Peter Kralchevsky, Krassimir Danov, Nikolai Christov and Mariana Boneva

1
Particles at Fluid Interfaces Electrodipping
Force, Bending Moments and Particle-Stabilized
Emulsions
Peter Kralchevsky, Krassimir Danov, Nikolai
Christov and Mariana Boneva Laboratory of
Chemical Physics and Engineering Faculty of
Chemistry, University of Sofia, Bulgaria (Lecture
at the Eleventh International Conference on
Organized Molecular Films (LB11), Sapporo,
Hokkaido, Japan, June 26-30, 2005)
(1) Capillary forces between colloidal particles
at a fluid interface (2) Particle-stabilized
emulsions (Ramsden, 1903 Pickering, 1907).
New Aspects Forces due to the particle surface
charges electrodipping force, and
electric-field induced capillary attraction.
2
Kinds of Capillary Forces
KEY The lateral capillary forces are due to the
overlap of the menisci formed around the separate
particles attached to a fluid interface.
3
Convective Self-Assembly of Colloids and Proteins
Role of Water Evaporation Drives convective flow
from the suspension toward array. N. Denkov et
al., Nature 361 (1993) 26.
(Yoshimura et al.) Protein ferritin, 2R 12 nm
?
Latex beads, 2R 1.7 ?m ?
(substrate fluorinated oil)
4
Electric-Field-Induced Capillary Forces
Nikolaides, Weitz et al., Nature (2002)
299301 Long-distance ordering of charged latex
particles at a decalin/water interface ?
Suggested Hypothesis Interplay of electrostatic
repulsion and capillary attraction.
The electric force (rather than weight) pushes
each particle toward the water phase. The
overlap of the interfacial distortions around the
two particles leads to a strong lateral capillary
attraction.
Oil
Colloidal particles Water
F(el) can be present for sub-?m particles
(negligible F(g))
5
(1) Are there electrically induced interfacial
deformations? (2) Is the deformation of
sufficiently long-range?
Our Theoretical Analysis
(1) Electric force at particle/water interface
p 16CkT(??pw)2/(4eC)2 11/2 ? 1 (?pw
charge density C salt concentration),
? - Debye screening parameter, ? R gtgt 1
(2) Electric force at particle/oil interface
?pn charge density particle/oil f(?, ?p/?n)
universal function
Both F(w) and F(n) push the particle into water !
Danov, Kralchevsky, Boneva, Langmuir 20 (2004)
6139.
6
Origin of F(n)
Origin of F(w)
Oil Particle No Debye screening The
electrostatics is long-range! ?w gtgt ?n, ?oil ?
Image forces push the particle into water.
Curvature effect PN(R) lt PN(?) F(w)
?rc2PN(?) PN(R)
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Normal balance of forces acting on the particle
Slope angle ?
(1) ? R0 (2) ? R1 (3) ?
R2
(1) Term originating from the electric field in
water (independent of R dependent on salt
concentration, C)
(2) Term originating from the electric field in
oil (proportional to R independent of salt
concentration C)
(3) Term due to gravity (F(g) ? R3 ),
proportional to R2 dominates ? for R ? 1 mm
8
Experiment
interfacial tension ? 52.2 mN/m ?oil 0.763
g/cm3 ?p 2.62 g/cm3
Experiment ? 12.9? vs. ? 0.75? if
the deformation were due to particle weight alone
(!)
silanized glass spheres ? 115?, rc 226 ?m
The difference between the experimental and
gravitational ? can be attributed to the
action of normal electric force (electrodipping
force)
Danov, Kralchevsky, Boneva, Langmuir 20 (2004)
6139
9
Effect of NaCl in the Water Phase
F(el) is independent of NaCl ? F(el) ? F(n)
With typical parameter value ?pw 90 nm2 (C 
0.1 mM, pH  5.8), we calculated F(w) 0.07 ?N,
in agreement with the the result that F(w) ltlt
F(n).
10
F(el) ? F(n) ? in our case, the electrodipping
force is due to charges at the particle-oil
interface
From the experimental F(n) we calculate ?pn
70.9 ?C/m2 For silanized silica/oil it was
determined ?pn 80 ?C/m2 (Horozov, Aveyard,
Clint, Binks, Langmuir 19 (2003) 28222829
Long-range ordering of 1 ?m silica particles at
the octane-water interface, which is insensitive
to the concentration of NaCl in the water, up to
1 M NaCl ? 129o. An effect due to electric
charges at the particle-oil interface.
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Range of the Interfacial Deformation
Laplace equation with electric term
q2 ??g/? effect of gravity
gravitational profile ?
Conclusions The electric deformation has medium
range it is significant for r lt 4R and decays as
1/r4. The resulting attractive capillary force
has a similar range.
? electric deformation ?(r) ? 1/r4
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Capillary Force between Two Particles
(Friction force Capillary force due to
gravity) (the inertial term is negligible)
Experimental results At long distances the
capillary force due to gravity is predominant. At
shorter distances, indication about the action of
an additional strong attractive force is found
(electrocapillary force). The latter dominates
the direct electric repulsion and the
hydrodynamic interaction between the two spheres.
13
Particle-Stabilized Emulsions Curvature Effects
The experiment indicates that Hydrophilic
particles (? lt 90 ?) stabilize O/W
emulsions Hydrophobic particles (? gt 90 ?)
stabilize W/O emulsions.
Expectation In analogy with surfactant
molecules, the monolayers will curve such that
the larger area of the particle surface remains
on the external side, giving rise to o/w
emulsions when ? lt 90? and w/o emulsions when ? gt
90?.
Question Does the curvature (bending) energy
determine emulsion type, or the two factors just
correlate because they are both governed by a
third factor ?
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Interfacial Bending Moment and Bending Elasticity
Work of interfacial deformation
Surface free energy
B Interfacial bending moment A Area
H Mean curvature
B0 B of flat interface ks Bending
elasticity H0 Spontaneous curvature

• Non-Closely Packed Monolayer
• B0 ? ?4ksH0 0 (no spontaneous curvature!)
• ?12 30 mN/m, a 50 nm,
• ?a 0.7 and sin? 1
• ? ks 4.8 ? 103 kT (negligible effect)

15
Closely Packed Monolayer Considerable bending
moment B0 and spontaneous curvature
H0 Bending elasticity fraction at close
packing ? 60?, ?12 30 mN/m, a 50 nm ?
B0 1.5 ? 10?9 N
The effect of B0 is significant The effect of ks
is of higher order and is negligible.
? This is in agreement with the experimental
dependence of emulsion stability on ?.
For ? lt 90?, B0 gt 0 Stabilizing effect For
? gt 90?, B0 lt 0 Destabilizing effect
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Work of Bending vs. Work of Dilatation (closely
packed monolayer, ? lt 90?)
Work of interfacial deformation
?W gt 0 ? stabilizing effect opposes
flocculation ?Wb dominates ?W for small
deformations ?Wdil dominates ?W at larger
deformations ?W is greater for smaller drops.
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Work of Bending vs. Work of Dilatation (closely
packed monolayer, ? gt 90?)
Work of interfacial deformation
?W gt 0 ? destabilization promotes
flocculation ?Wb lt 0, ?Wdil gt 0 ?W has a
minimum at ?Wmin gtgt kT ? stable flocs
18
B gt 0
B lt 0
Flocculation of the emulsion
Stabilization of the emulsion
Kralchevsky, Ivanov, et al., Langmuir 21 (2004)
50
19
Summary and Conclusions

• Electrodipping force (EDF) experimental proof
  and theoretical expressions.
• Charges at the particle-oil interface dominate
  the EDF (in our case).
• Medium range (r lt 4R) of the electric interfacial
  deformation and of the capillary force.
• Electrocapillary force (ECF) experimental
  proof for its existence.
• Bending moment due to closely-packed particle
  monolayers stabilizing or destabilizing effect
  depending on the contact angle.

20
Comparison of Oil-Water and Air-Water Interfaces
The electro-dipping force is considerably smaller
for particles at air-water interface, in
comparison with oil-water interface this can be
attributed to smaller ?pn at the particle-air
interface
21
Electrostatic Problem in the Water Phase Thin
EDL ?R gtgt 1
Maxwell stress tensor
? - electric potential
The normal pressure PN(R) at particle surface is
lower than the bulk pressure PN(?)!
Then, the force pulling the particle into water
is F(w) ? rc2 ?PN
where p 16CkT(??pw)2/(4eC)2 11/2 ? 1
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Electrostatic Problem in the Nonpolar Phases
Glass and Oil
?? ?pw ? ?nw
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Numerical Solution
Second order difference scheme Linear system of
20301 equations Exact solution - band diagonal
systems of equations
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Origin of the Lateral Capillary Force
F(1) F(2) F
F F(?) F(p)
F(?)
F(p)
(force due to surface tension) (force due
to pressure)
Presence of second particle breaks the axial
symmetry ? nonzero integral force