Physical Chemistry
Lecture 22
Surface Phases
Phase equilibrium
Describes the molar energy needed for
a system to exist at certain conditions
Equilibrium between phases described
by equality of chemical potentials
µ
α
= µ
β
Surface tension
The properties of molecules near a surface are
different from those in the bulk
Account for the different energies at the
surface by work of creating the surface
dU
= TdS
− PdV
+ γdA
γ is the surface tension, the work to create a
unit surface area
Free-energy changes
dAHelmholtz
= − SdT
dG = − SdT
− PdV
+ γdA
+ VdP + γdA
Surface tension of various
a
liquids against air at 20°C
Liquid
γ (dyne/cm)b
Liquid
γ (dyne/cm)b
Isopropanol
21.7
Benzene
28.9
Methanol
22.6
m-Xylene
28.9
Ethanol
22.8
o-Xylene
30.1
Isobutanol
23.0
Ethylbenzene
29.2
Acetone
23.7
Chlorobenzene
33.6
n-Propanol
23.8
Pyridine
38.0
n-Butanol
24.6
Bromine
40.9
p-Xylene
28.4
Water
72.8
Toluene
28.5
Mercury
a
435.
Source: R. C. Weast and M. J. Astle, Eds., CRC Handbook of Physics and Chemistry, 63rd Edition, CRC
Press, Boca Raton, Florida, 1982.
b
1 dyne/cm = 1erg/cm2 = 10-3joule/m2 = 10-3 N/m = 10-3 Pa-m
Thermodynamics of surfaces
Surface tension is a derivative
γ
 ∂U 
= 

∂
A

 S ,V
 ∂A 
=  Helm 
 ∂A T ,V
 ∂H 
= 

A
∂

T , P
By Maxwell’s relations, one can define
surface properties related to the surface
tension
SA
 ∂S 
=  
 ∂A T ,V
 ∂γ 
= − 

 ∂T T , A
Thermodynamics of surfaces
Pressure inside a bubble
The surface has an effect on the stability of a
bubble
Volume and surface area of a bubble
4 3
πr
Vbubble =
Abubble = 4πr 2
3
This relates the change of the volume of the
bubble to the change of the area:

 2γ
dAHelm
= − SdT
+ 
− P dV

 r
This pressure outside the bubble must
exactly balance the second term to maintain
equilibrium or the bubble collapses
Excess pressure in bubbles
For a bubble inside a condensed
phase such as a liquid, there is a
single surface
P − Pexternal
=
2γ
r
For a soap bubble in air, there is
an inner and outer surface, both
of which present the excess
pressure
2γ
∆P = 2
r
=
4γ
r
Capillary rise
Surface tension
causes capillary
rise
Balance of force
of gravity and the
surface force
ρgV
= ρghA =
2γ
A
r
Capillary rise used
to determine γ
γ
=
ρgr
2
h
Condensed phase equilibria
The coexistence curve of two phases is
specified by equality of µ
µα = µ β
For condensed phases, assuming
incompressibility
µ α ,θ (T ) + Vmα ( P − Pθ ) = µ β ,θ (T ) + Vmβ ( P − Pθ )
There is only a single pressure for a
given temperature at which the two
phases will coexist
“Clausius-Clapeyron equation”
for condensed phases
Equality of chemical potentials gives
relation between T and P on coexistence
curve
dP
dT
=
∆H m , transition
T ∆Vm , transition
Commonly used to find change in
melting point with pressure
 Tf
ln θ
T
 f

 =


( P − Pθ )∆ f Vm
∆ f Hm
Summary
Surface phases have “excess” energy due to
work of creating the surface

Surface tension
The criterion for equilibrium between phases
gives a requirement that pressure in a bubble
must be greater than the external pressure
Phase equilibrium applies to a wide variety of
situations, not just liquid-gas or solid-liquid




Bubbles and a bulk phase
Surface phase equilibrium
Solid-solid transition
Liquid-liquid crystal