Bhushan B. Nanotribology and Nanomechanics: An Introduction

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10 Interfacial Forces and Spectroscopic Study of Conﬁned Fluids 535

0.5

Elapsed time t (s)

Normalized dissipative force

1000

1.5

250 500 750

0.5

1000

1.5

250 500 750

0.5

1.5

12.5 25 37.5

40302010

Fig. 10.10a–d. The prominence of ﬂuctuations for water conﬁned in a Janus interface is

illustrated. In panels (a)–(c), the viscous forces, normalized to the mean (at 1.3 Hz), are plot-

ted against time elapsed. In panel (a), the surfaces were ﬁrst wetted with ethanol to remove

adsorbed gas, then ﬂushed with degassed, deionized water. In panel (b), the ethanol rinse

was omitted. Panel (c) shows a long-time trace for data taken under the same conditions

as for panel (b). Panel (d) illustrates that water conﬁned between symmetric hydrophilic–

hydrophilic surfaces (panel (d)) did not display noisy responses. Conﬁned ethanol ﬁlms like-

wise failed to display noisy responses (not shown). After [52] with permission

a quintessential instance of competing terms in the free energy, to satisfy which

there may be many metastable states that are equally bad (or almost equally bad)

compromises[91,92]. This suggests the physical picture of ﬂickering capillary-type

waves, sketched hypotheticallyin Fig. 10.11. These proposed long-wavelengthcap-

illary ﬂuctuationswould diﬀer profoundlyfrom thoseat the free liquid–gasinterface

because they would be constricted by the nearby solid surface.

The power spectrum is the decomposition of the traces into their Fourier com-

ponents whose squared amplitudes are plotted, on log–log scales, against Fourier

frequency in Fig. 10.11. In the power spectrum one observes, provided the Fourier

frequency is suﬃciently low, a high level of “white” frequency-independent noise.

But the amplitude began to decrease beyond a threshold Fourier frequency

(f ≈ 0.001Hz), about 10

times less than the drive frequency. Other experiments

536 Y. Elaine Zhu et al.

4

14

f (Hz)

S(f )

15

4

9

8

7

6

5

3

2

1

2

Fig. 10.11. The power spectrum for deionized water and the hydrophobized surface com-

prised of OTE deposited by the LB technique (squares); degassed deionized water and the hy-

drophobized surface comprised of an octadecanethiol monolayer (circles); and water contain-

ing 25 mM NaCl conﬁned between symmetric hydrophilic–hydrophilic surfaces (diamonds).

To calculate the power spectra the time elapsed was at least 10

s (the complete time series is

not shown). The power-law exponent is close to −2. After [52] with permission

(not shown) showed the same thresholdFourierfrequency when the drivefrequency

was raised from 1.3 to 80 Hz, and therefore it appears to be a characteristic fea-

ture of the system. It deﬁnes a characteristic time for rearrangement of some kind

of structure, ≈ 10

/2πs; we tentatively identify this with the lifetime of bubbles or

vapor (see below). The subsequent decay of the power spectrum as roughly 1/ f

suggests that these ﬂuctuations reﬂect discrete entities, as smooth variations would

decay more rapidly. Noise again appeared to become “white” but with an amplitude

times smaller at a Fourier frequency of f > 0.1Hz but the physical origin of this

is not evident at this time.

The possible role of dissolved gas is clear in the context of our proposed physi-

cal explanation. Indeed, submicron-sized bubbles resulting from dissolved air have

been proposed to explain the anomalously long range of the hydrophobic attrac-

tion observed between extended surfaces [48, 51, 70–72]. To test this idea, we

performed control experiments using degassed water. The power spectrum, shown

in Fig. 10.12, was nearly the same. Althoughwe cannotexcludethat a small amount

of residualdissolved gas was responsible,this method of degassingis reportedto re-

movelong-range hydrophobicattraction [71], whereas the comparison in Fig. 10.12

shows the consequence in the present situation to be minor. We conclude that the

eﬀects reported in this chapter do not appear to stem from the presence of dissolved

gas.

From recent theoretical analysis of the hydrophobic interaction the expectation

of dewetting emerges – it is predicted that an ultrathin gas gap, with a thickness on

10 Interfacial Forces and Spectroscopic Study of Conﬁned Fluids 537

Hydrophilic

Hydrophobic

Fig. 10.12. Schematic il-

lustration of the capillary

waves of water meeting the

hydrophobic surface with

a ﬂickering vapor phase in

between

the order of 1 nm, forms spontaneously when an extended hydrophobic surface is

immersed in water [50,61,67]. The resulting capillary-wave spectrum does not ap-

pear to have yet been considered theoretically, but for the related case of the free

water–vapor interface, measurements conﬁrm that capillary waves with a broad

spectrum of wavelengths up to micrometers in size contribute to its width [93].

On physical grounds, the thin gas gap suggested by our measurements should also

be expected to possess soft modes with ﬂuctuations whose wavelength ranges from

small to large. From this perspective,we then expectthat the experimentalgeometry

of a Janus-type water ﬁlm, selected for experimentalconvenience,was incidental to

the main physical eﬀect.

This has evident connections to understanding the long-standing question of the

structure of aqueous ﬁlms near a hydrophobic surface and may have a bearing on

understanding the structure of water ﬁlms near the patchy hydrophilic–hydrophobic

surfaces that are so ubiquitous in proteins.

10.4 Ultrafast Spectroscopic Study of Conﬁned Fluids:

Combining Ultra-Fast Spectroscopy with Force Apparatus

The surface forces apparatus (SFA) modiﬁed to measure interfacial rheology has

been used widely in last few years to study the viscoelasticity of molecularly thin

ﬂuid ﬁlms [1–4, 94–98]. A recent application of this technique is described in

Sect. 10.3. Though the force-based techniques are powerful and sensitive, they are

indirect. The observation of structure-related transitions, e.g., oscillatory forces [1],

conﬁnement-inducedsolidiﬁcation [4,94,95], and stick–slip motion in SFA experi-

ments [17,96,97] have not been directly veriﬁed experimentally using an indepen-

dent technique.

The power of scattering, microscopyand spectroscopic techniquesin the studies

of conﬁned ﬂuids has been of speculativeinterest for a long time.However, thereare

only a few reported successes, primarily because of technicaldiﬃculties of combin-

ing these forms of techniques with SFA. Neutron and X-ray diﬀraction methods are

538 Y. Elaine Zhu et al.

very powerful for direct determination of structures at the nanoscale. Recently de-

veloped X-ray surface forces apparatus permits simultaneous X-ray diﬀraction and

direct normal and lateral forces measurements of complex ﬂuids under shear and

conﬁnement [98]. Saﬁnya et al. have investigated the structure of thin liquid crystal

ﬁlms under conﬁnement using this apparatus [99]. The deep penetrating power of

neutrons and the ability to substitute hydrogen with deuterium in many liquid sys-

tems can be exploited to measure the molecular density and orientation of conﬁned

ﬂuidsby using neutrondiﬀraction[100].The structureof end-graftedpolymerbrush

layers have been investigated in this manner. Successful utilization of this method

requires one to devise an apparatus that can keep single-crystal substrates of quartz

or sapphire with areas up to tens of square centimeters parallel at controlled and

well-deﬁned separations [101]. So far, both neutron and X-ray conﬁnement cells

are limited to conﬁning gaps ranging from several hundred angstroms to millime-

ters and are not capable of studying ultrathin (≈ nm) liquid ﬁlms. This intermediate

length scale is more suited to study complex ﬂuids, e.g., long polymer chains, col-

loidal particles and biological cells, where self-organized structures of larger scale

come into play. For simple ﬂuids, the diﬃculty arises because, as the ﬁlm thick-

ness decreases, the total number of scatterers decreases and the signal-to-noise ratio

presents severe limitations. It is diﬃcult to distinguish with suﬃcientconﬁdence the

structure of a molecularly thin ﬂuid ﬁlm from that of the thicker solids that envelop

it. Synchrotron X-ray sources, such as the advanced photon source at Argonne Na-

tional Laboratory have suﬃcient ﬂux for experiments of extremely conﬁned liquid

ﬁlms possible. Recent X-ray reﬂectivity experiments have conﬁrmed the expected

layering in the direction perpendicular to the conﬁning surfaces [102],but questions

about in-plane order and responses to external ﬁelds remain conjectural.

The interaction of light with matter – for example Raman and infrared – has

impressive potential, but the problem is to distinguish the signal (the ﬂuid mono-

layer) from all the noise (the sliding surfaces and the solids beneath them). The

microrheometerdeveloped by Dhinojwala et al. can readily be combinedwith spec-

troscopy (Fourier-transform infrared spectroscopy and dielectric spectroscopy) or

scattering (X-ray and neutron) techniques [103]. It uses two parallel optically ﬂat

windows plates whose separation can be controlled from a few tens of nm to tens

of µm, but is more suited to thicker (0.1–10µm) ﬁlms. It has been used for in situ

study of shear-induced molecular orientation of nematic liquid crystals by using

Fourier-transform infrared time-resolved spectroscopy (FTIR-TRS) synchronized

with the shear motion [104]. By replacing one of the plates with a prism, recently

it has been shown that this rheometer can be combined with the surface-sensitive

technique of infrared-visible sum-frequency generation (SFG) in the total internal

reﬂection (TIR) geometry [105]. This combination can be used to probe the orien-

tation, alignment and relaxation modes of organic molecules at the buried interface

in a condition of ﬂow or shear. Some years back it was shown that SFG can be

combined with the surface forces apparatus to study nanometer-thick ﬁlms of self-

assembled monolayer conﬁned between atomically smooth mica surfaces [106], but

10 Interfacial Forces and Spectroscopic Study of Conﬁned Fluids 539

implementation of this approach to other experimental situations, such as conﬁned

ﬂuids still presents signiﬁcant challenges.

Another problematic issue arises in interpreting experiments that measure me-

chanical properties, such as the SFA or AFM. The measurement generates a single

number, the force, but although the surface separations are molecular, the areas of

interaction are macroscopic. So this force is the result of the average response of

a large collection of molecules. Recent advances in optical spectroscopy and mi-

croscopy have made it possible not only to detect and image single molecules, but

to conduct spectroscopic measurements and monitor dynamic processes as well at

the level of single (or a handful of) molecules [107, 108]. These studies illustrate

their utility to dissect the distributions around the average for processes such as dif-

fusion or chemical reactions. In many of these experiments, a ﬂuorescent molecule

is doped into the sample, which acts as a probe of its local environment[109]. Mon-

itoringmotions of the probeovertime and in the presenceof externalﬁelds can oﬀer

insightsinto changesin this localenvironmentwithin whichthe dye moleculeis em-

bedded.However,to integrateforce measurementsusing SFA withconcurrentmeas-

urements using ﬂuorescence spectroscopy required signiﬁcant modiﬁcation of the

usual methods [110]. In the following we discuss the challenges of combining SFA

with single-molecule-sensitive spectroscopy techniques. This section is adapted

from discussions in several primary accounts published previously [109,110].

10.4.1 Challenges

Oneofthemajordiﬃculties is to detect and collect ﬂuorescence eﬃciently and

to separate it from background noise. Background originates from many sources:

Raman and Rayleigh scattering, ﬂuorescence owing to impurities in the solvent,

and from the substrates, which includes the lens, glue and mica (the glue attaches

a cleaved mica sheet onto the supporting cylindrical lens in SFA experiments).Typ-

ical background counts can far exceed those from a dilute concentration of ﬂuo-

rophore molecules doped inside the sample of interest.

Another type of challenge comes from the limited photochemical lifetime of

a ﬂuorophore.A common ﬂuorophore photobleachesirreversibly after emitting a ﬁ-

nite number of photons (10

–10

). This problem becomes severe in ultrathin ﬁlms,

where the dynamics can become slower and a dye molecule resides for a long time

within the laser focus.

A third diﬃculty is the necessity to perform spectroscopy at the same time as

multiple-beam interferometry (MBI) to determine the ﬁlm thickness. Traditionally

a silver coating of thickness ≈ 63 nm is used at the back side of mica for the purpose

of MBI, but the high reﬂectivity of silver from the infrared to UV regime excludes

this possibility here.

Theﬁnal challengeis to incorporatethe SFA and the neededoptics.As the signal

must be as large as possible, the maximum possible amount of ﬂuorescence from

the ﬂuorophore of interest should be detected for a successful experiment. A high

numerical aperture (N.A.) objective is desirable but such objectives have a very

540 Y. Elaine Zhu et al.

small working distance (≈ 1−2mm). This requires signiﬁcant modiﬁcation of the

traditional SFA in order to make it possible to focus the laser beam on the sample.

We recently succeeded in implementing the technique of ﬂuorescence correla-

tion spectroscopy (FCS), which can measure the translational diﬀusion with surface

forces measurement and friction studies within the SFA [111]. The scientiﬁc objec-

tive of building this integrated platform was to answer questions such as: how is

the rate of molecular probe diﬀusion, within a conﬁned ﬂuid, related to the stress

relaxation time? Is there signiﬁcant collective molecular motion or dynamical het-

erogeneity? What happens to the molecules during the stick–slip motion? The prin-

ciple of the FCS technique and the experimental set-up of the combined platform

are described below.

10.4.2 Principles of FCS Measurement

Fluorescence correlation spectroscopy (FCS) is an experimental method to extract

information on dynamical processes from the ﬂuctuation of ﬂuorescence inten-

sity [112]. The technique has enjoyed widespread application recently in the ﬁeld of

chemical biology because of its ability to access to a multitude of parameters with

biologicalrelevance[113,114].The ﬂuctuationof ﬂuorescence,whendye molecules

are dilute, can in principle result from diﬀusion, aggregation, or chemical reaction.

Compared to other techniques for studying diﬀusion problems, such as quasi-elastic

light scattering (QELS), ﬂuorescence recovery after photobleaching (FRAP), and

laser-induced transient grating spectroscopy, FCS presents the unique capability of

measuring extremely dilute systems with high spatial resolution (downto the optical

diﬀraction limit). On the average there can be as few as 1–5 dye molecules within

the ≈ 1 fl volume element of the focused laser beam. However, these dye molecules

move in and out due to Brownian motion, causing intensity ﬂuctuations which can

be observed as low-frequency noise on the mean ﬂuorescence signal (Fig. 10.13).

By inspecting the autocorrelation function of this ﬂuctuation,

G(τ) ≡δI(t)δI(t+ τ)/δI(t)

, (10.4)

(here I denotes ﬂuorescence intensity and t is the time variable), and by choosing

a suitable model to analyze it, the rate of dynamic process is obtained [112]. If the

primary reason for ﬂuctuation is translational diﬀusion, and assuming that the ﬂu-

orescence characteristics of the diﬀusing molecules do not change while traversing

the laser volume, one can use Fick’s second law to calculate the translational diﬀu-

sion coeﬃcient (D) from the autocorrelation function by using the relation [115],

G(τ) = G(0)/



1+ 8Dτ/ω



. (10.5)

This result follows from the convolution of the concentration correlation with the

spatial proﬁle of the laser focus, which has been assumed to be a two-dimensional

Gaussian of width ω

. The magnitude of the autocorrelation function at time zero,

G(0), is related to the averagenumber of ﬂuorophores(N) in the observationvolume

10 Interfacial Forces and Spectroscopic Study of Conﬁned Fluids 541

by the relation [116]

G(0) = 1/(2

√

2N) . (10.6)

Molecular mobilities can be measured over a wide range of characteristic time con-

stants from ≈10

−3

to 10

ms by using this technique.

Fluctuation analysis is best performed if the system under observation is re-

stricted to very small ensembles and if the background is eﬃciently suppressed.

These can be accomplished by a combination of very low sample concentrations (≈

nanomolar) with extremely small measurements volumes (≈femtoliter). The excita-

tion of the ﬂuorophores can be performed either with two photons using a pulsed

laser or with one photon using continuous-wave lasers [115]. In one-photon FCS,

spatial resolution is obtained with a confocal set-up, in which a small pinhole in-

serted into the image plane can reject the out-of-focusﬂuorescence. For two-photon

excitation on the other hand, simultaneous (within ≈ 10

−15

s) absorption of two

lower-energyphotonsof approximatelytwicethe wavelengthis requiredfor a transi-

tion to the excited state. Mode-locked lasers providing short pulses (≈10

−13

s) with

a high repetition rate (10

Hz) can provide suﬃcient photon ﬂux densities for two-

photon processes. As the excitation probability is proportional to the mean square

of the intensity, it results in inherent depth discrimination. Additionally, two-photon

excitationimprovesthe signal-to-backgroundratioconsiderably.As the mostpromi-

nent scattering came from the incident light, which is well separated in wavelength

from the induced ﬂuorescence, this makes it easy to separate the ﬂuorescence emis-

sion from the excitation light and the scattered light. However, the photobleaching

rates with two-photon excitation are signiﬁcantly enhanced with respect to one-

photon excitation at comparable photon-emission yields [117].

10.4.3 Experimental Set-up

A schematic diagram of the method of combing ﬂuorescence correlation spec-

troscopy with the surface forces apparatus is shown in Fig. 10.12. The FCS por-

tion of the set-up consists of three major parts: light source, microscope and data

acquisition [110]. A femtosecond Ti:sapphire laser, which typically generates laser

pulses with full width at half maximum (FWHM) of 100 fs at a repetition rate of

80MHz can be used for the two-photon excitation of the ﬂuorophores. An inverted

microscope serves as the operational platform for the whole experiment. The exci-

tation light is focused onto the sample with an objective lens of high N.A. and the

emitted light is collected through the same objective and is detected by a photomul-

tiplier tube (PMT) or avalanche photodiode (APD). The photon counting output is

recorded by an integrated FCS data-acquisition board and data analysis can be per-

formed with commercial or home-written software. By introducing the laser beam

through the objective lens, a small excitation volume (≈1fl) is generated within the

sample.The lateral dimension of the excitation spot is about ≈0.5 µm, which can be

determined by a calibration experiment using widely used dyes, such as ﬂuorescein,

whose diﬀusion coeﬃcient in water is known to be ≈ 300µm

/s. The excitation

542 Y. Elaine Zhu et al.

power at the sample needs to be less than 1 mW to avoid photobleaching and heat-

ing eﬀects of the sample.

The modiﬁed surface forces apparatus sat directly on the microscope stage.

The traditional crossed-cylindrical geometry produced a circular contact of parallel

plates when the crossed cylinders were squeezed together such that they ﬂattened

at the apex. Using an inchworm motor, separation of the surfaces can be controlled

from nanometers to millimeters. To determine the separation between the surfaces,

the traditional silver sheets for interferometric measurements of surface spacing in

the SFA need to be replaced by multilayer dielectric coatings [118]. These multi-

layers can be produced by successive evaporation of layers (typically 13 or 15) of

TiO

and Al

by electron-beam evaporation. The optical thickness of each layer

was approximately λ/4(λ ≈ 650nm), as determined by the optical monitor within

the coating chamber. The thickness of each coating determines the windows of re-

ﬂectivity and translucency. This approach can produce high reﬂectivity in the region

600–700nm, as well as translucent windows in the region ≈ 800nm (to allow ﬂu-

orescence excitation) and 400–550nm (to detect ﬂuorescence). The reﬂectivity as

a function of wavelength is shown in Fig. 10.13 for the bare mica surface and for

surfaces with diﬀerent numbers of multilayers.

The same set-up (Fig. 10.14) with some modiﬁcation can be used to probe

molecular rotational diﬀusion. In the ground state ﬂuorophores are all randomly

oriented. When excited by polarized light, only those ﬂuorophores that have their

dipole moments oriented along the electric vector of the incident light are prefer-

5

ô (s)

g(ô)

0.75

0.25

0.5

1

4

3

2

1200200 600

Time (ms)

Count

b)a)

Fig. 10.13a–d. Schematic illustration of the utility of ﬂuorescence correlation spectroscopy

in a conﬁned geometry: (a) A ﬂuorescent molecule is doped within an ultrathin ﬁlm of ﬂuids

(e.g., simple alkanes, polymers, colloidal particles) conﬁned between two solid surfaces. Pho-

ton emission counts can ﬂuctuate with time (c) resulting from the diﬀusion of ﬂuorophores

through the laser focus (b). From the autocorrelation function of this ﬂuctuation G(τ), the

rate of dynamic process can be obtained (d). Calculated G(τ) for pure Brownian diﬀusion

(dashed curve) and ﬂow superimposed with diﬀusion (solid curve)areshown

10 Interfacial Forces and Spectroscopic Study of Conﬁned Fluids 543

SFA with

shear assembly

Inverted

microscope

Femtosecond

laser

Fig. 10.14. Schematic diagram of the assembly used to perform ﬂuorescence correlation

spectroscopy within a surface forces apparatus equipped for shear experiments. A miniatur-

ized surface forces apparatus sits on a microscope stage. A femtosecond pulsed laser excites

ﬂuorescent dye molecules within a molecularly thin liquid ﬁlm contained between two op-

posed surfaces of muscovite mica. Colored ﬁlter (A) to remove the residual excitation light

(λ = 800 nm) from the ﬂuorescence light (400–550 nm) which is collected by the single-

photon counting module (D). Dichroic mirror (B) and the objective lens (C) used to focus

and collect the light. An inchworm motor (E) controls the separation of the surfaces from

nanometers up to several micrometers

entially excited. So the excited-state population is not randomly oriented, instead

there is a larger number of excited molecules having their transition moments ori-

ented along the polarization direction of the incident light. This anisotropy of orien-

tation can be determined by measuring the intensity of light polarized parallel to the

incident light and perpendicular to the incident light. This preferential anisotropy

at time zero decays due to the rotational diﬀusion of the dye molecule, following

an exponential law with a characteristic rotation time (τ). As the typical rotational

timeranges from picosecondsto nanoseconds,the dynamicson much smaller length

scales, that of only one or two nm, can be investigated by this method. Translational

diﬀusion experimentsby FCS, on the other hand, (as discussed in the following sec-

tions) involves a large distance – the probe molecules travel hundreds of nm into

and out of the laser spot – to produce a signal. Therefore, it is more sensitive to the

global environmentof the molecules.

10.5 Contrasting Friction with Diﬀusion

in Molecularly Thin Films

In FCSexperiments,the magnitudeof the ﬂuctuationautocorrelationfunction scales

inversely with the number of ﬂuorescent molecules in the observation volume

(10.6). Large ﬂuorophore concentrations more than micromolar are not eﬃcient in

544 Y. Elaine Zhu et al.

FCS, because G(0) eventually becomes too small for ﬂuctuation analysis. Typical

dye concentration for conﬁned ﬂuid experiments is kept at 50nM. A key point for

these experiments is to ﬁnd systems in which adsorption of the ﬂuorophore would

not complicate the situation. In other words, the ﬂuids themselves, not the ﬂuo-

rophores, should be attracted preferentially to the conﬁning solid surfaces [111].

This point can be veriﬁed by scanning the laser focus vertically from within the

mica, through the surface, into the bulk ﬂuids, and observing that there is no jump

in ﬂuorescence counts as the surface is crossed. Finally, one needs to be sensitive

to the concern that, when using ﬂuorophores to probe local micro-environments,

micro-environments might be perturbed by their presence. Therefore, it is essen-

tial to perform normal and shear force experiments with and without the presence

of dye molecules to verify that these are not aﬀected. This section is adapted from

discussions in several primary accounts published previously [111].

In SFA experiments, a drop of the ﬂuid for study is placed between the two

mica sheets, oriented as crossed cylinders so that in projection the geometry os

a sphere against a ﬂat (Fig. 10.16). In the study of surface forces, it is well known

that, as surfaces separated by ﬂuid are brought together, ﬂuid drains smoothly until

a thickness of 5–10 molecular dimensions, at which point the ﬂuid supports stress

owing to packing of molecules at the surface [1]. When rounded surfaces of this

kind are pressed together, separated by ﬂuid, the curved surfaces ﬂatten at the apex

to form parallel plates. The resulting inhomogeneous pressure distribution over the

contact region is well known in the ﬁeld of tribology. It is approximately Hertzian;

zero at the edges of the contact zone and, at the center, 3/2 the mean value [119].

The Hertzian model is generally a good approximation in the absence of strongly

attractive forces.

Figure 10.15 shows results for two diﬀerent ﬂuid systems: (a) propane diol con-

taining ≈ 50nM rhodamine 123, and (b) octamethylcyclotetrasiloxane (OMCTS),

containing ≈ 50nM coumarin. Propane diol is a low-viscosity ﬂuid (≈ 0.4Poise)

with a glass-transition temperature far below room temperature (T

= −105

◦

C).

The OMCTS molecule is ring-shaped; it is the cyclic tetramer of dimethylsilox-

ane. It has a viscosity much like water (≈ 0.002Poise) and possesses the intriguing

featurethat it crystallizes at 1atm near room temperature(T

= 17

◦

C), thusenhanc-

ing the possibility that a conﬁnement-induced elevation of the melting temperature

might be detected. There is a long tradition of considering it to constitute a model

system when studying friction and surface-induced structure of nonpolar conﬁned

ﬂuids because numerous computer simulations designed to model lubrication have

concerned particles of spherical shape [2,95,120]. As the typical size of the con-

tact area is ≈ 50 µm and the size of the laser spot is ≈ 0.5µm, it is possible to scan

the laser focus laterally, as sketched in Fig. 10.14. From time series of ﬂuctuations

of the ﬂuorescence intensity, the intensity–intensity autocorrelation function can be

calculated and is plotted against logarithmic time lag. From Fig. 10.15 it is obvious

that the characteristic diﬀusion time increased with increasing proximity to the cen-

ter of the contact. Their physical meaning is to describe the time to diﬀuse through

the spot of calibrated diameter, ≈ 0.5 µm, at which the interrogatory laser beam was