# Rubber adhesion and friction: role of surface energy and contamination films

A. Tiwari  MultiscaleConsulting, Wolfshovener Str 2, 52428 Jülich, Germany  T.
Tolpekina  Apollo Tyres Global R&D B.V., P.O. Box 3795, 7500 DT — Colosseum 2,
7521 PT Enschede, The Netherlands  Hans van Benthem  Apollo Tyres Global R&D
B.V., P.O. Box 3795, 7500 DT — Colosseum 2, 7521 PT Enschede, The Netherlands
M.K. Gunnewiek  Apollo Tyres Global R&D B.V., P.O. Box 3795, 7500 DT —
Colosseum 2, 7521 PT Enschede, The Netherlands  B.N.J. Persson
MultiscaleConsulting, Wolfshovener Str 2, 52428 Jülich, Germany  PGI-1, FZ
Jülich, Germany

###### Abstract

We study the influence of the surface energy and contamination films on rubber
adhesion and sliding friction. We find that there is a transfer of molecules
from the rubber to the substrate which reduces the work of adhesion and makes
the rubber friction insensitive to the substrate surface energy. We show that
there is no simple relation between adhesion and friction: adhesion is due to
(vertical) detachment processes at the edge of the contact regions (opening
crack propagation), while friction in many cases is determined mainly by
(tangential) stick-slip instabilities of nanosized regions, within the whole
sliding contact. Thus while the pull-off force in fluids may be strongly
reduced (due to a reduction of the work of adhesion), the sliding friction may
be only slightly affected as the area of real contact may be dry, and the
frictional shear stress in the contact area nearly unaffected by the fluid.

1 Introduction

The friction and adhesion between rubber materials and a counter surface have
many practical applications, e.g., for tires, conveyor belts, rubber seals and
pressure sensitive adhesives. The adhesion and friction of rubber is a very
complex topic because of the temperature and frequency dependency, and the
non-linearity, of the stress-strain relation. In addition, all solids have
surface roughness, usually extending from the linear size of the object down
to atomic distances, which strongly influence the contact mechanics[1, 2, 3,
4, 5, 6, 7, 8].

In this paper we will study the influence of the substrate surface energy on
adhesion and friction. We use surfaces with the same topography but different
surface energy, namely smooth and sandblasted glass surfaces without and with
hydrophobic coating (monolayers of grafted molecules). We will also study how
the transfer of rubber to the track may influence the friction for another
rubber compound on the surface contaminated by the first compound.

This paper is organized as follows. In Sec. 2 we present a qualitative
discussion about rubber friction. In Sec. 3 we describe the rubber compounds
used in the study. In Sec. 4 we show the surface roughness power spectra of
the sandblasted glass surfaces, and of a smooth and a rough rubber surface.
Sec. 5 describe the procedure used to prepare hydrophobic glass surfaces. In
Sec. 6 we present adhesion results between clean and silanized glass balls and
rubber, which illustrate the influence on the adhesion by contamination films,
formed by transfer of molecules from the rubber to the glass surface. In Sec.
7 we present Fourier-transform infrared spectroscopy data which shows that the
contamination film is a wax, which is added to the rubber to protect against
ozone. Similarly, during sliding of rubber blocks, contamination films
(derived from the rubber) form on the countersurface, even for the silanized
glass surfaces. This is discussed in Sec. 8 where we present experimental
results for the velocity dependent friction coefficient for rubber blocks
sliding on smooth and sandblasted glass surfaces, both “clean” and silanized.
We will also study how the transfer of molecules from a rubber compound A to a
concrete surface influence the friction for another rubber compound B on the
surface contaminated by the compound A. Sec. 9 present a discussion, and Sec.
10 the summary and conclusion.

Figure 1:  The contribution to the friction coefficient from viscoelastic
deformations $\mu_{\rm vis}$, and from the area of real contact $\mu_{\rm
con}$, as function of sliding speed in a typical case at room temperature.
Figure 2:  The contribution to the friction from the area of real contact
depends on surface energies, contamination films and slip (or shear) planes.
In (a) a thin strongly bound contamination film occur on the substrate
surface. In (b) a thicker contamination film occur, e.g. due to transfer of
molecules from the rubber to the glass surface. In (c) the glass surface is
silanized which may result in slip between the contamination film and the
silanized glass surface (pink).

2 Rubber friction: qualitative discussion

Fig. 1 shows schematically the contribution to the friction coefficient
$\mu=\mu_{\rm vis}+\mu_{\rm con}$ from viscoelastic deformations $\mu_{\rm
vis}$, and from the area of real contact $\mu_{\rm con}$, as function of
sliding speed in a typical case of rubber sliding on a rough rigid
countersurface at room temperature[9].

The contribution from the area of real contact may involve shearing a thin
contamination film, or processes where polymer segments (or nanosized rubber
patches) undergoes cyclic stick-slip events[10, 11, 12], or where hard filler
particles at the rubber surface scratches the substrate (plowing friction).
The viscoelastic contribution to the friction result from the time-dependent
deformations of the rubber by the substrate asperities, and occurs on many
length scales[13]. In what follows we will focus mainly on the contribution to
the friction from the area of real contact.

We can write $\mu_{\rm con}=\tau_{\rm f}A$, where the area of real contact $A$
depends on the contact pressure, temperature and the sliding speed. The
frictional shear stress $\tau_{\rm f}$ can originate from different processes
which we now discuss.

Fig. 2 shows schematically the contribution to the friction from the area of
real contact, which depends on surface energies, contamination films and the
location of slip (or shear) planes. In (a) a thin, strongly bound,
contamination film (usually water and polar molecules with a hydrocarbon part)
occur on the surface. In (b) a thicker contamination film occur, which could
result from transfer of molecules from the rubber to the glass surface. In (c)
the glass surface is silanized, and hence covered by an inert grafted
monolayer (pink region), which may result in slip between the contamination
film and the silanized surface.

If the contamination film is very thin (some nanometers), and the molecules
bound strongly enough to the substrate surface (here glass), slip will occur
between the rubber and the contamination film (see Fig. 2(a)). In this case
the contribution from the area $A$ of real contact to the friction may involve
interfacial processes where polymer segments, or nanosized patches of the
rubber, attach, stretch, snap-off and re-attach to the substrate[10, 11, 12].
During the rapid snap-off the elastic energy in the stretched polymer chains
are converted into heat. Theoretical[10, 11, 12] and experimental[14, 15]
studied have shown that this result in a frictional shear stress which is well
approximated by a Gaussian-like function of the logarithm of the sliding speed
$v$, with a width of order several decades in velocity:

$\tau_{\rm f}\approx\tau_{0}\ {\rm exp}\left(-c\left[{\rm log}{v\over
v^{*}}\right]^{2}\right)$ $None$

where $v^{*}$ is a reference velocity which depends on the temperature but
which for $T\approx 20^{\circ}{\rm C}$ typically is of order $1\ {\rm mm/s}$.

If the contamination film is thicker (see Fig. 2(b)) it may behave as a
(usually shear thinning) viscous fluid, and the shear stress acting on the
rubber surface will be determined by the viscosity (and shear rate) of the
fluid:

$\tau_{\rm f}\approx{\eta_{0}\dot{\gamma}\over
1+(\eta_{0}/B)\dot{\gamma}^{n}}$ $None$

where $B$ is a shear-thinning constant and $\dot{\gamma}=v/d$ the shear rate
($d$ is the film thickness). For polymer fluids the exponent $n$ is typically
in the range $0.7-1$ [16, 17], where the larger $n$ correspond to longer chain
molecules.

For a silanized glass surface (see Fig. 2(c)) some of the slip may be
localized to the interface between the hydrophobic coating and the
contamination film[18], but the experimental results presented below indicate
that the main slip again occur either within the contamination film or at the
interface between the rubber and the contamination film. We will show below
that the contamination film may be derived mainly from the rubber rather than
from other origins.

If the substrate is perfectly smooth there is no viscoelastic contribution
$\mu_{\rm vis}$ to the friction. This is the case even if the rubber surface
has roughness. Several of the experiments reported on below use very smooth
glass surfaces, and in these cases $\mu\approx\mu_{\rm con}$.

3 Rubber compounds

We have used 3 different rubber compounds denoted A, B and C. B is a summer
tread compound filled with carbon black. A is a summer tread compound filled
with silica and containing a traction resin. C is a winter tread compound,
filled with silica and containing a traction resin (same as in A in the same
quantity).

Table 1 gives a summary of the glass transition temperature $T_{\rm g}$ and
the maximum of ${\rm tan}\delta$ for all the compounds as obtained from
Dynamic Machine Analysis (DMA) measurements of the viscoelastic modulus (see
Ref. [19]). The values in the parenthesis are from measurements performed one
year earlier on nominally identical rubber compounds from a different batch.

Table 1: Summary of the glass transition temperatures of the A, B and C compounds. The glass transition temperature is defined as the maximum of $\rm{tan}\delta$ as a function of temperature for the frequency $\omega_{0}=0.01\ \rm{s}^{-1}$. The values in the parenthesis are from measurements performed one year earlier on nominally identical rubber compounds from a different batch[19]. compound | $T_{\rm g}$ | maximum of $\rm{tan}\delta$
---|---|---
A |  $-28.2^{\circ}{\rm C}$ ($-30.4^{\circ}{\rm C}$) | 0.61 (0.53)
B |  $-39.4^{\circ}{\rm C}$ ($-40.5^{\circ}{\rm C}$) | 0.57 (0.52)
C |  $-46.2^{\circ}{\rm C}$ ($-47.2^{\circ}{\rm C}$) | 0.46 (0.41)
Figure 3:  The 1D surface roughness power spectrum of the sandblasted glass
plate 1 (red) and glass plate 2 (green). The rms roughness of both plates is
$\approx 15\ {\rm\mu m}$.  Figure 4:  The 1D surface roughness power spectrum
of the sandblasted glass surface (red) and of the smooth (before tests) rubber
surface (blue and pink), and of the rubber surface after the sliding friction
measurements on the sandblasted surface (green).

4 Surface roughness power spectrum

The surface roughness is of crucial importance for the sliding friction[8,
20]. The most important quantity is the surface roughness power spectrum. The
two-dimensional (2D) surface roughness power spectrum $C(q)$, which enters in
the Persson contact mechanics theory, can be obtained from the height profile
$z=h(x,y)$ measured over a square surface unit. However, for surfaces with
roughness with isotropic statistical properties, the 2D power spectrum can be
calculated from the one-dimensional (1D) power spectrum obtained from a line-
scan $z=h(x)$ (see [21, 22]).

The smooth glass surface can be considered as perfectly smooth with vanishing
surface roughness power spectrum. We prepared several sandblasted glass
surfaces. The glass plates ($16\ {\rm cm}\times 36\ {\rm cm}$ and $0.5\ {\rm
cm}$ thick) where sandblasted “by hand” for 5 minutes each. This may result in
some variation in the surface topography but the surface roughness power
spectrum of the plates are nearly identical (see Fig. 3). The power spectra
shown in Fig. 3 was calculated from $25\ {\rm mm}$ long line scans, and
averaged over 5 different line scans obtained at different locations on the
glass surfaces.

We also measured the surface topography of a rubber surface before and after
sliding it on the sandblasted glass surface. Sliding on the sandblasted
surface resulted in some wear and increased surface roughness. Fig. 4 shows
the power spectra of the smooth (before tests) rubber surface (blue and pink),
and of the rubber surface after the sliding friction measurements on the
sandblasted surface (green). The figure also shows the surface roughness power
spectrum of the sandblasted glass surface (red), as obtained from the average
over the two power spectra shown in Fig. 3. The root-mean-square (rms)
roughness of the sandblasted glass surface is $\approx 15\ {\rm\mu m}$.

Figure 5:  Water contact angle of glass surface cleaned with acetone and
isopropanol (left), and silanized glass surface i.e., a glass surface covered
by hydrophobic grafted monolayer (right).

5 Preparation of silanized glass surfaces

We have prepared silanized (hydrophobic) glass surfaces using Rain-X. Rain-X
is most commonly used on glass automobile surfaces, and result in a
hydrophobic coating which causes water to bead. Rain-X’s primary active
ingredient are polysiloxanes, the primary one being hydroxy-terminated
polydimethylsiloxane. The polysiloxanes have functional groups that bind to
the hydroxyl group of the glass surface. In addition Rain-X contains acetone
and water, but the exact ratio is a trade secret.

The glass surfaces was first cleaned with acetone and isopropanol, and then
ultrasonic cleaned in distilled water. After drying the surface with a paper
towel we immediately applied the Rain-X. Next the glass surface was wiped with
a paper towel for 5 minutes using a firm, circular and overlapping motion.
Finally, the coated surface was left for 24 hours, washed with distilled water
and dried. In addition, in a few studies the silanized glass surfaces were
ultrasonic cleaned in distilled water to make sure just a monolayer of
chemically attached polydimethylsiloxane molecules occur on the glass surface.

Fig. 5 shows the water contact angle on a glass surface cleaned with acetone
and isopropanol (left), and a glass surface covered by hydrophobic monolayer
(right) using Rain-X.

Figure 6:  The interaction force between a glass ball and the rubber compound
A as a function of time. Results are shown in dry condition (red) and when
immersed in water (green). The rubber surface was cleaned with hot water and
the glass ball with acetone. The glass ball moved up and down with the speed
$5\ {\rm\mu m/s}$.  Figure 7:  The work of adhesion between a glass ball and
the rubber compound B, C and A for dry contact and in water. The rubber
surfaces are smooth and cleaned with hot water just before start of the
experiments. The glass ball was cleaned with acetone. The pull-off speed
$v_{z}=5\ {\rm\mu m/s}$ and the temperature $T=20^{\circ}{\rm C}$.  Figure 8:
The work of adhesion between a glass ball and the rubber compound C for dry
contact (squares) and in water (stars). In (a) the rubber surface is smooth
and cleaned with hot water just before start of the experiment. In (b) the
rubber surface was roughened by sandpaper just before start of the experiment.
The red symbols are for a glass ball cleaned with acetone and isopropanol. The
green symbols are for a silanized glass ball prepared using Rain-X. The pull-
off speed $v_{z}=5\ {\rm\mu m/s}$ and the temperature $T=20^{\circ}{\rm C}$.

6 Role of contamination on adhesion

We have performed adhesion experiments where a glass ball with a few cm
diameter is moved repeatedly up and down making first repulsive contact with
the rubber substrate (typical repulsive force $0.1\ {\rm N}$) and then pulled-
off[19]. The glass ball was cleaned with acetone just before start of the
experiment, and moved up and down with the vertical speed $5.0\ {\rm\mu m/s}$.

The rubber surface is either smooth (but with some roughness due to the
roughness of the mold) or roughened by sandpaper P180. The smooth rubber
surfaces were cleaned with hot water just before the start of the experiments.
This removed a gray film from the rubber surface (probably wax, see Sec. 7),
and made the rubber surfaces appear shining black, but after a few hours the
rubber surface appeared gray again. This shows that mobile molecules diffuse
to the rubber surface from inside the rubber, which probably is the origin of
the time dependency of the adhesion observed below.

Fig. 6 shows the interaction force between a glass ball and the rubber
compound A as a function of time. Results are shown in dry condition (red) and
when immersed in water (green).

Fig. 7 shows the work of adhesion between an (originally) cleaned glass ball
and the rubber compound B, C and A for dry contact and in water. Note the
continuous decrease in the work of adhesion with the number of contacts (and
hence increasing time) which we attribute to diffusion of mobile molecules to
the rubber surface and to transfer of molecules from the rubber to the glass
surface. This is observed even in water. Note also that adhesion in water is
much smaller than in the dry state.

We have performed a set of experiments using rubber from a new (nominally
identical) batch produced one year after the rubber used in Fig. 7. Fig. 8
shows the work of adhesion between a glass ball and the rubber compound C for
dry contact (squares) and in water (stars). In (a) the rubber surface is
smooth and cleaned with hot water just before start of the experiment. In (b)
the rubber surface was roughened by sandpaper just before start of the
experiment. The red symbols are for a glass ball cleaned with acetone and
isopropanol. The green symbols are for a silanized glass ball prepared using
Rain-X (see Sec. 5).

Note that for the roughened rubber surface the (macroscopic) adhesion nearly
vanish. This is due to the reduction in the area of real contact, and (more
importantly) due to the elastic deformation energy stored at the interface
which is “given back” during pull-off, and help to break the adhesive bonds.
However, even when there is no macroscopic pull-off force, at short enough
length scale adhesion is still strong, and result in an increase in the
contact area[23].

Fig. 8(a) shows that for the smooth rubber surface the work of adhesion in the
dry state is initially much larger for the clean glass ball than for the
silanized glass ball, which we mainly attribute to a larger surface energy of
the clean glass ball then the silanized ball. However, the rubber surface is
not perfectly smooth and the surface roughness will affect (reduce) the work
of adhesion and this effect may differ for the two cases.

For the (initially) clean glass ball the work of adhesion decreases with
increasing number of contacts which we attribute to a decrease in the surface
energy of the glass ball due to transfer of molecules from the rubber to the
glass ball. For the silanized glass ball the work of adhesion is nearly
constant, both in the dry state and in water. This could indicate that no
molecules are transferred from the rubber to the silanized glass ball.
However, with increasing number of contacts the work of adhesion for the
(originally clean) glass ball approach the work of adhesion for the silanized
glass ball, so that even if molecules are transferred to the silanized glass
ball they may result in a negligible change in the ball surface energy. Since
the transferred molecules most likely are wax molecules (see Sec. 7) this is
not unexpected due to the inert nature of wax.

In water there is a huge difference between the clean glass ball and the
silanized glass ball. For the clean glass ball the adhesion nearly vanish
which result from the hydrophilic nature of the glass surface (water molecules
bind strongly to the glass surface) which, in the case of complete wetting,
favor a thin (nanometer or less) water film between the glass and the rubber
in the rubber-glass contact region, resulting in nearly vanishing adhesion.
The silanized glass surface is hydrophobic and the water does not like (from
an energetic point of view) to stay between the rubber and the glass surface,
i.e., a dewetting transition occurs, resulting in strong adhesion even in
water.

Figure 9:  Surface contamination of the rubber compound A. The infrared
absorption spectra from (a) a not-cleaned rubber surface, (b) a rubber surface
cleaned with acetone, (c) the contamination film left on a glass surface after
sliding of compound A and (d) anti-ozone wax.

7 Infrared spectroscopy of contamination film

We have performed Fourier-transform infrared (FTIR) spectroscopy from the
contamination film left on the glass surface after (sliding) contact with the
rubber. In Fig. 9 we show the FTIR spectra from (a) a not-cleaned rubber
surface (compound A), and in (b) from a rubber surface cleaned with acetone,
and in (c) from the contamination film left on a glass surface after sliding
of compound A. The FTIR spectra of the anti-ozone wax, which is added to the
rubber compounds, is shown in Fig. 9(d). We conclude that the contamination
film on the glass surface (and on the rubber surface) is a wax, which is added
to protect the rubber against ozone. The wax molecules are mobile in the
rubber matrix and even if removed from the surface of the rubber using, e.g.,
acetone or hot water, it will rapidly diffuse to the surface of the rubber
where it form a thin film which protect the rubber against the influence of
ozone[24].

8 Sliding friction on smooth and sandblasted hydrophilic and hydrophobic glass

In this section we present results for the friction force when rubber blocks
are sliding on smooth (Sec. 8.1 and 8.3) and sandblasted (Sec. 8.2) glass
surfaces which are either clean and hydrophilic, or made hydrophobic as
described in Sec. 5. We also study how the transfer of rubber to a concrete
surface may influence the friction for another rubber compound on the surface
contaminated by the first compound (Sec. 8.4). We note that rubber friction
measurements on smooth substrates are very sensitive to the thickness and
nature of contamination films, and to (unavoidable) variations in the
roughness of the rubber block. Thus, we observe relative large variations in
the friction force when repeating the experiments under nominally identical
conditions. In what follows we therefore focus mainly on general trends rather
than exact numerical values of the friction coefficients. Sliding friction
measurements on rough surfaces, e.g., concrete surfaces, are much easier to
perform, and result in more reproducible results.

Figure 10:  The measured friction coefficient for compound A on smooth silica
glass plates as a function of the logarithm of the sliding speed. The red
symbols are the measured friction coefficient on a glass surface ultrasonic
cleaned in distilled water, and then with distilled water. The green symbols
was obtained on the same type of glass plate cleaned in the same way and then
covered by an inert monolayer film using Rain X. The blue symbols is for a
thick film of Rain X. The nominal contact pressure $p=0.06\ {\rm MPa}$ and the
temperature $T=20^{\circ}{\rm C}$.  Figure 11:  The measured friction
coefficient for compound C on smooth silica glass plates as a function of the
logarithm of the sliding speed. The rubber surface was cleaned in hot water
and then dried just before start of the experiment. The squares are for dry
surfaces and the stars in water. The red symbols are the measured friction
coefficient on a glass surface cleaned by ultrasound in water. The green
symbols was obtained on the same type of glass plate cleaned in the same way
and then covered by an inert thin film using Rain X. The nominal contact
pressure $p=0.05\ {\rm MPa}$ and the temperature $T=17^{\circ}{\rm C}$.

8.1 Sliding friction on smooth glass surfaces

We have studied the rubber sliding friction on smooth and sandblasted glass
surfaces using the Leonardo da Vinci set up (see [19]). We have used clean
glass and silanized glass surfaces and studied both dry and wet friction.

Fig. 10 shows the measured friction coefficient for the compound A on smooth
silica glass plates as a function of the logarithm of the sliding speed. The
red symbols are the measured friction coefficient on a glass surface
ultrasonic cleaned in water. The green symbols was obtained on the same type
of glass plate cleaned in the same way and then covered by an inert monolayer
film using Rain X. The blue symbols is for a thick film of Rain X. The nominal
contact pressure $p=0.06\ {\rm MPa}$ and the temperature $T=20^{\circ}{\rm
C}$.

Note that the friction coefficient before run-away is the same on the “clean”
and (monolayer) silanized glass surface, but extend to higher sliding speeds
for the silanized surface. Optical (reflected light at grazing incidence)
pictures of the glass surfaces after the friction studies shows that a very
thin contamination film is transferred from the rubber to the glass surface,
probably already at the front edge of the rubber-glass asperity contact
regions. We propose that the friction is due to sliding on, or shearing of,
this transfer film which is effectively pinned at the glass surface, even for
the silanized glass surfaces.

That a thin molecular film is transferred from the rubber to the
countersurface even for silanized glass was also proved by letting a small
water droplet slide on the tilted glass surface: the droplet moved quickly on
the silanized glass surface in the regions which had not been in contact with
the rubber, but stopped to move, or moved in a slow and irregular way, on the
regions of the glass surface which had been in sliding contact with the
rubber. As shown in Sec. 7 the contamination film is a wax.

For the silanized glass surface which was not washed (cleaned) with distilled
water after being exposed to the Rain X liquid, we observed much lower
friction than for the monolayer silanized surface (see Fig. 10). We attribute
this to a relative thick (maybe micrometer) film of polydimethylsiloxane,
which act as a viscous lubrication film resulting in a hydrodynamical (but
shear thinning) frictional shear stress as indicated in Fig. 2(b).

Fig. 11 shows similar results as in Fig. 10 but now for the compound C. The
squares are for dry surfaces and the stars in water. The red symbols are the
measured friction coefficient on a glass surface cleaned by ultrasound in
water. The green symbols was obtained on the same type of glass plate cleaned
in the same way and then covered by an inert thin film using Rain X.

For the compound C the friction coefficient on the dry silanized glass surface
is lower at low sliding speed than for the clean glass surface, but larger at
the highest sliding speeds. Again we believe a very thin contamination film
(maybe just a few monolayers) is transferred from the rubber to the glass
surface already at the front edge of the rubber-glass asperity contact
regions, and the friction is due to shearing of this film. The lower friction
on the silanized surface indicate that some slip may occur between the
contamination film and the silanized glass surface, at least at low sliding
speed.

For the compound C (smooth) we observe before run-away the same friction
coefficient in water as on the dry surface for both the clean glass surface
and the silanized glass surface (see Fig. 11). This indicate that in both
cases the water is removed from the rubber-glass interface. This is expected
for the silanized glass surface which is hydrophobic. In fact, Fig. 8(a) shows
that for the silanized glass the rubber-glass adhesion in water is very
strong. However, for the clean glass surface the adhesion in water is very
weak, but the friction for low sliding speeds is the same as for the dry
surface. We believe this is due to a combination of fluid squeeze-out by the
applied normal pressure, and dewetting driven by the (small) adhesion observed
also in water (see Fig. 8(a)). Note, however, that for the clean glass surface
the sliding in water is stable only for sliding speeds $v<10^{-5}\ {\rm m/s}$
while in the dry state stable sliding occur up to $v\approx 10^{-3}\ {\rm
m/s}$. We interpret this difference as due to forced wetting, which is
expected for high enough sliding speed[25], and which will occur at lower
sliding speed when the adhesion in water is reduced. In forced wetting the
fluid (here water) is dragged in to the contact by the sliding motion,
resulting in viscous hydroplaning and a decreasing friction force with
increasing sliding speed and run-away. Forced wetting is due to a competition
between a liquid invasion induced by shear and spontaneous dewetting of the
liquid driven by the (negative) spreading pressure. A similar effect (forced
wetting) was found in an earlier study with rubber sliding on a concrete
surface in glycerol[26].

We have repeated the experiment for compound C (not shown) and found more
noisy results than in Fig. 11, but qualitatively the same behavior except that
for hydrophobic glass in water the run-away occurred at much lower friction
coefficient than found above ($\mu\approx 1.5$ instead of $\mu\approx 2.8$ in
Fig. 11). The two experiments was performed at different environmental
temperatures ($T=22^{\circ}{\rm C}$ and $T=17^{\circ}{\rm C}$), but this is
unlikely to be the origin of the different results in water. A more likely
explanation is that the mass load (here a lead block) in the two experiments
was located at slightly different position on the wood plate, which could tilt
the plate such that the rubber-glass contact pressure was higher at the front
edge than at the exit (in the sliding direction) in the set-up used in the
experiment reported on in Fig. 11, which could reduce or remove the liquid
invasion. This tilting-problem would be absent if instead of rectangular
rubber blocks one would use (half) cylinder shaped rubber samples.

Figure 12:  The measured friction coefficient for compound C on smooth silica
glass plates as a function of the logarithm of the sliding speed. The rubber
surface was roughened by sand paper. The squares are for dry surfaces and the
stars in water. The red symbols are the measured friction coefficient on a
glass surface cleaned by ultrasound in water. The green symbols was obtained
on the same type of glass plate cleaned in the same way and then covered by an
inert thin film using Rain X. The nominal contact pressure $p=0.05\ {\rm MPa}$
and the temperature $T=17^{\circ}{\rm C}$.

Fig. 12 shows the measured friction coefficient for compound C (rough) on
smooth silica glass plates as a function of the logarithm of the sliding
speed. The rubber surface was roughened by sand paper. The squares and
triangles are for dry surfaces and the stars in water. The red symbols are the
measured friction coefficient on a glass surface cleaned by ultrasound in
water. The green symbols was obtained on the same type of glass plate cleaned
in the same way and then covered by an inert thin film using Rain X.

Figure 13:  Rubber-glass asperity contact regions in water. At short enough
length scale the contact pressure becomes so high that the contact area
(locally) percolate. When the contact is formed in water, pressurized water
may occur in the sealed-off regions. In this case part of the external load
will be carried by the water resulting in a reduced rubber-glass contact area
and a reduced sliding friction.

Note that for the dry clean and silanized glass surfaces the velocity
dependency of the friction coefficient for the roughened rubber surface (Fig.
12) is similar to for the smooth rubber surface (Fig. 11), but the friction
coefficient is smaller for the rough rubber surface as expected because of the
smaller area of real contact. However, in water the results are very
different. Thus for the clean glass surface the friction is only weakly
velocity dependent, and similar in magnitude to the sliding friction on the
dry surface at the lowest sliding speed. For the hydrophobic glass surface the
friction in water is smaller than for the dry state but exhibit a similar
velocity dependency. The reduction in the friction coefficient in water for
the rough rubber surface may be due to water trapped in sealed-off regions
which carry part of the external load, and hence reduces the area of real
contact. In the present case the applied squeezing pressure is not high, but
the local pressure in asperity contact regions will be high and, at short
enough length scale, the contact area may percolate in the asperity contact
regions, resulting in water filled sealed-off regions (see Fig. 13).

8.2 Sliding friction on sandblasted glass surfaces

Fig. 14 shows the measured friction coefficient for compound C sliding on a
sandblasted silica glass plate as a function of the logarithm of the sliding
speed. The squares are for dry surfaces and the stars in water. The red
symbols are the measured friction coefficient on a glass surface ultrasonic
cleaned in water and then with distilled water. The green symbols was obtained
on the same type of glass plate cleaned in the same way, and then covered by
an inert monolayer film using Rain X.

Figure 14:  The measured friction coefficient for compound C on sandblasted
silica glass plates as a function of the logarithm of the sliding speed. The
squares are for dry surfaces and the stars in water. The red symbols are the
measured friction coefficient on a glass surface ultrasonic cleaned in water.
The green symbols was obtained on the same type of glass plate cleaned in the
same way), and then covered by an inert thin film using Rain X. The nominal
contact pressure $p=0.05\ {\rm MPa}$ and the temperature $T=22^{\circ}{\rm
C}$.  Figure 15:  The measured friction coefficient for compound A on
sandblasted silica glass plates as a function of the logarithm of the sliding
speed. The red squares are the measured friction coefficient on a glass
surface ultrasonic cleaned in water. The green squares was obtained on the
same type of glass plate cleaned in the same way), and then covered by an
inert thin film using Rain X. The nominal contact pressure $p=0.11\ {\rm MPa}$
and the temperature $T=16^{\circ}{\rm C}$.

The friction coefficient is very similar for the clean and silanized glass
surfaces in spite of the fact that the work of adhesion for the (smooth) clean
glass is twice as high as for the silanized glass surface (see Fig. 8). This
indicate again the transfer of a contamination film to the glass surface from
the rubber and that the film is effectively pinned at the glass interface even
for the silanized glass surface. For sliding in water, for the low sliding
speed prevailing in the experiments, the water is likely to be squeezed out
from the asperity contact regions. In this case it appears as if no islands of
trapped (sealed-off) water occur. This may be due to the increased surface
roughness which result in a smaller contact area and in larger non-contact
channels where the water can be removed.

Fig. 15 shows the measured friction coefficient for compound A on sandblasted
silica glass plates as a function of the logarithm of the sliding speed. Again
the rubber friction on the clean glass surface and the silanized glass is
nearly the same. Finally we note that on the sandblasted glass surface there
will be a viscoelastic contribution to the friction, which does not exist on
the smooth glass surfaces even when the rubber surface is rough.

Figure 16:  The friction coefficient as a function of the logarithm of the
sliding speed for the compound B. The red squares are on a dry glass surface
cleaned by acetone and isopropanol and then ultrasonic cleaned in distilled
water. The green squares are for a hydrophobic (silanized) glass. The rubber
block surface is roughened by sand paper. The nominal contact pressure
$p=0.06\ {\rm MPa}$ and the temperature $T=20^{\circ}{\rm C}$.  Figure 17:
The friction coefficient as a function of the logarithm of the sliding speed
for the compound C on sandblasted glass. The red squares are on a dry glass
surface cleaned by acetone and isopropanol and then ultrasonic cleaned in
distilled water. The green squares are for a hydrophobic (silanized) glass.
The square symbols are for dry contact and the stars in water. The nominal
contact pressure $p=0.06\ {\rm MPa}$ and the temperature $T=20^{\circ}{\rm
C}$.

8.3 Results obtained using a linear friction slider

We have also performed friction studies using a (low-temperature) linear
friction tester (see Ref. [19]). Fig. 16 shows the friction coefficient as a
function of the logarithm of the sliding speed for the compound B on a dry
smooth glass surface cleaned by acetone and isopropanol and then ultrasonic
cleaned in distilled water (red), and on a hydrophobic (silanized) glass
surface (green). The rubber block surface is roughened by sand paper, which
removes a thin surface layer of rubber, which may have different properties
from the bulk rubber.

Note that in the present case the dry “clean” glass surface exhibit nearly the
same friction as for the silanized surface, as also observed in the Leonardo
da Vinci study (not shown).

Fig. 17 shows the friction coefficient as a function of the logarithm of the
sliding speed for the compound C on sandblasted glass. The red squares are on
a dry glass surface cleaned by acetone and isopropanol and then ultrasonic
cleaned in distilled water. The green squares are for a hydrophobic
(silanized) glass. The square symbols are for dry contact and the stars in
water. The friction coefficients are similar to obtained in Fig. 14 using the
Leonardo da Vinci set up but at the higher sliding speeds the hydrophobic
glass gives slightly smaller friction than the clean glass, both in the dry
state and in water. Also, in the water the friction is smaller than in the dry
state. We believe the difference between the results in water in Fig. 14 and
Fig. 17 is due to differences in the stiffness of the two experimental set-up
and a (related) slight tilting of the rubber blocks which effect the removal
of the water between the two surfaces.

Figure 18:  The friction coefficient at the sliding speed $v=1\ {\rm cm/s}$ as
a function of the number of sliding cycles for compound B (red) and A (blue)
sliding on two different concrete blocks denoted a and b, respectively.
Figure 19:  Picture of concrete block a after run-in of compound B.  Figure
20:  The friction coefficient as a function of the logarithm of the sliding
speed. The solid lines are for the compound B (red line) and A (blue line)
sliding on two different concrete blocks (a and b, respectively) after run-in
on the same concrete blocks (resulting in “contaminated” concrete surfaces).
The red dashed line is for compound B sliding on the concrete block b after it
was contaminated by the compound A. The blue dashed line is for compound A
sliding on the concrete block a after it was contaminated by the compound B.

8.4 Sliding friction on contaminated concrete

It is often stated in F1-racing that transfer of rubber to the racing track
can have a strong influence on the sliding friction or grip. In particular,
when changing to new tires with a different rubber tread compound the friction
can be reduced compared to clean road surface. In an earlier study we observed
a strong drop in the friction when a rubber block was slid on a concrete
surface contaminated by first sliding a block made from another rubber
compound on the concrete surface[19].

We have performed a set of experiments to study the role of rubber
contamination films on rubber friction on a concrete surface. In the
experiments we first run-in the rubber compounds B and A on two different
concrete surfaces a and b. The run-in consisted of 11 forwards and backwards
sliding events (sliding speed $v=1\ {\rm cm/s}$) of compound B on surface a,
and similar for compound A on surface b. Fig. 18 shows the friction
coefficient as a function of the number of sliding cycles for compound B (red)
and A (blue) sliding on the two different concrete surfaces a and b. The two
concrete surfaces are nominally identical so the small difference in the
friction observed may be attributed to the different rubber compounds. Note
that during run-in there is an increase in the friction by $\sim 20\%$ in both
cases. This may be due to removing a thin skin layer on the rubber blocks or
due to the influence on the friction by a thin contamination film deposited on
the concrete surface. Fig. 19 shows a picture of the concrete block a after
run-in of compound B.

Next we measured the friction force for compound B on surface a for sliding
speeds from $1\ {\rm\mu m/s}$ to $1\ {\rm cm/s}$, and the same experiment was
carried out for compound A on the surface b. The results are given by the
solid red and blue lines in Fig. 20. Next we measured the friction for the
same velocity interval for compound B on the concrete surface b contaminated
by compound A (red dashed line in Fig. 20). Finally, we performed a similar
experiment for compound A on the concrete surface a already contaminated by
the compound B (blue dashed line in Fig. 20). As shown in the figure, within
the noise of the measured data, the friction coefficient is nearly the same
for compound B when sliding on surface a contaminated by compound B, as on
surface b contaminated by the compound A (red lines). The same is true for
compound A (blue lines). However, in all cases the compound A gives higher
friction than the compound B, but the difference is rather small at the
highest sliding speed, where the difference is consistent with the friction
observed during run-in.

We have shown that the friction changes very little when sliding compound B on
the concrete surface first contaminated by compound A, and the same was
observed also in the opposite case. This indicate that either the
contamination film is sheared as in Fig. 2(b), in which case the frictional
shear stress may be independent of the rubber compound used, or the chain
interdiffusion mentioned above may occur in a similar way for the compound B
in contact with the transfer film from compound A as with the transfer film
from compound B. Alternatively, during sliding of compound B on the concrete
surface contaminated by the compound A there is a new transfer film of
compound B deposited on the concrete surface which could result in a contact
which is effectively the same in both cases.

9 Discussion

We have found above that for smooth and sandblasted glass surfaces the
friction force for compounds A and B is nearly the same on the “clean” glass
surfaces as on the silanized glass surfaces. For compound C the same is true
on the sandblasted glass surface in the Leonardo da Vinci set up, but for the
smooth glass surface the silanized surface exhibit lower friction at low
sliding speed. Optical pictures show that molecules are transferred from the
rubber to the glass surface, and FTIR spectra shows that the contamination
film is a wax. If we assume that negligible slip occur at the interface
between the contamination film and the clean or silanized glass surface, then
the friction force will be the same on both glass surfaces. Only if we assume
this to be the case is it possible to explain the great similarity in the
observed friction coefficient on the two different surfaces for compounds A
and B. Thus, for these compounds in both cases we propose that most of the
slip may occur at the interface between the rubber and the contamination film
[see Fig. 2(a)], or result from shearing the lubrication film as in Fig. 2(b).
On the silanized surface the contamination film binds weaker than on the clean
surface but, nevertheless, it appear that in many cases there is negligible
slip between the contamination film and the silanized glass surface. This
differ from the result of a recent study where slip was observed between a
rubber stopper and a glass barrel with baked-on silicone oil[27].

In wet conditions the silanazed glass surface result in a higher maximum
friction coefficient than the hydrophilic glass surface. We interpret this as
resulting from forced wetting. In forced wetting the water is dragged into the
contact by the sliding motion, resulting in viscous hydroplaning and a
decreasing friction force with increasing sliding speed. Forced wetting is due
to a competition between a liquid invasion induced by shear and spontaneous
dewetting of the liquid driven by the (negative) spreading pressure.

Figure 21:  There is in general no simple relation between adhesion (pull-off
force) and sliding friction. (a) The pull-off force depends on breaking the
bonds in the normal direction at the edges of the contact region (opening
crack propagation). (b) The friction force depends on energy dissipation at
the opening and closing crack tips, and in addition on shearing the area of
real contact, i.e., on processes occurring everywhere within the contact
region. In many cases this latter contribution will give the most important
contribution to the friction force[30].

For the clean glass surface the drop in the work of adhesion between dry
contact and contact is in water (see Fig. 7) is much higher than the change in
the the friction force between dry and wet condition. Hence, there is no
simple relation between adhesion (pull-off force) and sliding friction. This
is easy to understand (see Fig. 21) because the pull-off force depends on
breaking the bonds in the normal direction at the edges of the contact region,
while the frictional shear stress depends mainly on shearing the contact area,
i.e., on processes occurring everywhere within the contact region. The latter
may not even “know” that there is fluid (water) outside the asperity contact
regions, which may strongly reduce the bond-breaking at the edges of the
contact regions.

When the substrate has surface roughness (as in Fig. 21) there will also be a
contribution to the friction from the opening crack tip on the exit side of
the sliding rubber-substrate contact regions[28], but for small contacts the
latter contribution will be reduced due to finite size effects[29], and
experiments[30] indicate that, in most practical applications, the main
contribution to the friction arises from the inner region of the asperity
contact regions.

10 Summary and conclusion

In this article we have presented results for rubber adhesion and friction
against glass in dry and wet conditions. The surface energy and topography of
the glass was changed by application of hydrophobic coating (silanization) and
sandblasting.

We found in many cases that changing the surface energy of the glass by
silanizing does not affect the magnitude of rubber friction on smooth and
sandblasted glass. We believe that this is due to sliding on, or shearing of,
a contamination film derived from the rubber, with negligible slip at the
glass-contamination film interface, even for the silanized glass surfaces.
This indicate that for dry surfaces the surface energy of the substrate may be
irrelevant for rubber friction in many practical cases. Infrared light
absorption measurements shows that the contamination film is a wax, which was
added to the rubber compounds to protect against ozone.

The magnitude of rubber friction for smooth glass depends on whether the
rubber is smooth or roughened prior to friction measurements. Smooth rubber
showed higher friction as compared to the roughened rubber. We attribute the
decrease in the friction for roughened rubber to the reduced area of contact.

When rubber slides on a clean smooth glass in the wet state we observe runaway
instabilities at low sliding speed. We attribute this to forced wetting, where
water is dragged into the sliding interface during sliding motion.

When the rubber or countersurface are rough the rubber friction is lower in
water than that in the dry state. We attribute this to a trapped islands of
pressurized water, which carry part of the external load and hence reduces the
area of real contact. The trapped islands of water form at short enough length
scale (observed at high enough magnification), where the rubber-substrate
contact area percolate.

We have shown that the transfer of rubber to a concrete track has only a small
influence the friction for another rubber compound and vice verse. However,
more studies of this, using rubber compounds with bigger difference in the
chemical composition, are necessary in order to determine how general this
conclusion is.

Our study demonstrate that there is no simple relation between adhesion and
friction. Thus, adhesion is due to (vertical) detachment processes at the edge
of the contact regions (opening crack propagation), while friction in many
cases is determined mainly by (tangential) stick-slip instabilities within the
whole sliding contact.

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