Bhushan B. Nanotribology and Nanomechanics: An Introduction

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10 Interfacial Forces and Spectroscopic Study of Conﬁned Fluids 525

much exceeds shear rate in those laboratory experiments that the direct connec-

tion to experiment is not evident. To quantify the inﬂuence of surface roughness,

Fig. 10.4 considers the limit up to which predictions based on the classical no-slip

boundary condition still described the data in Fig. 10.3. Since the no-slip boundary

condition still held, it was valid [7–9] to calculate the shear rate and shear stress by

known equations.

The data show that deviations from the no-slip prediction began at very low

levels of hydrodynamic stress – on the order of only 1–10Pa. Beyond this point, in

some sense the moving ﬂuid was depinned from the surface.

Slip need not necessarily be predicated on having surfaces coated with self-

assembled monolayers to render them partially wetted, though this was the case in

most of the studies cited so far. The no-slip boundary condition switches to partial

slip when the ﬂuid contains a small amount of adsorbing surfactant [30,32].

10.2.4 Slip Can Be Modulated by Dissolved Gas

When experimental observations deviate from expectations based on the stick

boundary condition, there are at least two alternative scenarios with microscopic

interpretations. One might argue that the ﬂuid viscosity depends on distance from

the wall, but for Newtonian ﬂuids this would not be realistic. Why then do experi-

mental data appear to undergo shear thinning with increasing values of the param-

eter υ

peak

/D, if it is unreasonable to suppose that the viscosity really diminished?

Inspection shows that the data for smooth surfaces at high ﬂow rates are consistent

with a two-layer-ﬂuidmodel in whicha layer < 1nm thick,but with viscosity 10–20

times less than the bulk ﬂuid, adjoins each solid surface [9]. A possible mechanism

to explain its genesis was proposed by de Gennes [46], who conjectured that shear

may induce nucleation of vapor bubbles; once the nucleation barrier is exceeded

the bubbles grow to cover the surface, and ﬂow of liquid is over this thin gas ﬁlm

rather the solid surface itself. Indeed, it is likely that incomplete air removal from

the solid surfaces canprofoundlyinﬂuenceﬁndings in thesesituationswhere surface

roughness is so low. This has been identiﬁed by recent research as a likely source

of the misnamed long-range hydrophobic attraction [47,48]; gases also appear to

inﬂuence the sedimentation rate of small particles in liquid [49].

Accordingly, similar experiments were performed, in which the surface forces

apparatus was used to measure hydrodynamic forces of Newtonian ﬂuids that had

been purged with various gases. Dissolved gas strongly inﬂuences hydrodynamic

forces, in spite of the fact that gas solubility is low.

Figure 10.5 (top panel) illustrates experiments in which a simple nonpolar ﬂuid

(tetradecane) was placed between a wetted mica surface on one side, and a partially

wetted methyl-terminated surface on the other, using methods described in detail

elsewhere [8,9]. The surface–surface spacing of 10–100nm substantially exceeded

the size of the ﬂuid molecules. The spacings were vibrated with small amplitude

at these spacings where the ﬂuid responded as a continuum, and the magnitude of

hydrodynamic force was measured as a function of the ratio υ

peak

/D suggested by

(10.2). The experiments showed that, whereas textbook behavior [10] was nearly

526 Y. Elaine Zhu et al.

Flow rate u

peak

/D (s

-1

)

H, peak

(mN)

0.1

101

Water

100

Tetradecane

Fig. 10.5. Illustration that the onset of slip depends on dissolved gas, when simple Newtonian

ﬂuids ﬂow past atomically smooth surfaces, either wetted or partially wetted. On log–log

scales, the hydrodynamic force F

H,peak

is plotted against reduced ﬂow rate, ν

peak

/D,such

that a straight line of slope unity would indicate the no-slip condition assumed by (10.1). The

vibration frequency is 9 Hz. Top panel: tetradecane ﬂowing between the asymmetric case

of a wetted mica surface on one side, a partially wetted surface of methyl-terminated self-

assembled monolayer on the other side, prepared as described elsewhere [33]. Filled symbols,

tetradecane saturated with carbon dioxide; open symbols, tetradecane saturated with argon.

Bottom panel: deionized water ﬂowing between mica surfaces that are wetted by this ﬂuid.

The hatched region of the graph shows the range of irreproducible results obtained when the

gas dissolved in the water was not controlled. Filled symbols, water saturated with carbon

dioxide; open symbols, water saturated with argon. After [7] with permission

followed when the tetradecane had been saturated with carbon dioxide gas, massive

deviations from this prediction were found when the tetradecane was saturated with

argon. This makes it seem likely that argon segregated to the solid walls, creating

a low-viscosity boundary layer, in this way greasing the ﬂow of ﬂuid past that sur-

face. Presumably, the amount of segregation is a material property of the ﬂuid, the

chemical makeup of the surface, and the chemical identity of the dissolved gas. In

this example, the fact that argon possesses low solubility in tetradecane may have

made it more prone to segregate to the surfaces.

10 Interfacial Forces and Spectroscopic Study of Conﬁned Fluids 527

Indeed, when a solid wall is hydrophobic and immersed in water, the ideas of

Chandler andcoworkers[50] suggestthat thermodynamicsmay assist the formation

of a vaporphase near the wall. Recent forcemeasurementssupport this idea [51,52].

10.2.5 Slip Past Wetted Surfaces

The inﬂuence of dissolved gas (just discussed) casts doubt on a traditional assump-

tion of work in this ﬁeld, which is that slip arises because ﬂuid–ﬂuid intermolecular

interactions are stronger than those between ﬂuid and surface, i.e. that the surface

must be wetted only partially. Yet for severalyears, therehavebeen prominentcoun-

terexamples [28, 41]. Recent experiments show that dissolved gases can mediate

apparent slip even for solid surfaces that are fully wetted by the ﬂowing ﬂuid.

Figure 10.5 (bottom panel) summarizes experiments in which deionized water

was placed between wetted surfaces of mica and the surface–surface spacing of 10–

100 nm was vibrated with small amplitude in the manner described previously [7–9,

31–34]. Hydrodynamic force is plotted against the ratio, ν

peak

/D. It is obvious that

the prediction based on (10.2), a straight line on the log–log plot with a slope of

unity, was violated systematically when the hydrodynamic force reached a critical

level. An intriguing point is that initial ﬁndings were found to be irreproducible

(they varied within the range marked by the hatched lines in the graph) but became

reproducible when the water was ﬁrst deliberately saturated with gas. One observes

that water saturated with argon appeared to slip at a slightly higher level of shear

stress than water saturated with carbon dioxide, and that in both cases the limiting

hydrodynamic force was larger than when the nature of the dissolved gas was not

controlled.

This rich and complex sensitivity to the detailed materials chemistry of the sys-

tem disappears, unfortunately, when surfaces are so rough that the stick boundary

condition is produced trivially by the inﬂuence of surface roughness [7,8,22–24].

Therefore for scientiﬁc and practical reasons alike, these issues of ﬂow past nearly

smooth surfaces comprise fertile ground for future work.

10.2.6 The Purposeful Generation of Slip

Inspired by these ideas to design new engineering structures, one might strive to

“grease” the ﬂow of liquids past solid surfaces by altering the boundary condition.

One strategy is to make the surfaces ultra-smooth [7–9]. Another (also mentioned

already) is to add processing aids that segregate to the surface [30,32,36]. A third

way is to purposefully use multicomponent ﬂuids to generate concentration gradi-

ents and diﬀerential wetting to generate slip, as can occur even if there is no velocity

gradient in the ﬂuid [38]. These methods could potentially be used in nanomotors

or nanopumps.

Alternatively, one may seek to maximize contact with air, which is exceedingly

solvophobic. Readers will have noticed that water ubiquitously beads up on the

leaves of plants. Some plants can display a contact angle that approaches 180

◦

,even

528 Y. Elaine Zhu et al.

though water at a smooth surface of the same chemical makeup displays a much

lower contact angle. A beautiful recent series of experiments from the Kao Corpora-

tion in Japan providedinsight into why [53] – the surfaces are rough on many length

scales [54,55] and trap air beneath them. Readers will have noticed that, if one tilts

a leaf, a drop of water on it rolls smoothly, because it rides mainly on a cushion of

air, whose eﬀect will be further discussed in the next section. It is the principle of

an ingenious method introduced recently to lower the viscous drag when ﬂuids [56]

are caused to ﬂow through pipes whose diameter is macroscopic. Of course, given

a long enough period of time it is likely that the trapped gas would dissolve into the

ﬂowing ﬂuid, but perhaps this eﬀect could be enhanced by placing air nozzles along

the walls of the tube and replenishing the trapped gas with a stream of inlet air.

A ﬁnal method by which ﬂow of a Newtonian ﬂuid past surfaces may be facil-

itated is to ciliate the surfaces by coating with chain molecules – polymers, pro-

teins, or sugars. Recent experiments using a surface forces apparatus (SFA) suggest

a similar (but less dramatic) rate-dependent slip in this case also [31]. This is pos-

sibly related to ﬂuid ﬂow in biological organs whose surfaces are also extensively

ciliated, such as blood vessels and the kidney [57].

10.2.7 Outlook

The textbook presentation of engineering ﬂuid mechanics is often of a subject thor-

oughly understood, but recent experiments and simulations using smooth surfaces

show behavior that is richer and more complex than had been supposed. The cor-

rect boundary condition appears to depend on physical chemical properties of the

solid–liquid interface that are susceptible to rational control.

10.3 Hydrophobic Interaction and Water

at a Hydrophobicity Interface

The role of water in physical situations from biology to geology is almost univer-

sally thought to be important but the details are disputed [1,48,50–52,58–72]. For

example, as concerns proteins, the side-chains of roughly half the amino acids are

polar while the other half are hydrophobic; the non-mixing of the two is a major

mechanism steering the folding of proteins and other self-assembly processes. As

a second example, it is an everyday occurrence to observe beading-up of raindrops,

on raincoats or leaves of plants. Moreover, it is observed theoretically and experi-

mentally that, when the gap between two hydrophobic surfaces becomes critically

small, water is ejected spontaneously [50,51,70–72] whereas water ﬁlms conﬁned

between symmetric hydrophilic surfaces are stable [1]. Despite its importance, wa-

ter exhibits many anomalous behaviors when compared to other ﬂuids. Particularly,

it presents some even more puzzling behaviors near hydrophobic surfaces. This

section is adapted from discussions in several primary accounts published previ-

ously [51,52].

10 Interfacial Forces and Spectroscopic Study of Conﬁned Fluids 529

In its liquid form, water consists of an ever-changing three-dimensional net-

work of hydrogen bonds. Hydrophobic surfaces cannot form hydrogen bonds, and

the hydrogen-bonding network must be disrupted. So what happens when water is

compelled to be close to a hydrophobic surface? Energetically, it is expected that

the system forms as many hydrogen bonds as possible, resulting in a preferential

ordering of the water. Entropically, it is expected that the system orients randomly

and thus samples the maximum number of states. Which of these two competing

interactions dominates? What eﬀect does the competition have on the dynamic and

equilibrium properties of the system? The answers to these questions are still hotly

debated. To help resolve this debate, static and dynamic interaction of water con-

ﬁned to a hydrophobic surface is studied by SFA.

10.3.1 Experimental

The atomically smooth clay surfaces used in this study, muscovite mica (hy-

drophilic) and muscovite mica blanketed with a methyl-terminated organic self-

assembled monolayer (hydrophobic), allowed the surface separation to be meas-

ured, by multiple beam interferometry, with a resolution of ±2−5 Å. Surfaces were

brought to the spacings described below using a surface forces apparatus modiﬁed

for dynamic oscillatory shear [44,73]. A droplet of water was placed between the

two surfaces oriented in a crossed cylinder geometry. Piezoelectric bimorphs were

used to produce and detect controlled shear motions. The deionized water was pre-

viously passed through a puriﬁcation system, Barnstead Nanopure II (control ex-

periments with water containing dissolved salt were similar). In experiments using

degassed water, the water was either ﬁrst boiled, then cooled in a sealed container,

or vacuumed for 5–10h in an oven at room temperature. The temperature of meas-

urements was 25

◦

In order to determine ﬁrmly that ﬁndings did not depend on details of surface

preparation,three methods were used to render one surface hydrophobic.In order of

increasing complexity, these were: (a) atomically smooth mica coated with a self-

assembled monolayer of condensed octadecyltriethoxysilane (OTE), using meth-

ods described previously [44]; (b) mica coated using Langmuir–Blodgett methods

with a monolayer of condensed octadecyltriethoxysilane; and (c) a thin ﬁlm of sil-

ver sputtered onto atomically smooth mica, then coated with a self-assembled thiol

monolayer. In method (a), the monolayer quality was improved by distilling the

OTE before self-assembly. In method (b), OTE was spread onto aqueous HCl (pH

= 2.5), 0.5 h was allowed for hydrolysis, the ﬁlm was slowly compressed to the sur-

face pressure π = 20mN/m (3–4 h), and the close-packed ﬁlm was transferred onto

mica by the Langmuir–Blodgetttechniqueat a creep-up speed of2 mm/min. Finally

the transferred ﬁlms were vacuum baked at 120

◦

C for 2h. In method (c), 650Å of

silver were sputtered at 120V (1 Å/s) onto mica that was held at room temperature,

and then octadecanethiol was deposited from 0.5 mM ethanol solution. In this case,

AFM (atomic force microscopy; Nanoscope II) showed the rms (root mean square)

roughness to be 0.5nm. All three methods led to the same conclusions, summarized

below.

530 Y. Elaine Zhu et al.

10.3.2 Hydrophobic Interaction

A puzzling aspect of the hydrophobic attraction is that its intensity and range ap-

pear to be qualitatively diﬀerent as concerns extended surfaces of large area, and

small molecules of modest size [50,60,67,74]. One diﬀerence is fundamental: the

hydrogen-bond network of water is believed for theoretical reasons to be less dis-

rupted near a single alkane molecule than near an extended surface [50,60,67,74].

A second diﬀerence is phenomenological: direct measurement shows attractive

forces between extended surfaces starting at separations too large to be reason-

ably explained by disruption of the hydrogen-bondnetwork. This conclusion comes

from 20years of research using the surface forces apparatus (SFA) and, more re-

cently, atomic force microscopy (AFM). The onset of attraction, ≈10nm in the ﬁrst

experiments [69,75–78], soon increased by nearly an order of magnitude [79–81]

and has been reported, in the most recent work, to begin at separations as large

as 500nm [71]. This has engendered much speculation because it is unreasonably

large compared to the size of the water molecule (≈ 0.25 nm). The range of interac-

tion decreases if the system (water and the hydrophobic surfaces) are carefully de-

gassed [48,82–86]. Water in usual laboratoryexperimentsis not degassed, however,

so it is relevantto understandthe origin of long-rangeattraction in that environment.

A recent review summarizes the experimental and theoretical situation [81].

In the course of experiments intended to probe the predicted slip of water over

hydrophobicsurfaces [9,45] (seethe previoussection), weakeningof the long-range

hydrophobic force to the point of vanishing was observed when the solid surfaces

experienced low-level vibrations around a mean static separation.

The attraction recorded during the approach of OTE surfaces with a droplet of

deionized water in between is plotted in Fig. 10.6 as a function of surface–surface

separation (D). D = 0 here refers to a monolayer–monolayer contact in air. In wa-

ter, the surfaces jumped into adhesive contact at 0 ±2Å. This jump in was very

slow to develop, however. The pull-oﬀ force to separate the surfaces from contact

at rest (113mN/m in Fig. 10.6) implies, from the Johnson–Kendall–Roberts (JKR)

theory [76], the surface energy of about 12mJ/m

(and up to about 30% less than

this when oscillations were applied). The onset of attraction at 650nm for the hy-

drophobic surfaces at rest is somewhat larger than in any past study of which we are

aware. However, we emphasize that the level of pull-oﬀ force was consistent with

the prior ﬁndings of other groups using other systems [1,60–72].

These observations clearly imply some kind of rate-dependent process. As

shown in Fig. 10.7, the force F diminished with increasing velocity and its mag-

nitude at a given D appeared in every instance to extrapolate smoothly to zero. The

possible role of hydrodynamic forces was considered but discarded as a possible

explanation. Similar results (not shown) were also obtained when the surfaces were

vibratedparallel to oneanotherrather thanin the normaldirection.Some precedence

is found in a recent AFM study that reported weakened hydrophobic adhesion force

with increasing approach rate [85].

These observations remove some of the discrepancy between the range of hy-

drophobic forces between extended surfaces of macroscopic size [1,60–72] and the

10 Interfacial Forces and Spectroscopic Study of Conﬁned Fluids 531

25

Distance D (nm)

F/R (mN/m)

20

15

10

5

200 400 600 800

Fig. 10.6. Force–distance proﬁles of deionized water between hydrophobic surfaces (OTE

monolayers on mica). Force F, normalized by the mean radius of curvature (R ≈ 2cm)of

the crossed cylinders, is plotted against surface separation. Forces were measured during

approach from static deﬂection of the force-measuring spring, while simultaneously applying

small-amplitude harmonic oscillations in the normal direction with peak velocity v

peak

d ×2π f where d denotes displacement amplitude and f denotes frequency. This velocity

was zero (solid squares), 7.6nm/s(d = 1.6nm, f = 0.76 Hz; circles), 26 nm/s(d = 3.2nm,

f = 1.3Hz;up triangles), 52 nm/s(d = 3.2nm, f = 2.6Hz;down triangles). The pull-oﬀ

adhesion forces (“jump out”), measured at rest and with oscillation, are indicated by the

respective semi-ﬁlled symbols. The approach data follow the straight line with slope K

(drawn separately as a guide to the eye), indicating that they represented a spring instability

(“jump in”) such that the gradient of the attractive force exceeded the spring constant (K

930 N/m. After [51] with permission

25

peak

(nm/s)

F/R (mN/m)

25

20

15

10

5

0123456

Fig. 10.7. The attractive

force (F/R)atsevendiﬀer-

ent surface separations (D)

is plotted against peak ve-

locity. The ﬁlm thickness

was D = 720 nm (squares),

540 nm (circles), 228 nm (up

triangles), 116 nm (down tri-

angles), 63 nm (diamonds),

17 nm (crosses), 5 nm (stars).

After [51] with permission

532 Y. Elaine Zhu et al.

range that is expected theoretically [50,60,67,74]. A tentative explanation is based

on the frequent suggestion that the long-range hydrophobic attraction between ex-

tended surfaces stems from the action of microscopic or submicron-sized bubbles

that arise either from spontaneous cavitation or the presence of adventitious air

droplets that form bridges between the opposed surfaces [48, 81,83–86]. The ex-

periments reported here show that this eﬀect required time to develop. Hydrophobic

attraction at long range was softened to the point of vanishing when the solid sur-

faces were not stationary.

10.3.3 Hydrophobicity at a Janus Interface

Due to the strong propensity to repel water completely out of two hydrophobicsur-

faces, it is then interesting to consider the antisymmetric situation, a hydrophilic

surface on one side (A) and a hydrophobic surface (B) on the other. The surface A

prevents water from being expelled, to successfully retain a stabilized aqueous thin

ﬁlm at intimately close contact. The surface B introduces the hydrophobic eﬀect.

This Janus situation is shown in the cartoon of Fig. 10.8.

Similar to the force between two OTE surfaces, long-range attraction was also

observed at the Janus interface, as shown in the inset of Fig. 10.8. The opposed

surfaces ultimately sprang into contact from D ≈ 5nm and upon pulling the sur-

faces apart, an attractive minimum was observed at D = 5.4nm. The surfaces could

be squeezed to a lower thickness, D ≈ 2.0nm. Knowing that the linear dimension

of a water molecule is ≈ 0.25nm [1], the thickness of the resulting aqueous ﬁlms

amounted to the order of 5–20 water molecules, although (see below) it is not clear

that molecules were distributed evenly across this space. Below we discuss shear

results.

In the shear measurements, the sinusoidal shear deformations were gentle – the

signiﬁcance of the resulting linear response being that the act of measurement did

not perturb their equilibrium structure (linear responses were veriﬁed from the ab-

sence of harmonics in the time dependence of shear motion). Using techniques

that are well known in rheology, from the phase lag and amplitude during oscil-

latory excitation the responses to shear excitation were decomposed into one in-

phase component (the elastic force, f



) and one out-of-phase component (the vis-

cous force, f



) [87]. Figure 10.8 (main portion) illustrates responses at a single

frequencyand variable thickness. The shear forces stiﬀened by more than one order

of magnitude as the ﬁlms were squeezed. It is noteworthy that, when molecularly

thin aqueous ﬁlms are conﬁned between clay surfaces that are symmetrically hy-

drophilic, deviations from the response of bulk water appear only at smaller separa-

tions [88]; evidently the physical origin is diﬀerent here. Moreover, at each separa-

tion the elastic and viscous forces were nearly identical. The equality of elastic and

viscous forces proved to be general, not an accident of the shear frequency chosen.

Again this contrasts with recent studies of molecularly thin water ﬁlms between sur-

faces that are symmetrically hydrophilic [88]. The magnitudes of the shear moduli

in Fig.10.8are “soft”– somethinglikethoseof agaror jelly. Theywere considerably

softer than for molecularly thin aqueous ﬁlms between symmetrically hydrophilic

10 Interfacial Forces and Spectroscopic Study of Conﬁned Fluids 533

D (nm)

f', f'' (mN)

3 4 5 6

0 200 400 600 800

D (nm)

Inward

Jump out

30

28

15

10

5

F/R (mN/m)

Hydrophilic

Hydrophobic

Fig. 10.8. Deionized water conﬁned between a hydrophilic surface on one side and a hy-

drophobic surface on the other (cartoon). The cartoon is not to scale because the gap thick-

ness is nanometers at closest approach and the droplet size (≈2 mm on a side) vastly exceeds

the contact zone (≈ 10 µm on a side). The main ﬁgure shows the time-averaged viscous (cir-

cles) and elastic (squares) shear forces measured at 1.3Hzand0.3-nm deﬂection, plotted

semilogarithmically against surface separation for deionized water conﬁned between OTE

deposited onto mica using the Langmuir–Blodgett (LB) technique (shear impulses were ap-

plied to this hydrophobic surface). The inset shows the static force–distance relations. Force,

normalized by the mean radius of curvature (R ≈ 2 cm) of the crossed cylinders, is plotted

against the thickness of the water ﬁlm (D = 0 refers to contact in air). The pull-oﬀ adhesion

at D ≈ 5.4 nm is indicated by a star.Thestraight line with slope K

/R indicates the on-

set of a spring instability where the gradient of attractive force exceeds the spring constant

), 930 N/m. Following this jump into contact, ﬁlms of stable thickness resulted, whose

thickness could be varied in the range D = 1−4 nm with application of compressive force.

After [52] with permission

surfaces. This again emphasizes the diﬀerent physical origin of shear forces in the

present Janus situation.

Figure 10.9 illustrates the unusual result that the shear forces scaled in mag-

nitude with the same power law, the square root of excitation frequency. This be-

havior, which is intermediate between solid and liquid, is often associated in other

systems with dynamical heterogeneity [89,90]. By known arguments it indicates

a broad distribution of relaxation times rather than any single dominant one [87].

The slope of 1/2 is required mathematically by the Kramers–Kronig relations if



(ω) = G



(ω) [87]; its observation lends credibility to the measurements. Fig-

ure 10.9 (main panel) illustrates this scaling for an experiment in which data were

averaged over a long time. The inset shows that the same was observed using other

methods to prepare a hydrophobic surface. In all of these instances, ω

1/2

scaling

534 Y. Elaine Zhu et al.

3.5

4.5

5.5

3.50.5 1 1.5 2 2.5 3

log w (rad/s)

log G', G'' (Pa)

4.5

5.5

0.5 0 0.5 1 1.5 2 2.5 3

Fig. 10.9. The frequency dependence of the momentum transfer between the moving sur-

face (hydrophobic) and the aqueous ﬁlm with an adjoining hydrophilic surface is plotted on

log–log scales. Time-averaged quantities are plotted. On the right-hand ordinate scale are the

viscous, g



(circles), and elastic, g



(squares) spring constants. The equivalent loss moduli,



eﬀ

(circles), and elastic moduli, G



eﬀ

(squares), are on the left-hand ordinate. All measure-

ments were made just after the jump into contact shown in Fig. 10.6, i.e. at nearly the same

compressive pressure ≈3 MPa. The main panel, representing LB-deposited OTE, shows ω

1/2

scaling after long-time averaging, 0.5–1 h per datum. The inset shows comparisons with us-

ing other methods to produce a hydrophobic surface. In those experiments the thickness was

generally D = 1.5−1.6 nm but occasionally as large as 2.5 nm when dealing with octade-

canethiol monolayers. Symbols in the inset show data averaged over only 5–10 min with

hydrophobic surfaces prepared with (a) a self-assembled monolayer of OTE (half-ﬁlled sym-

bols), (b) Langmuir–Blodgett deposition of OTE (crossed symbols), or (c) deposition of oc-

tadecanethiol on Ag (open symbols). As in the main ﬁgure, circles denote viscous forces,

squares denote elastic forces. Scatter in this data reﬂects shorter averaging times than in the

main part of this ﬁgure (Fig. 10.8). After [52] with permission

was observed regardless of the method of renderingthe surface hydrophobic.But to

observe clean ω

1/2

scaling required extensive time averaging – see later.

In repeated measurements at the same frequency, we observed giant ﬂuctuations

(±30−40%) arounda deﬁnite mean, as illustrated in Fig. 10.10, although water con-

ﬁned between symmetric hydrophilic–hydrophilic surfaces (bottom panel) did not

display this. It is extraordinary that ﬂuctuations did not average out over the large

contact area (≈ 10µm on a side) that far exceeded any molecular size. The struc-

tural implication is that the conﬁned water ﬁlm comprised some kind of ﬂuctuating

complex – seeking momentarily to dewet the hydrophobic side by a thermal ﬂuctu-

ation in one direction, but unable to because of the nearby hydrophilicside; seeking

next to dewet the hydrophobic side by a thwarted ﬂuctuation in another direction;

and so on. Apparently, nearby hydrophobic and hydrophilic surfaces may produce