Chemistry Reference
In-Depth Information
where
µ
n
represent the vapour and nuclei chemical potentials, respectively.
The chemical potential expresses the work associated with changing the number of
particles in the phase, vapour or solid.
µ
v
and
, also called supersaturation, appears as
the thermodynamic driving force of the crystallization process.
µ
γ
and
γ
⊥
denote the
interfacial energies per unit area (in units of J m
−
2
Nm
−
1
) of planes parallel and
=
perpendicular to the substrate surface, respectively.
γ
is the variation of the free
energy per unit area of the substrate interface associated with the replacement of
the substrate/vapour interface with free energy
γ
sv
by the substrate/nucleus (
γ
ns
)
γ
is given by the expression
γ
=
γ
nv
+
γ
ns
−
γ
sv
, making patent this balance, and can be expressed via the
specific free energy of adhesion
γ
nv
) interfaces. The value of
and nucleus/vapour (
γ
ad
. This magnitude represents the work per unit in-
terface area that has to be performed in order to achieve reversible isothermal separa-
tion of the nucleus from the substrate.
γ
can be expressed as
γ
=
2
γ
nv
−
γ
ad
since
γ
ad
=
γ
nv
+
γ
sv
−
γ
ns
. When the adhesion is strong (weak),
γ
<
0
(
γ
>
0), leading to complete (incomplete) wetting.
γ
⊥
=
3
γ
⊥
nv
+
γ
⊥
n
σ
−
γ
⊥
σ
v
, where
γ
⊥
σ
v
represent the nucleus edge/vapour, nucleus edge/
step and step/vapour interface tensions, respectively. The factor 3 results from the
choice of nucleus shape, in this case a parallelepiped, and is thus model-dependent.
Values of
γ
⊥
nv
,
γ
⊥
n
σ
and
1Jm
−
2
) (Northrup
et al
., 2002; Verlaak
et al
., 2003). According to first-principles pseudopotential DFT
calculations (Northrup
et al
., 2002) the (001) surface of pentacene is found to be
the lowest in energy, having a formation energy of 0.15 eV per surface unit cell.
This translates into a surface energy
γ
nv
for several MOMs lie below 0.7 eV nm
−
2
(
∼
0
.
γ
nv
of 0.31 eV nm
−
2
. On the other hand the
(010) surface of pentacene has a formation energy of 0.75 eV per surface unit cell,
corresponding to 0.64 eV nm
−
2
. Inorganic solids exhibit surface energies of the
order of 5-10 eV nm
−
2
.
Equation (5.1) describes the size effects associated with the presence of a finite
nucleus and reflects the balance between bulk and surface contributions. The lim-
iting case
L
represents the ideal formation of a film under complete wetting.
The convention is that the system evolves towards negative values of
G
. When
G
→∞
0 the interface term dominates over the bulk term (low
L
values) while the op-
posite situation is found for
G
>
<
0 (higher
L
values). Under the condition
∂
G
/∂
L
=
0,
G
c
and the critical length
L
c
of nucleation, are given by the expressions:
h
2
4
2
⊥
γ
G
c
=
h
µ
−
γ
,
(5.2a)
h
2
γ
⊥
L
c
=
µ
−
γ
.
(5.2b)
h
