Thin liquid film lubrication under external electrical fields: Roles of liquid intermolecular interactions Guoxin Xie, a) Jianbin Luo, b) Shuhai Liu, Dan Guo, and Chenhui Zhang State Key Laboratory of Tribology, Tsinghua University, Beijing 100084, China (Received 10 January 2011; accepted 8 April 2011; published online 1 June 2011) One of the important features of the nanoscale liquid film lubrication is the formation of ordered layers at the solid/liquid interface. In this paper, the effect of the intermolecular interaction in liquid lubricant films on the formation of ordered layers after applying external electric fields (EEFs) has been investigated by measuring the central-film-thicknesses of liquids in concentrated point contacts and then inferring the thin film rheology. It has been found that the film formation properties of both pure liquid n-alkanes and liquid n-alcohols with relatively long chains have weak responses to EEFs, while those of their mixed solutions could be enhanced more notably by EEFs. In addition, the effect of the dispersive interactions between solvent molecules on the formation of ordered layers in thin lubrication films under EEFs was also discussed. V C 2011 American Institute of Physics. [doi:10.1063/1.3587477] I. INTRODUCTION Understanding the nanoscale properties of thin liquid films is of great importance in a wide variety of applications such as lubrication, spreading and adhesion, etc. 1,2 With the development of micro/nanomachining techniques, the tribo- surfaces of ultraprecise instruments are often molecularly smooth, and the gap between the surfaces is usually at the nanometer scale. The lubricant film confined in such a nar- row gap behaves differently from the expectations of classi- cal lubrication theories. 3,4 Different kinds of experimental techniques have been applied to investigate the behaviors of nanoscale liquid films in lubricated contacts. 5–8 It has been shown 8–14 that the behaviors of the molecules in the confined liquid film are dependent on the physicochemical properties of the liquid, the solid surface properties, and the interactions between the liquid molecules and the solid surfaces. More recently, the effect of an external electrical field (EEF) on the properties of thin liquid films has attracted much attention. 16–22 One of the important findings in these studies was that the EEF could enhance the degree of molec- ular ordering in polar liquid films or nonpolar solution films with polar additives. As a result, similar to the action of an EEF on liquid crystals, the electroviscosity effect of these liquid films due to the formation of ordered layers or electri- cal double layers near the surfaces of tribopairs could be expected. However, the EEF effect on the liquid films with longer alkyl chains was found to be less noticeable in our previous study, 20 suggesting that the interactions between liquid molecules should be adequately considered for under- standing the behaviors of confined liquid films. Therefore, the investigations of how the interfacial ordered layers in liq- uid films are affected by the interactions between liquid mol- ecules under the influence of EEFs are very interesting. However, it is rarely discussed. In the present study, the relative optical interference intensity (ROII) technique was employed to investigate the EEF effects on confined films of simple n-alkanes, n-alcohols, and their mixtures by meas- uring the central-film-thickness in the concentrated point contact and then calculating the effective viscosity. II. EXPERIMENT The scheme of the experimental setup is shown in Fig. 1. A circular contact region is formed when a high precision steel ball in a liquid cup is pressed against a glass disk coated with a semireflective chromium (Cr) layer. The test liquid in the oil cup is entrained into the contact region with the rota- tion of the ball driven by the disk. Then, a liquid film is established in the contact region. The state of the liquid film in the contact region can be monitored with the interference patterns obtained from a microscope and a charge coupled device camera. The central-film-thickness, h, in the contact region is obtained with the ROII technique. A detailed meas- uring mechanism of the film thickness can be seen in Refs. 8 and 15. The roughness, R a , values of the undeformed surfa- ces of the steel ball and the Cr layer are about 3.7 nm and 1.0 nm, respectively. The Young’s moduli of the steel ball and the glass disk are 205.8 and 72.0 GPa, respectively. The val- ues of Poisson’s ratio of the steel ball and the glass disk are 0.30 and 0.17, respectively. The applied load was 28 N. The corresponding contact radius was about 125.56 lm. The ball was replaced and the disk was carefully cleaned after each test. In order to expose the liquid film to an EEF, the nega- tive pole of direct current power remains in contact with the Cr layer, and the positive one is in contact with the steel ball. Three sets of liquid mixtures were used: (I) n-decanol (Sinopharm Chemical Reagent, purity: >99%) in n-heptane (Sinopharm Chemical Reagent, purity: >99%) mixtures with solute concentrations of 5, 10, 25, 37.5, 50, and 75 vol. %; (II) n-decanol in n-hexadecane (Haltermann, purity: >99%) mixtures with solute concentrations of 10 and 50 vol. %; (III) n-decanol in octamethylcyclotetrasiloxane (OMCTS) a) Electronic mail: [email protected]. b) Author to whom correspondence should be addressed. Electronic mail: [email protected]. 0021-8979/2011/109(11)/114302/6/$30.00 V C 2011 American Institute of Physics 109, 114302-1 JOURNAL OF APPLIED PHYSICS 109, 114302 (2011) Downloaded 05 Jul 2011 to 166.111.200.172. Redistribution subject to AIP license or copyright; see http://jap.aip.org/about/rights_and_permissions
6
Embed
Thin liquid film lubrication under external electrical ...Thin liquid film lubrication under external electrical fields: Roles of liquid intermolecular interactions Guoxin Xie,a) Jianbin
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Thin liquid film lubrication under external electrical fields: Roles of liquidintermolecular interactions
Guoxin Xie,a) Jianbin Luo,b) Shuhai Liu, Dan Guo, and Chenhui ZhangState Key Laboratory of Tribology, Tsinghua University, Beijing 100084, China
(Received 10 January 2011; accepted 8 April 2011; published online 1 June 2011)
One of the important features of the nanoscale liquid film lubrication is the formation of ordered
layers at the solid/liquid interface. In this paper, the effect of the intermolecular interaction in
liquid lubricant films on the formation of ordered layers after applying external electric fields
(EEFs) has been investigated by measuring the central-film-thicknesses of liquids in concentrated
point contacts and then inferring the thin film rheology. It has been found that the film formation
properties of both pure liquid n-alkanes and liquid n-alcohols with relatively long chains have
weak responses to EEFs, while those of their mixed solutions could be enhanced more notably by
EEFs. In addition, the effect of the dispersive interactions between solvent molecules on the
formation of ordered layers in thin lubrication films under EEFs was also discussed. VC 2011American Institute of Physics. [doi:10.1063/1.3587477]
I. INTRODUCTION
Understanding the nanoscale properties of thin liquid
films is of great importance in a wide variety of applications
such as lubrication, spreading and adhesion, etc.1,2 With the
development of micro/nanomachining techniques, the tribo-
surfaces of ultraprecise instruments are often molecularly
smooth, and the gap between the surfaces is usually at the
nanometer scale. The lubricant film confined in such a nar-
row gap behaves differently from the expectations of classi-
cal lubrication theories.3,4 Different kinds of experimental
techniques have been applied to investigate the behaviors of
nanoscale liquid films in lubricated contacts.5–8 It has been
shown8–14 that the behaviors of the molecules in the confined
liquid film are dependent on the physicochemical properties
of the liquid, the solid surface properties, and the interactions
between the liquid molecules and the solid surfaces.
More recently, the effect of an external electrical field
(EEF) on the properties of thin liquid films has attracted
much attention.16–22 One of the important findings in these
studies was that the EEF could enhance the degree of molec-
ular ordering in polar liquid films or nonpolar solution films
with polar additives. As a result, similar to the action of an
EEF on liquid crystals, the electroviscosity effect of these
liquid films due to the formation of ordered layers or electri-
cal double layers near the surfaces of tribopairs could be
expected. However, the EEF effect on the liquid films with
longer alkyl chains was found to be less noticeable in our
previous study,20 suggesting that the interactions between
liquid molecules should be adequately considered for under-
standing the behaviors of confined liquid films. Therefore,
the investigations of how the interfacial ordered layers in liq-
uid films are affected by the interactions between liquid mol-
ecules under the influence of EEFs are very interesting.
However, it is rarely discussed. In the present study, the
relative optical interference intensity (ROII) technique was
employed to investigate the EEF effects on confined films of
simple n-alkanes, n-alcohols, and their mixtures by meas-
uring the central-film-thickness in the concentrated point
contact and then calculating the effective viscosity.
II. EXPERIMENT
The scheme of the experimental setup is shown in Fig.
1. A circular contact region is formed when a high precision
steel ball in a liquid cup is pressed against a glass disk coated
with a semireflective chromium (Cr) layer. The test liquid in
the oil cup is entrained into the contact region with the rota-
tion of the ball driven by the disk. Then, a liquid film is
established in the contact region. The state of the liquid film
in the contact region can be monitored with the interference
patterns obtained from a microscope and a charge coupled
device camera. The central-film-thickness, h, in the contact
region is obtained with the ROII technique. A detailed meas-
uring mechanism of the film thickness can be seen in Refs. 8
and 15. The roughness, Ra, values of the undeformed surfa-
ces of the steel ball and the Cr layer are about 3.7 nm and 1.0
nm, respectively. The Young’s moduli of the steel ball and
the glass disk are 205.8 and 72.0 GPa, respectively. The val-
ues of Poisson’s ratio of the steel ball and the glass disk are
0.30 and 0.17, respectively. The applied load was 28 N. The
corresponding contact radius was about 125.56 lm. The ball
was replaced and the disk was carefully cleaned after each
test. In order to expose the liquid film to an EEF, the nega-
tive pole of direct current power remains in contact with the
Cr layer, and the positive one is in contact with the steel ball.
Three sets of liquid mixtures were used: (I) n-decanol
(Sinopharm Chemical Reagent, purity: >99%) in n-heptane
(Sinopharm Chemical Reagent, purity: >99%) mixtures with
solute concentrations of 5, 10, 25, 37.5, 50, and 75 vol. %;
(II) n-decanol in n-hexadecane (Haltermann, purity: >99%)
mixtures with solute concentrations of 10 and 50 vol. %;
(III) n-decanol in octamethylcyclotetrasiloxane (OMCTS)
a)Electronic mail: [email protected])Author to whom correspondence should be addressed. Electronic mail:
(Fluka, purity: >99%) mixtures with solute concentrations
of 10 and 50 vol. %. The bulk viscosity, g0, was measured
using a rheometer (Anton Paar, MCR301). The boiling
points at atmospheric pressure of n-heptane, n-hexadecane,
and OMCTS are 98.4, 287, and 175.5 �C, respectively. The
relevant physical parameters of the test liquids are summar-
ized in Table I. All of the experiments were conducted at a
temperature of 25 6 1 �C.
III. RESULTS AND DISCUSSION
The central-film-thicknesses, h, of the n-decanol/n-heptane
mixtures against rolling speed at different external voltages are
shown in Fig. 2. According to the elastohydrodynamic (EHD)
lubrication theory, the film thickness, h, depends upon the
speed, u, and the lubricant bulk viscosity, g0, according to
Ref. 3
h ¼ a ug0ð Þb; (1)
where the constant, a, is related to the geometry and the elas-
tic modulus of the tribopair, the pressure-viscosity coeffi-
cient of the lubricant and load, etc. The index, b, normally
ranges from 0.6 to 0.75 for different liquids in the EHD
lubrication regime.9 The fluid washing effect is strong and
the fluid film acts predominantly in the lubricated contact in
this lubrication regime.8 It can be inferred from Eq. (1) that
the plot of log (h) versus log (u) should be linear. The theo-
retically fitted lines (dashed lines) of the film thicknesses at
higher speeds investigated under no EEF according to Eq.
(1) are plotted in Fig. 2. As shown, the straight lines in the
plots have different theoretical gradients due to the differen-
ces in the index, b, and the gradients for some liquids are
smaller than 0.6 within the investigated speed range. The
gradient smaller than the typical one in the EHD lubrication
regime may arise from the decrease in the fluid washing
effect and the increase in the effect of solid surface proper-
ties on the film formation properties. Furthermore, such an
analysis done by fitting the measured film thickness over a
power law of speed would bring some uncertainty to the
comparison between the film formation properties of differ-
ent liquids. However, it does not affect the estimation of the
changes in the film formation properties for a given liquid af-
ter exposure to EEFs.
The deviation of the measured film thicknesses in Fig.
2(a) from the theoretically fitted values of pure n-heptane is
unnoticeable, and the differences between the film thicknesses
at different voltages are very small. For n-decanol/n-heptane
mixtures of low solute concentrations (5, 10, 25, and 37.5 vol.
%), the relationships between log (h) and log (u) at low
speeds exhibit deviations from linearity, i.e., the gradients of
the plot of log (h) versus log (u) reduce [Figs. 2(b)–2(e)]. The
measured film thicknesses under no EEF are several nano-
meters larger than the theoretical ones. After exposure to the
EEFs, the films become thicker in varying degrees. Most dra-
matically, the film thicknesses increase by more than 10 nm
at 30 V for 25 and 37.5 vol. % n-decanol/n-heptane mixtures.
In contrast, nearly linear relationships of log (h) versus log
(u) under no EEF can be observed for 50 and 75 vol. % n-dec-
anol/n-heptane mixtures within the investigated speed range
[Figs. 2(f) and 2(g)]. After exposure to the EEFs, the film
thicknesses increase by 2–3 nm, as a whole. For pure n-dec-
anol, the measured film thicknesses under no EEF are slightly
larger than the theoretical values at low speeds. However,
very small changes in the film thicknesses can be observed
under the influence of EEFs [Fig. 2(h)].
A further analysis of Eq. (1) indicates that if the pres-
sure-viscosity coefficient of the lubricant is assumed to be
invariant when the lubricant is confined in a narrow gap, the
deviation of the gradient of log (h) versus log (u) from the
typical value in the EHD lubrication regime at low speeds
can be ascribed to the change in the lubricant viscosity. This
is due to the fact that other operating conditions, e.g., load
and rolling speed, are unchanged. Thus, the effective viscos-
ity of the confined liquid film can be obtained by rearranging
Eq. (1) as,
geff �1
u
h
a
� �1=b
: (2)
In order to give a clearer demonstration of the EEF effect on
the characteristics of confined lubricant films, the effective
viscosity, geff, will be discussed in the following text. The
calculated effective viscosities of the n-decanol/n-heptane
TABLE I. Some relevant physical parameters of test liquids.
Bulk viscosity,
g0 (mPa � s)
Refractive
index
n-heptane 0.39 1.39
n-decanol 10.90 1.43
n-hexadecane 3.59 1.43
OMCTS 2.40 1.40
n-decanol/n-heptane (5 vol. %) 0.88 1.39
n-decanol/n-heptane (10 vol. %) 1.17 1.39
n-decanol/n-heptane (25 vol. %) 1.85 1.41
n-decanol/n-heptane (37.5 vol. %) 3.66 1.41
n-decanol/n-heptane (50 vol. %) 4.62 1.41
n-decanol/n-heptane (75 vol. %) 6.16 1.43
n-decanol/n-hexadecane (10 vol. %) 4.73 1.43
n-decanol/n-hexadecane (50 vol. %) 6.43 1.43
n-decanol/OMCTS (10 vol. %) 3.25 1.42
n-decanol/OMCTS (50 vol. %) 5.63 1.42
FIG. 1. The schematic diagram of the experimental setup.
114302-2 Xie et al. J. Appl. Phys. 109, 114302 (2011)
Downloaded 05 Jul 2011 to 166.111.200.172. Redistribution subject to AIP license or copyright; see http://jap.aip.org/about/rights_and_permissions
films by using Eq. (2) are shown in Fig. 3. Since the EEF
effect on the film thickness of pure n-heptane is not remark-
able and the data are also somehow scattered, the effective
viscosities of the n-heptane film were not calculated. As
shown in Fig. 3(a), the effective viscosity under no EEF
gradually increases with the decreasing film thickness for the
5 vol. % n-decanol/n-heptane film, and a double increase,
compared with the bulk value at the film thickness of 5 nm,
is present. Larger increases in the effective viscosity of the
5 vol. % n-decanol/n-heptane film can be observed after ex-
posure to EEFs. The effective viscosity at 30 V increases by
six times compared with the bulk value at the film thickness
of 8 nm. Similarly, the EEF effect on the effective viscosity
at the small film thickness is also very evident for the n-dec-
anol/n-heptane films with solute concentrations of 10, 25,
and 37.5 vol. % [Figs. 3(b)–3(d)]. Most dramatically, the
effective viscosity at 30 V increases by more than ten times
compared with the bulk value for the 25 vol. % n-decanol/
FIG. 2. (Color online) Central-film-
thicknesses vs rolling speed of the n-dec-
anol/n-heptane films with different sol-
ute concentrations: (a) 0, (b) 5, (c) 10,
(d) 25, (e) 37.5, (f) 50, (g) 75, and (h)
100 vol. % at various voltages. The theo-
retically fitted lines (dashed lines) of the
film thicknesses at 0 V at high speeds,
investigated according to Eq. (1), are
also shown.
114302-3 Xie et al. J. Appl. Phys. 109, 114302 (2011)
Downloaded 05 Jul 2011 to 166.111.200.172. Redistribution subject to AIP license or copyright; see http://jap.aip.org/about/rights_and_permissions
n-heptane film. In the cases of the n-decanol/n-heptane films
with higher solute concentrations (50 and 75 vol. %) and the
pure n-decanol film, the EEF effects on the effective viscos-
ity are not as remarkable as those for films with low solute
concentrations, as shown in Figs. 3(e)–3(g).
It was previously proposed that the larger film thick-
nesses than the theoretically predicted ones under no EEF
are due to the formation of ordered layers in the liquid film
near solid surfaces.8 In the presence of an EEF, polar mole-
cules with permanent dipoles can be adsorbed and reoriented
to more easily increase the number of interfacial ordered
layers.15 However, the EEF effects on the adsorption and ori-
entation of the molecules in pure polar liquid films become
less pronounced when the alkyl chain is longer.20 Such phenom-
ena were proposed to be a result of the intermolecular interac-
tions in the liquid film, mainly including the dipole-dipole
FIG. 3. (Color online) Normalized
effective viscosity vs film thickness of
the n-decanol/n-heptane films with dif-
ferent solute concentrations: (a) 5, (b)
10, (c) 25, (d) 37.5, (e) 50, (f) 75, and
(g) 100 vol. % at various voltages. The
solid curve (0 V), long-dashed curve (10
V), short-dashed curve (20 V), and dot-
ted curve (30 V) were drawn by hand to
guide the eye.
114302-4 Xie et al. J. Appl. Phys. 109, 114302 (2011)
Downloaded 05 Jul 2011 to 166.111.200.172. Redistribution subject to AIP license or copyright; see http://jap.aip.org/about/rights_and_permissions
interactions [the shadow circular regions of Fig. 4(a)] and
the dispersive interactions between alkyl chains [the regions
denoted as dashed circles of Fig. 4(a)]. Large intermolecular
interactions would result in high potential barriers for the
breaking of monomers and the following rotation of partially
liberated monomers. Hence, the EEF effect on the effective vis-
cosity of the pure n-decanol film is not very remarkable. For
the reasonably dilute n-heptane solutions in which n-decanol
is the solute (e.g., the solute concentrations are 5, 10, 25, and
37.5 vol. %), the intermolecular self-association can be mini-
mized in the following way: The dipole-dipole interactions,
or rather hydrogen bonds between alcohol molecules,
become weak in a dilute nonpolar n-alkane solution. Then,
the hydroxyl groups have a larger rotational freedom, and
the permanent dipoles can be reoriented more easily by the
electrical force. More ordered layers could be formed near
the solid surfaces due to the solid/liquid interfacial interac-
tions, e.g., the ion-dipole interaction. Therefore, a greater
effective viscosity and thus, a larger film thickness can be
expected, as schematically shown in Fig. 4(b).
Next, the mixtures of n-decanol in n-hexadecane, which
has a longer alkyl chain than n-heptane, will be discussed. The
dispersive interactions between alkyl chains in n-hexadecane
are stronger than those in n-heptane, and it can be intuitively
shown by the difference in the boiling points of the two
liquids. The n-hexadecane will have a lower solvation power
than n-heptane, and n-decanol will be less well solvated in
n-hexadecane.23 In other words, n-decanol molecules will be
more aggregated and curled up in n-hexadecane than in
n-heptane.24 Hence, the hydrogen bonds between n-decanol
molecules in n-hexadecane are stronger since the number of
hydroxyl groups per unit volume is constant at the same sol-
ute concentration. More energy is then needed to compensate
for the larger entropy loss associated with the alignment by
EEFs for n-decanol molecules in the n-hexadecane solution,
i.e., the n-decanol molecules display a lower capacity for
being reoriented by EEFs. Therefore, the n-decanol/n-hexa-
decane film should have a weaker response to the EEF than
the n-decanol/n-heptane film at the same solute concentration.
Such a speculation is in agreement with the experimental
results in Fig. 5, where the EEF effect on the effective viscos-
ity of the n-decanol/n-hexadecane films is less remarkable.
Finally, OMCTS, a model liquid with quasispherical
molecules, was used as the solvent. The relationships
between the effective viscosity and the film thickness of
OMCTS, and n-decanol/OMCTS mixtures with solute con-
centrations of 10 and 50 vol. % are shown in Fig. 6. The
effective viscosity of the pure OMCTS film under no EEF
becomes increasingly larger with the decreasing film thick-
ness when the film thickness is smaller than 12 nm. It is pri-
marily due to the formation of molecular layers in the
OMCTS film near the solid surfaces, and similar results were
also observed in previous studies9,10,25–27 However, no no-
ticeable change in the effective viscosity of the OMCTS film
can be observed after the film has been exposed to EEFs.
The variations in the effective viscosity of the n-decanol/
OMCTS films with the film thickness become less noticeable
under no EEF, indicating that n-decanol probably destroys
the molecular ordering in the OMCTS film. However, the
EEF effect on the effective viscosities of the n-decanol/
OMCTS films is more remarkable than that of the OMCTS
film. For instance, the effective viscosity of the 50 vol. % n-
decanol/OMCTS film increases dramatically with the
decreasing film thickness at 30 V. Moreover, it can be found
that the response of the effective viscosities of the n-decanol/
OMCTS films to EEFs is more pronounced than that of the
n-decanol/n-hexadecane films but less than that of the n-decanol/
n-heptane film at the same solute concentration. Such a phenom-
enon is primarily due to the difference in the strengths of the
FIG. 4. (Color online) The schematic diagrams of (a) pure n-decanol and
(b) n-decanol/n-heptane films with low solute concentrations under EEFs.
FIG. 5. (Color online) Normalized effective viscosity vs film thickness of (a) n-hexadecane film, (b) 10 vol. % n-decanol/n-hexadecane film, and (c) 50 vol. %
n-decanol/n-hexadecane film at various voltages. The exponents, b, used in Eq. (2) were 0.60, 0.56, and 0.60 for these lubricant films, respectively. The solid
curve (0 V), long-dashed curve (10 V), short-dashed curve (20 V), and dotted curve (30 V) were drawn by hand to guide the eye.
114302-5 Xie et al. J. Appl. Phys. 109, 114302 (2011)
Downloaded 05 Jul 2011 to 166.111.200.172. Redistribution subject to AIP license or copyright; see http://jap.aip.org/about/rights_and_permissions
dispersive interactions between solvent molecules. It can be
inferred from the boiling points that the dispersive interactions
between OMCTS molecules are smaller than those between n-
hexadecane molecules, while larger than those between n-
heptane molecules. As discussed above, the larger the dispersive
interactions between solvent molecules, the lower the solvation
power of the solvent and the stronger the hydrogen bonds
between the hydroxyl groups in the n-decanol/solvent films.
IV. CONCLUSIONS
In summary, the effect of intermolecular interactions on
the formation of ordered layers in nanoliquid lubrication
films under EEFs has been investigated through measuring
the film thickness under pure rolling conditions. Experimen-
tal results indicate that the film formation properties of a rea-
sonably dilute n-alkane solution in which the solute is a long
liquid alcohol can be enhanced more remarkably by EEFs
than those of the pure solvent and the pure solute due to the
reduction in the intermolecular self-association. After en-
hancing the dispersive interactions between solvent mole-
cules, the number of the interfacial ordered layers in the
nanoliquid film decreases and the promotion of the film for-
mation properties by EEFs would weaken. The present work
suggests that properly incorporating the intermolecular inter-
actions into the lubricant design is of practical significance
for desirable control over the lubrication properties of thin
liquid films by EEFs.
ACKNOWLEDGMENTS
The work is financially supported by the National Natu-
ral Science Foundation of China (Grant Nos. 51021064 and
50823003). The authors are also grateful to the NSK Ltd. for
providing high precision steel balls.
1D. T. Wasan and A. D. Nikolov, Nature (London) 423, 156 (2003).2M. Urbakh, J. Klafter, D. Gourdon, and J. Israelachvili, Nature (London)
430, 525 (2004).3B.J. Hamrock and D. Dowson, ASME J. Lubr. Technol. 99, 264 (1977).4F. P. Bowden and D. Tabor, The Friction and Lubrication of Solids(Oxford University Press, London, 1954).
5I. Krupka, M. Hartl, and M. Liska, Trans. ASME, J. Tribol. 127, 890 (2005).6F. Guo and P. L. Wong, Proc. Inst. Mech. Eng., Part J: J. Eng. Tribol. 216,
281 (2002).7H. A. Spikes and P. M. Cann, Proc. Inst. Mech. Eng., Part J: J. Eng. Tribol.
215, 261 (2001).8J. B. Luo, S.Z. Wen, and P. Huang, Wear 194, 107 (1996).9H. A. Spikes and M. Ratoi, Tribol. Interface Eng. Ser. 38, 359 (2000).
10M. Hartl, I. Krupka, and M. Liska, Sci. China Ser. A-Math., Phys.,
abstract376450.shtml.11S. H. Liu, L. R. Ma, C. H. Zhang, and X.C. Lu, Appl. Phys. Lett. 91,
253110 (2007).12S. H. Liu, G. X. Xie, D. Guo, and Y. H. Liu, J. Appl. Phys. 107, 104323 (2010).13Y. Z. Hu and S. Granick, Tribol. Lett. 5, 81 (1998).14A. Martini and A. Vadakkepatt, Tribol. Lett. 38, 33 (2010).15J. B. Luo, M. W. Shen, and S. Z. Wen, J. Appl. Phys. 96, 6733 (2004).16R. Verma, A. Sharma, K. Kargupta, and J. Bhaumik, Langmuir 21, 3710 (2005).17D. Bratko, C. D. Daub, K. Leung, and A. Luzar, J. Am. Chem. Soc. 129,
2504 (2007).18H. B. Zeng, Y. Tian, T. H. Anderson, M. Tirrell, and J. N. Israelachvili,
Langmuir 24, 1173 (2008).19D. Bratko, C. D. Daub, and A. Luzar, Phys. Chem. Chem. Phys.10, 6807
(2008).20G. X. Xie, J. B. Luo, D. Guo, and S. H. Liu, Appl. Phys. Lett. 96, 043112
(2010); G. X. Xie, J. B. Luo, S. H. Liu, D. Guo, and C. H. Zhang, Soft
Matter 7,4453 (2011).21I. Bou-Malham and L. Bureau, Soft Matter 6, 4062 (2010).22S. Srivastava, P. D. S. Reddy, C. Wang, D. Bandyopadhyay, and A.
Sharma, J. Chem. Phys. 132, 174703(2010).23H. J. Butt and M. Kappl, Surface and Interfacial Forces (Wiley-VCH,
Weinheim, 2010).24M. G. Martin, N. D. Zhuravlev, B. Chen, P. W. Carr, and J. I. Siepmann,
J. Phys. Chem. B 103, 2977 (1999).25J. Klein and E. Kumacheva, Science 269, 816 (1995).26Y. Zhu and S. Granick, Langmuir 19, 8148 (2003).27L. Bureau, Phys. Rev. Lett. 104, 218302 (2010).
FIG. 6. (Color online) Normalized effective viscosity vs film thickness of (a) pure OMCTS film, (b) 10 vol. % n-decanol/OMCTS film, and (c) 50 vol. % n-
decanol/OMCTS film at various voltages. The exponents, b, used in Eq. (2) were 0.67, 0.75, and 0.67 for these lubricant films, respectively. The solid curve (0
V), long-dashed curve (10 V), short-dashed curve (20 V), and dotted curve (30 V) were drawn by hand to guide the eye.
114302-6 Xie et al. J. Appl. Phys. 109, 114302 (2011)
Downloaded 05 Jul 2011 to 166.111.200.172. Redistribution subject to AIP license or copyright; see http://jap.aip.org/about/rights_and_permissions