126
5 Nucleation of Gas Hydrates
or more than 25 orders of magnitude larger than the experimentally derived kinetic
factor. In short, the frequency with which the system “attempts” to surmount the
activation barrier is 25–30 orders of magnitude lower in reality.
One way to account for this very large discrepancy between the theoretically calculated and the experimentally determined kinetic parameters is to assume a much
smaller “real” system size in which a small number of active nucleation sites are
concentrated than is expected from a uniform distribution of nucleation sites over
the nominal size that characterizes the system [54]. The basic idea is that dividing
the experimentally determined nucleation rate by a much smaller “real” system size
would lead to a much greater normalized nucleation rate. Then, dividing the experimentally determined nucleation rate by a much smaller “real” system size would
yield a much greater normalized nucleation rate.
If the locations of the potential nucleation sites were limited to the three-phase
lines, as we assumed, it would substantially lower the total number of potential nucleation sites in the system and hence would bring the agreement between the experimentally determined and theoretically expected kinetic factors closer. However, this
factor alone is unlikely to be sufficiently large to bridge the gap of more than 20
orders of magnitude [56]. If we assume that the relevant interfacial area in a quiescent sample is the length of the three-phase lines multiplied by the diffusive length
of the guest gas, that would lower the kinetic parameter by 4–5 orders of magnitude
[56]. Of course, we could further assume that the width of such a band in a quiescent
sample that can contribute to the nucleation of clathrate hydrate is narrower than the
diffusive length of the guest gas and bring the agreement still closer. This assumption could be warranted because nucleation rate exponentially falls with diminishing
supersaturation of the guest gas and the concentration gradient exists in a direction
perpendicular to the three-phase lines. However, there is a problem in this approach.
First of all, bridging of the discrepancy of more than 20 orders of magnitude
would require an unphysical assumption that the width of the band to be smaller than
the size of an atom. Second, we used nominal lengths of the three-phase lines for the
normalization of the nucleation rate that do not account for any surface roughness
that would render the “real” lengths of the three-phase lines much longer [48]. Such
longer “real” lengths of the three-phase lines would effectively render the “real”
system size larger, which would worsen the discrepancy.
Then there is the issue of silver iodide (AgI). Silver iodide is a salt of particular
interest in the context of nucleation although it is sparingly soluble in water. Silver
iodide is also not very hydrophilic (water still wets silver iodide: the contact angle
of water on AgI is about 15°). Sowa et al. reported that an addition of silver iodide
did not have appreciable impact on the nucleation probability of natural clathrate
hydrates [57]. Silver iodide is perceived to be an excellent nucleation agent of ice
due to its lattice matching and has long been used as a cloud seeding agent, and ice
has been considered to be an excellent nucleation agent of clathrate hydrates [58,
59]. The negative results of Sowa et al. thus suggest that either silver iodide is a
poor nucleation promotor of clathrate hydrates despite its lattice matching with ice
or a sufficient number of ubiquitous active nucleation sites already exist in a typical
clathrate hydrate system that would mask any additional effect of silver iodide. If a
5 Nucleation of Gas Hydrates
or more than 25 orders of magnitude larger than the experimentally derived kinetic
factor. In short, the frequency with which the system “attempts” to surmount the
activation barrier is 25–30 orders of magnitude lower in reality.
One way to account for this very large discrepancy between the theoretically calculated and the experimentally determined kinetic parameters is to assume a much
smaller “real” system size in which a small number of active nucleation sites are
concentrated than is expected from a uniform distribution of nucleation sites over
the nominal size that characterizes the system [54]. The basic idea is that dividing
the experimentally determined nucleation rate by a much smaller “real” system size
would lead to a much greater normalized nucleation rate. Then, dividing the experimentally determined nucleation rate by a much smaller “real” system size would
yield a much greater normalized nucleation rate.
If the locations of the potential nucleation sites were limited to the three-phase
lines, as we assumed, it would substantially lower the total number of potential nucleation sites in the system and hence would bring the agreement between the experimentally determined and theoretically expected kinetic factors closer. However, this
factor alone is unlikely to be sufficiently large to bridge the gap of more than 20
orders of magnitude [56]. If we assume that the relevant interfacial area in a quiescent sample is the length of the three-phase lines multiplied by the diffusive length
of the guest gas, that would lower the kinetic parameter by 4–5 orders of magnitude
[56]. Of course, we could further assume that the width of such a band in a quiescent
sample that can contribute to the nucleation of clathrate hydrate is narrower than the
diffusive length of the guest gas and bring the agreement still closer. This assumption could be warranted because nucleation rate exponentially falls with diminishing
supersaturation of the guest gas and the concentration gradient exists in a direction
perpendicular to the three-phase lines. However, there is a problem in this approach.
First of all, bridging of the discrepancy of more than 20 orders of magnitude
would require an unphysical assumption that the width of the band to be smaller than
the size of an atom. Second, we used nominal lengths of the three-phase lines for the
normalization of the nucleation rate that do not account for any surface roughness
that would render the “real” lengths of the three-phase lines much longer [48]. Such
longer “real” lengths of the three-phase lines would effectively render the “real”
system size larger, which would worsen the discrepancy.
Then there is the issue of silver iodide (AgI). Silver iodide is a salt of particular
interest in the context of nucleation although it is sparingly soluble in water. Silver
iodide is also not very hydrophilic (water still wets silver iodide: the contact angle
of water on AgI is about 15°). Sowa et al. reported that an addition of silver iodide
did not have appreciable impact on the nucleation probability of natural clathrate
hydrates [57]. Silver iodide is perceived to be an excellent nucleation agent of ice
due to its lattice matching and has long been used as a cloud seeding agent, and ice
has been considered to be an excellent nucleation agent of clathrate hydrates [58,
59]. The negative results of Sowa et al. thus suggest that either silver iodide is a
poor nucleation promotor of clathrate hydrates despite its lattice matching with ice
or a sufficient number of ubiquitous active nucleation sites already exist in a typical
clathrate hydrate system that would mask any additional effect of silver iodide. If a