Direct Measurement of Sub-Debye-Length Attraction between Oppositely Charged Surfaces

Article (PDF Available)inPhysical Review Letters 103(11):118304 · September 2009with45 Reads
DOI: 10.1103/PhysRevLett.103.118304 · Source: PubMed
Abstract
Using a surface force balance with fast video analysis, we have measured directly the attractive forces between oppositely charged solid surfaces (charge densities sigma(+), sigma(-)) across water over the entire range of interaction, in particular, at surface separations D below the Debye screening length lambda(S). At very low salt concentration we find a long-ranged attraction between the surfaces (onset ca. 100 nm), whose variation at D<lambda(S) agrees well with predictions based on solving the Poisson-Boltzmann theory, when due account is taken of the independently-determined surface charge asymmetry (sigma(+) not equal to |sigma(-)|).
Direct Measurement of Sub-Debye-Length Attraction between Oppositely Charged Surfaces
Nir Kampf,
1
Dan Ben-Yaakov,
2
David Andelman,
2
S. A. Safran,
1
and Jacob Klein
1,
*
1
Department of Materials and Interfaces, Weizmann Institute of Science, Rehovot 76100, Israel
2
Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Ramat Aviv, Tel Aviv 69978, Israel
(Received 15 May 2009; published 11 September 2009)
Using a surface force balance with fast video analysis, we have measured directly the attractive forces
between oppositely charged solid surfaces (charge densities
þ
,
) across water over the entire range of
interaction, in particular, at surface separations D below the Debye screening length
S
. At very low salt
concentration we find a long-ranged attraction between the surfaces (onset ca. 100 nm), whose variation at
D<
S
agrees well with predictions based on solving the Poisson-Boltzmann theory, when due account is
taken of the independently-determined surface charge asymmetry (
þ
j
j).
DOI: 10.1103/PhysRevLett.103.118304 PACS numbers: 82.70.y, 07.10.Pz, 82.45.Mp
The Debye-Hu
¨
ckel, and more generally the Derjaguin-
Landau-Verwey-Overbeek approach, based on lineariza-
tion of the Poisson-Boltzmann (PB) theory, are used clas-
sically to calculate the repulsive interactions between
uniform symmetrically-charged surfaces, and their predic-
tions have been amply verified [1,2]. In 1972, Parsegian
and Gingell [3] extended this to interactions between un-
equally-charged surfaces in the low surface potential limit
(as may result from strong electrostatic screening at high
salt concentration c
b
). In that limit (where the theory may
be linearized) the range of the interaction scales with the
Debye screening length
S
¼ð""
0
k
B
T=2e
2
c
b
Þ
1=2
; here "
0
is the permittivity of free space, " is the dielectric constant,
k
B
the Boltzmann constant, T the absolute temperature,
and e the electronic charge. For unequally-charged sur-
faces the forces may be attractive or repulsive [3], but in
the case of surfaces whose charge densities are equal and
opposite (i.e., antisymmetric),
þ
¼j
j, the forces are
monotonically attractive as a function of D.ForD>
S
,
such attraction is predicted to decay exponentially with D
[3]. Qualitatively, this attraction may be viewed [4] as due
to the entropy gain arising through release of counterion
pairs from the intersurface gap into the surrounding reser-
voir, as the surfaces approach. Direct measurements [59]
of forces between approaching, oppositely charged sur-
faces in the Parsegian-Gingell regime reveal the onset of
measurable attraction at D ð1:53Þ
S
, followed by
jumps into contact from these separations due to mechani-
cal instability of the measuring devices [10]; the magnitude
of the attraction during the jumps could not be measured.
Recently the case of oppositely charged surfaces across
water at very low bulk salt concentration c
b
was treated
theoretically [4,11,12], where the high surface potential
c
necessitates solution of the PB equation:
r
2
c
¼ð2ec
b
=""
0
Þ sinhðe
c
=k
B
TÞ: (1)
This low-salt regime is of special interest because the
attraction between the surfaces can be significant over a
surface separation range of order 50 nm or more, which is
nonetheless smaller than the screening length
S
(recalling
S
/ c
1=2
b
). In this regime the attraction predicted by the
nonlinear theory [Eq. (1)] scales approximately as (1=D
2
)
[4]. Here we measure directly the forces between two
oppositely charged surfaces as a function of their separa-
tion across water with no added salt. Our results reveal a
long-ranged attraction, which at its onset (at D ¼ ca:
100 nm) is many orders of magnitude larger than van der
Waals (vdW) attraction. Using fast video recording we are
able to characterize the attraction between the surfaces
continuously as they come into contact. We find that the
measured forces agree well with the variation given by the
PB theory [Eq. (1)] [1214] at all surface separations D,
particularly at D<
S
where its predictions diverge from
those of the linearized treatment [3], when proper account
is taken of the (independently-determined) asymmetry in
the surface charge density.
We use a surface force balance (SFB) [15] (see sche-
matic inset to Fig. 1), with high sensitivity in measuring
both normal forces, F
n
ðDÞ, and especially shear forces,
F
S
ðDÞ, between two molecularly smooth, curved mica
surfaces (curvature radius R 1cm) as a function of their
absolute separation D. The high sensitivity, necessary for
detailed examination of the forces, requires a weak force-
measuring spring K
n
, which in turn leads to a spontaneous
jump-in of the surfaces [10] as in previous studies [7,9].
We measure forces during the jump-in via a dynamic
measurement, using fast video recording of the SFB optical
interference fringes which, with frame grabbing and solu-
tion of the optical equations, reveals the variation with time
t of the separation DðtÞ of the surfaces. From DðtÞ the
resulting normal force F
n
ðDÞ between the surfaces is eval-
uated from the instantaneous balance of forces [16], using
Eq. (2) below:
F
n
ðDÞ¼m
d
2
D
dt
2
K
n
ðDðtÞÞþ6R
2

dD
dt

DðtÞ
;
(2)
where m is the total mass of the (moving) lower surface, K
n
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0031-9007=09=103(11)=118304(4) 118304-1 Ó 2009 The American Physical Society
is the normal spring constant (150 N=m), and is the
viscosity of the liquid in the gap ( ¼
water
¼
0:85 10
3
Pa:s). DðtÞ is the deflection of the spring,
given by DðtÞ¼D
t¼0
DðtÞþv
app
t, where v
app
is the
inward applied velocity (in the range 1020 nm= sec , see
also inset to Fig. 1), and is determined from the video
recording at large separations where F
n
ðDÞ0. The first
and second terms on the right-hand side of Eq. (2) are the
inertial and spring-bending contributions to the force,
while the third is the Reynolds-Taylor hydrodynamic lu-
brication force between the moving surfaces [17].
Force profiles between mica surfaces in pure water
(Milli-Q Gradient A10 purification system, water resistiv-
ity 18:2M and total organic content 34 ppb) were
measured as previously detailed [16]. Mica loses surface
K
þ
ions in water to become negatively-charged, with
consequent repulsive forces F
n
ðDÞ between two similar
surfaces (the K
þ
ions disperse throughout the volume
and contribute negligibly to the effective salt concentra-
tion). The effective salt concentration is evaluated via the
far-field decay length
S
of the forces, while the effective
charge density
on each bare mica surface may be
extracted via a fit to the F
n
ðDÞ profiles based on the PB
equation (1) with the condition of constant surface charge.
Following this, one surface was then removed and coated
with chitosan [18], a positively-charged polysaccharide.
The chitosan adsorbs from aqueous solution (followed by
washing to remove excess), as previously described [18], to
form a thin layer which reverses the charge on the mica,
through charge overcompensation, from net negatively
charged to net positively charged, as seen at once from
the resulting forces. Atomic force microscopy (not shown)
was used to characterize the chitosan layer topography,
revealing a uniformly coated surface smooth to 2 0:4nm
rms over a 1 1 m
2
area.
Figure 1 shows normalized force profiles F
n
ðDÞ=R be-
tween the bare mica surfaces measured across pure water
in the usual quasistatic way, i.e., via monitoring of the
spring bending during stepwise changes in D [15]. A
long-ranged repulsion due to counterion osmotic pressure
is observed (star symbols), with measurable forces setting
on from D ¼ ca: 200 nm, with a Debye length
S
¼ 68
8nmevaluated from the far-field regime (D>
S
). This
value corresponds to an effective salt concentration of ð2
0:5Þ10
5
M 1:1 electrolyte (attributed to dissolved at-
mospheric CO
2
, the extent of which may be evaluated from
the slightly acidic pH of our solutions, pH ¼ 5:8 0:2,
and residual ions leached from the glassware [19]). Using
this value for c
b
we extract the effective bare mica surface
charge density j
e=ð66:5nm
2
Þ through a best fit of
the data using the PB equation [Eq. (1)] with constant
surface charge (augmented by a vdW attraction term [2]
F
vdW
ðDÞ=R ¼ðA=6D
2
Þ, with A ¼ 2 10
20
J), shown
as the solid curve in the upper part of the figure. As in
earlier studies [16] the surfaces jump under vdW attraction
from a separation 3 0:5nminto adhesive contact. After
coating the upper surface with chitosan to reverse its
charge a monotonic attraction, larger than the scatter in
the data, sets on at D 100 nm, with the surfaces jumping
[10] from D ¼ ca: 60 nm into an adhesive contact at D ¼
2 0:3nm(a measure of the thickness of the compressed
chitosan coating). The dashed curve is the predicted attrac-
tion based on solving the PB equation, Eq. (1) (for c
b
¼
2 10
5
M), for antisymmetric surface charge densities,
i.e.
þ
¼j
j ( ¼ e=ð66:5nm
2
Þ), neglecting any vdW
contribution. We see that indeed the onset of attraction
and its magnitude are reasonably predicted by this ap-
proach, and in particular that the jumps-in to contact
(arrows in Fig. 1) occur roughly where the slope of the
predicted F
n
ðDÞ curve equals K
n
, as expected [10]. We
0100200300
-3000
-2000
-1000
0
1000
2000
σ
= e/66.5 nm
2
(c
b
=2x10
-5
M)
F
n
/R (
µ
N/m)
D (nm)
J
λ
s
D
K
n
K
s
D
K
n
PZT
K
s
v
app
FIG. 1. Normal force profiles F
n
ðDÞ=R between curved mica
surfaces (mean radius R) across water with no added salt. w, q:
interactions between bare mica surfaces (from independent ex-
periments, i.e., different pairs of mica sheets). The solid curve is
the prediction based on the PB equation [Eq. (1)] with constant
surface charge density
¼ e=ð66:5nm
2
Þ,a1:1 electrolyte
concentration c
b
¼ 2 10
5
M (derived from the Debye screen-
ing length at D
S
) and a vdW attraction F
vdW
ðDÞ=R ¼
A=6D
2
, with A ¼ 2 10
20
J. Solid black symbols (from
different experiments and contact points): interactions between
a chitosan-coated and a bare mica surface; the arrows indicate
the jump-in (J) at the point of mechanical instability, expected
for ð@F
n
=@DÞK
n
. Broken curve: predicted interaction [4,12]
based on antisymmetric surface charge densities,
þ
¼j
e=ð66:5nm
2
Þ. Dotted curve: vdW attraction F
vdW
ðDÞ=R ¼
A=6D
2
, with A ¼ 2 10
20
J. (asterisks and diamonds: 2nd
approach of surfaces at 2 different contact points in different
experiments; circles and triangles: 1st and 6th approaches,
respectively, at a given contact point in a different experiment).
The inset shows the schematic of the SFB with the two surfaces
facing each other in a crossed-cylinder configuration; K
n
and K
s
are the constants of the normal and shear springs, respectively,
PZT is the sectored piezocrystal, and v
app
the applied velocity
of the normal spring mount (bottom) in the dynamic mode [see
Eq. (2)].
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118304-2
emphasize that there is negligible, if any, transfer of chi-
tosan between the bare and coated mica surfaces when they
come into contact; this is demonstrated by the fact that 1st,
2nd and 6th approaches (Fig. 1 caption) of the surfaces at
given contact points show very similar attractive profiles.
To proceed, we confirm that the onset of the measured
long-ranged attraction is not due to large, positively-
charged polymer loops extending from the adsorbed chi-
tosan layers, which are known to lead to long-ranged
attractive bridging forces [20] (bearing in mind the large
radius of gyration of the chitosan, R
g
100 nm [18]). To
do this we measure the shear forces between the bare mica
and the chitosan-bearing mica. The resulting shear force
traces are shown in Fig. 2, and reveal that there is little
shear force between the surfaces as they approach down to
the jump-in separation. By clamping the normal force
springs, we are also able to suppress the jump-in, and
thus to show that shear forces are within the scatter down
to D<ca: 3 nm. Since shear forces are very sensitive to
any bridging by the polymer chains [21,22], this confirms
that loops from the chitosan layer do not extend beyond a
few nm from the mica surface, and that the long-ranged
attraction is due purely to electrostatic effects.
To obtain the F
n
ðDÞ profile over the entire range of the
interaction—including, in particular, the jump-into-contact
regime—we carried out dynamic measurements using fast
video recording and frame-grabbing analysis described
above [Eq. (2)]. The results are shown in Fig. 3. For the
symmetric (mica-mica) repulsive regime (large open
circles and squares) the dynamic data are within the scatter
of the quasistatic force profiles from Fig. 1, and very close
to the predicted variation (dashed top curve, taken from
Fig. 1). For the case of attracting oppositely charged sur-
faces, the dynamic profiles all fall within a small range
(diamonds and empty circles show profiles at the extremes
of the range, with the striped region including 3 other
dynamic profiles, not shown for clarity). The five attractive
profiles summarized in Fig. 3 include interactions both on a
first approach as well as on subsequent approaches: We
found no systematic differences between a first approach
and second or subsequent approaches at the same contact
point, indicating that little if any transfer of the polyelec-
trolyte was occurring between the surfaces. The range of
0
100 200 300
0.0
0.1
0.2
0.3
5
10
15
20
F
s
( N)
D (nm)
D
J
X
0
X
0
= 30nm
2 sec
F
s
=10 N
J
FIG. 2. Shear force F
s
ðDÞ profiles between a chitosan-coated
surface and a bare mica surface sliding past it at separation D,
where X
0
is the applied lateral motion. The cartoon illustrates the
adsorption on the lower mica surface of the positively charged
chitosan, interacting with the negatively charged upper mica
surface. The right inset shows the actual traces, the top one
being the back-and-forth sliding motion of the top surface, and
the lower trace being the shear force transmitted between the
surfaces. When the lower surface is free (filled circles) there is
little shear force above the noise until the surfaces jump into
contact at J. On clamping the lower surface (squares) to suppress
any jump-in, F
s
is measurable—revealing little shear force
above the noise—right down to D 3nm.
0100200
-3000
-2000
-1000
0
1000
2000
F
n
/R ( N/m)
D (nm)
s
Chitosan
vs. chitosan
Chitosan
vs. mica
Mica vs. mica
0 100 200
100
1000
FIG. 3. Normal force profiles F
n
ðDÞ=R between two mica
surfaces (either bare or coated with chitosan) measured dynami-
cally via fast-rate video recording across water with no added
salt. Repulsive profiles between bare mica surfaces are shown by
the open circles and squares (from independent experiments, i.e.,
different pairs of mica sheets), and the dashed curve is the
theoretical prediction from Fig. 1. All attractive profiles between
a bare and a chitosan-coated mica surface fall in the striped
region shown: diamond and empty circles are data for dynamic
profiles at the two extremes of this spread, which include 3
additional dynamic profiles (not shown for clarity). The grey
band is the range of measured quasistatic profiles from Fig. 1.
Dotted curve: predicted forces for antisymmetric case
þ
¼
j
e=ð66:5nm
2
Þ as in Fig. 1 but augmented by vdW
attraction F
vdW
ðDÞ=R ¼A= 6D
2
, with A ¼ 2 10
20
J.
Solid curve: predicted forces (based on solution of the PB
Eq. (1) with constant charge condition) for the asymmetric
case
þ
¼ e=ð90 nm
2
Þ, j
e=ð66:5nm
2
Þ and c
b
¼
2 10
5
M, augmented by F
vdW
ðDÞ=R as above. Inset:
Quasistatically measured F
n
ðDÞ=R profiles between two
chitosan-coated mica surfaces (different symbols are for differ-
ent contact points). The curve is the prediction based on solution
of the PB [Eq. (1)] with constant charge condition and c
b
¼
2 10
5
M and
þ
¼ e=ð90 nm
2
Þ on both surfaces, augmented
by F
vdW
ðDÞ=R as above.
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dynamic profiles is also similar to the quasistatic data from
Fig. 1, indicated as a lightly-shaded region in Fig. 3, where
they overlap prior to the jump-in. The dynamic profiles
show a rapid increase in attraction at lower D values (D<
ca: 15 nm), indicating the importance of accounting for
vdW attraction. This is implemented in the dotted curve,
which represents the antisymmetric prediction
þ
¼j
j
from Fig. 1 augmented by a vdW attraction term
F
vdW
ðDÞ=R as in Fig. 1. The agreement with the data is
then improved, but a discrepancy remains over the range
10 nm <D<60 nm where the antisymmetric prediction
is outside the range of the measured profiles. To account
for this we must consider the possibility that the opposing
charge densities may be asymmetric,
þ
j
j. This is
done by measuring independently, in a separate (quasi-
static) experiment, the normal force profile between two
similarly chitosan-coated surfaces across water, inset to
Fig. 3. Fitting this profile using the PB equation [Eq. (1)]
with constant surface charge, augmented with the same
vdW attraction as above, then yields a surface density
þ
¼ e=½ð90 10Þ nm
2
. This independently determined
value of
þ
for the chitosan-coated surface, together with
for the mica taken at its value determined from the
bare-mica/bare-mica profiles, and incorporating vdW at-
traction as above, is then used to calculate the profile
shown as the solid curve in Fig. 3. Agreement of the theory
with experiment over almost all the range of attraction then
becomes much closer. We remark that the crossover from
attractive to repulsive electrostatic interaction expected
theoretically [3] for the asymmetric case
þ
j
j is
predicted to occur in the range D<ca: 10 nm already
dominated by the vdW attraction, and so is not seen in
the calculated curve.
In conclusion, we have measured directly the forces
between oppositely charged surfaces across water as a
function of their surface separation D, at low salt concen-
trations where the Debye screening length
s
70 nm
comprises a substantial part of the range of measurable
attraction (ca. 100 nm). Dynamic surface force balance
measurements, using a rapid video recording technique,
enabled a detailed examination of the attractive forces,
particularly in the regime D<
s
, inaccessible to earlier
studies. Our results, taking due account of the indepen-
dently determined charge asymmetry on the interacting
surfaces, are in close agreement with predictions [1114]
of the Poisson-Boltzmann theory for interactions in this
regime.
We thank the Israel Science Foundation (grants to J. K.,
to D. A. and to S. A. S.), the Minerva Foundation and the
Schmidt Minerva Center for Supramolecular Architecture
at the Weizmann Institute (J. K.), and the US-Israel
Binational Science Foundation (grants to D. A. and to
S. A. S.) for their support of this work. D. A. thanks the
Weizmann Institute. This research was made possible in
part by the historic generosity of the Harold Perlman
Family.
*Jacob.klein@weizmann.ac.il
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Interfaces And Membranes (Addison-Wesley, New York,
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[2] J. N. Israelachvili, Intermolecular And Surface Forces
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[3] V. A. Parsegian and D. Gingell, Biophys. J. 12, 1192
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[4] S. A. Safran, Europhys. Lett. 69, 826 (2005).
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[18] The chitosan used and the adsorption procedure are iden-
tical to that described in N. Kampf, U. Raviv, and J. Klein,
Macromolecules 37, 1134 (2004); it has average molecu-
lar mass M ¼ 6 10
5
Da and 85% degree of deacetyla-
tion.
[19] While the level of residual ions is difficult to control, there
is substantial reproducibility between different experi-
ments in water with no added salt (S. Perkin et al.,
Langmuir 22, 6142 (2006)); this is true particularly for a
given set of experiments using mica from the same batch
as in the present study, as seen in different force profiles in
Figs. 1 and 3.
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118304-4
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