Bhushan B. Nanotribology and Nanomechanics: An Introduction

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10 Interfacial Forces and Spectroscopic Study of Conﬁned Fluids 545

Wavelength (nm)

Transmittance (%)

1200400 600 800 1000

TiO

Air

Mica

Fig. 10.15. Optical transmittance of mica coated with a multilayer dielectric, showing the

feasibility of performing optical spectroscopies in the region 400–600 nm while also meas-

uring surface–surface separation by multiple beam interferometry in the region 650–750 nm.

Bare mica (solid line), mica coated with 7 layers of coating (dotted line) and with 13 layers of

coating (dash-dot line). The window of optical transmission is adjustable through variations

of multilayer dielectric. (Inset) The schematic diagram of the dielectric coating, composed of

alternate layers of TiO

and Al

» 20µm

Fig. 10.16a,b. Experimental scheme. (a) Crossed-

cylinder conﬁguration. Droplets of ﬂuids were

placed between crossed cylinders of mica as a drop

and force is applied in the normal direction, caus-

ing the formation of a circular area of ﬂattened

contact. (b) Fluorescence correlation spectroscopy

(FCS) is performed after compressing the ﬁlms

with a mean normal pressure of 2–3 MPa. The se-

quence of smaller circles illustrate that the focus

of the laser beam (diameter ≈0.5 µm) was scanned

across the contact (radius ≈ 10 µm), enabling spa-

tially resolved measurements. After [111] with per-

mission

focused. The time scale of these processes, which can be estimated as the time at

which the autocorrelation function decayed to one half of its initial value, slowed

for example from 2ms (rhodamine123 in bulk propane diol) to 800ms (the slowest

curve shown in Fig. 10.15a).

For quantitative analysis, one can ﬁt these curves to the standard model for two-

dimensional Fickian diﬀusion and assume a single diﬀusion process; the imper-

fect ﬁts towards the center of the contact zone are discussed below. Figure 10.18

shows D/D

bulk

, the relative diﬀusion coeﬃcient, plotted against position within the

contact on semi-logarithmic scales; the logarithmic scale is needed because the de-

pendence was so strong. Equivalently, assuming a Hertzian contact-pressure distri-

546 Y. Elaine Zhu et al.

bution, D/D

bulk

is plotted against relative pressure within the contact in Fig. 10.18

(inset). A separate controlexperimentin which the bulk pressure was variedshowed

the diﬀusion in propane diol slowed by a much smaller amount, a factor of only 1.5,

when the pressure was raised to 7 MPa. Evidently the ﬁndings described in this re-

port are signiﬁcantly larger than those produced by compressibility of the bulk ﬂuid

under isotropic pressure, and a diﬀerent sort of explanation is needed.

Postulating that D

eﬀ

was proportional to a Boltzmann factor in energy (ΔE/kT,

where E is the energy, k the Boltzmann constant, and T the absolute temperature,

which was constant), ΔE can be regardedas the net diﬀerential normal pressure, Δp,

times an activation volume, ΔV

act

. Figure 10.18 (inset) shows that the data are con-

sistent with the impliedexponentialdecreaseof D

eﬀ

with p, in spite of the fact that p

is mechanical pressuresqueezing the conﬁnedﬂuid, not the usual isotropic pressure.

From the slope in Fig. 10.18, one deduces that ΔV

act

= 15−20nm

. It is intriguingly

close to the activation volume obtained some years ago from independent friction

measurements [121]. In the bulk, by contrast, the activation volume for diﬀusion

is only ≈ 0.2nm

, the size of a ﬂuid molecule. This analysis highlights one of the

key conclusions that diﬀusion appeared to involve cooperative rearrangements of

many molecules. But this concept assumes a single reaction coordinate and a fully

equilibrated homogeneous system. Therefore, it may not seem physically meaning-

ful to identify the deduced activation volume with the lateral size of cooperatively

rearranging regions within the conﬁned ﬁlms.

The inﬂections in the intensity–intensity autocorrelation functions of Fig. 10.17

are quantitatively reproducible on diﬀerent days with fresh samples. They refer to

the same data-acquisition time, ≈ 45 min. Near the edges of the contact this time is

enough to produce an autocorrelation curve that conformedwell to expectations for

adiﬀusion process with a single diﬀusion rate. But in the same system, at the same

ﬁlm thickness, at the same temperature, and in the same experiment, the autocorre-

lation curves deviatedfrom this expectationmore and more, the higher the local me-

chanicalpressure. The resultssuggest that thesystem became increasinglyheteroge-

neous with increasing pressure, so much so that the spatial resolution of this exper-

iment sampled zones of slightly diﬀerent dynamical response. Molecules diﬀused

at one rate through a certain micro-environment, then entered another. Physically,

this signiﬁes some kind of long-lived but quantitatively reproducible heterogeneity,

which becomes increasingly intense when moving from the edges of the contact to-

wards the center. To make this more precise, it is worth remembering that molecules

in conﬁned ﬂuid ﬁlms are known to organize into layers parallel to the conﬁning

surfaces, in which local density diﬀers. In this scenario, the multiple processes sug-

gested in the autocorrelation curves signify that translational diﬀusion rates diﬀered

in these layers. For example, for OMCTS the slowest curve in Fig. 10.17b can be

decomposed into sub-processes with D

eﬀ

= 0.1, 0.7, 2.9, and 40 µm

/s, the average

being 5.5µm

/s because the slowest two processes had the smallest amplitude and

contributed least. This interpretation is consistent with the observation that the het-

erogeneity was more pronounced for OMCTS than for 1,2-propane diol, which is

not expected to organize so deﬁnitively into distinct layers. From another perspec-

10 Interfacial Forces and Spectroscopic Study of Conﬁned Fluids 547

OMCTS

5

ô (s)

(ô)

0.25

0.5

0.75

3

1

4

2

ô (s)

(ô)

0.25

0.5

0.75

3

Propane diol

2

1

Fig. 10.17a,b. Fluorescence

autocorrelation functions,

normalized to unity, are

plotted against logarithmic

time for rhodamine 123 in

1,2-propane diol (a)and

coumarin 153 in OMCTS (b).

The focus was at distance a

from the center of the contact

and the ratio x ≡ a/r was

considered, where r is the

contact radius. In panel (a),

x ≈ 0.95 (circles), 0.82 (down

triangles), 0.7(squares),

and 0.6(up triangles). In

panel (b), x ≈ 0.95 (circles),

0.8(up triangles), and 0.7

(squares). Lines through the

autocorrelation curves are the

least-squares ﬁt to a single

Fickian diﬀusion process. Af-

ter [111] with permission

tive, these data are qualitatively reminiscent of the ‘cage’ slowing down observed

in autocorrelation curves from dynamic light scattering (DLS) studies of colloidal

glasses – some kind of incipient but incomplete solidiﬁcation [122]. From the avail-

able data it is diﬃcult so far to assess the relative importance of these two scenarios,

but one conclusion is ﬁrm: the scale of heterogeneity must have been impressively

large, when one considers that these heterogeneities did not average out in spite of

the long averaging time and the fact that the laser beam spot (≈ 500−nm diameter)

exceeded the size of the diﬀusing molecules by so much.

Concerning the question of how the diﬀusion of individual molecules is related

to friction, these results suggest that the slit-averaged retardation of diﬀusion is

much less than the conﬁnement-induced enhancement of eﬀective viscosity, which

is known to be at least 6–7 orders of magnitude [94,95]. However, the generality

of the observation has been cast into doubt recently by mechanical experiments,

which showed that the solidity of molecularly thin ﬁlms using mica as substrates

depends on a particular method of surface preparation [124]. Mica recleaved im-

mediately before an experiment to minimize potential exposure to airborne contam-

548 Y. Elaine Zhu et al.

0.6

3

a/r

eff

bulk

0.01

0.1

10.7 0.8 0.9 0

0.90.3 0.6

0.01

0.1

0.3

0.60

0.1

0.7 0.8 0.9

0.01

Propane diol

a) b)

OMCTS

Fig. 10.18a,b. Quantiﬁcation of the eﬀective diﬀusion coeﬃcients (D

eﬀ

) inferred from the

raw data in the previous ﬁgure. (a) The ratio, D

eﬀ

bulk

, is plottedagainst focus position, a/r.

(b) The ratio, D

eﬀ

bulk

, is plotted against relative pressure squeezing the surfaces together,

≡ P/P

max

≈ 4 MPa) assuming a Hertzian pressure distribution. Open circles (main

ﬁgures) denote rhodamine 123 in 1,2-propane diol (D

bulk

≈ 8 µm

/s). Filled circles (insets)

denote coumarin 153 in OMCTS (D

bulk

≈ 190 µm

/s). After [123] with permission

inants, is reported to produce very low friction [125]. These results are consistent

with the spectroscopyexperiments,with molecular dynamicssimulation and dielec-

tric measurements, none of which had observed divergence of relaxation times, or

conﬁnement induced solidiﬁcation.

10.6 Diﬀusion of Conﬁned Molecules During Shear

In most previous friction experimentsusing the traditional mica cleaving procedure,

static friction (a mechanically solid state) was found to give way, under sliding, to

kinetic friction (a mechanically molten state) [126]. The transition from mechani-

cal solidity to ﬂuidity has been interpreted to suggest a shear-induced phase tran-

sition. The premise was that, if the hypothesis of shear-melting held, shear should

induce considerable quickening of the intensity–intensity autocorrelation function

time scale of the dye molecule. Shear forces in SFA experiments are generated by

sliding the top cylindrical lens, which is suspended from the upper portion of the

apparatus by two piezoelectric bimorphs, mounted symmetrically to the two ends

of the mount (Fig. 10.14). Shear forces were generated by one of the piezoelectric

bimorphs(the “sender”), and the response of the device induced a voltage across the

right-hand bimorph (the “receiver”). A typical frequency range is 0.1–256Hz, with

shear displacement amplitude of 0.1–10µm. These forces were usually sinusoidal

in time but sometimes were a triangular ramp of constant slope, for better compar-

ison with nanotribology measurements and simulations that employed a constant

sliding velocity. The triangular ramp produced nearly constant velocity except for

a slight acceleration to prevent stick–slip. This section is adapted from discussions

in several primary accounts published previously [123].

10 Interfacial Forces and Spectroscopic Study of Conﬁned Fluids 549

Figure 10.19 shows representative autocorrelation curves of the ﬂuorescence

ﬂuctuations. In Fig. 10.20, the ratio of D

eﬀ

during sliding to D

eﬀ

at rest is plotted

against the shear rate; the main ﬁgure shows the entire range of shear rate and the

inset magniﬁes the regime of small shear rate. One sees that shear speeded up this

measure of the time scale of the autocorrelationfunction by less than a factor of 5 in

every case [123]. The signiﬁcance is that this aﬀords a direct (negative) test of the

common hypothesisthat the transition from rest to sliding reﬂects shear melting that

is analogous to the melting transition of a solid. The reason that the autocorrelation

functionswere unaﬀectedby motion is believedto be that the ﬂuid undergoespartial

slip when the moving surface is smooth; the same conclusion follows from friction

measurements in similar systems.

Taken together, these ultrafast spectroscopy experiments show that these com-

plex molecularly thin systems retain a high degree of ﬂuidity at the molecular level.

While it is true that the structure factor of in-plane correlation is predicted from

computer simulations to be enhanced relative to the bulk and that the activation vol-

ume for diﬀusion exceeds that in the bulk liquid by about three orders of magnitude,

indicating a higher degree of order than in the bulk ﬂuid, shear does not appear to

substantially modify the degree of ﬂuidity inferred by direct measurements of the

diﬀusion of individual molecules. An agenda for future investigation will be to un-

5

ô (s)

(ô)

0.2

0.4

0.6

0.8

1.0

4

3

2

1

Fig. 10.19. Illustrative ﬂuorescence intensity–intensity autocorrelation functions, g

(τ), nor-

malized to unity at short time and plotted against logarithmic time lag τ. The thickness of

the liquid ﬁlm was 3.0±0.4 nm relative to air, corresponding to ≈3−4 molecular layers. The

curves compare diﬀusion at rest in the unconﬁned bulk (circles; D = 180 µm

/s) and at two

radial positions (“a”) within the contact zone of radius r ≈ 25 µm; a/r = 0.7(triangles)and

a/r = 0.5(squares). These data are taken at rest (open symbols) and while sliding (ﬁlled sym-

bols) at shear rates of 10

and 10

−1

, respectively. Sliding was performed at 1–256 Hz such

that it was unidirectional for half the period then reversed direction, and so on repetitively;

for the data shown here, it was 256 and 32 Hz, respectively. Lines through the data for the

bulk are ﬁts to a single diﬀusion process. After [111] with permission

550 Y. Elaine Zhu et al.

Shear rate (s

1

)

rel

6.0´10

2.0´10

4.0´10

3.0´10

0 6.0´10

Fig. 10.20. The ratio (D

rel

)

of the eﬀective diﬀusion

coeﬃcient during sliding

(deﬁned in text) to that at

rest, plotted against peak

shear rate. The data represent

the average of more than 30

experiments, with error bars

indicated. The inset shows the

low-shear part of this data.

After [123] with permission

derstand better the relationship between the mechanical friction response, which is

an ensemble average, and measurements such as those presented here, which refer

to the motion of individual molecules.

10.7 Summary

We have reviewed some recent advances in the experimental study of conﬁned ﬂu-

ids. Some important questions involving thin liquid ﬁlms with broad applications

from biology to tribology have been addressed with complementary approaches.

Surface and interfacial forces of liquids in intimate contact with surfaces can be di-

rectly measured by SFA, AFM and other force-based techniques. Meanwhile, scat-

tering, microscopic and spectroscopic techniques combined with the surface forces

apparatushave been developedto provideunique experimentalplatformsin orderto

understand the structure, the phase behavior, and the dynamical responses of ﬂuids

conﬁned between surfaces whose spacing becomes comparable to the correlation

length of short-range packing, the size of supramolecular structures, and/or the size

of the molecules.Taking all the eﬀorts together,the study of ﬂuid molecules in close

proximity to surfaces and under conﬁnement gets us to the nitty-gritty of the beauty

and distinction of the nano-world and nanotechnology.

Acknowledgement. Y. Elaine Zhu gratefully acknowledges the ﬁnancial support from the

US Department of Energy, Division of Materials Science (Grant No. DE-FG02-07ER46390)

and the National Science Foundation (Grant No. CBET-0651408 and CBET-0730813). Ashis

Mukhopadhyay acknowledges the supports of the American Chemical Society Petroleum

Research fund (PRF No. 44953-G5) and National Science Foundation (Grant No. DMR-

0605900). Steve Granick appreciates ﬁnancial support from the NSF (Surface Engineering

program) and also from the NSF (Polymers Program, Grant No. DMR-0605947).

10 Interfacial Forces and Spectroscopic Study of Conﬁned Fluids 551

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