Surface Forces and Liquid Films

1
Surface Forces and Liquid Films
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
Sofia University
2
Surface Force, Disjoining Pressure and
Interaction Energy
gas
? ?
Example Foam Film stabilized by
ionic surfactant
Disjoining pressure, ? Surface force acting
per unit area of each surface of a liquid film
1-4
h
liquid
? ?
? gt 0 repulsion ? lt 0 attraction
gas
? depends on the film thickness? ?(h)
At equilibrium, ?(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
Foam is composed of liquid films and Plateau
borders
3
DLVO Surface Forces (DLVO Derjaguin, Landau,
Verwey, Overbeek)
Their combination leads to a barrier to
coagulation
(1) Electrostatic repulsion
(2) Van der Waals attraction
NonDLVO Surface Forces
(5) Hydrophobic attraction in water films between
hydrophobic surfaces
(4) Steric interaction due to adsorbed polymer
chains
(3) Oscillatory structural force (films with
particles)
(6) Hydration repulsion
4
(1) Electrostatic (Double Layer) Surface Force
?el excess osmotic pressure ofthe ions in the
midplane of asymmetric film (Langmuir, 1938)
5-7
n0
n1m, n2m
n1m, n2m concentrations of (1) counterions
and (2) coions in the midplane. n0
concentration of the ions in the bulk
solution ?m potential in the midplane.
?el gt 0 ? repulsion!
For solution of a symmetric electrolyte Z1
?Z2 Z Z is the valence of the
coions.Boltzmann equation Fm dimensionless
potential in the midplane (Fm ltlt 1).
5

Verwey Overbeek Formula (1948)
?(h) ?
Near single interface, the electric potential of
the double layer is 7
Superposition approximation in the midplane ?m
2?1 6
More salt ? Greater ? ? Smaller ?el


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(2) Van der Waals surface force
AH Hamaker constant (dipole-dipole attraction)
Hamakers approach 8 The interaction energy is
pair-wise additive Summation over all couples of
molecules.Result 8,9
Symmetric film phase 2 phase 1 For symmetric
films always attraction! Asymmetric films, A11
gt A33 gt A22 ? repulsion!
7
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 e1,
e2 and e3 (ii) Refractive indexes of the
phases n1, n2 and n3
Zero-frequency term orientation
inductioninteractionskT thermal energy.
Dispersion interaction term ?e 3.0 x 1015 Hz
main electronic absorption frequencyhP 6.6 x
10 34 J.s Plancks const.
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Derjaguins Approximation (1934)
The energy of interaction, U, between two bodies
across a film of uneven thickness, h(x,y), is
11
where f(h) is the interaction free energy per
unit area of a plane-parallel film
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
From planar films, f(h) to spherical particles,
U(h0).
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DLVO Theory The electrostatic barrier
The secondary minimum could cause coagulation
only for big (1 µm) particles.
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)
11
The Critical Coagulation Concentration (ccc) 6,7
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DLVO Theory 6,7 Equilibrium states of a
free liquid film
Born repulsion
Electrostatic component of disjoining pressure
Van der Waals component of disjoining pressure
(2) Secondary film (1) Primary film
h film thickness AH Hamaker constant ?
Debye screening parameter
13
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.

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OscillatoryStructural Surface Force
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.
For details see the book by Israelachvili 1
15
Oscillatory structural forces 1 were observed
in liquid films containing colloidal particles,
e.g. latex surfactant micelles Nikolov et al.
16,17.
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 lt 0.
Oscillatory-structuraldisjoiningpressure
Depletion minimum
16
Metastable states of foam films containing
surfactant micelles
Oscillatory-structuraldisjoiningpressure
Foam film from a micellar SDS solution
(movie) Four stepwise transitions in the film
thickness are seen.
17
OscillatoryStructural Surface Force Due to
Nonionic Micelles
Ordering of micelles of the nonionic surfactant
Tween 20 19. MethodsMysels-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)
18
Steric interaction due to adsorbed polymer chains
l the length of a segmentN number of
segments in a chainIn a good solvent L gt L0,
whereas in a poor solvent L lt L0. L depends on
adsorption of chains, ? 1,21. ? Alexander de
Gennes theory for the case of good solvent
22,23
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.
19

Steric interaction poor solvent
Plot of experimental data for measured forces,
F/R ? 2?f 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.
20

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 (12 nm)
w 10?50 mJ/m2 and ? 1?2 nm
(2) Long-range Hphb force (h 2 20 nm)
proton-hopping polarizability of water (?)
(3) Long-range Hphb force (h 100 200 nm)
electrostatic mosaic patches and/or bridging
cavitation


21
Hydration Repulsion
At Cel lt 10?4 M NaCl, a typical DLVO maximum is
observed. At Cel ? 10?3 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
Important fel decreases, whereas fhydr increases
with the rise of electrolyte concentration! Differ
ent hypotheses (1) Water-structuring models (2)
Discreteness of charges and dipoles (3) Redu-ced
screening of the electrostatic repulsion 27.
22
Example Data from 27 by the MyselsJones (MJ)
Porous Plate Cell 20
SE cell ? lt 85 Pa(thickness h vs. time) MJ
cell ? gt 6000 Pa (!) (? vs. thickness h)
(1) Electrostatic repulsion (2) Hydration
repulsion.
23
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)
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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.
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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.
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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.
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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, 299308. 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, 51122. 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.