Transcript Surface Forces and Liquid Films Peter A. Kralchevsky Fluids and Solid Interfaces

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 3
sandwiched between
phases 1 and 2
Sofia University
Surface Force, Disjoining Pressure and Interaction Energy
gas
Π
h
liquid
gas
Π
Example: Foam Film stabilized
by ionic surfactant
Disjoining pressure, Π
= Surface force acting per unit area
of each surface of a liquid film [1-4]
Π>0
Π<0
– repulsion
– attraction
Π depends on the film thickness:
Π = Π(h)
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 :

Foam is composed of liquid films
and Plateau borders
f (h0 )    (h) dh
h0
DLVO Surface Forces (DLVO = Derjaguin, Landau, Verwey, Overbeek)
uij (r )  
(1) Electrostatic repulsion
 ij
r6
Their combination leads to
a barrier to coagulation
(2) Van der Waals attraction
Non–DLVO Surface Forces
hydrophobic
interface
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
Πel = excess osmotic pressure of
the ions in the midplane of a
symmetric film (Langmuir, 1938) [5-7]:
n0
n1m, n2m
 el  kT n1m  n2m  2n0 
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.
Πel > 0  repulsion!
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).
n1m  n0 exp(  m );
n2m  n0 exp(  m );


 el  2n0 kT cosh  m  1  n0 kT 2m  0


Ze m
m 
kT
 2m
cosh  m   1 
 O( 4m )
2
Π(h) = ?
Verwey – Overbeek Formula (1948)
Near single interface, the electric
potential of the double layer is [7]:
Zeψ1
h

 γ exp   κ 
4kT
2

Superposition approximation
in the midplane: ψm = 2ψ1 [6]:
Ze
h

 m  2ψ1
 8γ exp   κ 
kT
2

 el (h)  n0 kT 2m  64n0kTγ 2 exp( κ h)
More salt  Greater κ  Smaller Πel
Zeψ1
In the midplane
 1
4kT
 Ze s 
  tanh 

 4kT 
2e 2 I
κ 
εε 0 kT
2
1
I   Z i2ci
2 i
(ionic strength)
(2) Van der Waals surface force:
AH
 vw (h)  
6 h3
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]:
uij (r )  
α ij
r6
(i, j  1, 2, 3)
AH  A12  A23  A31  A33
Aij   2 i  j ij ;
Aij  ( Aii A jj )1 / 2
Symmetric film: phase 2 = phase 1
For symmetric films: always attraction!
AH  A11  2 A13  A33 

1/ 2
A11


1/ 2 2
A33
0
Asymmetric films, A11 > A33 > A22  repulsion!
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:


 
3hP e n12  n32 n22  n32
3  1   3    2   3 
 
 
AH  A132  kT 
4  1   3    2   3  16 2 n 2  n 2 3 / 4 n 2  n 2
1
3
2
3

Zero-frequency term:
( 0)
A132
orientation & induction
interactions;
kT – thermal energy.
Dispersion interaction term:


3/ 4
( 0)
A132
νe = 3.0 x 1015 Hz – main electronic
absorption frequency;
hP = 6.6 x 10– 34 J.s – Planck’s const.
Derjaguin’s Approximation (1934):
The energy of interaction, U, between
two bodies across a film of uneven
thickness, h(x,y), is [11]:
U   f (h( x, y )) dx dy
where f(h) is the interaction free energy
per unit area of a plane-parallel film:

~ ~
f ( h )    ( h ) dh
h
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:

2 R1 R2
U h0  
f h  dh

R1  R2 h
0
From planar films, f(h) to spherical particles, U(h0).
DLVO Theory: The electrostatic barrier
 B  h
AH 

U (h)   R 2 e 
12 h 

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)
U (hmax )  0;
dU
dh
0
h hmax
The Critical Coagulation Concentration (ccc) [6,7]
B
U (hmax )  0 
dU
dh
2
0 
h  hmax
B

e  hmax 
e
 hmax
AH
12 hmax
AH

2
12 hmax
Two equations for determinin g B and hmax
( B  64n0kT 2 )
 ccc  n0 
ccc 
1
Z
6

(64 12π) 2 γ 4 (ε 0ε)3 (kT )5
23 e 2
AH2 ( Ze)6
4
3
5
γ
(
ε
ε
)
(
kT
)
0
 98.5 103
AH2 ( Ze)6
Rule of Schulze (1882) [12] and Hardy (1900) [13]
Na : Mg
2
: Al
3
1
1
1 1
 ccc  1 : 6 : 6  1 : :
64 729
2 3
DLVO Theory [6,7]: Equilibrium states of a free liquid film
(h)   el (h)   vw (h)
Born repulsion
Electrostatic component of disjoining pressure:
 el (h)  B exp(  h) (repulsion )
Van der Waals component
of disjoining pressure:
 vw (h)  
(2) Secondary film
(1) Primary film
h – film thickness; AH – Hamaker constant;
κ – Debye screening parameter
AH
6 h3
(attractio n)
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
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
For details – see the book by Israelachvili [1]
force.
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.
Oscillatorystructural
disjoining
pressure
Depletion
minimum
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.
Metastable states of foam films containing surfactant micelles
Oscillatorystructural
disjoining
pressure
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],
Theoretical curve – formulas by Trokhimchuk et al. [18].
The micelle aggregation number, Nagg = 70, is determined [19].
(the micelles are modeled as hard spheres)
and
Scheludko- Exerowa
(SE) capillary cell [14].
Steric interaction due to adsorbed polymer chains
L  L0  l N 1/ 2 (ideal solvent)
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.
 2L 9 / 4
g
 
 st h   kT  3 / 2 
 h 

for h  2Lg ;
 h 


 2Lg 


3/ 4 
 
Lg  N l
5 1/ 3



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].
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].
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)
f hb (h)  2weh / λ
w = 1050 mJ/m2 and  = 12 nm
proton-hopping polarizability of water (?):
p


H 2O  H 2O  OH  H3O 
(3) Long-range Hphb force (h = 100 – 200 nm):
electrostatic mosaic patches and/or bridging cavitation:
+–+–+
–+–+–
(2) Long-range Hphb force (h = 2 – 20 nm)
Hydration Repulsion
At Cel < 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
Important: fel decreases, whereas fhydr increases
with the rise of electrolyte concentration!
Different hypotheses: (1) Water-structuring models;
interaction free energy per unit area:
f hydr  f 0 exp( h / 0 )
(2) Discreteness of charges and dipoles; (3) Redu-
0  0.6  1.1 nm
ced screening of the electrostatic repulsion [27].
f 0  3  30 mJ/m 2
Disjoining pressure,  (Pa)
7000
1 mM SDP-3S
100 mM MCl
6000
5000
LiCl
NaCl
KCl
RbCl
CsCl
4000
3000
Example:
Data from [27] by the
Mysels–Jones (MJ)
Porous Plate Cell [20]
SE cell: Π < 85 Pa
(thickness h vs. time)
2000
MJ cell: Π > 6000 Pa (!)
1000
(Π vs. thickness h)
0
10
11
12
13
Film thickness, h (nm)
(1) Electrostatic repulsion;
(2) Hydration repulsion.
14
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.