In a homogeneous multicomponent system, all extensive properties can be related by U =
U(S,V,N
i
,…N
r
,Q)
∂
U
∂
S
⎛
⎝
⎜
⎞
⎠
⎟
V
,
N
i
, ...,
N
r
,
Q
≡
T
∂
U
∂
V
⎛
⎝
⎜
⎞
⎠
⎟
S
,
N
i
, ...,
N
r
,
Q
≡−
P
∂
U
∂
N
i
⎛
⎝
⎜
⎞
⎠
⎟
V
,
S
,
Q
≡
µ
∂
U
∂
Q
⎛
⎝
⎜
⎞
⎠
⎟
S
,
N
i
,...,
N
r
,
V
≡
F
j
Where U is the internal energy, V is the volume, N
i
is the number of moles of species i, S is
entropy, and Q is charge.
We can focus in on the internal energy of a surface by assuming zero volume and zero moles on
the interface.
The intensive variables are defined as the partial derivatives of the internal energy with respect to
their conjugate extensive variables, with all other variables held constant. This is how we define
the interfacial surface tension
γ
LV
, interfacial chemical potential
µ
i
LV
, interfacial surface
temperature T
LV
, and interfacial electrical potential
φ
LV
.
The differential form of the interface internal energy can then be written for a liquidvapor
interface as the Gibbs dividing surface equation:
dU
LV
= T
LV
dS
LV
+
γ
LV
dA
LV
+
Σµ
i
LV
dN
i
LV
+
φ
LV
dQ
LV
Rearranging, we obtain the Gibbs Absorption Equation:
γ
LV
= SdT
LV

ΣΓ
i
d
µ
i
LV
 q
LV
d
φ
LV
Here,
Γ
is the surface fraction due to nonadsorbed chains.
The total entropy of the system is the sum of the entropies of the liquid phase, the vapor phase,