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sat).
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77953164699
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-a d a is the gamma function.
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Note
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This manuscript follows the common practice of writing nucleation kinetics in terms of a relative supersaturation defined in terms of concentrations. Strictly speaking, the driving force for nucleation should be written in terms of the chemical potential difference or a ratio of activities of the substance in the solid and liquid states; for example, see Mullin, J. W.; Sohnel, O. Chem. Eng. Sci. 1977, 32, 683, which can be important at high solute concentrations. The stochastic model and associated analysis are valid for nucleation kinetics written in terms of chemical potential, activities, or absolute supersaturation, with obvious modifications
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a is the diffusion activation energy
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68149171797
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For variation in the surface energy and/or diffusion activation energy during an experiment (such as in
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0347308440
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the variation on temperature and/or solute concentration would be included explicitly, which would be written as a function of time for each drop as computed from mass and/or energy conservation equations.
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Bhamidi, V.; Varanasi, S.; Schall, C. A. Cryst. Growth Des. 2002, 2, 395), the variation on temperature and/or solute concentration would be included explicitly, which would be written as a function of time for each drop as computed from mass and/or energy conservation equations.
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77950553955
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The model and analysis apply to other nucleation expressions as well, and to systems in which the overall nucleation rate decreases with time due to partial rehydration of the droplet (such as in;;;;;) or the nucleation rate decreases with increased solute concentration. The latter could occur, for example, due to the formation of a glassy state.
-
The model and analysis apply to other nucleation expressions as well, and to systems in which the overall nucleation rate decreases with time due to partial rehydration of the droplet (such as in Talreja, S.; Perry, S. L.; Guha, S.; Bhamidi, V.; Zukoski, C. F.; Kenis, P. J. A. J. Phys. Chem. B 2010, 114, 4432) or the nucleation rate decreases with increased solute concentration. The latter could occur, for example, due to the formation of a glassy state.
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Because of the low number of parameters, Eq 21 was solved by gridding over the model parameters A and B.
-
Because of the low number of parameters, Eq 21 was solved by gridding over the model parameters A and B.
-
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58
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-
77953153575
-
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Note
-
The mean induction time (13) was numerically computed using the Matlab quad problem to find the value of inner integral and trapz to find the value of the outer integral, as well as by solving an equivalent system of two ordinary diffusion equations (ODEs) using ode45; one ODE for the inner integral and the second ODE for the outer integral. The same numerical method used for finding the mean can be used to determine the variance (15).
-
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59
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77953160830
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Note
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a as a function of the solute concentration.
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