5.2 Nucleation Rate of Gas Hydrates
117
experimental techniques detailed in Chap. 2 can be applied to the investigations of
nucleation of clathrate hydrates.
5.2.1 Unique Attributes of Gas Hydrate Nucleation
We start from highlighting the unique attributes of clathrate hydrate nucleation
that are different from ice nucleation. Clathrate hydrate is, by definition, a multicomponent system. The concentrations of a guest gas that can be contained inside
clathrate hydrate are many orders of magnitude higher than the solubility of the
same gas in liquid water at the same pressure and temperature. This much greater
gas contents in the clathrate form than the solubility of the same guest gas in liquid
water renders clathrate hydrate thermodynamically stable at temperatures higher than
the ice point of around 273 K, as we saw in Chap. 3. However, this essential feature
of clathrate hydrates inevitably leads to the fact that the concentration of the guest
gas in the aqueous phase is not uniform but has a spatial gradient that becomes the
highest at the guest–aqueous interface, under a static, isothermal and isobaric condition. Stirring of the aqueous phase and turbulent flows could somewhat mitigate the
steepness of the spatial concentration gradient of the guest gas in water but a spatial
concentration gradient nevertheless remains. A salient point here is that the driving
force for nucleation is implicitly assumed to be spatially uniform throughout the
metastable phase in Eq. (1.2.4), but this is clearly not the case for clathrate hydrates.
Whether such an intrinsic spatial inhomogeneity within a system under thermodynamic equilibrium can be treated by assuming local equilibria in different sections
of the system remains an unresolved issue [21].
This inevitable spatial concentration gradient of a guest gas in liquid water and
the resulting spatial gradient in the driving force for nucleation have important implications to the nucleation rate of clathrate hydrates. The supersaturation and hence
the driving force for nucleation becomes the greatest (i.e., G* activation in Eq. (1.2.6)
becomes the smallest) at a guest–aqueous interface and diminishes (i.e., G* activation
increases) with the distance from the interface. The exponential dependence of the
nucleation rate to G* activation in Eq. (1.2.6) thus means that homogeneous nucleation
in the conventional sense cannot occur for clathrate hydrates because the nucleation
rate exponentially diminishes as one moves away from the interface.
Even for a single-component system that has a spatially uniform driving force,
it has been postulated that homogeneous nucleation of a crystal from a liquid of
a finite size preferentially occurs at the liquid–vapor interface where the system
symmetry breaks [1, 2]. It follows that the homogeneous nucleation rate scales not
with the system volume but with the interfacial area in many systems [1, 2]. Then,
strictly speaking, “truly” homogeneous nucleation (i.e., nucleation is equally likely
throughout the system volume) can only occur in an infinitely large system. For ice,
it has been known that the so-called “contact nucleation” (heterogeneous nucleation
of ice in the presence of a solid wall at an air–liquid interface) is more efficient than
“immersion nucleation” (heterogeneous nucleation of ice in the presence of a solid
117
experimental techniques detailed in Chap. 2 can be applied to the investigations of
nucleation of clathrate hydrates.
5.2.1 Unique Attributes of Gas Hydrate Nucleation
We start from highlighting the unique attributes of clathrate hydrate nucleation
that are different from ice nucleation. Clathrate hydrate is, by definition, a multicomponent system. The concentrations of a guest gas that can be contained inside
clathrate hydrate are many orders of magnitude higher than the solubility of the
same gas in liquid water at the same pressure and temperature. This much greater
gas contents in the clathrate form than the solubility of the same guest gas in liquid
water renders clathrate hydrate thermodynamically stable at temperatures higher than
the ice point of around 273 K, as we saw in Chap. 3. However, this essential feature
of clathrate hydrates inevitably leads to the fact that the concentration of the guest
gas in the aqueous phase is not uniform but has a spatial gradient that becomes the
highest at the guest–aqueous interface, under a static, isothermal and isobaric condition. Stirring of the aqueous phase and turbulent flows could somewhat mitigate the
steepness of the spatial concentration gradient of the guest gas in water but a spatial
concentration gradient nevertheless remains. A salient point here is that the driving
force for nucleation is implicitly assumed to be spatially uniform throughout the
metastable phase in Eq. (1.2.4), but this is clearly not the case for clathrate hydrates.
Whether such an intrinsic spatial inhomogeneity within a system under thermodynamic equilibrium can be treated by assuming local equilibria in different sections
of the system remains an unresolved issue [21].
This inevitable spatial concentration gradient of a guest gas in liquid water and
the resulting spatial gradient in the driving force for nucleation have important implications to the nucleation rate of clathrate hydrates. The supersaturation and hence
the driving force for nucleation becomes the greatest (i.e., G* activation in Eq. (1.2.6)
becomes the smallest) at a guest–aqueous interface and diminishes (i.e., G* activation
increases) with the distance from the interface. The exponential dependence of the
nucleation rate to G* activation in Eq. (1.2.6) thus means that homogeneous nucleation
in the conventional sense cannot occur for clathrate hydrates because the nucleation
rate exponentially diminishes as one moves away from the interface.
Even for a single-component system that has a spatially uniform driving force,
it has been postulated that homogeneous nucleation of a crystal from a liquid of
a finite size preferentially occurs at the liquid–vapor interface where the system
symmetry breaks [1, 2]. It follows that the homogeneous nucleation rate scales not
with the system volume but with the interfacial area in many systems [1, 2]. Then,
strictly speaking, “truly” homogeneous nucleation (i.e., nucleation is equally likely
throughout the system volume) can only occur in an infinitely large system. For ice,
it has been known that the so-called “contact nucleation” (heterogeneous nucleation
of ice in the presence of a solid wall at an air–liquid interface) is more efficient than
“immersion nucleation” (heterogeneous nucleation of ice in the presence of a solid