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