104
4 Interfacial Gaseous States
rather consists of patches of droplets [45] is consistent with the larger than expected
specific interfacial free energy values between ice and water. Clathrate hydrates are
similar to ice in many aspects [60], however, the specific interfacial free energy
between a clathrate hydrate and water is expected to be somewhat higher than that
between ice and water because most guest gases are hydrophobic. In other words, the
specific interfacial free energy between hydrate and water is expected to be greater
than 33 mJ/m
2 .
The broad similarity between γ ice-w and γ hw suggests that the number of the
bonds that will be broken to create a unit area of new surface is expected to be
similar between ice and clathrate hydrates. This similarity may be expected given
that (1) the structures of ice and clathrate hydrates are similar and the similarity
includes the close lattice matching between ice and clathrate hydrate, and (2) the
guest molecules trapped in a clathrate hydrate are not chemically bonded to water
and only the chemical and the hydrogen bonds among the water molecules would
contribute to the interfacial free energy.
The specific surface free energy of clathrate hydrate, γ gh (for the clathrate hydrate–
gas interface), is experimentally difficult to measure due to surface roughness and
other experimental complications, and no estimate has been reported in the literature
to date. To be fair, we note that the specific surface free energy of ice has also
been difficult to measure. An estimate reported is around 130 mJ/m
2 [61] but the
value varies wildly depending on the experimental techniques used. For example, a
vacuum cleavage of ice yielded a very high specific surface energy of ice that is over
a thousand mJ/m
2 , which has been attributed to electrostatic charging of the cleaved
ice surfaces [62].
If we can assume that γ gh of a clathrate hydrate surface is similar to that of
ice (≈130 mJ/m
2 ), and noting that the specific interfacial free energy between ice
and water is about 30 mJ/m
2 and that the surface tension of water is 72 mJ/m
2 ,
then Eq. (4.3.1) yields G surf ≈ −28 mJ/m
2 , which is negative. Even if we assume
a somewhat higher specific interfacial free energy between clathrate hydrate and
water of 40 mJ/m
2 , G surf is still negative: ≈ –18 mJ/m
2 . G surf will become positive only when the specific interfacial free energy between clathrate hydrate and
water approaches 60 mJ/m
2 , which would be higher than the specific interfacial free
energy between a typical oil and water. On the other hand, if the specific surface
free energy of clathrate hydrate, γ gh , is much lower than that of ice of 130 mJ/m
2
then G surf could still become positive for a realistic specific interfacial free energy
between clathrate hydrate and water. Pre-melting is expected to occur when G surf
is sufficiently negative that offsets the free energy cost of dissociation of clathrate
hydrate, G fus , below the thermodynamic dissociation temperature. These analyses
suggest that pre-melting of clathrate hydrates is likely, at least for temperatures close
to the thermodynamic dissociation temperature.
As detailed in [18], the G surf gain is proportional to the surface area whereas the
G fus penalty is proportional to the mass or volume of the clathrate hydrate to be
dissociated as a result of pre-melting. G fus becomes proportional to the thickness
of the film if we only consider a unit surface area. We may denote the number density
of water as ρ and the thickness of the film as h. Then the volume of the pre-melting
film on ice over a unit surface area is h and G per unit area is
4 Interfacial Gaseous States
rather consists of patches of droplets [45] is consistent with the larger than expected
specific interfacial free energy values between ice and water. Clathrate hydrates are
similar to ice in many aspects [60], however, the specific interfacial free energy
between a clathrate hydrate and water is expected to be somewhat higher than that
between ice and water because most guest gases are hydrophobic. In other words, the
specific interfacial free energy between hydrate and water is expected to be greater
than 33 mJ/m
2 .
The broad similarity between γ ice-w and γ hw suggests that the number of the
bonds that will be broken to create a unit area of new surface is expected to be
similar between ice and clathrate hydrates. This similarity may be expected given
that (1) the structures of ice and clathrate hydrates are similar and the similarity
includes the close lattice matching between ice and clathrate hydrate, and (2) the
guest molecules trapped in a clathrate hydrate are not chemically bonded to water
and only the chemical and the hydrogen bonds among the water molecules would
contribute to the interfacial free energy.
The specific surface free energy of clathrate hydrate, γ gh (for the clathrate hydrate–
gas interface), is experimentally difficult to measure due to surface roughness and
other experimental complications, and no estimate has been reported in the literature
to date. To be fair, we note that the specific surface free energy of ice has also
been difficult to measure. An estimate reported is around 130 mJ/m
2 [61] but the
value varies wildly depending on the experimental techniques used. For example, a
vacuum cleavage of ice yielded a very high specific surface energy of ice that is over
a thousand mJ/m
2 , which has been attributed to electrostatic charging of the cleaved
ice surfaces [62].
If we can assume that γ gh of a clathrate hydrate surface is similar to that of
ice (≈130 mJ/m
2 ), and noting that the specific interfacial free energy between ice
and water is about 30 mJ/m
2 and that the surface tension of water is 72 mJ/m
2 ,
then Eq. (4.3.1) yields G surf ≈ −28 mJ/m
2 , which is negative. Even if we assume
a somewhat higher specific interfacial free energy between clathrate hydrate and
water of 40 mJ/m
2 , G surf is still negative: ≈ –18 mJ/m
2 . G surf will become positive only when the specific interfacial free energy between clathrate hydrate and
water approaches 60 mJ/m
2 , which would be higher than the specific interfacial free
energy between a typical oil and water. On the other hand, if the specific surface
free energy of clathrate hydrate, γ gh , is much lower than that of ice of 130 mJ/m
2
then G surf could still become positive for a realistic specific interfacial free energy
between clathrate hydrate and water. Pre-melting is expected to occur when G surf
is sufficiently negative that offsets the free energy cost of dissociation of clathrate
hydrate, G fus , below the thermodynamic dissociation temperature. These analyses
suggest that pre-melting of clathrate hydrates is likely, at least for temperatures close
to the thermodynamic dissociation temperature.
As detailed in [18], the G surf gain is proportional to the surface area whereas the
G fus penalty is proportional to the mass or volume of the clathrate hydrate to be
dissociated as a result of pre-melting. G fus becomes proportional to the thickness
of the film if we only consider a unit surface area. We may denote the number density
of water as ρ and the thickness of the film as h. Then the volume of the pre-melting
film on ice over a unit surface area is h and G per unit area is