28
1 Nucleation Theory
Or, equivalently, the amount of n-octadecane in mole in a unit surface area (1 m
2 )
is
(αN A )
−1
= 7.9 × 10
−6 mol · m
−2
(1.4.11)
Then, the latent heat of fusion of 1 m
2 of a surface monolayer of n-octadecane
can be calculated as
L surface = (44 kJ/mol) ×
7.9 × 10
−6 mol · m
−2
= 0.348 J · m
−2
(1.4.12)
Then, dS, the change of entropy of a surface monolayer of n-octadecane from solid
to liquid at T m (≈301 K) for unit area (1 m
2 ) can be calculated using Eq. (1.4–1.12)
as
dS = L surface /T m = 0.348 J · m
−2
/301K = 1.16 × 10
−3 J · K
−1
· m
−2
(1.4.13)
This value is very similar to the absolute value of the surface excess entropy 1
× 10
−3 J K
−1 m
−2 found in Eq. (1.4.7). The surface of n-octadecane is thus indeed
frozen below the surface freezing point and its thickness is monomolecular. Such
truly two-dimensional (2D) solid layers are rare in nature, and other than the normal
alkanes, only limited number of straight-chain alcohols are known to form such twodimensional (2D) solid layers. These analyses further augment the idea that the use
of macroscopic specific interfacial free energy terms and surface entropy values are
surprisingly accurate approximations.
1.4.4 Nucleation of Two-Dimensional (2D) Solid Layers
Now we are ready to discuss the nucleation of two-dimensional (2D) solid layers.
That surface freezing has been observed on both liquid n-alkane beds [17] and solid
substrates of silica [26] and mica [33] suggests that the effect of a solid substrate or
the liquid bed of n-alkanes underneath the frozen surface monolayer may not be as
important as the lateral cohesion within the monolayer. An exception can occur when
the van der Waals adhesion of the n-alkane monolayer to the underlying substrate is
stronger than the lateral cohesion within the monolayer. The strong adhesion between
the alkyl chains of n-alkanes and a graphite substrate was found to render n-alkane
chains lie parallel to a graphite substrate [34], in contrast to the surface freezing in
which each n-alkane chain stands perpendicular to the surface of the monolayer and
to the surface of the underlying foreign substrate.
Thus, we conclude that, as pointed out by Frederick Fowkes [35], the strength
of lateral cohesion between the methylene chains (CH 2 –CH 2 ) stabilizes the frozen
monolayer against thermal motion. In bulk crystals, cohesion within each layer
(CH 2 –CH 2 ) is stronger than the cohesion between the successive layers (CH 3 –CH 3 )
because of the higher energy for the methylene group, which follows from Zisman’s
1 Nucleation Theory
Or, equivalently, the amount of n-octadecane in mole in a unit surface area (1 m
2 )
is
(αN A )
−1
= 7.9 × 10
−6 mol · m
−2
(1.4.11)
Then, the latent heat of fusion of 1 m
2 of a surface monolayer of n-octadecane
can be calculated as
L surface = (44 kJ/mol) ×
7.9 × 10
−6 mol · m
−2
= 0.348 J · m
−2
(1.4.12)
Then, dS, the change of entropy of a surface monolayer of n-octadecane from solid
to liquid at T m (≈301 K) for unit area (1 m
2 ) can be calculated using Eq. (1.4–1.12)
as
dS = L surface /T m = 0.348 J · m
−2
/301K = 1.16 × 10
−3 J · K
−1
· m
−2
(1.4.13)
This value is very similar to the absolute value of the surface excess entropy 1
× 10
−3 J K
−1 m
−2 found in Eq. (1.4.7). The surface of n-octadecane is thus indeed
frozen below the surface freezing point and its thickness is monomolecular. Such
truly two-dimensional (2D) solid layers are rare in nature, and other than the normal
alkanes, only limited number of straight-chain alcohols are known to form such twodimensional (2D) solid layers. These analyses further augment the idea that the use
of macroscopic specific interfacial free energy terms and surface entropy values are
surprisingly accurate approximations.
1.4.4 Nucleation of Two-Dimensional (2D) Solid Layers
Now we are ready to discuss the nucleation of two-dimensional (2D) solid layers.
That surface freezing has been observed on both liquid n-alkane beds [17] and solid
substrates of silica [26] and mica [33] suggests that the effect of a solid substrate or
the liquid bed of n-alkanes underneath the frozen surface monolayer may not be as
important as the lateral cohesion within the monolayer. An exception can occur when
the van der Waals adhesion of the n-alkane monolayer to the underlying substrate is
stronger than the lateral cohesion within the monolayer. The strong adhesion between
the alkyl chains of n-alkanes and a graphite substrate was found to render n-alkane
chains lie parallel to a graphite substrate [34], in contrast to the surface freezing in
which each n-alkane chain stands perpendicular to the surface of the monolayer and
to the surface of the underlying foreign substrate.
Thus, we conclude that, as pointed out by Frederick Fowkes [35], the strength
of lateral cohesion between the methylene chains (CH 2 –CH 2 ) stabilizes the frozen
monolayer against thermal motion. In bulk crystals, cohesion within each layer
(CH 2 –CH 2 ) is stronger than the cohesion between the successive layers (CH 3 –CH 3 )
because of the higher energy for the methylene group, which follows from Zisman’s