Surface Forces and Liquid Films

Sofia University

Peter A. Kralchevsky

Department of Chemical Engineering, Faculty of Chemistry

Sofia University, Sofia, Bulgaria

Lecture at COST D43 School Fluids and Solid Interfaces

Sofia University, Sofia, Bulgaria

12 – 15 April, 2011

Film of phase 3sandwiched between phases 1 and 2

Surface Force, Surface Force, Disjoining PressureDisjoining Pressure and and Interaction EnergyInteraction Energy

Π

Π

Example: Foam Film stabilized by ionic surfactant

Foam is composed of liquid films and Plateau borders

h Disjoining pressure, Π

= Surface force acting per unit area of each surface of a liquid film [1-4]

Π > 0 – repulsion Π < 0 – attraction

Π depends on the film thickness:Π = Π(h)

gas

gas

liquid

At equilibrium, Π(h) = Pgas – Pliquid

Interaction free energy (per unit area) f(h0)= Work to bring the two film surface from

infinity to a given finite separation h0 :

hhhfh

d)()(

0

0

DLVO Surface Forces DLVO Surface Forces (DLVO = Derjaguin, Landau, Verwey, Overbeek)(DLVO = Derjaguin, Landau, Verwey, Overbeek)

6)(

rru ij

ij

(1) Electrostatic repulsion (2) Van der Waals attractionTheir combination leads to a barrier to coagulation

Non–DLVO Surface ForcesNon–DLVO Surface Forces

hydrophobicinterface

bulk

(3) Oscillatory structural force

(films with particles)

(4) Steric interaction due to adsorbed polymer

chains

(5) Hydrophobic attraction in water

films between hydrophobic

surfaces (6) Hydration repulsion

(1) Electrostatic (Double Layer) Surface Force

0m2m1el 2nnnTk n1m, n2m

n0

Πel = excess osmotic pressure of

the ions in the midplane of a

symmetric film (Langmuir, 1938) [5-7]:

n1m, n2m – concentrations of (1) counterions

and (2) coions in the midplane.

n0 – concentration of the ions in the bulk

solution; ψm potential in the midplane.

For solution of a symmetric electrolyte: Z1 = Z2 = Z; Z is the valence of the coions.

Boltzmann equation; Φm – dimensionless potential in the midplane (Φm << 1).

kT

Zennnn m

mm0m2m0m1 );exp();exp(

)(2

1cosh 4m

2m

m

O 01cosh2 2m0m0el

kTnkTn

Πel > 0 repulsion!

Verwey – Overbeek Formula (1948)

Superposition approximation

in the midplane: ψm = 2ψ1 [6]:

Near single interface, the electric

potential of the double layer is [7]:

2κexpγ

4

ψ1 h

kT

Ze

14

ψmidplanetheIn 1

kT

Ze

)κexp(γ64)( 20

2m0el hkTnkTnh

kT

Ze

4tanh s

2κexpγ8ψ2 1mh

kT

Ze

Π(h) = ?

strength)(ionic

2

1

εε

2κ

2

0

22

iii cZI

kT

Ie

More salt Greater κ Smaller Πel

(2) Van der Waals surface force: 3H

vw6

)(h

Ah

AH – Hamaker constant (dipole-dipole attraction)

Hamaker’s approach [8]

The interaction energy is pair-wise additive:

Summation over all couples of molecules.

Result [8,9]:

)3,2,1,(α

)(6

jir

ru ijij

33312312H AAAAA

2/12 )(; jjiiijijjiij AAAA

Symmetric film: phase 2 = phase 1

For symmetric films: always attraction!

Asymmetric films, A11 > A33 > A22 repulsion!

0222/1

332/1

11331311H AAAAAA

Lifshitz approach to the calculation of Hamaker constant

E. M. Lifshitz (1915 – 1985) [10] took into account

the collective effects in condensed phases (solids,

liquids). (The total energy is not pair-wise additive

over al pairs of molecules.)

Lifshitz used the quantum field theory to derive

accurate expressions in terms of:

(i) Dielectric constants of the phases: ε1, ε2 and ε3 ;

(ii) Refractive indexes of the phases: n1, n2 and n3:

4/32

322

4/323

21

23

22

23

21eP

32

32

31

31132H

216

3

4

3

nnnn

nnnnhkTAA

Zero-frequency term:

orientation & induction

interactions;

kT – thermal energy.

)0(132A Dispersion interaction term:

νe = 3.0 x 1015 Hz – main electronic

absorption frequency;

hP = 6.6 x 10– 34 J.s – Planck’s const.

)0(132A

Derjaguin’s Approximation (1934): The energy of interaction, U, between

two bodies across a film of uneven

thickness, h(x,y), is [11]:

dydxyxhfU )),((

where f(h) is the interaction free energy

per unit area of a plane-parallel film:

hhhfh

~d)

~()(

This approximation is valid if the range of action

of the surface force is much smaller than the surface curvature radius.

For two spheres of radii R1 and R2, this yields:

dhhfRR

RRhU

h

021

210

2

From planar films, f(h) to spherical particles, U(h0).

DLVO Theory: The electrostatic barrier

The secondary minimum could cause

coagulation only for big (1 μm) particles.

h

ABRhU h

21e)( H

2

The primary minimum is the reason for

coagulation in most cases [6,7].

Condition for coagulation: Umax = 0

(zero height of the barrier to coagulation)

0d

d;0)(

max

max hhh

UhU

The Critical Coagulation Concentration (ccc) [6,7]

max

H2max 21

e0)( max

h

ABhU h

2max

H

21e0

d

dmax

max h

AB

h

U h

hh

62H

530

43

62H

530

4

23

2

0)(

)()εε(γ105.98

)(

)()εε(γ

e2

)π1264(

ZeA

kT

ZeA

kTnccc

[13] (1900)Hardyand]12[(1882)Schulze ofRule1

6Zccc

)64( 20 kTnB

maxandgdetermininforequationsTwo hB

729

1:

64

1:1

3

1:

2

1:1Al:Mg:Na

6632 ccc

DLVO Theory [6,7]: Equilibrium states of a free liquid film

Born repulsion Electrostatic component of disjoining pressure:

)(repulsion)exp()(el hBh

)()()( vwel hhh

Van der Waals component

of disjoining pressure:

n)(attractio6

)(3

Hvw

h

Ah

(2) Secondary film

(1) Primary film

h – film thickness; AH – Hamaker constant;

κ – Debye screening parameter

Primary Film (0.01 M SDS solution) Secondary Film (0.002 M SDS + 0.3 M NaCl)

Observations of free-standing foam

films in reflected light.

The Scheludko-Exerowa Cell [14,15]

is used in these experiments.

Oscillatory–Structural Surface Force

For details – see the book by Israelachvili [1]

A planar phase

boundary (wall) induces

ordering in the adjacent

layer of a hard-sphere

fluid.

The overlap of the

ordered zones near two

walls enhances the

ordering in the gap

between the two walls

and gives rise to the

oscillatory-structural

force.

The maxima of the oscillatory

force could stabilize

colloidal dispersions.

The metastable states of the

film correspond to the

intersection points of the

oscillatory curve with the

horizontal line = Pc.

The stable branches of the

oscillatory curve are those with

/h < 0.Depletion

minimum

Oscillatory structural forces [1] were observed in liquid films containing colloidal particles, e.g. latex & surfactant micelles; Nikolov et al. [16,17].

Oscillatory-structuraldisjoiningpressure

Oscillatory-structuraldisjoiningpressure

Metastable states of foam films containing surfactant micelles

Foam film from a micellar

SDS solution (movie):

Four stepwise transitions in

the film thickness are seen.

Oscillatory–Structural Surface Force Due to Nonionic Micelles

Ordering of micelles of

the nonionic surfactant

Tween 20 [19].

Methods:

Mysels-Jones (MJ)

porous plate cell [20],

and

Scheludko- Exerowa

(SE) capillary cell [14].

Theoretical curve – formulas by Trokhimchuk et al. [18].

The micelle aggregation number, Nagg = 70, is determined [19].

(the micelles are modeled as hard spheres)

Steric interaction due to adsorbed polymer chains

l – the length of a segment;

N – number of segments in a chain;

In a good solvent L > L0, whereas

in a poor solvent L < L0.

L depends on adsorption of chains,

[1,21].

Alexander – de Gennes theory

for the case of good solvent [22,23]:

solvent)(ideal2/10 NlLL

3/15gg

4/3

g

4/9g2/3

st

;2for

2

2

lNLLh

L

h

h

LTkh

The positive and the negative terms in the brackets in the above expression

correspond to osmotic repulsion and elastic attraction.

The validity of the Alexander de Gennes theory was experimentally confirmed;

see e.g. Ref. [1].

Steric interaction – poor solvent

Plot of experimental data for

measured forces, F/R 2f vs. h,

between two surfaces covered by

adsorption monolayers of the

nonionic surfactant C12E5 for

various temperatures.

The appearance of minima in the

curves indicate that the water

becomes a poor solvent for the

polyoxyethylene chains with the

increase of temperature; from

Claesson et al. [24].

Hydrophobic Attraction

After Israelachvili et al. [25] Discuss. Faraday Soc.

146 (2010) 299.

Force between two hydrophobic surfaces

across water.

(1) Short range Hphb force

Due to surface-oriented H-bonding of water molecules (1–2 nm)

λ/hb 2)( hwehf

w = 1050 mJ/m2 and = 12 nm

(2) Long-range Hphb force (h = 2 – 20 nm)

proton-hopping polarizability of water (?):

OHOHOHOH 322

p

(3) Long-range Hphb force (h = 100 – 200 nm): electrostatic mosaic patches and/or bridging cavitation:

+ – + – +

– + – + –

Hydration Repulsion

At Cel < 104 M NaCl,

a typical DLVO maximum is observed.

At Cel 103 M, a strong short-range

repulsion is detected by the surface

force apparatus – the hydration

repulsion [1, 26].

Empirical expression [1] for the

interaction free energy per unit area:

)/exp( 00hydr hff

20

0

mJ/m303

nm1.16.0

f

Important: fel decreases, whereas fhydr increases with

the rise of electrolyte concentration!

Different hypotheses: (1) Water-structuring models;

(2) Discreteness of charges and dipoles; (3) Redu-

ced screening of the electrostatic repulsion [27].

Film thickness, h (nm)

10 11 12 13 14

Dis

join

ing

pre

ssu

re,

(P

a)

0

1000

2000

3000

4000

5000

6000

7000

1 mM SDP-3S100 mM MCl

LiClNaClKClRbClCsCl

Example:

Data from [27] by the Mysels–Jones (MJ)

Porous Plate Cell [20]

SE cell: Π < 85 Pa(thickness h vs. time)

MJ cell: Π > 6000 Pa (!)

(Π vs. thickness h)

(1) Electrostatic repulsion;

(2) Hydration repulsion.

The total energy of interaction between two particles , U(h),

includes contributions from all surface forces:

U(h) = Uvw(h) + Uel(h) + Uosc(h) + Ust(h) + Uhphb(h) + Uhydr + …

DLVO forces Non-DLVO forces

(The depletion force is included in the expression for the oscillatory-structural energy, Uosc)

Basic References

1. J.N. Israelachvili, Intermolecular and Surface Forces, Academic Press, London, 1992.

2. P.A. Kralchevsky, K. Nagayama, Particles at Fluid Interfaces and Membranes,

Elsevier, Amsterdam, 2001; Chapter 5.

3. P.A. Kralchevsky, K.D. Danov, N.D. Denkov. Chemical physics of colloid systems and

Interfaces, Chapter 7 in Handbook of Surface and Colloid Chemistry", (Third Edition;

K. S. Birdi, Ed.). CRC Press, Boca Raton, 2008; pp. 197-377.

Additional References

4. B.V. Derjaguin, E.V. Obuhov, Acta Physicochim. URSS 5 (1936) 1-22.

5. I. Langmuir, The Role of Attractive and Repulsive Forces in the Formation of Tactoids,

Thixotropic Gels, Protein Crystals and Coacervates. J. Chem. Phys. 6 (1938) 873-896.

6. B.V. Derjaguin, L.D. Landau, Theory of Stability of Strongly Charged Lyophobic Sols

and Adhesion of Strongly Charged Particles in Solutions of Electrolytes, Acta

Physicochim. URSS 14 (1941) 633-662.

7. E.J.W. Verwey, J.Th.G. Overbeek, Theory of Stability of Lyophobic Colloids, Elsevier,

Amsterdam, 1948.

8. H.C. Hamaker, The London – Van der Waals Attraction Between Spherical Particles

Physica 4(10) (1937) 1058-1072.

9. B.V. Derjaguin, Theory of Stability of Colloids and Thin Liquid Films, Plenum Press:

Consultants Bureau, New York, 1989.

10. E.M. Lifshitz, The Theory of Molecular Attractive Forces between Solids, Soviet Phys.

JETP (English Translation) 2 (1956) 73-83.

11. B.V. Derjaguin, Friction and Adhesion. IV. The Theory of Adhesion of Small Particles,

Kolloid Zeits. 69 (1934) 155-164.

12. H. Schulze, Schwefelarsen im wässeriger Losung, J. Prakt. Chem. 25 (1882) 431-452.

13. W.B. Hardy, A Preliminary Investigation of the Conditions, Which Determine the

Stability of Irreversible Hydrosols, Proc. Roy. Soc. London 66 (1900) 110-125.

14. A. Scheludko, D. Exerowa. Instrument for Interferometric Measuring of the Thickness

of Microscopic Foam Films. C.R. Acad. Bulg. Sci. 7 (1959) 123-132.

15. A. Scheludko, Thin Liquid Films, Adv. Colloid Interface Sci. 1 (1967) 391-464.

16. A.D. Nikolov, D.T. Wasan, P.A. Kralchevsky, I.B. Ivanov. Ordered Structures in

Thinning Micellar and Latex Foam Films. In: Ordering and Organisation in Ionic

Solutions (N. Ise & I. Sogami, Eds.), World Scientific, Singapore, 1988, pp. 302-314.

17. A. D. Nikolov, D. T. Wasan, et. al. Ordered Micelle Structuring in Thin Films Formed

from Anionic Surfactant Solutions, J. Colloid Interface Sci. 133 (1989) 1-12 & 13-22.

18. A. Trokhymchuk, D. Henderson, A. Nikolov, D.T. Wasan, A Simple Calculation of

Structural and Depletion Forces for Fluids/Suspensions Confined in a Film,

Langmuir 17 (2001) 4940-4947.

19. E.S. Basheva, P.A. Kralchevsky, K.D. Danov, K.P. Ananthapadmanabhan, A. Lips,

The Colloid Structural Forces as a Tool for Particle Characterization and Control of

Dispersion Stability, Phys. Chem. Chem. Phys. 9 (2007) 5183-5198.

20. Mysels, K. J.; Jones, M. N. Direct Measurement of the Variation of Double-Layer

Repulsion with Distance. Discuss. Faraday Soc. 42 (1966) 42-50.

21. W.B. Russel, D.A. Saville, W.R. Schowalter, Colloidal Dispersions, Cambridge Univ.

Press, Cambridge, 1989.

22. S.J. Alexander, Adsorption of Chain Molecules with a Polar Head: a Scaling

Description, J. Phys. (Paris) 38 (1977) 983-987

23. P.G. de Gennes, Polymers at an Interface: a Simplified View, Adv. Colloid Interface

Sci. 27 (1987) 189-209.

24. P.M. Claesson, R. Kjellander, P. Stenius, H.K. Christenson,  Direct Measurement of

Temperature-Dependent Interactions between Non-ionic Surfactant Layers, J. Chem.

Soc., Faraday Trans. 1, 82 (1986), 2735-2746.

25. M.U. Hammer, T.H. Anderson, A. Chaimovich, M.S. Shell, J. Israelachvili,

The search for the Hydrophobic Force Law. Faraday Discuss. 2010, 146, 299–308.

26. R.M. Pashley, J.N. Israelachvili, Molecular layering of water in thin films between mica

surfaces and its relation to hydration forces. J. Colloid Interface Sci. 1984, 101, 511–22.

27. P.A. Kralchevsky, K.D. Danov, E.S. Basheva, Hydration force due to the reduced

screening of the electrostatic repulsion in few-nanometer-thick films.

Curr. Opin. Colloid Interface Sci. (2011) – in press.