24
1 Nucleation Theory
(C 44 H 90 ) and found the enthalpy of the surface freezing transition to be 142 J/g,
which is close to that of bulk freezing [18].
It has been known that long-chain liquid n-alkanes exhibit little bulk subcooling
when cooled from a high temperature before they begin to crystallize. It has been
suggested that surface freezing was responsible for this apparent absence of subcoolings of n-alkanes [19, 20]. The frozen surface monolayer has a similar structure and
density to those of the bulk rotator phase and forms a few Kelvins above T m . Then,
no further energy barrier would be required when the bulk rotator phase epitaxially grows from the already-present surface rotator phase as the system eventually
reaches T m . Although even-number alkanes form a bulk crystalline (triclinic) phase,
not a rotator phase, directly from the liquid phase at T m , the specific interfacial free
energy between the bulk rotator and the bulk crystalline phases of n-alkanes appears
very small [19]. It was reported that bulk crystallization of n-hexadecane indeed
proceeded via a transient bulk rotator phase [20]. A remarkable feature of surface
freezing is that such monomolecular thick two-dimensional solid layers exist above
the melting point in equilibrium, and its thickness remains constant as it is heated
from T m to T sf [16, 17]. We refer the readers to a comprehensive review article [21]
for details of experimental findings on surface freezing of normal alkanes.
Another important consequence of surface freezing is the absence of pre-melting
of long-chain n-alkanes below the bulk melting point, as noted in 1949 by Bradley
and Shellard [22]. As we will see in Chap. 4, the presence of pre-melting is of central
importance to the presence or absence of activation barrier and to nucleation of ice.
In short, both pre-melting of a solid surface and surface freezing of a liquid surface
are of central importance to nucleation of condensed phases. Below, we briefly cover
the theoretical background of surface freezing [21].
1.4.2 Estimation of the Contact Angle of Alkane Melt
on Frozen Alkane Monolayers
The central equation to set the criterion for surface freezing in terms of the specific
interfacial free energy is the Young equation [23]:
γ 1v cos θ = γ sv − γ s1
(1.4.1)
where the subscripts l, v, and s refer to liquid, vapor, and solid phases, respectively.
Formation of a solid-like monolayer must lower the free energy of the system for
surface freezing to materialize. Let us assume for the moment that the specific interfacial free energy of either side of the frozen monolayer can be expressed in terms
of the macroscopic (semi-infinite media) specific interfacial free energy. Then,
γ 1v > γ sv + γ s1
(1.4.2)
1 Nucleation Theory
(C 44 H 90 ) and found the enthalpy of the surface freezing transition to be 142 J/g,
which is close to that of bulk freezing [18].
It has been known that long-chain liquid n-alkanes exhibit little bulk subcooling
when cooled from a high temperature before they begin to crystallize. It has been
suggested that surface freezing was responsible for this apparent absence of subcoolings of n-alkanes [19, 20]. The frozen surface monolayer has a similar structure and
density to those of the bulk rotator phase and forms a few Kelvins above T m . Then,
no further energy barrier would be required when the bulk rotator phase epitaxially grows from the already-present surface rotator phase as the system eventually
reaches T m . Although even-number alkanes form a bulk crystalline (triclinic) phase,
not a rotator phase, directly from the liquid phase at T m , the specific interfacial free
energy between the bulk rotator and the bulk crystalline phases of n-alkanes appears
very small [19]. It was reported that bulk crystallization of n-hexadecane indeed
proceeded via a transient bulk rotator phase [20]. A remarkable feature of surface
freezing is that such monomolecular thick two-dimensional solid layers exist above
the melting point in equilibrium, and its thickness remains constant as it is heated
from T m to T sf [16, 17]. We refer the readers to a comprehensive review article [21]
for details of experimental findings on surface freezing of normal alkanes.
Another important consequence of surface freezing is the absence of pre-melting
of long-chain n-alkanes below the bulk melting point, as noted in 1949 by Bradley
and Shellard [22]. As we will see in Chap. 4, the presence of pre-melting is of central
importance to the presence or absence of activation barrier and to nucleation of ice.
In short, both pre-melting of a solid surface and surface freezing of a liquid surface
are of central importance to nucleation of condensed phases. Below, we briefly cover
the theoretical background of surface freezing [21].
1.4.2 Estimation of the Contact Angle of Alkane Melt
on Frozen Alkane Monolayers
The central equation to set the criterion for surface freezing in terms of the specific
interfacial free energy is the Young equation [23]:
γ 1v cos θ = γ sv − γ s1
(1.4.1)
where the subscripts l, v, and s refer to liquid, vapor, and solid phases, respectively.
Formation of a solid-like monolayer must lower the free energy of the system for
surface freezing to materialize. Let us assume for the moment that the specific interfacial free energy of either side of the frozen monolayer can be expressed in terms
of the macroscopic (semi-infinite media) specific interfacial free energy. Then,
γ 1v > γ sv + γ s1
(1.4.2)