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SURFACTANT ADSORPTION
Surfactant =substance composed of surface active molecules(spontaneously adsorb and decrease surface tension)
Why are the surfactants so important ?
Affect all foam properties!Can be used for control of foam behavior!
Ensure foam stability:
1. Low molecular mass (≈ 200 to 1000)
Ionic
Nonionic
Types of surfactant
2. Polymeric (including proteins)
FibrilarGlobular
3. Solid particles
Aims of presentation:1. To describe the phenomena of surfactant
adsorption and aggregation in solutions.
2. Role of surfactants in foams (introduction).
CONTENTS
A. Surface tension and surfactant adsorption.
B. Kinetics of surfactant adsorption.
C. Surfactants in foams – illustrative examples.
A. Surface tension and surfactant adsorption
Work = 2σAσ - interfacial energy per unit area [J/m2]
Surface tension - energetical and force approaches.
1. Energetical approach
Molecular interpretation of energetical approach
Intermolecular interaction energy
σ ≈ ≈ 20 / 200 mJ/msN u A
( ) ( )= µ − + µ −0 0 0 06 5B SG N u N u
Surface energyas an excess energy
( ) {=σµ
= µ − +142430 0 0
surface energy
6
B
TOT SA
N u N u
2. Force approach
Surface tension of liquids as a tangential force
= σ2F L
σ = (F / 2L) [N/m]
σ
= + π σ θ2 cosF mg R
F
σ
Where does this tangential force come from?
Surface tension of spread surfactant monolayers(Langmuir-trough)
( )= σ − σ0F L⎡ ⎤Γ ⎣ ⎦
2mol/m
surface concentration
( )Π ≡ σ − σ0SSurface pressure Related to Marangoni effect
⇒W/A W/S/A
Effect of surfactants
Analogy between surface and bulk pressures
Dilute monolayersIdeal adsorption layer
( )Π Γ = ΓS Bk T
( ) = BP C Ck TIdeal gas
Concentrated monolayers
( )( )∞Π −β − =2S BA A A k T - 2D van der Waals
- 3D van der Waals( ) ( )∞− − =2BP a v v v k T
Typical results for soluble surfactants and data interpretation
CMC
Micelle formation
Gibbs adsorption isotherm
lnBd d k Td Cσ = −Γ µ ≈ −Γ
(Gibbs-Duhem for the surface phase)
µ = µ +0 lnBk T C
Model adsorption isotherms
σ = − Γ lnBd k T d CLangmuir ( ) ∞Γ = Γ+1KCC
KC
Assumptions:
• Localized adsorption.
• Non-interacting molecules.
( ) ( )∞ ∞σ = σ − Γ = σ − Γ ++∫0 0
0
ln 11
C
B BKC k T dC k TK KCKC
Surface tension isotherm
Model adsorption isotherms
Type of isotherm
Surfactant adsorption isotherm Surface equation of state
Henry KC∞
Γ=Γ
Π = σ − σ = Γ0S Bk T
Langmuir KC∞
Γ=Γ − Γ
lnS Bk T ∞∞
∞
⎛ ⎞ΓΠ = Γ ⎜ ⎟Γ −Γ⎝ ⎠
Volmer expKC∞ ∞
⎛ ⎞Γ Γ= ⎜ ⎟Γ − Γ Γ − Γ⎝ ⎠
S Bk T ∞∞
ΓΠ = Γ
Γ − Γ
Frumkin 2expB
KCk T∞
⎛ ⎞Γ βΓ= −⎜ ⎟Γ − Γ ⎝ ⎠
2lnS Bk T ∞∞
∞
⎛ ⎞ΓΠ = Γ −βΓ⎜ ⎟Γ − Γ⎝ ⎠
van der Waals 2expB
KCk T∞ ∞
⎛ ⎞Γ Γ βΓ= −⎜ ⎟Γ − Γ Γ −Γ⎝ ⎠
2S Bk T ∞
∞
ΓΠ = Γ − βΓ
Γ − Γ
Gibbs elasticity of adsorption monolayers
lnGdE
d Aσ
= +Insoluble monolayer
ln lnS
GddE
d dΠσ
= − =Γ Γ
Soluble monolayer
Henry S B G Bk T E k TΠ = Γ ⇒ = Γ
Volmer ( )
2
2S B G Bk T E k T ∞∞
∞ ∞
ΓΓΠ = Γ ⇒ = Γ
Γ − Γ Γ − Γ
Examples
Methods for measuringthe surface tension
1. Wilhelmy plate
2. Pendant drop method
( )P z gz= ρ
1 2
1 1CP
R R⎛ ⎞
= σ +⎜ ⎟⎝ ⎠⎛ ⎞
⇒ σ ρ = ⎜ ⎟⎝ ⎠1 2
1 1/ ,g fR R
( ) − = 0CP z P P
z
Experimental determination of Γ(C):ellipsometry, neutron reflection, radioactivity…
B. Kinetics of surfactant adsorption
Interrelation between macroscopicand molecular levels of description
Two consecutive stagesStage 1 - adsorption from the "subsurface layer" onto surface.
Stage 2 - diffusion from the bulk to the subsurface layer
Possible additional stages
• Molecule rearrangement
• Formation of intermolecular bonds
Stages of dynamic adsoprion
Diffusion control of adsorption:large deviation from equilibrium
Γ = Γ(CS)
t = t1
δ(t1)
t = t2
δ(t2)
( )δ2 ~ 2t Dt
∞Γ δmax~ BC
2
diff1~
BD C∞⎛ ⎞Γ
τ ⎜ ⎟⎝ ⎠
Diffusion time
Diffusion control of adsorption:exact solution and asymptotics
∂ ∂=
∂ ∂
2
2C CDt x =
Γ ∂=
∂ 0x
d CDdt x ( )SCΓ = Γ
Diffusion equation Surface mass balance Adsorption isotherm
( ) ( ) ( )⎡ ⎤Γ = Γ + − τ⎢ ⎥
π − τ⎢ ⎥⎣ ⎦∫0
0 2t
Sb
C tDt C t dt
Solution (Ward & Tordai)
( ) 2 BDtt C tΓ ≈ ∝π
t → 0
( ) ( ) ( ) τσ⎛ ⎞∆σ = ∆Γ = ∆Γ ∝⎜ ⎟Γ π⎝ ⎠
10 ddt td t t
t → ∞
Barrier control of adsorption
( ) ( ),ads B desd V C VdtΓ= Γ − Γ
Surface mass balance
Example: Langmuir adsorption
( )ads ads 1BV k C ∞= − Γ Γ des desV k= ΓRate of adsorption Rate of desorption
( )( )
( )( )
exp0 0 b
t t t∆σ ∆Γ ⎛ ⎞= = −⎜ ⎟∆σ ∆Γ τ⎝ ⎠ des ads
bBk k C
∞
∞
Γτ =
Γ +
( )ads B ads B desd k C k C kdt ∞Γ= − Γ + Γ
Adsorption from micellar solutions
Characteristic times
τd – diffusion of monomers
τdm - diffusion of micelles
τmic - supply of monomersfrom the micelles
For ionic surfactants – msecFor nonionic surfactants - sec
Surfactant spreading and Marangoni effect
{ {surf viscsurface viscousstress stress
τ = τ
visc0
r
z
dVdz =
⎛ ⎞τ = µ⎜ ⎟⎝ ⎠
Stress balance
Viscous stress
Surface stress
σ − σστ = ≈ 0
surfddr r
( ) 1 20 1 4
1 2 1 234rV t −
⎡ ⎤σ − σ= ⎢ ⎥
ρ µ⎣ ⎦
Spreading velocity
Marangonieffect
Carlo Marangoni• James Thomson, "On certain curious motions observable
on the surfaces of wine and other alcoholic liquours,“Philosophical Magazine, 10, 330 (1855).
• Carlo Marangoni, "On the expansion of a drop of liquid floating in the surface of another liquid“, PhD Thesis, Pavia, Italy, 1865.
“Tears of wine” and Marangoni effect
1. Determine the equilibrium surface tension⇒ the static foam structure.
Water drainage:(ASJ, SCA – next week)
C. Role of surfactants in foams
Proteins: σ ~ 50 mN/mFluoro-surfactants: σ ~ 15 mN/m
Capillary pressure
Hydrostaticpressure
= σ2 /C BP R = ρHP gH
Height of the wet foam
2W
BH
gRσ
=ρ
2. Static stabilization of foam films
Static stabilization: ASJ and ND in Thursday
Electrostatic stabilization by ionic surfactants
Ionic surfactants
Steric stabilization by nonionic surfactants
Nonionic surfactants
3. Dynamic stabilization of the foam filmsby Marangoni effect
Damped local perturbations in the film thickness due to Marangoni effect
⇒ Slower film drainage and higher stability
4. Effect of surfactants on the dynamic phenomena in foams
Foaming – foam volume and bubble size.
Rate of water drainage from foams.
Rate of foam film thinning.
Viscous dissipation in foams.
Foam-wall friction.
Ostwald ripening.
Important role of dynamic surface tension and interfacial rheology!
5. Role of micelles in foams
(a) Reservoir of surfactant – dynamic surface tension.
(c) Solution rheology (shampoos, dish-washing gels)
higher solution viscosity
(b) Oscillatory forces in foam films (stratification).
Following related presentations:
ThursdayRole of surfactants in foam stabilization (including
antifoams)
Friday• Interfacial rheology
SINCERE THANKS
Dr. S. TcholakovaHelp in preparation of the presentation.
Miss M. ParaskovaPreparation of some of the figures.
Other colleaguesThe Laboratory of Chemical Physics & EngineeringFaculty of Chemistry, University of Sofia, Sofia, Bulgaria
Derivation of Gibbs adsorption isotherm
( ) ( )0
0
Sf f z f dz f z f dz∞
α β
−∞
⎡ ⎤ ⎡ ⎤= − + −⎣ ⎦ ⎣ ⎦∫ ∫
( ) ( )0
0i i i i in z n dz n z n dz
∞α β
−∞
⎡ ⎤ ⎡ ⎤Γ = − + −⎣ ⎦ ⎣ ⎦∫ ∫
( ) ( )0
0T TP z P dz P z P dz
∞α β
−∞
⎡ ⎤ ⎡ ⎤σ = − − − −⎣ ⎦ ⎣ ⎦∫ ∫
V V Vα β= +
Si i i iN N N Nα β= + +
SF F F Fα β= + +
SU U U Uα β= + +
Surface excess quantities
SS S S Sα β= + + ;i i i iF pV N F pV Nα α α β β β= − + Σµ = − + Σµ
S S SF U TS= −S S
i iF A N⇒ = σ +Σµ
;i i i idF s dT pdV dN dF s dT pdV dNα α α α β β β β= − − + Σµ = − − + Σµ
S S Si idF S dT dA dN⇒ = − +σ + Σµ
Si id S dT dσ = − −ΣΓ µ
, ,
i i
T V N
i i
dF SdT pdV dA dNFA
F PV A N
= − − + σ + Σµ
∂⎛ ⎞σ = ⎜ ⎟∂⎝ ⎠= − + σ + Σµ
Conditions for equilibrium:
T = const
µi = const
For the total system:
For the subsystems