Gibbs adsorption isotherm

Gibbs adsorption isotherm
@ liquid surface, surface and subphase are in equilibrium:exchange possible
Problem: Location of a surface at a liquid/vapor interface?
Liquid surface: interfacial region a few molecular diameters thick (nm)
Solid surface: interfacial region on a Å scale

Δ c(z) = c(z) −c
Δ c(z) = c(z) −c
∞
Γ = Γ = − + −
liq
vap
∫ ∫
0
(c(z) c )dz (c(z) c )dz
2 z
2
0
−∞
2
1 H O H O,v H O,liq
∞
∫ ∫
Γ = Γ = − + −
0
(c(z) c )dz (c(z) c )dz
0
−∞
2 SDS
z
SDS,v SDS,liq
c vap ~ 10 -2 (M)
Gibbs adsorption equation
z
z
∞
∫
∫ ∫
Γ= Δc(z)dz
−∞
∞ ∞
−∞
vap
−∞
liq
Γ= (c(z) − c )dz + (c(z) −c
)dz
= 0
dγ
= −Γ
dμ
SDS
1 dγ
Γ SDS = −
RT d lnc SDS

saturation
below cmc
Surface tension of surfactant solutions
c cmc
Slope
corresponds to
surface density

Surface tension of polyelectrolyt/surfactant solutions

surface tension / mN/m
70 C 12 TAB
60
50
40
30
10 -5
-
10 -4
cac
10 -3
10 -2
-
- +
PSS/C 12TAB 12TAB
5*10 -3
C 12 TAB concentration / mol/l
10 -1
A. Asnacios, R. v. K., D. Langevin, Coll. Surfaces A (2001)

*
A) Polyelectrolytes B) Surfactants (c

C 12 TAB / PAMPS
C 12 TAB / PAMPS
(75 – 750 ppm)
C 12 TAB / PAMPS
+ -
CnTAB TAB / PAMPS
C 12 TAB
C 16 TAB / PAMPS
C16TAB / PAMPS
cac cmc
(75 ppm) cac
KBr / PAMPS
CMC (C 12 TAB) = 15 mM
CMC (C 16 TAB) = 1 mM
PAMPS
C 16 TAB
cmc cmc‘
A. Asnacios, D. Langevin, J.-F. Argillier, Macromolecules (1996)
A. Asnacios, R. v. Klitzing, D. Langevin Coll. Surf. A (2000)

surface tension / mN/m
75
70
65
60
55
50
45
-
Low density
of binding sites
+ -
P(DADMAC-stat
P(DADMAC stat-NMVA)/SDS
NMVA)/SDS
Maximum in density at 50 %
0 20 40 60 80 100
polymer charge density / %
-
Coiled chains
*
C
H 3
Stretched chains
P(DADMAC-stat-NMVA)
-
N +
Cl
CH 3
f
O
n
*
N CH3
CH 3

Langmuir films
Preparation: dissolve insoluble amphiphiles in a volatile organic solvent
and deposit drops of solution onto the air/water interface
S>0 => spreading, evaporation of solvent => monolayer of amphiphiles
Pressure is needed to prevent film from spreading:
0
Π s = γ −γ

Collapse
Langmuir films
G: gas phase
L1: liquid expanded phase
(e.g. saturated unbranched
carbon chains: a 0 ≈30-50Å 2 )
L2: liquid condensed phase
(stronger molecular interactions,
lower compressibilty
S: solid (e.g. alcohols, esters:
a 0 ≈19 Å 2 )
G->L1: typical gas liquid transiton
like in 3D
L1->L2: transition not finally explained.

Effect of polymer charge on lipid/polyelectrolyte complexes @ air/water interface:
DPPA / PDADMAC–co-polymer
Thickness: Ellipsometry
n CP-47 =n CP-73 =1.35
d CP-73 =7.5 nm
d CP-47 =9.0 nm
Kerstin de Meijere et al. Macromolecules 1997

GID (grazing incidence diffraction)

Effect of polymer charge on lipid/polyelectrolyte complexes @ air/water interface:
DPPA / PDADMAC–co-polymer
GID:
α i =0.85α c
in plane
diffraction:
d hk =2π/Q xy
Kerstin de Meijere et al. Macromolecules 1997
DPPA
PDADMAC
Without
PDADMAC
With PDADMAC
Domains of
tilted chains