass% and higher. When the initial oxygen content was more than 0.045 mass% and higher, dendritic alumina formed at the position that was nearer to the interface than the position of spherical and polygonal inclusions. No inclusion was observed around the interface because of the re-dissolution of the inclusions. The initiating position of the inclusion formation was approximated by the reaction position, Zr, obtained from the model on the assumption that aluminum and oxygen contents at the reaction position were zero. Empirically, 0.9×Zr and 0.17×Zr expressed the initiating positions of formation and re-dissolution of inclusions respectively. The critical supersaturation ratio was estimated to be from 1 to 7.4×105, depending on the initial aluminum and oxygen contents.

Role of Orthophosphate As a Corrosion Inhibitor in Chloraminated Solutions Containing Tetravalent Lead Corrosion Product PbO2

Addition of orthophosphate has been commonly employed to suppress lead levels in drinking water. Its detailed mechanism and time required for it to become effective, however, have not been fully elucidated. In this study, we investigated the mechanistic role of orthophosphate as a corrosion inhibitor in controlling lead release from tetravalent lead corrosion product PbO(2) in chloraminated solutions, a system representing distribution networks experiencing disinfectant changeover from free chlorine to monochloramine. In all experiments with orthophosphate addition of at least 1 mg/L as P, peaking of soluble Pb(II) concentration within the first 24 h was observed before lead concentrations decreased and stabilized at levels lower than 15 μg/L. The variation of soluble Pb(II) concentration could be attributed to the dynamics between the rate of PbO(2) reductive dissolution, primarily induced by monochloramine decomposition, and that of chloropyromorphite (Pb(5)(PO(4))(3)Cl) precipitation, which did not occur until a critical supersaturation ratio of about 2.36 was reached in the solution. Our findings provide insights to how orthophosphate reduces lead levels under drinking water conditions and highlight the potential risk of short-term elevated lead concentrations. Intensive monitoring following the disinfectant changeover may be required to determine the overall lead exposure when using orthophosphate as a corrosion inhibitor.

Cubic SiC formation on the C-face of 6H–SiC (0 0 0 1) substrates

Nucleation and subsequent growth of cubic SiC (111) on Si- and C-faces of nominally on-axis 6H–SiC substrates was investigated. More uniform nuclei and twin boundary distribution was observed when 3C–SiC was grown on the C-face. This was attributed to a lower critical supersaturation ratio. A new type of defects which appear as pits in the C-face 3C–SiC layers related to homoepitaxial 6H–SiC spiral growth was found and described. The evaluation of the growth driving force for both polar faces showed that the homoepitaxial 6H–SiC spirals were not overgrown on the C-face due to low maximum supersaturation ratio. The XRD ω-rocking characterization shows a better structural quality of the 3C–SiC grown on the Si-face, however on the C-face the uniformity over the whole sample was higher. Unintentional doping by N (∼1016cm−3) was slightly higher on the C-face while Al doping was higher (∼1014cm−3) on the Si-face of the grown material, similarly to the doping of hexagonal SiC polytypes.

An evaluation and comparison of cloud condensation nucleus activity models: Predicting particle critical saturation from growth at subsaturation

The ability of particles to activate and form cloud droplets influences the functioning of the Earth's hydrological cycle. This work links the particle water uptake at subsaturation to the critical supersaturation ratio needed for particles to become cloud condensation nuclei (CCN). Five models using the particle hygroscopic growth at subsaturation for predicting the critical supersaturation needed for droplet activation were applied to a laboratory data set of inorganic and organic compounds and mixtures of them. The data set consisted of hygroscopicity tandem differential mobility analyzer measurements and CCN counter measurements. No chemical composition information was used when applying the models. All models tested were based on modifications of Köhler theory and gave similar results. The agreement between predicted and measured critical supersaturations was good, considering the relatively simple models used. A trend of overestimating the critical supersaturations was observed, typically by ∼15%. The best performing model gave on average only a 4% offset from experimental values; the model with the largest deviation was offset by 20%. A comparison was made between the number of soluble entities (ions or nondissociating molecules) estimated from the particle hygroscopic growth at 90% relative humidity (RH) and the number estimated from the particle critical supersaturation; a ∼35% increase was observed in the effective number of entities in solution when going from 90% RH to activation. For many types of aerosols, differences in the model approaches tested do not induce large differences in the predicted critical supersaturation. However, it is most important to follow the recommendations published with the respective models and not use them indiscriminately.

Reverse engineering the kidney: modelling calcium oxalate monohydrate crystallization in the nephron

Crystallization of calcium oxalate monohydrate in a section of a single kidney nephron (distal convoluted tubule) is simulated using a model adapted from industrial crystallization. The nephron fluid dynamics is represented as a crystallizer/separator series with changing volume to allow for water removal along the tubule. The model integrates crystallization kinetics and crystal size distribution and allows the prediction of the calcium oxalate concentration profile and the nucleation and growth rates. The critical supersaturation ratio for the nucleation of calcium oxalate crystals has been estimated as 2 and the mean crystal size as 1 mum. The crystal growth order, determined as 2.2, indicates a surface integration mechanism of crystal growth and crystal growth dispersion. The model allows the exploration of the effect of varying the input calcium oxalate concentration and the rate of water extraction, simulating real life stressors for stone formation such as dietary loading and dehydration.

Surface tensions of multi-component mixed inorganic/organic aqueous systems of atmospheric significance: measurements, model predictions and importance for cloud activation predictions

Abstract. In order to predict the physical properties of aerosol particles, it is necessary to adequately capture the behaviour of the ubiquitous complex organic components. One of the key properties which may affect this behaviour is the contribution of the organic components to the surface tension of aqueous particles in the moist atmosphere. Whilst the qualitative effect of organic compounds on solution surface tensions has been widely reported, our quantitative understanding on mixed organic and mixed inorganic/organic systems is limited. Furthermore, it is unclear whether models that exist in the literature can reproduce the surface tension variability for binary and higher order multi-component organic and mixed inorganic/organic systems of atmospheric significance. The current study aims to resolve both issues to some extent. Surface tensions of single and multiple solute aqueous solutions were measured and compared with predictions from a number of model treatments. On comparison with binary organic systems, two predictive models found in the literature provided a range of values resulting from sensitivity to calculations of pure component surface tensions. Results indicate that a fitted model can capture the variability of the measured data very well, producing the lowest average percentage deviation for all compounds studied. The performance of the other models varies with compound and choice of model parameters. The behaviour of ternary mixed inorganic/organic systems was unreliably captured by using a predictive scheme and this was dependent on the composition of the solutes present. For more atmospherically representative higher order systems, entirely predictive schemes performed poorly. It was found that use of the binary data in a relatively simple mixing rule, or modification of an existing thermodynamic model with parameters derived from binary data, was able to accurately capture the surface tension variation with concentration. Thus, it would appear that in order to model multi-component surface tensions involving compounds used in this study one requires the use of appropriate binary data. However, results indicate that the use of theoretical frameworks which contain parameters derived from binary data may predict unphysical behaviour when taken beyond the concentration ranges used to fit such parameters. The effect of deviations between predicted and measured surface tensions on predicted critical saturation ratios was quantified, by incorporating the surface tension models into an existing thermodynamic framework whilst firstly neglecting bulk to surface partitioning. Critical saturation ratios as a function of dry size for all of the multi-component systems were computed and it was found that deviations between predictions increased with decreasing particle dry size. As expected, use of the surface tension of pure water, rather than calculate the influence of the solutes explicitly, led to a consistently higher value of the critical saturation ratio indicating that neglect of the compositional effects will lead to significant differences in predicted activation behaviour even at large particle dry sizes. Following this two case studies were used to study the possible effect of bulk to surface partitioning on critical saturation ratios. By employing various assumptions it was possible to perform calculations not only for a binary system but also for a mixed organic system. In both cases this effect lead to a significant increase in the predicted critical supersaturation ratio compared to the above treatment. Further analysis of this effect will form the focus of future work.

Effect of ultrasound on the heterogeneous nucleation of BaSO4 during reactive crystallization

The effect of ultrasound on reactive crystallization is studied by measuring the induction time when nucleation is predominantly heterogeneous. Barium sulphate is used as the working substance precipitated by mixing aqueous BaCl2 and Na2SO4 solutions with relatively low concentrations compared to experiments for homogeneous nucleation. It is observed that at a given supersaturation level, the induction time significantly decreases with increasing ultrasonic energy input. The mechanism of the ultrasonic effect on heterogeneous nucleation is analyzed. The effect of ultrasound is to increase the diffusion coefficient (DAB) while reducing the contact angle (θ) and geometric factor (f). This gives rise to an increase in the heterogeneous nucleation rate and shorter induction time. The ultrasonic effect on critical supersaturation ratio (Scrit) is also investigated to determine the mechanism of ultrasonic effect on f and θ. Both the force from the cavitational bubble implosion and the nucleation process occurring at bubble/solution/foreign solid interface are proposed as the predominant reasons why contact angle (θ) decreases with the increase of energy input.

Relationship between Supersaturation Ratio and Supply Rate of Solute in the Growth Process of Monodisperse Colloidal Particles and Application to AgBr Systems

Supersaturation ratio, S, has been theoretically related to the supply rate of solute, Q, from growth rate and mass-balance equations in the quasi-steady state in the growth process of isotropic monodisperse particles. The derived equation, (S - 1) = (1/D + 1/kr)(Q/betaC(0)nr) + 2V(m)gamma/rRT, suggests a linear dependence of S on Q under constant n and r, where D is the diffusion coefficient, k is the rate constant for surface-reaction, C(0) is the solubility, n and r are the number and radius of growing particles, respectively, V(m) is the molar volume of particles, R is the gas constant, T is the absolute temperature, and beta is the shape factor defined by beta identical with (1/r(2)) dupsilon/dr, where upsilon is the volume of an individual particle. The equation was applied to the analysis of growth kinetics and determinations of critical supersaturation ratio in monodisperse AgBr particles in the controlled double-jet system with the assistance of a potentiometric supersaturation measurement. In both cubic and octahedral particles, growth rates were completely limited by diffusion and surface-reaction at pBr ( identical with -log[Br(-)]) 3.0 and 1.0, respectively, while the growths were intermediate of them at pBr 2.0 and 4.0. The growth parameters, DC(0) and kC(0), were experimentally determined. Also, critical supersaturation ratio was estimated as 1.28 as an average in the present study.

Scale inhibition study by turbidity measurement

The concept of a critical supersaturation ratio (CSSR) has been used to characterize the effectiveness of different types of scale inhibitors, inhibitor concentration, and precipitating solution pH in order to prevent the formation of barium sulfate scale. The scale inhibitors used in this work were aminotrimethylene phosphonic acid (ATMP), diethylenetriaminepentamethylene phosphonic acid (DTPMP), and phosphinopolycarboxylic acid polymer (PPCA). The CSSR at which barium sulfate precipitates was obtained as a function of time for different precipitation conditions and was used as an index to evaluate the effect of the precipitation conditions. The results showed that the CSSRs decrease with increasing elapsed time after mixing the precipitating solutions, but increases with increasing scale inhibitor concentration and solution pH. The CSSR varies linearly with the log of the scale inhibitor concentration and with the precipitating solution pH. A SEM analysis showed that the higher the scale inhibitor concentration and solution pH, the smaller and more spherical the BaSO 4 precipitates. Analysis of the particle size distribution revealed that increasing the elapsed time, the scale inhibitor concentration, and precipitating solution pH, all produce a broader particle size distribution and a smaller mean diameter of the BaSO 4 precipitates. DTPMP and PPCA were the most effective BaSO 4 scale inhibitors per ionizable proton and the most effective on a concentration basis, respectively.

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.

Scale formation in tubular heat exchangers—research priorities

The common case of CaCO 3 scale formation in pipe flow is considered in this paper. Results of experimental studies, mainly by the author and his collaborators, are reviewed from the standpoint of the main mechanisms involved, in order to identify key issues that require additional research. The discussion is focused on the initial deposition rate as well as on the morphology of growing crystalline deposits as a function of various process parameters. A critical supersaturation ratio ( S c∼7 for CaCO 3) represents a significant transition from one type of scale formation process to another, including the dominant mechanism, the growth rate, and the morphology of scale. As regards generic topics that need clarification, it is suggested that high priority should be placed on (a) the attachment phenomena of nuclei/crystals on the substrate and (b) the effect of particulate/colloidal matter on scale characteristics. Significant gaps also exist in our understanding of the effects of fluid physical and chemical properties, and of fluid mechanics, on elementary processes (e.g., crystal growth and morphology) and on scale characteristics. Clarifying these aspects of scale formation would facilitate the development of fouling mitigation methods. Modelling efforts addressing elementary processes as well as system (global) evolution are considered essential for developing improved predictive tools, and reliable techniques for estimating physical parameter values difficult to obtain by other means.

Potentiometric Determination of the Critical Supersaturation Ratio of Monodisperse Silver Chloride Grains in the Controlled Double-Jet Precipitation

Potentiometric Determination of the Critical Supersaturation Ratio of Monodisperse Silver Chloride Grains in the Controlled Double-Jet Precipitation

Simple Model of Aerosol Particle Formation by the Evaporation–Condensation Method

From an engineering point of view the present authors have proposed the simple model of a homogeneous nucleation relationship in the liquid phase that can predict the number concentration of nucleated particles in various operating conditions. Experiments of liquid-phase nucleation in which the precursor monomers were generated by several methods have successfully confirmed the predictions of the model. In the present paper, our previous model of homogeneous nucleation is extended to the case in which the precursor monomers are generated in a gas-phase system. First, a relationship between number concentration and mean volume diameter of nucleated aerosol particles and operating conditions is obtained considering the free molecular regime around the critical nuclei, which is the main difference with the liquid phase. Second, the validity of the relation lies in experimental use of dioctyl sebacate particles generated by evaporation–condensation. As a result, the predictions are in excellent agreement with the experimental results after considering substantial losses of monomers and particles to the walls of the experimental system because in the gasphase the diffusion velocity and the critical supersaturation ratio of monomer are higher than those in the liquid phase.

The adsorption and nucleation of water vapor on an insoluble spherical solid particle

A kinetic theory with consideration of surface migration is derived for heterogeneous nucleation of water on a smooth spherical solid particle. In this model, the adoption of the kinetic coefficient for the calculation of nucleation rate, whose value is somewhat uncertain, is avoided. The effects of particle size and contact angle between the condensate and particle surface on the critical supersaturation ratio were investigated. The calculated critical supersaturation is lower compared with that of the classical theory proposed by Fletcher, and higher than that obtained by Scheludko's theory, which took into account the effect of a negative line tension. A comparison with experimental data shows that the contact angle between water and Ag particles is about 40° and that for dioctyl phthalate (DOP) aerosol is about 5°. The results indicate that the assumption of a hydrophilic adsorbed layer on the DOP surface is not necessary. We also find that for the onset of heterogeneous nucleation processes, the indirect addition of the adsorbed molecules to the condensate nuclei by two-dimensional diffusion is more important than the direct addition of the molecules from the vapor phase. In general, the predicted critical supersaturation is higher than the experimental values and the discrepancy cannot be accounted for simply by the consideration of indirect addition of adsorbed molecules in this model.

Determination of the Critical Supersaturation Ratio in Heterogeneous Nucleation of Benzene Vapor on a Cold Substrate.

The heterogeneous nucleation of benzene from the vapor phase to the solid phase on a foreign substrate contacted with vapor phase was studied experimentally at reduced pressures by cooling the copper substrate. The critical substrate temperature corresponding to the onset of nucleation was determined at a given vapor pressure by observing both the rapid decrease in vapor pressure that occurred as the substrate was cooled past the critical point and the subsequent appearance of benzene crystals on the substrate. The experimental critical supersaturation ratios determined from observed critical substrate temperatures were found to increase as the cooling rate of the substrate increased. The dependences of critical supersaturation ratios on substrate temperatures could be explained qualitatively by a theoretical expression derived from the classical heterogeneous nucleation theory

Precipitation of calcium oxalate hydrate by titration of acidified calcium nitrate solutions with potassium oxalate

The precipitation of calcium oxalate during the titration of acidified solutions of calcium nitrate with potassium oxalate was studied in the temperature range 13–69°C by monitoring changes in pH with time. A critical supersaturation ratio of 30 for incipient precipitation of the solid phase at 25°C was measured that proved to be independent of the titration speed or initial calcium concentration. With increasing temperature this critical supersaturation is observed to decrease. An analysis of the observed change in supersaturation with titration time at relatively high supersaturation, but under conditions where three-dimensional nucleation is not possible, indicates that the rate of growth of the precipitated phase, calcium oxalate monohydrate, varies with the relative supersaturation raised to the power 3.4. This empirical result is different from the observed parabolic rate law in seeded growth experiments and can be explained by a layer-by-layer growth mechanism based on a polynuclear, surface nucleation model.