5.3 The Memory Effect
135
large that they may detach from the substrate due to buoyancy and be removed from
the system.
Shinoda showed that freezing of a non-gaseous, non-polar solute in a binary
solution decreased the solubility of the solute whereas freezing of the solvent (such
as ordering of water around non-polar solutes) in a binary solution increased the
solubility of the solute [81]. Consequently, the solubility of a non-gaseous, nonpolar
solute does not monotonically increase with heating but becomes rather constant
with temperature between the melting point of water and room temperature [81].
Although this mechanism also applies to gaseous, non-polar solutes in water, the
solubility of a gas in a liquid usually decreases with heating because the entropy of
the solute molecule is expected to be much greater in the gaseous state than in the
dissolved state and that the entropic contribution to the system free energy increases
with temperature. The effect of ordering of water around nonpolar solutes thus makes
the solubility of nonpolar liquid solutes to be rather temperature independent, but
the solubility of nonpolar gaseous solutes in water surely decreases with heating in
this temperature range. Methane, whose critical pressure of about 4.6 MPa, might
behave a gaseous solute or a liquid solute depending on the pressure.
The solubility of inert gases such as rare gases in water typically reaches a
minimum at around 300 K and then increases with heating at higher temperatures
[82–84]. At elevated pressures for which clathrate hydrate formation is possible, the
solubility of methane in water decreases with heating up to at least 313 K for the
pressures of up to 15 MPa [85]. On the other side, the solubility of methane in water
starts increasing with heating above 71 °C (344 K) for pressures greater than 20 MPa
[86]. Unfortunately, the precise location of the minimum is not clear in the literature
that reported the solubility of a guest gas in water at elevated pressures.
Meanwhile, the thermodynamic equilibrium dissociation temperature of clathrate
hydrate depends on the guest composition and the system pressure and is up to about
300 K [27]. Up until the temperature at which the solubility becomes a minimum,
the solubility of the guest gas decreases with heating. The interfacial gaseous states
will not go away while the solubility of the guest gas in the surrounding aqeueous
phase keeps falling. Above the expected minimum solubility temperature, however,
any further heating will cause the solubility of the guest gas in water to increase.
The interfacial gaseous states will then be deflated as the guest gas contained therein
will be dissolved into the surrounding aqueous phase. Therefore, heating to above
the expected solubility minimum of the guest gas would be required to erase the
memory effect. That the expected minimum solubility temperature of a typical guest
gas appears to be slightly higher than the thermodynamic equilibrium dissociation
temperature of clathrate hydrate renders the interfacial gaseous states hypothesis still
more plausible.
Another potential remaining loose end of the interfacial gaseous states hypothesis
could be that the memory effect was reported to occur in melted water from ice
that has no history of clathrate hydrate formation [62]. How can interfacial gaseous
states influence the memory effect of melted ice with no history of clathrate hydrate
formation? The answer might lie in the fact that freezing effectively degasses water
(i.e., it is impossible to freeze water without degassing it) [87].
135
large that they may detach from the substrate due to buoyancy and be removed from
the system.
Shinoda showed that freezing of a non-gaseous, non-polar solute in a binary
solution decreased the solubility of the solute whereas freezing of the solvent (such
as ordering of water around non-polar solutes) in a binary solution increased the
solubility of the solute [81]. Consequently, the solubility of a non-gaseous, nonpolar
solute does not monotonically increase with heating but becomes rather constant
with temperature between the melting point of water and room temperature [81].
Although this mechanism also applies to gaseous, non-polar solutes in water, the
solubility of a gas in a liquid usually decreases with heating because the entropy of
the solute molecule is expected to be much greater in the gaseous state than in the
dissolved state and that the entropic contribution to the system free energy increases
with temperature. The effect of ordering of water around nonpolar solutes thus makes
the solubility of nonpolar liquid solutes to be rather temperature independent, but
the solubility of nonpolar gaseous solutes in water surely decreases with heating in
this temperature range. Methane, whose critical pressure of about 4.6 MPa, might
behave a gaseous solute or a liquid solute depending on the pressure.
The solubility of inert gases such as rare gases in water typically reaches a
minimum at around 300 K and then increases with heating at higher temperatures
[82–84]. At elevated pressures for which clathrate hydrate formation is possible, the
solubility of methane in water decreases with heating up to at least 313 K for the
pressures of up to 15 MPa [85]. On the other side, the solubility of methane in water
starts increasing with heating above 71 °C (344 K) for pressures greater than 20 MPa
[86]. Unfortunately, the precise location of the minimum is not clear in the literature
that reported the solubility of a guest gas in water at elevated pressures.
Meanwhile, the thermodynamic equilibrium dissociation temperature of clathrate
hydrate depends on the guest composition and the system pressure and is up to about
300 K [27]. Up until the temperature at which the solubility becomes a minimum,
the solubility of the guest gas decreases with heating. The interfacial gaseous states
will not go away while the solubility of the guest gas in the surrounding aqeueous
phase keeps falling. Above the expected minimum solubility temperature, however,
any further heating will cause the solubility of the guest gas in water to increase.
The interfacial gaseous states will then be deflated as the guest gas contained therein
will be dissolved into the surrounding aqueous phase. Therefore, heating to above
the expected solubility minimum of the guest gas would be required to erase the
memory effect. That the expected minimum solubility temperature of a typical guest
gas appears to be slightly higher than the thermodynamic equilibrium dissociation
temperature of clathrate hydrate renders the interfacial gaseous states hypothesis still
more plausible.
Another potential remaining loose end of the interfacial gaseous states hypothesis
could be that the memory effect was reported to occur in melted water from ice
that has no history of clathrate hydrate formation [62]. How can interfacial gaseous
states influence the memory effect of melted ice with no history of clathrate hydrate
formation? The answer might lie in the fact that freezing effectively degasses water
(i.e., it is impossible to freeze water without degassing it) [87].