Page 1
Direct Measurement of Sub-Debye-Length Attraction between Oppositely Charged Surfaces
Nir Kampf,1Dan Ben-Yaakov,2David Andelman,2S.A. Safran,1and Jacob Klein1,*
1Department of Materials and Interfaces, Weizmann Institute of Science, Rehovot 76100, Israel
2Raymond 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 < ?Sagrees 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.103.118304PACS 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 cb). In that limit (where the theory may
be linearized) the range of the interaction scales with the
Debye screening length ?S¼ ð""0kBT=2e2cbÞ1=2; here "0
is the permittivity offree space, " is the dielectric constant,
kBthe 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), ?þ¼ j??j, the forces are
monotonically attractive as a function of D. For D > ?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 [5–9]
of forces between approaching, oppositely charged sur-
faces in the Parsegian-Gingell regime reveal the onset of
measurable attraction at D ? ð1:5–3Þ?S, followed by
jumps into contact from these separations due to mechani-
cal instability ofthe measuringdevices [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 cbwas treated
theoretically [4,11,12], where the high surface potential c
necessitates solution of the PB equation:
r2c ¼ ð2ecb=""0Þsinhðec=kBTÞ:
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
(1)
nonetheless smaller than the screening length ?S(recalling
?S/ c?1=2
nonlinear theory [Eq. (1)] scales approximately as (1=D2)
[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)] [12–14] at all surface separations D,
particularly at D < ?Swhere 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, FnðDÞ, and especially shear forces,
FSðDÞ, between two molecularly smooth, curved mica
surfaces (curvature radius R ? 1 cm) as a function of their
absolute separation D. The high sensitivity, necessary for
detailed examination of the forces, requires a weak force-
measuring spring Kn, 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,usingfast videorecordingofthe SFBoptical
interference fringes which, with frame grabbing and solu-
tion of the optical equations, reveals thevariation with time
t of the separation DðtÞ of the surfaces. From DðtÞ the
resulting normal force FnðDÞ between the surfaces is eval-
uated from the instantaneous balance of forces [16], using
Eq. (2) below:
?d2D
b
). In this regime the attraction predicted by the
FnðDÞ¼m
dt2
?
?Knð?DðtÞÞþ6?R2?
??dD
dt
??
DðtÞ
?
(2)
;
wherem is thetotal massof the(moving) lowersurface, Kn
PRL 103, 118304 (2009)
PHYSICALREVIEWLETTERS
week ending
11 SEPTEMBER 2009
0031-9007=09=103(11)=118304(4)118304-1
? 2009 The American Physical Society
Page 2
is the normal spring constant (150 N=m), and ? is the
viscosity of the liquid in the gap (? ¼ ?water¼
0:85 ? 10?3Pa:s). ?DðtÞ is the deflection of the spring,
given by ?DðtÞ ¼ Dt¼0? DðtÞ þ vappt, where vappis the
inward applied velocity (in the range 10–20 nm=sec, see
also inset to Fig. 1), and is determined from the video
recording at large separations where FnðDÞ ? 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 ? 3–4 ppb) were
measured as previously detailed [16]. Mica loses surface
Kþions in water to become negatively-charged, with
consequent repulsive forces FnðDÞ between two similar
surfaces (the Kþions 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 ?Sof the forces, while the effective
charge density ??on each bare mica surface may be
extracted via a fit to the FnðDÞ 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
washingtoremoveexcess),aspreviouslydescribed[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,
revealingauniformlycoated surfacesmoothto 2 ? 0:4 nm
rms over a 1 ? 1 ?m2area.
Figure 1 shows normalized force profiles FnðDÞ=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 ?S¼ 68 ?
8 nm evaluated from the far-field regime (D > ?S). This
value corresponds to an effective salt concentration of ð2 ?
0:5Þ ? 10?5M 1:1 electrolyte (attributed to dissolved at-
mosphericCO2, the extentof 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 cbwe extract the effective bare mica surface
charge density j??j ¼ e=ð66:5 nm2Þ through a best fit of
the data using the PB equation [Eq. (1)] with constant
surface charge (augmented by a vdW attraction term [2]
FvdWðDÞ=R ¼ ?ðA=6D2Þ, with A ¼ 2 ? 10?20J), shown
as the solid curve in the upper part of the figure. As in
earlier studies [16] the surfaces jump under vdWattraction
from a separation 3 ? 0:5 nm into 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 ? 0:3 nm (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 cb¼
2 ? 10?5M), for antisymmetric surface charge densities,
i.e. ?þ¼ j??j ( ¼ e=ð66:5 nm2Þ), 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 FnðDÞ curve equals Kn, as expected [10]. We
0 100 200 300
-3000
-2000
-1000
0
1000
2000
σ = e/66.5 nm
2 (cb=2x10
-5 M)
Fn/R (µN/m)
D (nm)
J
λs
DD
Kn
Kn
Ks
Ks
PZT
vapp
FIG. 1.
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=ð66:5 nm2Þ, a 1:1 electrolyte
concentration cb¼ 2 ? 10?5M (derived from the Debye screen-
ing length at D ? ?S) and a vdW attraction FvdWðDÞ=R ¼
?A=6D2, with A ¼ 2 ? 10?20J. 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@Fn=@DÞ ? Kn. Broken curve: predicted interaction [4,12]
based on antisymmetric surface charge densities, ?þ¼ j??j ¼
e=ð66:5 nm2Þ. Dotted curve: vdW attraction FvdWðDÞ=R ¼
?A=6D2, with A ¼ 2 ? 10?20J. (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; Knand Ks
are the constants of the normal and shear springs, respectively,
PZT is the sectored piezocrystal, and vappthe applied velocity
of the normal spring mount (bottom) in the dynamic mode [see
Eq. (2)].
Normal force profiles FnðDÞ=R between curved mica
PRL 103, 118304 (2009)
PHYSICALREVIEW LETTERS
week ending
11 SEPTEMBER 2009
118304-2
Page 3
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, Rg? 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 FnðDÞ 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
profilessummarizedinFig. 3includeinteractions both ona
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
100200300
0.0
0.1
0.2
0.3
5
10
15
20
Fs ( N)
D (nm)
D
J
X0
X0= 30nm
2 sec
Fs=10 N
J
FIG. 2.
surface and a bare mica surface sliding past it at separation D,
where X0is 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, Fs is measurable—revealing little shear force
above the noise—right down to D ? 3 nm.
Shear force FsðDÞ profiles between a chitosan-coated
0 100
D (nm)
200
-3000
-2000
-1000
0
1000
2000
Fn/R ( N/m)
s
Chitosan
vs. chitosan
Chitosan
vs. mica
Mica vs. mica
0 100200
100
1000
FIG. 3.
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 ?þ¼
j??j ¼ e=ð66:5 nm2Þ as in Fig. 1 but augmented by vdW
attraction
FvdWðDÞ=R ¼ ?A=6D2,
Solid curve: predicted forces (based on solution of the PB
Eq. (1) with constant charge condition) for the asymmetric
case
?þ¼ e=ð90 nm2Þ,
2 ? 10?5M, augmented by FvdWðDÞ=R as above. Inset:
Quasistaticallymeasured
FnðDÞ=R
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 cb¼
2 ? 10?5M and ?þ¼ e=ð90 nm2Þ on both surfaces, augmented
by FvdWðDÞ=R as above.
Normal force profiles FnðDÞ=R between two mica
with
A ¼ 2 ? 10?20J.
j??j ¼ e=ð66:5 nm2Þ
and
cb¼
profiles betweentwo
PRL 103, 118304 (2009)
PHYSICAL REVIEWLETTERS
week ending
11 SEPTEMBER 2009
118304-3
Page 4
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 ?þ¼ j??j
from Fig. 1 augmented by a vdW attraction term
FvdWðDÞ=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
?þ¼ e=½ð90 ? 10Þ nm2?. This independently determined
value of ?þfor 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 [11–14]
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
[1] S.A. Safran, Statistical Thermodynamics Of Surfaces,
Interfaces And Membranes (Addison-Wesley, New York,
1994).
[2] J.N. Israelachvili, Intermolecular And Surface Forces
(Academic Press Limited, London, 1992).
[3] V.A. Parsegian and D. Gingell, Biophys. J. 12, 1192
(1972).
[4] S.A. Safran, Europhys. Lett. 69, 826 (2005).
[5] K. Besteman et al., Phys. Rev. Lett. 93, 170802 (2004).
[6] K. Besteman, M.A.G. Zevenbergen, and S.G. Lemay,
Phys. Rev. E 72, 061501 (2005).
[7] M. Giesbers, J.M. Kleijn, and M.A. Cohen Stuart,
J. Colloid Interface Sci. 252, 138 (2002).
[8] P.G. Hartley and P.J. Scales, Langmuir 14, 6948 (1998).
[9] K. Lowack and C.A. Helm, Macromolecules 31, 823
(1998).
[10] Sensitivity in measuring forces FðDÞ between surfaces D
apart requires springs of low constant Kn, leading to Euler-
like instabilities and jumps-in whenever dF=dD > Kn.
[11] A.A. Meier-Koll, C.C. Fleck, and H.H. von Grunberg,
J. Phys. Condens. Matter 16, 6041 (2004).
[12] D. Ben-Yaakov et al., Europhys. Lett. 79, 48002 (2007).
[13] S.H. Behrens and M. Borkovec, Phys. Rev. E 60, 7040
(1999).
[14] D. McCormack, S.L. Carnie, and D.Y.C. Chan, J. Colloid
Interface Sci. 169, 177 (1995).
[15] J. Klein and E. Kumacheva, J. Chem. Phys. 108, 6996
(1998).
[16] U. Raviv et al., Langmuir 20, 5322 (2004).
[17] D.Y.C. Chan and R.G. Horn, J. Chem. Phys. 83, 5311
(1985).
[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 ? 105Da 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.
[20] J. Klein and P.F. Luckham, Nature (London) 308, 836
(1984).
[21] E. Eiser et al., Phys. Rev. Lett. 82, 5076 (1999).
[22] U. Raviv, R. Tadmor, and J. Klein, J. Phys. Chem. B 105,
8125 (2001).
PRL 103, 118304 (2009)
PHYSICALREVIEWLETTERS
week ending
11 SEPTEMBER 2009
118304-4
Download full-text