This paper is published as
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Water – From Interfaces to the
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and G. Zaccai, Faraday Discuss., 2009
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interfaces: peptides, proteins and cells
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Lugovoj, Yaxing Liu, Katrin Siefermann, Manfred
Faubel, Helmut Grubmüller, R. Benny Gerber, Yifat
Miller and Bernd Abel, Faraday Discuss., 2009
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Discussion
General discussion
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hydration shell of ubiquitin
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Martin Gruebele and Martina Havenith, Faraday
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Discussion
General discussion
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Papers
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Coarse-grained modeling of the interface between
Similarities between confined and supercooled
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water
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Maria Antonietta Ricci, Fabio Bruni and Alessia
Discuss., 2009
Giuliani, Faraday Discuss., 2009
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Water growth on metals and oxides: binding,
Structural and mechanical properties of glassy
dissociation and role of hydroxyl groups
water in nanoscale confinement
M. Salmeron, H. Bluhm, M. Tatarkhanov, G. Ketteler,
Thomas G. Lombardo, Nicolás Giovambattista and
T. K. Shimizu, A. Mugarza, Xingyi Deng, T. Herranz, S.
Pablo G. Debenedetti, Faraday Discuss., 2009
Yamamoto and A. Nilsson, Faraday Discuss., 2009
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Water nanodroplets confined in zeolite pores
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Mark Gallagher, Ahmed Omer, George R. Darling and
Vuilleumier, Alain H. Fuchs and Anne Boutin, Faraday
Andrew Hodgson, Faraday Discuss., 2009
Discuss., 2009
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What ice can teach us about water interactions: a
Dynamic properties of confined hydration layers
critical comparison of the performance of different
Susan Perkin, Ronit Goldberg, Liraz Chai, Nir Kampf
water models
and Jacob Klein, Faraday Discuss., 2009
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Aragones, Faraday Discuss., 2009
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Study of a nanoscale water cluster by atomic force
microscopy
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Manhee Lee, Baekman Sung, N. Hashemi and Wonho
melting
Jhe, Faraday Discuss., 2009
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Michaelides, E. G. Wang and B. Slater, Faraday
Water at an electrochemical interface—a simulation
study
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and David Chandler, Faraday Discuss., 2009
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Discussion
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PAPER
www.rsc.org/faraday_d | Faraday Discussions
Dynamic properties of confined hydration layers
Susan Perkin,*ab Ronit Goldberg,c Liraz Chai,c Nir Kampfc
and Jacob Klein*ac
Received 28th March 2008, Accepted 16th May 2008
First published as an Advance Article on the web 8th October 2008
DOI: 10.1039/b805244a
Prompted by the recent discovery that water and aqueous monovalent Na+
solutions remain fluid-like when confined to films of a few molecular layers
between mica surfaces,[Raviv et al., Nature, 2001, 413, 51–54; and Raviv and
Klein, Science, 2002, 297, 1540–1543] we now extend the previous study by
comparing the shear- and normal-force properties of 0.1 M Na+, Cs+ and Ni2+
salt solutions which demonstrate a diverse range of behaviours under
confinement. In the case of hydrated Na+ we extend the previous study to higher
pressures, up to 10 atmospheres, and record similar fluidity of the hydration
layers at these elevated pressures. Aqueous Cs+ films under confinement between
mica sheets have been found to be unable to support an applied load—that is to
say they do not demonstrate any hydration repulsion regime—as a result of their
lower hydration energy [see Goldberg et al., Phys. Chem. Chem. Phys., 2008, 10,
4939–4945] which contrasts with the properties of Na+. We show that 0.1 M Ni2+
solution remains close to its bulk viscosity down to nanometre thin films, but
does not demonstrate a hydration repulsion. By comparing the properties of this
range of cations, with differing valency and hydration, we aim to examine the
conditions under which ions serve as effective lubricants and what we call the
‘hydration lubrication’ mechanism.
1. Introduction
The forces that act between surfaces across liquid media have been studied extensively over the past century or so, not least because of their relevance to understanding and controlling colloidal and bio-colloidal stability.1,2 Direct force vs.
surface-separation measurements between well-characterised, molecularly smooth
surfaces across a variety of different liquids became possible with the development
of the mica surface force balance (SFB): some 30 years of experiments using various
forms of the SFB, as well as other methods, have achieved an extensive understanding
of many aspects of equilibrium normal surface forces in both non-aqueous and particularly aqueous systems.3–8 The Derjaguin–Landau–Verwey–Overbeek (DLVO)
theory of colloidal stability1,9—still the benchmark for interpreting surface interactions—has been demonstrated to apply well to certain aqueous systems at low ionic
strengths. In addition, the detailed direct studies of normal forces have revealed,
beyond the mean field theory, the importance of structural and hydration forces,10–12
especially at small surface separations, as well as of hydrophobic interactions.13,14
In contrast to normal forces between surfaces across thin aqueous films, which are
generally well understood, the issue of lateral forces across such films has been far
less studied.15–17 These reflect the dynamic rather than the equilibrium properties
a
Department of Physical and Theoretical Chemistry, University of Oxford, Oxford, UK
Department of Chemistry, University College London, UK
c
Department of Materials and Interfaces, Weizmann Institute of Science, Rehovot, Israel
b
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Faraday Discuss., 2009, 141, 399–413 | 399
of the confined films, with clear relevance to tribology, slip18 and lubrication issues.
In the past few years studies on the shear of thin water films have indicated that the
properties of these films differ significantly from those of non-aqueous solvents.19,20
In particular, water appears to retain its bulk fluidity even when confined by solid
surfaces to films of sub-nanometre thickness.19,21 This is in marked contrast to
organic solvents whose viscosity diverges for films thinner than a few nanometres,
and which tend to become solid-like under such confinements.22–24 The difference
has been attributed to the densification of liquid water under the van der Waals
attraction of the confining walls which suppresses its tendency to solidify, an effect
consistent with detailed molecular dynamics studies.20,25
A related but even more remarkable observation concerns recent experiments
demonstrating an extreme lubricating effect of hydrated ions26,27 and other hydrated
charged species28,29 when confined to nanometrically-thin films between charged
surfaces. Such films can support a normal load due to the presence of the trapped
hydrated ions and the resulting hydration repulsion. The central hypothesis put
forward to explain these first results is based on the thermodynamic stability of
the hydration sheath around the confined ions—which supports the normal
load—concurrent with the kinetic lability of the primary hydration sheath about
such ions, which facilitates rapid exchange of water molecules and thus results in
fluid-like response under shear.26,30 This effect has recently been invoked to explain
the extreme lubricity of charged, highly compressed polymer brushes.28 Very
recently, a massive reduction in friction by boundary lubricants under water has
also been attributed to the hydration of their polar head-groups, with a resulting
locally-fluid (and thus easily sheared) layer at the head-group/substrate interface.29
In the present work we inspect in more detail the normal and shear characteristics
of three contrasting hydrated metal cations between negatively charged (mica)
surfaces, extending the earlier studies21,26 and drawing conclusions through comparison of ions with differing hydration and dynamic characteristics.31 By increasing the
applied load we demonstrate the lubricating behaviour of aqueous Na+ up to pressures relevant in biological and mechanical shearing environments. The overall aim
of the present study is to demonstrate the contrast between Cs+, Na+ and Ni2+ ions,
and especially their lubrication behaviour, resulting from their differing charge and
hydration status at interfaces.
2. Experimental procedure
2.1 Force measurements
The surface force balance (SFB) used in this study to record normal and shear forces
between mica surfaces across electrolyte solutions has been described previously.23
To summarise: large (cm2) single-crystal facet mica sheets, of 1–2.5 mm thickness,
are back-silvered and mounted onto hemi-cylindrical lenses such that the mica sheets
face one another in a crossed-cylinder configuration. One of these lenses is then
translated relative to the other in normal and lateral directions by applying varying
voltages to the sectored piezoelectric tube upon which it is mounted. The distance
between the crossed cylinders at their point of closest separation, D, is measured
directly to 3 Å via fringes of equal chromatic order (FECO) observed in a grating
spectrometer.32 The shape of the FECO also reveals the interaction geometry. The
normal and lateral (shear) forces, FN and FS respectively, resulting from the normal
and lateral displacements are detected as the bending of springs either in the FECO
(normal forces) or by an air-gap capacitance probe (shear forces). Normal forces are
presented as normalised by the mean radius of curvature of the crossed cylinders, R,
i.e. as FN/R; this value is directly proportional to the interaction energy per unit area
between parallel plates.33 The resolution of the shear spring deflection, and therefore
shear force, depends on the isolation of the system from ambient vibrations: before
signal processing this is 4–20 nm (corresponding to 1–5 mN). This shear force data
400 | Faraday Discuss., 2009, 141, 399–413
This journal is ª The Royal Society of Chemistry 2009
collected as a capacitance signal is then Fourier transformed to give a frequency
spectrum. The amplitude of response at the frequency of applied shear motion, u0,
can then be extracted and normalised if necessary, as described earlier.21 Comparison
is then made between the response signals as a function of surface separation,
including at large separations where there is no direct shear coupling although
some response is observed due to indirect coupling through the apparatus. Within
each experiment the scatter is in this way reduced to dFS z 20–50 nN, with variation
from experiment to experiment due to differences in experimental setup leading to
differences in the through-apparatus indirect coupling of the shear motion.
Before each experiment stringent cleaning procedures for all glassware, tools and
apparatus parts were followed, involving strong oxidising (piranha) solutions followed by water and organic solvents, as described earlier.21 All preparation was
carried out in a laminar flow cabinet (Bassaire Ltd) to avoid particulate contamination. Each experiment involved calibration of the mica contacting geometry and mica
thickness in air, followed by similar calibration in pure ‘conductivity’ water. Only
if the normal forces were in agreement with DLVO theory and the shear response
showed no coupling in the last few nm of the water film before mica–mica
contact21 was the experiment deemed to be clean enough to proceed to the next stage.
Calibration of the mica–mica surface separation in water yields a value of approx.
5 5 Å relative to the air contact value, known to be due to dissolution in water of
the air-adsorbed carbonaceous and water layer.34 All measurements of surface separation (D) are relative to this point of mica–mica contact under water, D0 ¼ 0.0 nm.
Therefore a layer of solid-like bound water on the mica surface (as suggested in
X-ray reflectivity (XRR) measurements of the mica/water interface35), leading to
the possibility of a bilayer of water between the mica surfaces when in contact, is
included within this calibration of D0 and subsequent D values measured relative
to this (possible) water layer. For this reason we cannot detect the presence or
absence of this single water layer adsorbed onto the mica, which if present behaves
in a solid-like manner and can be considered as part of the solid crystal-lattice structure, in contrast to the adjacent liquid water.21,34,35
2.2 Materials
The pure ‘conductivity’ water used for these experiments was obtained by passing
tap water through a Millipore water purification apparatus, consisting of a RiOs5
and Milli-Q Gradient A10 system. The water has resistivity greater than 18.2 MU
cm, and a total organic content of 2–4 ppb. Mica was ruby muscovite, grade 1
(S&J Trading Inc., New York). The mica was cleaved for each experiment using
one of two possible methods: downstream melt-cutting and the torn method. These
methods were devised recently to avoid any possibility of the effect of Pt nanoparticles.34 Salts were as follows: NaCl 99.999%, Aldrich, crystals treated with UV
for 30–40 min before making up solutions; CsNO3 99.999%, Aldrich; Ni(NO3)2
99.999%, Aldrich.
3. Results
3.1 Normal forces in Na+ and Cs+ salt solutions
Experiments were conducted to measure the normal forces between mica surfaces
across aqueous Na+ and Cs+ salt solutions, each at 1 101 M concentration,
as a function of surface separation, and the results are presented in Fig. 1. Looking
first to the normal interaction force between the mica sheets across Na+ solution, we
see that the interaction is short-ranged—of the order of a few nm—and strongly
repulsive in agreement with previous studies. The confined hydrated Na+ ions resist
compression or squeeze-out from the film at all values of applied normal loads in this
investigation, which are an order of magnitude higher than those applied in previous
studies.26,27,36 The mica surfaces do not adhere and the forces are reversible. This is in
This journal is ª The Royal Society of Chemistry 2009
Faraday Discuss., 2009, 141, 399–413 | 401
Fig. 1 Normal interaction forces between mica sheets across 1.0 101 M aqueous solutions
of NaCl (all open symbols) and CsNO3 (all filled symbols). The main Figure compares the normalised F/R values as a function of surface separation in these two solutions on a linear scale.
The data for CsNO3, collected in two different laboratories, shows no interaction until the
surfaces are close to D ¼ 1.0–2.0 nm, at which point they are attracted into adhesive contact
at a separation of D ¼ +0.6 nm relative to the closest separation in pure water (before addition
of salt). The solid line in the main Figure represents a DLVO expression using the algorithm of
Chan et al.55 to solve the non-linear Poisson–Boltzmann equation for the electrostatic repulsion, fitted to the Cs+ data with J0 ¼ 10 mV and c ¼ 1.0 101 M monovalent salt, added
to the van der Waals interaction with AH(mica–water–mica) ¼ 2 1020 J. Due to the experimental scatter, the data supports values of J0 < 25 mV. The data for NaCl show a shortranged repulsion with no adhesion at small separations, down to 0.8 0.3 nm. This data is
shown on an extended and logarithmic scale in the inset. The dotted lines in both the main
Figure and the inset show a fit to the Na+ data using the DLVO expression as above, with
J0 ¼ 60 mV and c ¼ 0.6 101 M, and added to this an exponential term for the hydration
repulsion of Ehexp(D/Dh) with Eh ¼ 0.12 J m2, Dh ¼ 0.25 nm.
contrast to the mica–mica interaction in pure water or solutions of Na+ salts at
concentrations below the critical hydration concentration, where the surfaces
jump together from 2–7 nm into primary minimum contact under the influence of
the van der Waals interaction.3,33,37 This short-range repulsive interaction, observed
only above a critical value of the bulk salt concentration and not accounted for
within the DLVO theory, has been called the ‘hydration repulsion’36,38 to reflect
the suggestion that it is due to the tenaciously bound water surrounding the Na+
ions, preventing dehydration and condensation of the ions into the mica lattice.
Here we see that this hydration repulsion extends up to elevated normal force values
of FN/R z 105 mN m1. Using the theory of Hertz for a non-adhesive deformable
solid sphere in contact with a flat plate, we calculate the contacting area, A:33
A z p(RFN/K)2/3
where R is the radius of the sphere, corresponding to the mean radius of our crossed
cylinders at the contact region determined from the FECO, and K is related to the
effective modulus of the surfaces and has a value of K 1 109 Nm2. This method
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This journal is ª The Royal Society of Chemistry 2009
yields a value of A ¼ 1 109 m2 at this maximal applied FN, which is in accordance
with the value estimated from the flattening of the fringes viewed in the FECO and
corresponds to a mean pressure over the contacting area of 1.1 106 Pa. By
assuming an exponential dependence of the hydration force on the separation
between the mica plates, and that this additional force is additive with the mean-field
DLVO contribution, we deduce a value of J0 ¼ 60 mV for the surface potential of
the mica and 0.25 nm for the decay length of the hydration repulsion (see caption to
Fig. 1). These values are close to those observed in the past,26 and we show here that
this expression applies up to enhanced normal force values.
In contrast to this hydration-repulsive behaviour, the normal interaction force
between mica sheets across a 0.1 M Cs+ salt solution is quite different.27,31 We
observe no osmotic repulsion between the mica sheets within our force resolution
until at 1–2 nm a van der Waals attraction causes a small jump-in to contact at D
¼ +0.6 nm relative to mica–mica contact in salt-free water.39 At this point the
surfaces are observed to have a small flattened contact, indicating adhesion, and
indeed a finite pull-off force is required to separate the surfaces from this point:
from the pull-off force, Fpull-off, we calculate the solid–liquid surface tension, g ¼
Fpull-off/3pR ¼ 0.72 0.2 mN m1.31
The absence of osmotic repulsion between the surfaces in the case of Cs+, beyond the
scatter of the experimental data, implies that there is significantly reduced excess
concentration of ions in the electrical double layer at the mica surface. This in turn
implies a very low surface potential (and surface charge), relative to mica surfaces
in pure water, and is likely to be due to neutralisation of the mica (negative) surface
charge by adsorbed Cs+ ions. We can calculate an upper limit for (the modulus of)
the residual negative surface charge on the mica, smax
0 , due to the extensive neutralisation by Cs+ ions, using the experimental resolution-limited upper limit of surface
potential measured in our experiments, J0, and using the Grahame equation:33
smax
¼ (8kBT303rcN)1/2sinh(eJmax
0
0 /2kBT)
where kB is the Boltzmann constant, T the temperature, cN is the concentration
of bulk 1 : 1 salt solution, e is the charge of an electron and 30 and 3r are the permittivity of free space and relative permittivity of the medium respectively. From the
upper limit value of Jmax
¼ 25 mV (caption to Fig. 1) we find s0 < 0.02 Cm2 in
0
0.1 M Cs+ solution (with Debye length k1 ¼ 0.97 nm);31 compared to
0.06 Cm2 in equivalent Na+ solution and 0.002 Cm2 in pure water.
3.2 Shear forces in Na+ salt solutions
In order to investigate the dynamic properties of the film of confined hydrated Na+
ions within the regime of hydration repulsion described above, we have applied
a lateral shearing motion to one of the confining mica surfaces and recorded the
response of the other surface to this motion. The results of these measurements
are shown in Fig. 2. In all cases we observe no shear force response above the noise
level of the measurement, indicating high fluidity of the confined hydrated film
between the surfaces: At all of the shear rates and applied pressures investigated
the aqueous hydration film provides extremely efficient lubrication. From this observation we can extract an upper limit for the effective viscosity of the confined liquid
film, heff, between the surfaces, since:
ss ¼ heffg
where ss ¼ (Fs/A) is the transmitted shear stress in response to the applied shear rate
g ¼ (vs/D) where vs is the shear velocity. The shear force resolution of our measurement, dFS ¼ 30 nN (as outlined in the Figure caption), determines the upper limit
for the shear stress value, supper
, through supper
¼ dFS/A. Using the values from trace
s
s
This journal is ª The Royal Society of Chemistry 2009
Faraday Discuss., 2009, 141, 399–413 | 403
Fig. 2 Shear forces between mica sheets across films of aqueous Na+ solution at varying film
thicknesses. A: example of applied triangle-wave shearing motion, at 2 Hz and 330 nm peak-topeak shearing amplitude. The cartoon inset shows how one surface is sheared laterally relative
to the other (with lateral position Dx0), and any coupling of the surfaces at that point results in
the bending of a spring, by Dxb, which when multiplied by the spring constant, Ks, gives the
shear force, FS. B: shear force response to the applied shearing, with surfaces separated by
4.1 nm of aqueous solution, recorded using a capacitance probe to detect shear spring deflection and taken directly from the oscilloscope reading. To the right of the oscilloscope reading is
the Fourier transformation (FT) of this data showing a peak at the applied frequency of 2 Hz
(applied frequencies are indicated with arrows) due to indirect coupling of the surface through
the apparatus. This signal is identical to traces measured at all larger separations, within the
scatter of 30 nN. C: shear force response to the same applied shearing motion with the
surfaces separated by 0.5 0.3 nm of hydrated Na+ ions, representing a high shear rate of
2.9 103 s1. The FT of the oscilloscope reading, to the right-hand side, is shown with a solid
line and the FT of the ‘large D’ signal is superimposed with the dashed line. The FT traces are
identical within the 30 nN scatter. D and E: shear force response traces for mica surfaces separated by 0.5 and 0.8 nm (0.3 nm) respectively, with large applied normal force as shown on the
traces corresponding to the hydration repulsion regime. In each case the FT trace has the
frequency of applied shear marked with an arrow; the solid line is the FT of the response
data; and the dotted traces overlaid onto these are FTs of the shear force response to an identical applied shear amplitude and frequency when the surfaces are far apart.
C—corresponding to the highest shear rate applied in this study—we therefore find
the upper limit of viscosity: hupper
eff ¼ 0.03 Pa s. Although this value is 30 times higher
than the bulk viscosity of water of 0.001 Pa s, we emphasise that this is an upper
limiting value. In the lower two traces of Fig. 2 we show that by applying a normal
load to the confined hydrated film within the hydration repulsion regime as
described above, we were able to verify this fluidity of the film up to mean pressures
of 1 106 Pa. These data, measured in 4 separate experiments (different mica sheets)
and with different contact points within each experiment, corroborate the previous
report of fluidity of confined hydration layers26,34 and extend towards higher shear
rates and applied normal pressures within the hydration repulsion region.
3.3 Shear forces in Cs+ salt solutions
The shear forces between mica sheets approaching contact in Cs+ solutions and in
pure water are shown in Fig. 3. These very recent results31 demonstrate a significant
404 | Faraday Discuss., 2009, 141, 399–413
This journal is ª The Royal Society of Chemistry 2009
Fig. 3 Shear forces between mica sheets across films of pure water and aqueous Cs+ solution.
A: applied triangle-wave shear motion of the upper surface. B: shear force response between
mica sheets across pure water during approach of the surfaces. The shear force response is
below the noise-limited resolution from large separations (shown here are separations below
4.4 nm), beyond the point at which the surfaces jump into contact (shown with ‘J’), down to
mica–mica contact at D ¼ 0.2 0.3 nm, as shown. At this point the surfaces become instantly
rigidly coupled, and the lower surface moves in parallel with the upper one. C: shear force
response (to applied shear similar to that in A) between mica sheets across 1.0 101 M
CsNO3 during approach of the surfaces. As in pure water, there is no shear force response
measurable at all separations down to closest approach—this time at +0.6 0.3 nm—at which
point the surfaces become coupled. However, in contrast to the pure water case, the yield force
is lower and once the yield force is reached the surfaces slide across each other.
difference between the shear properties of mica sheets contacting across pure
salt-free water and across an aqueous 1.0 101 M solution of Cs+ ions. Additionally, in parallel with the normal force behaviour, we also see a significant contrast
with the results of similar shear measurements in 1.0 101 M Na+ solutions
(Fig. 2).
Fig. 3A shows the applied shear motion of the upper surface and Fig. 3B shows
the shear force response between mica sheets across pure water of film thicknesses
between 4.4 and 0.0 nm. This result, including in particular the jump of the
surfaces into adhesive contact at the point J on the trace, has been analysed in detail
previously.21 From these data, in conjunction with measurements of normal force
interactions in pure water,21 it has been shown that the viscosity of the water remains
close to the bulk value right down to D ¼ D0. At this point the surfaces spontaneously adhere under the influence of the van der Waals forces, and the shear response
demonstrates rigid coupling between the surfaces. Fig. 3C shows the shear behaviour
of mica surfaces approaching contact across 1.0 101 M solutions of CsNO3. The
shear response is within the very low noise level of the measurement at all separations, including during the small jump-in, to D ¼ +0.6 0.3 nm, corresponding
to the point at which the surfaces spontaneously flatten and the interaction becomes
adhesive. At this point the shear response changes spontaneously to a coupled
motion until the yield force is reached: the surfaces move together as one is translated by Dx0, with increasing shear force, FS ¼ KsDx0, until the shear force reaches
a ‘yield point’, FS ¼ Fy, at which point the surfaces slide past each other as seen by
the flat-topped part of the shear trace. This process then repeats itself as the translated surface moves back in the other direction. Fy values were measured in the range
15 mN < Fy < 21 mN. We note that these normal and shear measurements across
CsNO3 solutions involved over 10 independent experiments, with different mica
sheets, in two different laboratories.
This journal is ª The Royal Society of Chemistry 2009
Faraday Discuss., 2009, 141, 399–413 | 405
3.4 Normal and shear forces in Ni2+ salt solutions
Fig. 4 presents the normal and shear interactions between mica sheets across solutions of the divalent transition metal salt Ni(NO3)2. Fig. 4C shows the normal interaction forces across pure water and across 1.0 101 M Ni(NO3)2 solution. In both
cases the surface forces are repulsive, due to osmotic repulsion between the diffuse
double layers: in pure water the interaction is long-ranged, due to the low screening
and long Debye length, whereas in the 1.0 101 M Ni(NO3)2 solution the screening
of the surface charge results in the expected shorter-range repulsive interaction. At
small separations an attractive van der Waals force causes the surfaces to jump
together into contact to D ¼ D0, not only in pure water but also in the Ni2+ solution.
That is to say there is no hydration-repulsion regime in the Ni2+ solution at a bulk
concentration of 1.0 101 M. After attraction into contact the adhesion force
between the surfaces is measured by pulling the surfaces apart and recording the
jump-out distance. For mica sheets in 1.0 101 M Ni(NO3)2 solution we found
Fpull-off/R ¼ 25 mN m1 (a single measurement), from which we obtain the solid–
liquid surface tension, g ¼ 2.7 mN m1. This is within the range of values observed
for mica sheets adhered in pure water as measured in these and similar experiments.21
Fig. 4 A: applied triangle-wave shear motion (upper trace) and shear force response (lower
trace) between mica sheets across 1.0 101 M Ni(NO3)2 solution during approach of the
surfaces. At the point when the surfaces reach contact (after jump towards each other due to
van der Waals attraction) they become coupled and both surfaces move with identical
triangle-wave motion. Before that point there is no shear force response resolved above the
noise level. B: as for A, with solution concentration 1.0 104 M and high shear amplitude.
The inset within B shows a zoom-in of the response in the region before and immediately after
contact between the mica surfaces. The jump distance Dj ¼ 4.5 0.4 nm. To the right of the
oscilloscope shear response trace is an FT of the response signal up until the jump—shown
by the solid line—and, for comparison, the FT of a response signal when the surfaces are far
apart. The component at the applied frequency, u0 (indicated with an arrow), is identical for
these two traces within the scatter, leading to an upper limit for the shear force response before
the jump of dFS ¼ 40 nN. C: normal forces between mica sheets in pure water (crosses) and in
1.0 101 M Ni(NO3)2 solution. The grey line shows a DLVO fit to the water data using the
algorithm of Chan et al.55 to solve the non-linear Poisson–Boltzmann equation. The fitting
parameters are the surface potential, J0 ¼ 115 mV, and the bulk concentration of monovalent
ion, c ¼ 3.0 105 M.
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In Fig. 4A and B we present the shear force response between mica sheets across
solutions of Ni2+ salt solutions, at concentrations of 1.0 101 and 1.0 104 M
respectively, during the approach of the mica sheets from 6–8 nm separations
down to contact. The shear force response, FS, remains within the noise level of
the measurement, dFS, before and during the jump into contact of the mica surfaces,
at which point they become rigidly coupled with yield force greater than the
maximum applied shear force. The jump time is rapid—estimated to be within
0.1–0.3 s in each case—and the jump distances vary according to the concentration:
Dj ¼ 1.7 0.3 nm at [Ni2+]bulk ¼ 1.0 101 M, and Dj ¼ 4.5 0.4 nm at [Ni2+]bulk ¼
1.0 104 M. By performing a Fourier-transform analysis to extract the amplitude
of FS at the applied frequency of the shear, we find that there is no difference
between the response immediately before the jump into contact and the response
at large surface separations between the mica plates. That is to say, there is no shear
response within this improved sensitivity of dFS ¼ 40 nN for films of thicknesses
down to the point of the jump-in. In addition during the jump itself, while the
film thins from 4.5 nm to zero, FS remains within the noise level until the spontaneous rigid coupling of the surfaces at D ¼ D0.
4. Discussion
4.1 Normal forces in Na+ and Cs+ salt solutions
We begin with a comparison of the normal force between mica sheets across aqueous
Na+ and Cs+ solutions, which demonstrates two contrasting features. Whereas the
mica sheets experience an osmotic repulsion in the case of Na+, there is no measurable
repulsion between the mica surfaces across Cs+ solutions. And whilst the mica plates
are held apart by a film of hydrated Na+ ions at separations below 1.0 nm, there is
no hydration-repulsion regime for aqueous Cs+ confined between mica surfaces.31
The absence of hydration repulsion between mica surfaces across Cs+ solutions, as
well as the very low value of the surface charge, implies that Cs+ ions are not bound
to the mica surface in a fully hydrated state in the first solution layer adjacent to the
negative lattice site. Instead, the Cs+ ions appear to energetically favour either expulsion from the film or condensation into the mica lattice. In contrast, Na+ is observed
to form a molecular film of strongly bound and hydrated ions at the mica surface.
Expulsion of Cs+ from the film, by exchanging with a hydrated proton (H3O+) to
maintain charge neutrality, has until recently been the primary interpretation of
the fate of ions when mica surfaces contact across aqueous solution.40 However,
we suggest that a more likely explanation in the case of Cs+ is the condensation of
Cs+ into the mica-lattice negative sites in a partially de-hydrated or fully-dehydrated
state.31 The evidence for this is now discussed.
The Cs+ ion is large in size (r ¼ 0.169 nm)41 with single unit positive charge,
combining to give a small charge to radius ratio. This results in a relatively low
hydration energy, DGhyd,42 which can be interpreted in terms of the energy per coordination water: DGhyd/6–12 ¼ (24–47) kJ mol1;27,43 equivalent to 9–18 kBT at room
temperature. Therefore we expect the Coulombic interaction between the ion and
the surrounding dipolar water molecules to have significantly less effect on the
ordering of water molecules around a Cs+ ion compared to Na+ (DGhyd ¼ 24–
42 kBT per water molecule) or particularly in Ni2+ (DGhyd ¼ 139 kBT per water molecule). This simplistic argument is borne out in detailed simulations and studies.43–46
In relation to the present work, this explains the increased surface-bound concentration of Cs+ on mica relative to Na+: Cs+ is more favourably bound to the surface (as
a de-hydrated ion) due to its less thermodynamically favourable solvation. Indeed,
very recent studies using XRR suggest that Cs+ ions adsorb to mica (not under
confinement) with no intercalated water layer between the ion and the muscovite
negative surface site;47 and X-ray photoelectron spectroscopy (XPS) studies confirm
the ion-exchange of Cs+ on mica.31,48
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Faraday Discuss., 2009, 141, 399–413 | 407
This favourable dehydration and binding at the mica surface for Cs+ explains why
we do not observe the hydration repulsion regime in this case: the Cs+, sitting inside
the mica ditrigonal siloxane cavity,47 is not holding a sheath of water molecules
tightly around it and thereby allows the mica sheets to reach close contact without
repulsion. In addition, we note that this surface-binding of partially dehydrated Cs+
is likely to occur on the mica irrespective of confinement—in the XRR study there
was no confinement—and so the mica surface charge is neutralised by the Cs+
without the need for charge-regulation (condensation due to counterion osmotic
pressure) arguments. Therefore this also accounts for the lack of double-layer repulsion between the surfaces in CsNO3 solution at all surface separations as well as the
low surface charge density, s0.
We observe a significantly lower adhesion value for mica sheets reaching contact
across Cs+ solution compared to pure water, and in addition the closest separation
(at which the adhesion takes place) is some 0.6 nm further apart in Cs+ solution
compared to pure water. We again attribute these observations to the presence of
dehydrated Cs+ ions at the mica surfaces when the surfaces reach contact, as
follows:31 the large Cs+ cation (rCs+ ¼ 0.169 nm) occupying the ditrigonal mica sites
would lead to (i) distortion of the mica lattice structure relative to its bond lengths
and angles with the natural K+ counterion (rK+ ¼ 0.133 nm); and (ii) protrusion of
the Cs+ outside of the mica lattice. These two factors combine to result in the
observed reduced adhesion, at a closest separation of 0.6 nm, and reduced sliding
friction (discussed below) between the mica sheets, since the mica sheets are not
able to reach the same intimate contact as in pure water.
4.2 Shear forces in Na+ salt solutions
We have shown that molecularly thin films or ‘hydration layers’ containing Na+ ions
and water confined between mica surfaces 0.8 0.3 nm apart and under pressures
up to 10 times atmospheric pressure remain fluid-like with an upper limit of viscosity
hupper no larger than 30 times that of bulk water.
This highly fluid behaviour under extreme confinement and shear is in direct
contrast to the performance of non-associating simple liquids, such as octamethylcyclotetrasiloxane (OMCTS), cyclohexane or toluene, under similar conditions:
these non-associating liquids undergo liquid-to-solid phase transition, resulting in
a finite yield stress once confined to 6–9 molecular layers.22,23 We suggest that
the lubricity of hydrated films of Na+ relies upon two factors: the capacity of water
to retain its bulk fluidity under confinement and in hydration layers around
charged species;21,26 and the strong binding of water molecules within the hydration
shell around Na+ which supports an applied load, therefore preventing primary
minimum contact (which is adhesive and leads to high shear forces)31 between
the mica surfaces. The shear lubricity of these load-bearing hydrated films have
been rationalised in terms of the rapid kinetics of exchange of water molecules
within hydration spheres with adjacent water molecules, as well as the rapid
rotational dynamics and diffusivity of the water molecules within the thin film.
The bulk water exchange rate, kex, for a water ligand in the primary hydration
sphere of Na+ is 109 s1, a factor of at least 104 faster than the fastest shear rates
accessible in this experiment. In addition, the rotational relaxation time of water
molecules, 1011 s in bulk water, is thought to be a factor in the persistent fluidity
of the confined hydration layers.30
Recent experiments of Sakuma et al.49 and simulations of Leng and Cummings25,30
have corroborated these results for Na+ hydration layers of $ 0.92 nm thickness.
This is in good agreement with the surface separation at which we find the highly
fluid hydration layer between mica surfaces: D values measured are 0.5–1.0 nm in
Na+ salt within the hydration-repulsion region of the interaction profile, at F/R
values up to 105 mN m1. We note that there may additionally be one water layer
at each surface not accounted for within the D values quoted in the SFB
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measurement if bound water remains at the surfaces during calibration of D0 of mica
contact in water (as discussed in the methods section).
A less fluid layer is described in the simulations of thinner films; rotational relaxation times of water in films of ‘bilayer ice’ (D # 0.6 nm) was found to be up to 105 s
and viscosity is significantly increased at this separation.25 It is interesting that this
seemingly ‘critical separation’ for fluidity occurs at the same separation value as
the steep repulsive wall observed in normal force measurements. This corroborates
our conclusion that the presence of hydrated ions—cations coordinated to the negative mica sites but surrounded by a sheath of water molecules—constitutes the lubricating layer. At closer separations, not accessible in the present experiments due to
the steep repulsive wall of hydration repulsion, the cations are presumably stripped
of their hydration layers and the lubricating fluidity may not occur.
4.3 Shear forces in Cs+ salt solutions
In contrast to the shear forces across Na+ solutions at small separations discussed above, mica sheets shearing across Cs+ solutions exhibit discontinuous
behaviour: The shear force remains below our detection limit for D $ 0.6 0.3 nm, while at D ¼ 0.6 0.3 nm—the closest separation of the surfaces—
a shear force is transmitted between the surfaces with yield force in the range
15.0 mN < Fy < 21.5 mN.
We can also compare this behaviour in Cs+ solution with the shear forces in pure
water (Fig. 3B), to find that (i) the separation of the mica sheets at which the shear
stress increases above the experimental resolution is larger in Cs+ than in pure water
(by 0.6 nm), and (ii) in Cs+ solution the yield stress at the closest separation is
significantly decreased compared to micas reaching contact from pure water.
In the discussion of normal forces above we arrived at the conclusion that Cs+ ions
reside at the mica surfaces in an un-hydrated form, particularly when the mica sheets
are brought to sub-nanometre separations. This conclusion is strongly supported by
these shear force measurements, since the nature of the contacting mica sheets is
clearly different when contact occurs from Cs+ solution. The bound Cs+ ions must
be un-hydrated for geometrical reasons: hydrated Cs+ would not fit inside the mica
sites nor fit between the mica sheets at this closest separation. Therefore it appears
that unhydrated Cs+ ions, incorporated into the mica lattice but extending outwards
from it, are leading to a reduction in the shear stress sustainable between the Cs-mica
sheets. We note that variations in the value of Fy could result from variation in
the mica–mica twist angle, which was not finely controlled in these experiments.50
4.4 Normal and shear forces in Ni2+ salt solutions
The short-ranged (2–5 nm) small repulsive interaction between mica sheets across
1.0 101 M Ni(NO3)2 solution is in broad agreement with previous studies of divalent ions.12,51 At a surface separation of 1.7 0.3 nm the interaction becomes attractive, and the surfaces are pulled into contact at D ¼ D0. The interaction cannot be
well explained using the mean-field DLVO theory; the attractive interaction appears
to be accounted for only by invoking a correlation interaction due to the divalent
nature of the ions,12,52,53 although we do not discuss this further here. Our main focus
is the absence of hydration repulsion at 1.0 101 M solution and the resulting shear
forces as the surfaces approach contact.
We have argued above that the hydration repulsion is observed in Na+ solution
but not in Cs+ as a result of the repulsion between strongly bound hydration sheaths
of water molecules around the Na+ ions. However, we now look to the case of Ni2+,
which has a hydration energy value 5 times higher than Na+ (DGhyd(Ni2+) ¼ 2068 kJ
mol1, due to the double charge and small ionic radius of 0.07 nm,42 compared to
DGhyd(Na+) ¼ 411 kJ mol1) and see no hydration-repulsion regime at this bulk
concentration. We suggest that this may be due to the less strong coordination of
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the highly hydrated Ni2+ ions with the mica sites—due to the less (enthalpically)
favourable partial-dehydration required for closest approach of the ion to the
surface—resulting in attraction of the surfaces to D ¼ D0 and balance of the mica
charge by protons at D0 as the hydrated Ni2+ ions are expelled from the confined
film. This conclusion is additionally backed up by the observations that the adhesion
force after jump-in to contact and the surface separation at this point of closest
approach are within the boundaries of values measured in pure water, confirming
that the Ni2+ ions are unlikely to be held between the mica surfaces at this point
in contrast to what we have seen in the case of Cs+.
We now calculate the effective viscosity of the Ni2+ solution confined to a film
between the surfaces before the jump-in to contact. It has been demonstrated recently
how the effective viscosity of the film, heff, can be calculated by analysis of the
dynamics of the escaping hydration film during the jump together of the surfaces
into mica–mica contact under influence of van der Waals interactions.21 The ‘jumptime’, tj, is related to the viscosity of the film according to the following expression:
tj ¼ (18pRheff/A)[Dj2 D02]
where A is the Hamaker constant determining the van der Waals interaction. Using
the experimentally measured value of the jump distance of 1.7 nm in 1 101 M
Fig. 5 Cartoon, approximately to scale, indicating the contrasting behaviour of ions at mica
surfaces. On the left-hand side the negatively charged mica surface is neutralised by counterions
in pure water (top), 1 101 M Cs+ ions (middle), and 1 101 M Na+ ions (bottom). On the
right-hand side we show two mica surfaces in contact, with different counterions between the
surfaces, and their differing degrees of hydration, as discussed in the text.
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Ni(NO3)2 solution and the experimentally estimated jump times of 0.3 0.2 s, we
determine the effective viscosity of the film in these two cases to be 1.2 < heff <
6.1 mPa s.54 These results suggest that the film of hydrated Ni2+ ions squeezing
out from between the mica surfaces has viscosity close to that of bulk water, and
to that expected for bulk 1 101 M Ni(NO3)2 solution.42
This study of Ni(NO3)2 solution demonstrates that although 1 101 M Ni(NO3)2
solution remains highly fluid in thin films between mica sheets, this very strongly
hydrated ion does not provide ‘hydration lubrication’ at this bulk concentration
due to its apparent weaker interaction with the mica surface compared to Na+
and Cs+ ions.
5. Conclusion
The three ions investigated in this study, each at 1 101 M concentration, demonstrate three very different behaviours with respect to confinement in thin films
and the resulting lubrication of the shearing surfaces. We tentatively attribute these
contrasting properties as demonstrated with a schematic cartoon in Fig. 5. Na+
appears to remain bound to the mica surfaces, in hydrated form, on confinement
to a film of thickness 0.8 0.3 nm and under external applied loads of up to 10
atmospheres pressure. Under this confinement the hydrated film remains fluid in
the shear plane, with viscosity close to that of bulk solution, and thereby provides
effective lubrication of the shearing surfaces by relieving the applied shear stress
with little frictional dissipation. Cs+ also remains bound to the mica surfaces under
molecular level confinement—a conclusion derived from the shear behaviour of the
surfaces at closest approach, the distance of closest approach and the adhesion
value—but in contrast to Na+ films, the Cs+ ion does not hold a bound hydration
layer. As the mica surfaces approach, the van der Waals attraction between
them is sufficient to expel all water from the film, whereupon a finite yield stress is
recorded between the shearing surfaces. Ni2+ solutions at similar 1 101 M concentrations demonstrate an example of hydrated ions which are not bound to the mica
surfaces on close approach of the surfaces: the hydrated ions are expelled from the
film as the mica surfaces come into lattice-lattice contact. Although the aqueous Ni2+
film is demonstrated to have low viscosity until the point of jump into contact of the
surfaces, there is no lubrication between the surfaces at their closest separation (at
this bulk concentration) since no fluid hydration layer is present. The adhesion,
shear force and surface separation of the mica sheets at this point of adhesive contact
all corroborate the suggestion that Ni2+ does not remain between the surfaces—in
contrast to Cs+—and the negative mica sites are neutralised instead by protons
when the mica sheets come into contact. This study has allowed us to formulate
two conditions which must be satisfied in order for ‘hydration lubrication’ to take
place: (i) ions must remain bound to the shearing surfaces under confinement; and
(ii) the surface-bound ions must retain their hydration sheath under confinement
and applied load. When these conditions are fulfilled, hydration lubrication is mediated by the (thermodynamically) bound and (kinetically) fluid hydration layers
attached to interfacial charged species. This mechanism is likely to occur also at
more complex shearing, strongly hydrated interfaces, such as occur in synovial joints
and mucosal surfaces, and sliding over wet sand at high pressures.
Acknowledgements
We thank Merton College, Oxford (for SP Fellowship), the EPSRC (UK), the Israel
Science Foundation and the Minerva Foundation at the Weizmann Institute for
support of this work and donors of the American Chemical Society Petroleum
Research Fund for support under grant 45694-AC 7. We thank Ben Ocko and Jia
Wang for useful discussions and suggestions concerning caesium hydration.
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Faraday Discuss., 2009, 141, 399–413 | 411
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