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Noriaki Kubota - One of the best experts on this subject based on the ideXlab platform.
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Monte Carlo simulation of Induction Time and metastable zone width; stochastic or deterministic?
Journal of Crystal Growth, 2018Co-Authors: Noriaki KubotaAbstract:Abstract The Induction Time and metastable zone width (MSZW) measured for small samples (say 1 mL or less) both scatter widely. Thus, these two are observed as stochastic quantities. Whereas, for large samples (say 1000 mL or more), the Induction Time and MSZW are observed as deterministic quantities. The reason for such experimental differences is investigated with Monte Carlo simulation. In the simulation, the Time (under isothermal condition) and supercooling (under polythermal condition) at which a first single crystal is detected are defined as the Induction Time t and the MSZW ΔT for small samples, respectively. The number of crystals just at the moment of t and ΔT is unity. A first crystal emerges at random due to the intrinsic nature of nucleation, accordingly t and ΔT become stochastic. For large samples, the Time and supercooling at which the number density of crystals N/V reaches a detector sensitivity (N/V)det are defined as t and ΔT for isothermal and polythermal conditions, respectively. The points of t and ΔT are those of which a large number of crystals have accumulated. Consequently, t and ΔT become deterministic according to the law of large numbers. Whether t and ΔT may stochastic or deterministic in actual experiments should not be attributed to change in nucleation mechanisms in molecular level. It could be just a problem caused by differences in the experimental definition of t and ΔT.
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Analysis of the effect of volume on Induction Time and metastable zone width using a stochastic model
Journal of Crystal Growth, 2015Co-Authors: Noriaki KubotaAbstract:Abstract The effect of sample volume on Induction Time and metastable zone width (MSZW) is discussed theoretically by using a stochastic model. The effect of sample volume on Induction Time and MSZW is different depending on the detection criterion of nucleation used. The Induction Time and MSZW both decrease with an increase in sample volume when these values are determined on the basis of total number of crystals per sample N (an extensive variable). However, when the number density of crystals N / V (an intensive variable) is used, both of them remain unchanged even when the volume is changed. Although nucleation is stochastic by nature, the Induction Time and the MSZW, which are both nucleation-related, are not always observed as stochastic. In case of small samples, the stochastic aspects are usually observed, because a single crystal or a small number of crystals are used as a detection criterion of nucleation. Even for large samples, the stochastic aspect could be observed in theory. However, it is not usually the case in actual experiments because a small number of crystals are rather difficult to detect when the sample is large. The stochastic Induction Time and MSZW are mathematically related to the deterministic Induction Time and MSZW, respectively.
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Effects of detector sensitivity and resolution on Induction Time reading
CrystEngComm, 2014Co-Authors: Noriaki Kubota, Masanori Kobari, Izumi HirasawaAbstract:The effects of sensitivity and resolution of a nucleation detector on Induction Time were mathematically analysed. The Induction Time was defined here as the Time at which the number density of crystals nucleated under isothermal conditions had reached the minimum detectable number density of crystals (N/M)det. The value of (N/M)det depends on the detector used, and therefore can be called the detector sensitivity. Meanwhile, the detector resolution is defined as the minimum detectable crystal size Ld. The equation for Induction Time tind was derived for a simplified case wherein secondary nucleation and concentration reduction were both neglected. For a more general case where such a simplification cannot be made, the Induction Time tind was calculated numerically. The sensitivity and resolution had effects on Induction Time. The Induction Time increased as the sensitivity decreased (i.e., the value of (N/M)det increased). It also increased with a decrease in the resolution (i.e., an increase in the minimum detectable size Ld). The effect of nucleus size L0 on Induction Time tind was also analysed. The analysis suggested that the Induction Time in an actual experiment, where the minimum detectable size Ld would be much larger than the nucleus size L0, was independent of nucleus size itself but was affected by the resolution Ld. The interfacial energy of a crystal nucleus in solution that is deduced from the widely used plot of ln tindvs. 1/(ln S)2 (S: supersaturation ratio) was pointed out to be questionable. The effect of agitation rate (or stirrer speed) on Induction Time was also discussed.
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secondary nucleation mediated effects of stirrer speed and growth rate on Induction Time for unseeded solution
CrystEngComm, 2012Co-Authors: Masanori Kobari, Noriaki Kubota, Izumi HirasawaAbstract:Simulation of Induction Time for nucleation was performed under isothermal conditions for unseeded aqueous solutions of different concentrations. The effects of stirrer speed and growth rate on Induction Time were both explained with the proposed secondary nucleation-mediated mechanism. The effect of stirrer speed Nr was incorporated into the simulation with an empirical relation of kb2 ∝ Nrj, where kb2 is the coefficient in the secondary nucleation rate equation B2 = kb2 (ΔT)b2μ3, ΔT is supercooling, j and b2 are empirical constants and μ3 is the third moment of crystal size distribution. The simulated Induction Time decreased with an increase in stirrer speed at lower supercoolings, while it remained unchanged at higher supercoolings. Such action of stirrer speed was similar to that observed in the literature data. The growth rate effect was considered to be caused by a faster increase in the secondary nucleation rate via a faster increase in μ3. The simulated Induction Time decreased with an increase in crystal growth rate. This type of growth rate effect is completely different from the existing mechanism considering the Time needed for invisible nuclei to grow to a detectable size.
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Effect of sample volume on metastable zone width and Induction Time
Journal of Crystal Growth, 2012Co-Authors: Noriaki KubotaAbstract:Abstract The metastable zone width (MSZW) and the Induction Time, measured for a large sample (say>0.1 L) are reproducible and deterministic, while, for a small sample (say
J. L. Yordan - One of the best experts on this subject based on the ideXlab platform.
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Induction Time measurements for the quartz amine flotation system
Joint International Conference on Information Sciences, 1991Co-Authors: R H Yoon, J. L. YordanAbstract:Abstract An Induction Time apparatus which has a sensitivity limit of 100–150 μs has been constructed in the present work. The basic unit is similar to the one used by Eigeles and Volova and Trahar, but it operates with a microcomputer and has a greater sensitivity. Using this apparatus, the flotation chemistry of the quartz—amine system has been studied. It has been found that at a given dodecylaniminium hydrochloride concentration, the Induction Time is at a minimum at approximately pH 10.5. At this pH, the collector hydrolizes to form neutral amine and the flotation recovery reaches a maximum, suggesting that ionomolecular species are the surface-active species responsible for flotation. This finding confirms the earlier conclusions obtained using the surface tension and contact angle techniques. Induction Time measurements have also been conducted as a function of particle size, collector concentration, indifferent electrolyte concentration, bubble change, and temperature. The results are compared with flotation data, and the activation energy for the bubble—particle adhesion has been calculated.
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Induction Time measurements for the quartz—amine flotation system
Journal of Colloid and Interface Science, 1991Co-Authors: R H Yoon, J. L. YordanAbstract:Abstract An Induction Time apparatus which has a sensitivity limit of 100–150 μs has been constructed in the present work. The basic unit is similar to the one used by Eigeles and Volova and Trahar, but it operates with a microcomputer and has a greater sensitivity. Using this apparatus, the flotation chemistry of the quartz—amine system has been studied. It has been found that at a given dodecylaniminium hydrochloride concentration, the Induction Time is at a minimum at approximately pH 10.5. At this pH, the collector hydrolizes to form neutral amine and the flotation recovery reaches a maximum, suggesting that ionomolecular species are the surface-active species responsible for flotation. This finding confirms the earlier conclusions obtained using the surface tension and contact angle techniques. Induction Time measurements have also been conducted as a function of particle size, collector concentration, indifferent electrolyte concentration, bubble change, and temperature. The results are compared with flotation data, and the activation energy for the bubble—particle adhesion has been calculated.
Izumi Hirasawa - One of the best experts on this subject based on the ideXlab platform.
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Effects of detector sensitivity and resolution on Induction Time reading
CrystEngComm, 2014Co-Authors: Noriaki Kubota, Masanori Kobari, Izumi HirasawaAbstract:The effects of sensitivity and resolution of a nucleation detector on Induction Time were mathematically analysed. The Induction Time was defined here as the Time at which the number density of crystals nucleated under isothermal conditions had reached the minimum detectable number density of crystals (N/M)det. The value of (N/M)det depends on the detector used, and therefore can be called the detector sensitivity. Meanwhile, the detector resolution is defined as the minimum detectable crystal size Ld. The equation for Induction Time tind was derived for a simplified case wherein secondary nucleation and concentration reduction were both neglected. For a more general case where such a simplification cannot be made, the Induction Time tind was calculated numerically. The sensitivity and resolution had effects on Induction Time. The Induction Time increased as the sensitivity decreased (i.e., the value of (N/M)det increased). It also increased with a decrease in the resolution (i.e., an increase in the minimum detectable size Ld). The effect of nucleus size L0 on Induction Time tind was also analysed. The analysis suggested that the Induction Time in an actual experiment, where the minimum detectable size Ld would be much larger than the nucleus size L0, was independent of nucleus size itself but was affected by the resolution Ld. The interfacial energy of a crystal nucleus in solution that is deduced from the widely used plot of ln tindvs. 1/(ln S)2 (S: supersaturation ratio) was pointed out to be questionable. The effect of agitation rate (or stirrer speed) on Induction Time was also discussed.
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secondary nucleation mediated effects of stirrer speed and growth rate on Induction Time for unseeded solution
CrystEngComm, 2012Co-Authors: Masanori Kobari, Noriaki Kubota, Izumi HirasawaAbstract:Simulation of Induction Time for nucleation was performed under isothermal conditions for unseeded aqueous solutions of different concentrations. The effects of stirrer speed and growth rate on Induction Time were both explained with the proposed secondary nucleation-mediated mechanism. The effect of stirrer speed Nr was incorporated into the simulation with an empirical relation of kb2 ∝ Nrj, where kb2 is the coefficient in the secondary nucleation rate equation B2 = kb2 (ΔT)b2μ3, ΔT is supercooling, j and b2 are empirical constants and μ3 is the third moment of crystal size distribution. The simulated Induction Time decreased with an increase in stirrer speed at lower supercoolings, while it remained unchanged at higher supercoolings. Such action of stirrer speed was similar to that observed in the literature data. The growth rate effect was considered to be caused by a faster increase in the secondary nucleation rate via a faster increase in μ3. The simulated Induction Time decreased with an increase in crystal growth rate. This type of growth rate effect is completely different from the existing mechanism considering the Time needed for invisible nuclei to grow to a detectable size.
Sattar Ghader - One of the best experts on this subject based on the ideXlab platform.
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Interpreting the effect of operating variable, seed, and impurity on the Induction Time of silver nanoparticles precipitation by cluster coagulation models
2018Co-Authors: Negin Hatami, Sattar GhaderAbstract:This paper reports the effect of temperature, presence of impurity (Fe3+), and crystal seed on the Induction Time of silver nanoparticles. In this study, Ag precipitation was achieved by solution reduction and the experimental Induction Time was measured by monitoring the absorption of the solution after creation of supersaturation. Experimental Induction Time was compared to the cluster coagulation models (the Smoluchowski model and its’ variation cluster coagulation model) and the conclusion is that the conventional Smoluchowski coagulation model works better than the modified version.
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Induction Time of silver nanoparticles precipitation: Experiment and modeling
Crystal Research and Technology, 2009Co-Authors: N. Hatami, Sattar GhaderAbstract:This paper describes the measurement of Induction Time in precipitation of silver nanoparticles at different temperatures and supersaturations, and models it with Smoluchowski's coagulation theory. Silver nanoparticles are synthesized by reaction of silver nitrate with hydrazine in the presence of sodium citrate as stabilizer. The rate of association between clusters is found to depend on temperature and their sizes. The activation energy for the association between two clusters and interfacial tension of silver nanoparticles were also estimated. The results also show that Induction Time decreases with increasing supersaturation and temperature. (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
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Induction Time of Reaction Crystallization of Silver Nanoparticles
Chemical Engineering & Technology, 2007Co-Authors: Sattar Ghader, Mehrdad Manteghian, Mehrdad Kokabi, Rasool Sarraf MamooryAbstract:This paper describes the measurement of Induction Time in the reaction crystallization of silver nanoparticles at different temperatures and supersaturations, and compares it with classical nucleation theory. Silver nanoparticles are synthesized by a reaction of silver nitrate with hydrazine in the presence of sodium citrate as stabilizer. Induction Time is estimated from an absorption-Time graph obtained by monitoring the absorption of the solution after creation of supersaturation. The results show that Induction Time decreases with increasing supersaturation and temperature. The classical nucleation theory can well predict experimental data. Interfacial tension is estimated at different temperatures and compared with two correlations for calculation of interfacial tension.
Michael C. Weinberg - One of the best experts on this subject based on the ideXlab platform.
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Induction Time for crystal growth
Journal of Non-Crystalline Solids, 1994Co-Authors: Michael C. WeinbergAbstract:Abstract An expression is derived for the Induction Time for crystal growth. It is shown that this Induction Time is not uniquely determined, and is dependent on experimental conditions. Induction Time for crystal growth, unlike the Induction Time for nucleation, becomes unbounded if defined rigorously.
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Induction Time in transient nucleation theory
The Journal of Chemical Physics, 1992Co-Authors: Vitaly A. Shneidman, Michael C. WeinbergAbstract:We derive an exact expression for the Induction Time associated with the Zeldovich nucleation equation in terms of rapidly convergent integrals. Also, we consider an asymptotic approximation of the exact expression which is obtained in the limit of a high nucleation barrier and derive explicit formulas for several widely employed nucleation models. We demonstrate that analytical results are in excellent agreement with numerical results of the present and previous studies.
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Transient nucleation Induction Time from the birth-death equations
The Journal of Chemical Physics, 1992Co-Authors: Vitaly A. Shneidman, Michael C. WeinbergAbstract:For the set of finite‐difference equations of Becker–Doring an exact formula for the Induction Time, which is expressed in terms of rapidly convergent sums, is presented. The form of the result is particularly amenable for analytical study, and the latter is carried out to obtain approximations of the exact expression in a rigorous manner and to assess its sensitivity to the choice of the nucleation model. The Induction Time, tind, is found to be governed by two main nucleation parameters, Φ*/kT, the normalized barrier height, and g*, the number of molecules in the critical cluster. The ratio of these two parameters provides an assessment of the importance of discreteness effects. We study the exact expression in both the continuous (g*→∞) and the asymptotic (Φ*/kT→∞) limits. Asymptotic results for tind are compared with those previously reported from simulation studies as well as with tind obtained numerically from the exact expression in the present study. Also, the accuracy of the Zeldovich equation, w...