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1 Nucleation Theory
spontaneous emulsifications in the presence and in the absence of dissolved atmospheric gases, in which the nucleation became more homogeneous after the removal
of dissolved atmospheric gases. In short, removal of dissolved atmospheric gases
resulted in larger numbers of smaller and more uniformly sized droplets [15].
The larger numbers of smaller and more uniformly sized droplets after degassing
suggest that the nucleation of the oil droplets after degassing became more homogeneous in nature, which underscores our point that ubiquitous atmospheric gases
should be regarded as impurities that offer potential heterogeneous nucleation sites
for spontaneous emulsification. Removal of any impurities that could act as heterogeneous nucleation sites is expected to allow further diffusion of the oil-in-ethanol
solution into the aqueous phase before the oil precipitates out of the aqueous phase.
Such enhanced diffusion of the oil-in-ethanol solution not only would distribute the
oil over a larger space in the aqueous phase but also would help attain a higher
supersaturation of the oil in the aqueous solution.
For a sufficiently large supersaturation of the oil, the driving force for precipitation
may approach that of the homogeneous nucleation. In this situation, the Boltzmann
distribution of the clusters of the oil molecules may show that the driving force is
so large that the probability of finding a critically sized cluster is significant. Then,
any small fluctuations in the concentration of the oil molecules that can perturb
the Boltzmann distribution may trigger the homogeneous nucleation. An important
consequence of formation of a nucleus is depletion of the oil monomers from its
surroundings (because they are used up for the formation of said nucleus). Then, the
next nearest homogeneous nucleation can only occur some distance away from an
existing nucleus where the concentration of the oil molecules has not depleted. The
end result is that homogeneous nucleation results in the formation of larger numbers
of smaller oil droplets that are spatially more uniformly distributed compared to
emulsions formed by heterogeneous nucleation. In short, the spontaneous emulsification before degassing is still heterogeneous nucleation, with the dissolved gases
acting as heterogeneous nucleation sites, and the spontaneous emulsification after
degassing is closer to “truly” homogeneous nucleation as a result of reaching the
spinodal limit.
Thus, an important conclusion of this section is that “truly” homogeneous nucleation might never occur in a natural system given that even ubiquitous dissolved
atmospheric gases (mainly nitrogen gas) can make a measurable difference to homogeneous nucleation of oil droplets in water. In other words, homogeneous nucleation
rates of a given system reported in the literature could be overestimated by a significant margin, i.e., “true” homogeneous nucleation would require a greater supersaturation and “true” nucleation rates would be lower than what has been reported
for a given supersaturation.
Other than the general point made above, the implications of these results to
the nucleation of clathrate hydrates are fairly clear. In a multi-component system,
nucleation of solutes will deplete solute monomers from the surrounding solution,
which will in turn lower the chemical potential of the solute monomers. It follows that
homogeneous nucleation of the solutes or its crystal growth cannot proceed without
timely replenishment of the solute monomers to the depleted region of the system.
1 Nucleation Theory
spontaneous emulsifications in the presence and in the absence of dissolved atmospheric gases, in which the nucleation became more homogeneous after the removal
of dissolved atmospheric gases. In short, removal of dissolved atmospheric gases
resulted in larger numbers of smaller and more uniformly sized droplets [15].
The larger numbers of smaller and more uniformly sized droplets after degassing
suggest that the nucleation of the oil droplets after degassing became more homogeneous in nature, which underscores our point that ubiquitous atmospheric gases
should be regarded as impurities that offer potential heterogeneous nucleation sites
for spontaneous emulsification. Removal of any impurities that could act as heterogeneous nucleation sites is expected to allow further diffusion of the oil-in-ethanol
solution into the aqueous phase before the oil precipitates out of the aqueous phase.
Such enhanced diffusion of the oil-in-ethanol solution not only would distribute the
oil over a larger space in the aqueous phase but also would help attain a higher
supersaturation of the oil in the aqueous solution.
For a sufficiently large supersaturation of the oil, the driving force for precipitation
may approach that of the homogeneous nucleation. In this situation, the Boltzmann
distribution of the clusters of the oil molecules may show that the driving force is
so large that the probability of finding a critically sized cluster is significant. Then,
any small fluctuations in the concentration of the oil molecules that can perturb
the Boltzmann distribution may trigger the homogeneous nucleation. An important
consequence of formation of a nucleus is depletion of the oil monomers from its
surroundings (because they are used up for the formation of said nucleus). Then, the
next nearest homogeneous nucleation can only occur some distance away from an
existing nucleus where the concentration of the oil molecules has not depleted. The
end result is that homogeneous nucleation results in the formation of larger numbers
of smaller oil droplets that are spatially more uniformly distributed compared to
emulsions formed by heterogeneous nucleation. In short, the spontaneous emulsification before degassing is still heterogeneous nucleation, with the dissolved gases
acting as heterogeneous nucleation sites, and the spontaneous emulsification after
degassing is closer to “truly” homogeneous nucleation as a result of reaching the
spinodal limit.
Thus, an important conclusion of this section is that “truly” homogeneous nucleation might never occur in a natural system given that even ubiquitous dissolved
atmospheric gases (mainly nitrogen gas) can make a measurable difference to homogeneous nucleation of oil droplets in water. In other words, homogeneous nucleation
rates of a given system reported in the literature could be overestimated by a significant margin, i.e., “true” homogeneous nucleation would require a greater supersaturation and “true” nucleation rates would be lower than what has been reported
for a given supersaturation.
Other than the general point made above, the implications of these results to
the nucleation of clathrate hydrates are fairly clear. In a multi-component system,
nucleation of solutes will deplete solute monomers from the surrounding solution,
which will in turn lower the chemical potential of the solute monomers. It follows that
homogeneous nucleation of the solutes or its crystal growth cannot proceed without
timely replenishment of the solute monomers to the depleted region of the system.