On some probabilistic aspects of the nucleation process

Nucleation of lysozyme crystals in quiescent solutions at a regime of progressive nucleation is investigated under an optical microscope at conditions of constant supersaturation. A method based on the stochastic nature of crystal nucleation and using discrete time sampling of small solution volumes for the presence or absence of detectable crystals is developed. It allows probabilities for crystal detection to be experimentally estimated. One hundred single samplings were used for each probability determination for 18 time intervals and six lysozyme concentrations. Fitting of a particular probability function to experimentally obtained data made possible the direct evaluation of stationary rates for lysozyme crystal nucleation, the time for growth of supernuclei to a detectable size and probability distribution of nucleation times. Obtained stationary nucleation rates were then used for the calculation of other nucleation parameters, such as the kinetic nucleation factor, nucleus size, work for nucleus formation and effective specific surface energy of the nucleus. The experimental method itself is simple and adaptable and can be used for crystal nucleation studies of arbitrary soluble substances with known solubility at particular solution conditions.

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“…As nuclei appear randomly in time, the probability P to form at least one supernucleus until time t is given by [2][3][4]7]:…”

Section: Theoretical Basismentioning

confidence: 99%

“…Relevant probabilistic approaches have already been used in nucleation studies of water [2], tin [3], electrocrystallization of mercury [4], amino acids [5], and isonicotinamide [5,6] in stirred solutions.…”

mentioning

confidence: 99%

Probabilistic approach to lysozyme crystal nucleation kinetics

2015

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“…Note that To.s differs from the mean time Tn = IIJS of nucleation, as pointed out by Toshev et al (30) The time lapse To.s can be determined at different overpotentials. Figure 5 shows a In J vs. I/'T1c plot of data obtained in this way.…”

Section: The Experimental Investigation Of the Kinetics Of Twodimensimentioning

confidence: 96%

“…The shape of the i-t curves obviously follows the growth and decay of the peripheral edge of the spreading monolayer growing over and out of the face boundaries. (25)(26)(27) In the beginning, before the step has reached the face boundaries, the current should follow the linear law (30) where b is the same geometrical factor defined previously in Section 3.1.1. From the slope (di/ dt)t=o, the propagation velocity v of the step can be evaluated if the geometrical form of the spreading layer is known.…”

Section: The Experimental Determination Of the Rate Of Step Propagationmentioning

confidence: 99%

Deposition and Dissolution of Metals and Alloys. Part A: Electrocrystallization

Budevski

1983

Comprehensive Treatise of Electrochemistry

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“…Previous research on hydrate nucleation has in general reached the same conclusion that compared to hydrate growth, nucleation is a stochastic process. As has been pointed out in the literature [11], "Stochastic Nucleation" has very rich meanings. Not only the number of nuclei formed in a saturated solution within a certain period of time is stochastic, but the time point for the first nuclei to appear is unpredictable.…”

Section: Introductionmentioning

confidence: 99%

The Effect of Molar Liquid Water-Gas Ratio on Methane Hydrate Formation

Ke¹,

Svartaas²

2013

JMSE-B

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Experimental results and analysis among different hydrate research groups are very often not transplantable, partly due to the intrinsic stochastic nature of hydrate formation, partly due to different experimental conditions, gas compositions and analyzing techniques used or applied. In the present work the effect of the molar liquid water-gas ratio (γ m ) on both nucleation and growth of methane hydrate has been examined. Structure I methane hydrates were formed under isochoric conditions in stirred cell during constant cooling, and the point of spontaneous nucleation (PSN) was recorded. The results show that change of γ m gave no significant effect on average induction time, average nucleation rate or average sub-cooling at PSN. Nevertheless, nucleation behaved more stochastic when the volume fraction of water and γ m increased. Moderate γ m values that were closer to the theoretical hydration number (5.9 to 6 at the experimental conditions) could achieve larger total gas consumption and higher hydrate formation rate. "Imbalanced" γ m values (either highly water-excess or highly gas-excess) may however lead to smoother behavior of crystal growth.

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On some probabilistic aspects of the nucleation process

Cited by 125 publications

References 4 publications

Probabilistic approach to lysozyme crystal nucleation kinetics

Probabilistic approach to lysozyme crystal nucleation kinetics

Deposition and Dissolution of Metals and Alloys. Part A: Electrocrystallization

The Effect of Molar Liquid Water-Gas Ratio on Methane Hydrate Formation

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