112
5 Nucleation of Gas Hydrates
course, this usage of the terminology is how we have consistently applied in our past
publications. For clathrate hydrate nucleation, this effect is further compounded by
the limitation in the availability of the guest gas, as we will see in the next section.
Second, experimentally, nucleation rate is determined under the assumption that
only one supernucleus induces a nucleation event for the whole system. Even if
multiple nucleation events were to occur simultaneously, the resulting growth of the
thermodynamically stable phase from each nucleation site would merge with each
other and result in only one experimentally detectable phase transition. In short,
multiple simultaneous nucleation events would be counted as one event and the rest
would be effectively neglected. It is impossible to independently detect each of such
possible simultaneous nucleation events for the reasons we detailed in Chap. 2. The
consequent potential undercounting of nucleation events would lead to an underestimation of nucleation rates. In short, the “real” nucleation rate could have been higher
if each such individual nucleation event had been separately detectable.
Third, any cooperative phenomena would steer the system away from the totally
random Arrhenius behavior that forms the basis of classical nucleation theory [3].
Since classical nucleation theory is built on the random probabilistic nature of
surmounting of an activation energy barrier, as we detailed in Chap. 1, a presence of
cooperative phenomena in a system would invalidate the foundation of the applicability of classical nucleation theory. An extreme unrealistic case (yet another thought
experiment) will make this point abundantly clear: if the size distribution of the clusters were not of the Boltzmann form but uniform (independent of their sizes) then
no activation barrier would exist and no nucleation would be required for the phase
transition.
With these three general points in mind, we briefly review three aspects of ice
nucleation in this section; (1) physical properties of H 2 O, (2) nucleation of ice from
liquid water, and (3) nucleation of ice from water vapor.
5.1.2 Physical Properties of H 2 O
Water has many unusual attributes that could be relevant to nucleation of ice. H 2 O has
a non-zero entropy at 0 K [4]. The coordination number of H 2 O only changes from
about 4.0 to about 4.4 when ice melts [5], which shows that liquid water is highly
structured due to the hydrogen bonding. Each –OH bond is approximately 1/3 ionic
and 2/3 covalent in nature. Each H 2 O molecule in ice has four nearest neighbors and
acts as a hydrogen donor to two of them and acts as a hydrogen acceptor to the other
two. The H–O–H bond angle in the water molecule is very close to the tetrahedral
angle of 109.5° [6].
Many physical properties of subcooled water exhibit a pronounced temperature
dependence. Liquid water above 273 K expands and becomes more compressible as
it is cooled and becomes less viscous when compressed. Water’s unusual physical
properties at ambient conditions, such as the fact that it becomes less compressible
when heated, can be traced to more pronounced anomalies at lower temperatures
5 Nucleation of Gas Hydrates
course, this usage of the terminology is how we have consistently applied in our past
publications. For clathrate hydrate nucleation, this effect is further compounded by
the limitation in the availability of the guest gas, as we will see in the next section.
Second, experimentally, nucleation rate is determined under the assumption that
only one supernucleus induces a nucleation event for the whole system. Even if
multiple nucleation events were to occur simultaneously, the resulting growth of the
thermodynamically stable phase from each nucleation site would merge with each
other and result in only one experimentally detectable phase transition. In short,
multiple simultaneous nucleation events would be counted as one event and the rest
would be effectively neglected. It is impossible to independently detect each of such
possible simultaneous nucleation events for the reasons we detailed in Chap. 2. The
consequent potential undercounting of nucleation events would lead to an underestimation of nucleation rates. In short, the “real” nucleation rate could have been higher
if each such individual nucleation event had been separately detectable.
Third, any cooperative phenomena would steer the system away from the totally
random Arrhenius behavior that forms the basis of classical nucleation theory [3].
Since classical nucleation theory is built on the random probabilistic nature of
surmounting of an activation energy barrier, as we detailed in Chap. 1, a presence of
cooperative phenomena in a system would invalidate the foundation of the applicability of classical nucleation theory. An extreme unrealistic case (yet another thought
experiment) will make this point abundantly clear: if the size distribution of the clusters were not of the Boltzmann form but uniform (independent of their sizes) then
no activation barrier would exist and no nucleation would be required for the phase
transition.
With these three general points in mind, we briefly review three aspects of ice
nucleation in this section; (1) physical properties of H 2 O, (2) nucleation of ice from
liquid water, and (3) nucleation of ice from water vapor.
5.1.2 Physical Properties of H 2 O
Water has many unusual attributes that could be relevant to nucleation of ice. H 2 O has
a non-zero entropy at 0 K [4]. The coordination number of H 2 O only changes from
about 4.0 to about 4.4 when ice melts [5], which shows that liquid water is highly
structured due to the hydrogen bonding. Each –OH bond is approximately 1/3 ionic
and 2/3 covalent in nature. Each H 2 O molecule in ice has four nearest neighbors and
acts as a hydrogen donor to two of them and acts as a hydrogen acceptor to the other
two. The H–O–H bond angle in the water molecule is very close to the tetrahedral
angle of 109.5° [6].
Many physical properties of subcooled water exhibit a pronounced temperature
dependence. Liquid water above 273 K expands and becomes more compressible as
it is cooled and becomes less viscous when compressed. Water’s unusual physical
properties at ambient conditions, such as the fact that it becomes less compressible
when heated, can be traced to more pronounced anomalies at lower temperatures