1 Institute of Biocolloid Chemistry of National Academy of Sciences of Ukraine, 03142 Kiev, Ukraine...

1

Institute of Biocolloid Chemistryof National Academy of Sciences of Ukraine,

03142 Kiev, Ukraine

Dilatational rheology of complex fluid-fluid interfaces

V.I. Kovalchuk

2

Scope

Diffusion and mixed relaxation kinetics in adsorption layers

Dilatational rheology of complex fluid-fluid interfaces

Dilatational rheology of thin liquid films

Summary and conclusions

V.I. Kovalchuk, Dilatational rheology – Lorentz Workshop, Leiden-2011

Effect of equilibrium thermodynamic properties

Particles at interfaces

Relaxation in mixed adsorption layers

3

Interfacial rheology


Expansion / Compression

Shear

Elasticity

Viscosity

4

A

Surface dilational modulus

E - characterizes the response of the surface tension against relative surface

area change A:


iAln

iiE

tFi

tAlnFiAln

t

tdtAlnttEt

where iEFtE 1

A(t) can be arbitrary function of time ir EiEiE

rE - surface dalational elasticity

i

d

E - surface dalational viscosity

5

A

Purely diffusion relaxation of adsorption layers


2

2

yC

DtC

Diffusion in the bulk phase:

Boundary conditions:

0CC y

yC

Ddt

AdA1

0y

Initial condition:

2

tCtC

Additional conditions – surface tension and adsorption isotherms:

SC

6

A



2

2

yC

DtC



0CC y

yC

Ddt

AdA1

0y

Initial condition:

2

tCtC


SC

7



2

2

yC

DtC



0CC y

yC

Ddt

AdA1

0y

Initial condition:

2

tCtC


SC

2D

ddC

i11

1d

dE

Sln

Dilational elasticity modulus:

or:

20 221i1

EE

where:

ln/ ddE0

21

S

2D

ddC

/

J. Lucassen and M. van den Tempel, Chem. Eng. Sci., 27 (1972) 1283; J. Colloid Interface Sci., 41 (1972) 491

8

Lucassen – van den Tempel model:


//

/

DD

D0r 221

1EE

ln/ ddE0

2D

ddC

2

SD

//

/

DD

D0i 221

EE

Maxwell model:

2

2

0r 1EE

20i 1

EE

Kelvin-Voigt model:

KVKV iEE constEKV constKV

- limiting elasticity

- characteristic frequency of diffusion relaxation

9

Lucassen – van den Tempel model:


0.0 0.5 1.0

-1.0

-0.5

0.0

0.5 Ei

Er

Lucassen-van den Tempelmodel

Maxwellmodel

2E

2E

E2E

E20

2

0i

2

0r

Maxwell model:

4

EE

2E

E202

i

2

0r

2E

2E

O 00 ,2

ER 0

0

2E

O 0 ,2E

R 0

Cole-Cole plot:

10

Microgravity experiments during the STS-107 space shuttle mission

Real part of complex surface dilatational modulus vs. frequency for different C12DMPO

concentrations. V.I. Kovalchuk et al. / Journal of Colloid and Interface Science 280 (2004) 498–505

0.01 0.1 1 10 1000

20

40

60

0.013 mmol/l 0.019 mmol/l 0.026 mmol/l 0.038 mmol/l 0.064 mmol/l 0.115 mmol/l 0.22 mmol/l 0.42 mmol/l

r , m

N/m

Frequency, Hz


11


Imaginary part of complex surface dilatational modulus vs frequency for different

C12DMPO concentrations. V.I. Kovalchuk et al. / Journal of Colloid and Interface Science 280 (2004) 498–505

0.01 0.1 1 10 1000

5

10

15 0.013 mmol/l 0.019 mmol/l 0.026 mmol/l 0.038 mmol/l 0.064 mmol/l 0.115 mmol/l 0.22 mmol/l 0.42 mmol/l

i , m

N/m

Frequency, Hz


12


Cole-Cole diagram for complex surface dilatational modulus for different C12DMPO

concentrations.


0.00 0.02 0.04 0.060.000

0.005

0.010

0.015

Ei,

mN

/m

Er, mN/m

0.013 mmol/l 0.019 mmol/l 0.026 mmol/l 0.038 mmol/l 0.064 mmol/l 0.115 mmol/l 0.22 mmol/l

13

A

Diffusion from two adjacent phases


Effective diffusion coefficient:

20 221i1

EE

2D

ddC ef

2

SD

2ef DKDD

D

D

0

0

C

CK

Surfactant distribution coefficient:

14

Mixed adsorption kinetics


2

2

yC

DtC


yC

Ddt

AdA1

SC

B.A. Noskov, Adv. Colloid Interface Sci., 69 (1996) 63.

- no equilibrium at the interface

2/)i1(i1

2/)i1(iEE 0

Relaxation time:

desSad k1Ckdt

d

1addes ckk

/

15

Micellar solutions – Lucassen equation


J. Lucassen, Faraday Discuss. Chem. Soc., 59 (1975) 76.

disturbance time is much larger than the characteristic time of the “slow process”

- for ordinary surfactants of the order of milliseconds and characterizes the change in the number of micelles

12/122/10 m1m1)i1(1EE

D/DM2 - the ratio of micelles to monomers diffusion coefficients

m - the aggregation number

KK0 CCC / , CK = CMC (critical micelle concentration)

21

S

2D

ddC

/

Effective diffusion coefficient:

Dm1m1DD 2eff

16

Effect of equilibrium thermodynamic properties

ln/ ddE0

2D

ddC

2

SD

- limiting elasticity

- characteristic frequency of diffusion relaxation

SC

Equilibrium surface tension and adsorption isotherms:


17

Frumkin adsorption model


= 0 - the surface coverage

0 - the molar area

2

01

alnRT

)a2exp(1

bc

- surface pressure isotherm (equation of state)

- adsorption isotherm

a - the interaction constant

b - the adsorption equilibrium constant

18V.I. Kovalchuk, Dilatational rheology – Lorentz Workshop, Leiden-2011

0

50

100

150

0.001 0.01 0.1 1

c, mmol/l

E0,

mN

/m

1E-06

1E-05

1E-04

1E-03

0.001 0.01 0.1 1

c, mmol/l

d/d

c, m

Frumkin model: Γ = const, Ω = 1/Γ = const

Intrinsic compressibility model: Ω = 1/Γ = Ω0(1 – εΠ)

(ε – intrinsic 2D monolayer compressibility)

C12DMPOC12DMPO

lnd

dE0

V.I. Kovalchuk et al. / Journal of Colloid and Interface Science 280 (2004) 498–505

Intrinsic 2D monolayer compressibility

ir

2i

2r

0 EE

EEE

2

D

E

EE

dc

d

i

ir

Theory:

Experiment:Experiment:

SdCd

Theory:

19

= 0(1 – εΠ)

ε – intrinsic 2D monolayer compressibility, – surface pressure

The area occupied by a molecule on the interface can continuously change with the surface pressure.

V.I. Kovalchuk, R. Miller, V.B. Fainerman and G. Loglio / Advances in Colloid and Interface Science, 114-115 (2005) 303.





Frumkin model: Γ = const, Ω = 1/Γ = constIntrinsic compressibility model: Ω = 1/Γ = Ω0(1 – εΠ)

V.I. Kovalchuk et al. / Journal of Colloid and Interface Science 280 (2004) 498–505

0

50

100

150

0.001 0.01 0.1 1

c, mmol/l

E0,

mN

/m

The surface rheological characteristics are much more sensitive to the state and

interaction of molecules in the adsorption layer than equilibrium isotherms!

0

10

20

30

1E-4 1E-3 1E-2 1E-1

c, mmol/l

,

mN

/m


Dependence of C14TAB adsorption on activity c*: neutron reflection data ( )

and calculations according to Frumkin and compressibility model.

0E+00

1E-06

2E-06

3E-06

4E-06

5E-06

0,000 0,001 0,002 0,003 0,004 0,005

c*, mol/l

, mol

/m2

Intrinsic 2D monolayer compressibility - C14TAB adsorption

V.I. Kovalchuk, R. Miller, V.B. Fainerman and G. Loglio / Advances in Colloid and Interface Science, 114-115 (2005) 303.

22

Reorientation model

Adsorbed molecules can acquire two (or more) orientation states with respect to the interface.

V.B. Fainerman, S.A. Zholob, E.H. Lucassen-Reynders and R. Miller, J. Colloid Interface Sci., 261 (2003) 180.


2S0SS0 a1

RT ln

S

0

1

S

01 a21

bc01exp/

S

0

2

S12

02 a21

bc02exp

/ /

23

Protein Adsorption Layers


- the total surface coverage

- the molar area in state i ( )

with

2PPP0PP

0 a11RT

/ln

n

1iPiiPPP

PPjP

P

PjPPPj a2

1cb

Pj

/exp/

01i 1i ni1

01 1n max1min and

V.B. Fainerman, E.H. Lucassen-Reynders and R. Miller, Adv. Colloid Interface Sci., 106 (2003) 237.


Relaxation in mixed adsorption layers


)aaaa(DD

ia

D

ia

D

i

lnB

1

)aaaa(DD

ia

D

ia

D

i

lnB

1E

21122211

21

2222

121

12

21122211

211

212

211

11

1

2

jkcjiij )c(a

)aaaa()DDi(aDiaDi1B 2112221121222111 where:

21

ln

12

ln

and,

Viscoelasticity of mixed adsorption layers

This expression includes 6 parameters determined from surface tension and adsorption isotherms:

Jiang Q, Valentini JE, Chiew YC. J. Colloid Interface Sci. 174 (1995) 268.


Viscoelasticity of mixed adsorption layers

P. Joos, Dynamic Surface Phenomena, 1999

where:

212

1211

1

20

121

2122

2

10

di

Dd

i

D1

lnB

1

di

Dd

i

D1

lnB

1E

1

2

)dddd(DD)i/1(i/Ddi/Dd1B 21122211212221110

jk

jiij cd

/

21

ln

12

ln

and,

This expression also includes 6 parameters determined from surface tension and adsorption isotherms:


0

10

20

30

1E-02 1E-01 1E+00f (Hz)

|E| (

mN

/m)

7/200

3/200

5/200

3/500

2/500

5/2000

E.V. Aksenenko, V.I. Kovalchuk, V.B. Fainerman and R. Miller / J. Phys. Chem. C, 111 (2007) 14713

Dilational elasticity of mixed adsorption layers:Mixture of C10DMPO and C14DMPO

C14DMPO/C10DMPO concentrations in µmol/l

28

Mixtures of proteins and surfactants

Protein/non-ionic surfactant

Protein/ionic surfactant

Cs. Kotsmar, et al. / Advances in Colloid and Interface Science 150 (2009) 41–54



where:

S = SS - surface coverage by surfactant molecules;

SPPS2SS

2PPP0PSP

*0 2)/1()1ln(

RT

P = PP - total surface coverage by protein molecules;

SPSPP1P/SP

1PPP1P 2)/(2exp

1cb

P1

PPSSSSP

SSS 22exp

1cb

Adsorption isotherms:

These tree equations allow one to calculate the necessary 6 partial derivatives

Equation of state for protein/non-ionic surfactant mixtures

E.V. Aksenenko et al. / Advances in Colloid and Interface Science 122 (2006) 57–66

30

Dilational elasticity modulus |E| vs. frequency f at various C10DMPO concentrations (in mmol/l) in the β-LG/C10DMPO mixtures. Experimental data from R. Miller et al., Tens. Surf. Deterg. 40 (2003) 256.

V.I. Kovalchuk et al., in Progress in Colloid and Interface Science, Vol.1, Brill, Leiden-Boston, 2009, p. 332-371.

Dilational rheology of mixed adsorption layers:Mixture of C10DMPO and β-lactoglobulin

0

20

40

60

80

100

1E-03 1E-02 1E-01 1E+00 1E+01 1E+02

f, Hz

|E| ,

mN

/m0.02; 0.04; 0.1; 0.2; 0.4; 0.7



Particles at interfaces

Position of a spherical particle at the water/air interface (top) andmodification of particles via adsorption of ionic surfactants (bottom).

R. Miller et al: Project Proposal for the Investigation of Particle-Stabilised Emulsions and Foams by Microgravity Experiments,Microgravity sci. technol. XVIII-3/4 (2006) 104-107

32

Particles at the interface


coh0 AA

1kT

ln

0 - the molar area of solvent molecules

A - the available surface area per particle

- the molar area of particles

coh - the cohesion pressure

V.B. Fainerman, V.I. Kovalchuk, D.O. Grigoriev, M.E. Leser and R. Miller / NATO Science Series, Vol. 228, 2006, P. 79-90

33

Dependence of surface pressure on the monolayer coverage for polymeric particles 113 nm in diameter without dispersant (▲) and with dispersant (■). Experimental data according to E. Wolert

et al., Langmuir 17 (2001) 5671.

V.B. Fainerman, V.I. Kovalchuk, D.O. Grigoriev, M.E. Leser and R. Miller / NATO Science Series, Vol. 228, 2006, P. 79-90

Surface pressure in a monolayerof polymeric particles

0

10

20

30

40

50

0 10 20 30 40 50

Area [m2/g]

Sur

face

Pre

ssur

e [m

N/m

]


34



J. Lucassen, Colloids Surfaces, 65(1992) 139

Apparent dilatation modulus of composite monolayers:

n

1 i

i

E

X

E

1

Xi is the surface fraction having the dilatational modulus Ei.

Corresponds to the case of particles which do not interact and do not move but are characterized by a certain internal compressibility.

For incompressible particles:

P

S

S

S

1

E

X

EE

P is the surface coverage for particles, Es is the local elasticity of

interparticle space (e.g. covered by surfactants).

- excluded area effect

35



R. Miller et al., Adv. Colloid Interface Sci., 128–130 (2006) 17–26

Alternatively, for a mixed particle-surfactant layers the surface elasticity can be obtained by considering the surface pressure as a function of two variables:

PS ,

where θP and θS is the surface coverage by particles and surfactant.

Ad

d

Ad

d

Ad

dE P

P

S

SSP

ln

ln

lnln

ln

lnln

For insoluble surfactant molecules and particles:

1Ad

d

Ad

d PS

ln

ln

ln

lnand

SPPS

PS EEE

lnln

36



R. Miller et al., Adv. Colloid Interface Sci., 128–130 (2006) 17–26

For a mixed particle-surfactant layers described by the surface pressure isotherm:

the partial elasticities are:

)c(a)/1(1lnkT

Scoh2SSS0SPSP

0

S

coh2SS

S

0S

SP

S0S d

da21

1EE

ln

SP

SPP0P 1

EE

with 00 kTE /

For fast oscillations: PS EEE

For slow oscillations: SP

PP E

1EE

37



38


F F

FF

Δγf Δγf

Alnd

dE ff

γf = 2γ

Film elasticity: Δγf ≠ 2Δγ

Ef ≠ 2E


39

Film elasticity vs. thickness dependencies for normal alcohols: n-hexanol, n-octanol, n-decanol; films with initial surface pressure 0 = 42 mN/m and initial thickness h0 = 10 m

V.I. Kovalchuk et al., in Progress in Colloid and Interface Science, Vol.1, Brill, Leiden-Boston, 2009, p.476-518.


1E-7 1E-6 1E-50

50

100

150

200

250

300C10-OH

C8-OH

C6-OH

h0 = 10 m

0 = 42 mN/m

Ef,

mN

/m

h, m

hcrh0


40

Effect of characteristic disturbance time on film elasticity modulus (full lines) and its imaginary part Ei (dotted lines). Frumkin isotherm with the parameters for C8 (octanol), h0 = 10 m, 0 = 42 mN/m.

V.I. Kovalchuk et al., in Progress in Colloid and Interface Science, Vol.1, Brill, Leiden-Boston, 2009, p.476-518.

Film elasticity – time effect of disturbances

hcrh0

1E-6 1E-50

100

200

300

EGibbs

2E0

1000 Hz

100 Hz

10 Hz

|Ef|,

Ei m

N/m

h, m

fE

1

0f D

i

2

h

i

D

d

dc1E2E

tanh


41

Summary and conclusions

Surface tension studies provide general information about the formation of adsorption layers.

However, interfacial rheology gives more insight into the details of single and mixed adsorption layers.

The study of interfacial rheological properties represents a versatile and very sensitive experimental tool to investigate the adsorption layer properties. This techniques requires, however, quantitative theories combining interfacial dynamics and mass transfer aspects.


42

Acknowledgements

Financial support by

Max-Planck-Institute of Colloids and Interfaces

and

COST D-43 Action

is gratefully acknowledged.


August 2008

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