# Structural Lubricity and Molecular Contamination: Rejuvenation, Aging, and
Friction Switches

Wai H. Oo  Department of Mechanical Engineering, University of California
Merced, Merced, California 95343, USA  Hongyu Gao  Department of Materials
Science and Engineering, Saarland University, Saarbrücken, Saarland 66123,
Germany<EMAIL_ADDRESS>Martin H. Müser  Department of Materials
Science and Engineering, Saarland University, Saarbrücken, Saarland 66123,
Germany  Mehmet Z. Baykara  Department of Mechanical Engineering, University
of California Merced, Merced, California 95343, USA
<EMAIL_ADDRESS>
###### Abstract

Using atomic force microscopy experiments and molecular dynamics simulations
of gold nanoislands on graphite, we investigate why ultra-small friction
commonly associated with structural lubricity can be observed even under
ambient conditions. Measurements conducted within a few days after sample
synthesis reveal previously undiscovered phenomena in structurally lubric
systems: rejuvenation, a drop in kinetic friction of an order of magnitude
shortly after the onset of sliding; aging, a significant increase in kinetic
friction forces after a rest period of 30 minutes or more; switches,
spontaneous jumps between distinct friction branches. These three effects are
drastically suppressed a few weeks later. Imaging of a contamination layer and
simulations provide a consistent picture of how single- and double-layer
contamination underneath the gold nanoislands as well as contamination
surrounding the nanoislands affect structural lubricity but not lead to its
breakdown.

###### keywords:

atomic force microscopy, friction, molecular contaminants, molecular dynamics,
nanotribology, superlubricity

These authors contributed equally to this work These authors contributed
equally to this work

Research on structural lubricity, an ultra-low friction state arising due to
the systematic annihilation of lateral forces in atomically flat interfaces
formed by two incommensurate surfaces 1, 2, 3, is accelerating in recent years
4, 5. Although the concept came about as a theoretical exercise 1, 2, atomic-
force-microscopy (AFM) experiments on the friction between a graphene flake
and graphite under dry nitrogen atmosphere confirmed the geometrical
explanation of miniscule friction due to rotation-induced lattice mismatch 6.
More recently, other observations of ultra-low friction attributed to
structural lubricity between carbon-based materials have been reported 7, 8,
complemented by reports of structural lubricity at hetero-interfaces formed by
two-dimensional materials 9, 10. Likewise, theoretical predictions of surface
contamination leading to a breakdown of structural lubricity 11 were supported
through AFM experiments performed on antimony nanoislandsAAAFor simplicity,
‘island’ will be used in place of ‘nanoisland’ hereafter. . on gold,
contrasting UHV with ambient conditions 12. Remarkably, similar experiments
performed on noble metal islands on graphite demonstrated that structural
lubricity is not restricted to the pristine UHV environment. Comparable values
of friction force and the sub-linear scaling of friction force as a function
of contact area were also observed under uncontrolled ambient conditions 13,
14. This leaves open the questions of when contaminants destroy structural
lubricity and how they affect friction otherwise, which is relevant for the
potential exploitation of superlubricity outside of UHV chambers.

Contaminating interfacial particles were expected to destroy superlubricity
because their mobility allows them to adopt positions, which are energy minima
of both surfaces simultaneously, whereby the surfaces interlock 11. One reason
why this argument may not always hold is that extremely smooth surfaces like
that of graphite do not provide energy barriers large enough to substantially
counteract sliding of an adsorbed or rather “between-sorbed” layer. Another
one is that organic molecules adsorbed on graphite form highly ordered
domains. 15 They might act similarly to two-dimensional solids, whereby
individual molecules have an additional constraint in the presence of another
surface, which reestablishes, to a significant degree, the systematic
annihilation of lateral forces at pristine interfaces formed by smooth,
incommensurate surfaces. Which effect dominates might depend on the structure
and chemical nature of the counterface to graphite.

To illuminate the role of contamination in superlubricity, we present results
of AFM-based sliding (i.e., nanomanipulation) experiments on gold islands. In
contrast to other experiments on this system, we chose the tip-on-top16 rather
than the previously used and easier-to-implement push-from-the-side approach,
13, 14 because it allows islands to be dragged back and forth under a
controlled load in a controlled direction, with controlled speeds. We also
report results of molecular dynamics (MD) simulations mimicking the
experiments, albeit using smaller islands and nine-order-of-magnitude larger
velocities. Thus, direct quantitative comparisons are not possible and would
remain questionable even when using scaling arguments. Nonetheless, relative
trends of how contamination affects friction can certainly be contrasted,
whereby MD can offer possible explanations for experimental observations.

Before presenting the results of the nanomanipulation experiments regarding
friction forces, we first briefly describe the associated data acquisition
procedure. First, individual line scans of lateral force, such as those shown
in Figure 1d are recorded. In accordance with established procedures, 17 half
of the difference between trace (i.e., forward) and retrace (i.e., backward)
scans are plotted for all lines (n = 1, 2, …, 256), yielding maps of friction
like those shown in Figure 1c,f. While some friction maps are homogeneous
(Figure 1c), some reveal two clearly distinct domains of high and low
friction, as indicated by bright and light colors, respectively (Figure 1f).
Data points in the remaining panels of Figure 1 represent the average over
such friction domains. Since no scan produced more than two domains, one scan
can result in one (Figure 1a,b) or two (Figure 1e) friction values. Arrows
next to friction maps (Figure 1c,f) indicate the slow scan direction, while
arrows in the plot shown in Figure 1e indicate the jumps from low to high
friction domains.

Figure 1: (a) Friction force as a function of scan number extracted from the
nanomanipulation of a freshly deposited island. (b) Same as (a) but repeated
on the same island and area after a 30 minute waiting time. (c) Friction-force
map associated with scan 5 in (b). (d) Lateral forces extracted along single
scan lines in the forwards and backwards directions, along the two traces
shown with black lines in (f), located in high and low friction domains,
respectively. (e) Friction force as a function of scan number extracted from
the nanomanipulation of another gold island. During the scan, friction jumped
from low to high as shown in the friction-force map of panel (f).

Gold islands, when measured within a few days after synthesis, always produce
relatively high friction during the first (areal) scan. However, friction
drops substantially during the second scan, i.e., by one order of magnitude
and can remain low in all subsequent scans, as is depicted in Figure 1a. When
repeating the experiments on the same island and same scan area, after waiting
times ranging from 30 minutes to 18 hours, similar results were obtained
(Figure 1b). Differences between the average friction of the very initial scan
and the first scan after $\geq 30$ minute waiting times were on the order of
15%. The average friction of subsequent scans were again reduced by about an
order of magnitude with respect to the first one as in the initial set of
experiments. Interestingly, stiction peaks were observed neither at the onset
of a first scan (initial and after waiting) nor after the periodic pauses (on
the order of 10 ms) at the end of scan lines, where the sliding direction
changes.

An increase of friction force with waiting time has been known since Coulomb’s
classical friction experiments 18 and is commonly referred to as aging 19,
while the reduction of friction during sliding is called rejuvenation 20 and
captured in rate-and-state models of friction. 21, 22 However, typical results
reveal changes on the order of 10% rather than by a factor of ten. Prominent
examples are rough glassy polymer sliding past smooth silanized glass with
nominal contact areas of order millimeter 20 as well as material systems meant
to mimic the friction of tectonic plates 21, 22. Given the dramatic difference
in the observed effect, common explanations of aging and rejuvenation 23 do
not seem plausible for our experiments. This suggests a rather large gap of
understanding of the physical mechanisms underlying our observations at the
small nanoscale.

In addition to rejuvenation and aging, we encountered “friction switches”,
i.e., spontaneous jumps between low and high friction forces within a single
scan, (see Figure 1e,f). A combination of all three effects is frequently
observed within the same experiment, even with the same island on the same
area (see Figure S5). Since graphite has a homogeneous surface away from steps
and operating conditions are mild, surface contamination appears to be the
most likely candidate to cause aging, rejuvenation, and friction switches in
our system, which is why it is investigated next.

To gain information on contamination of our samples, we used AFM-based
topographical and phase imaging. As opposed to topographical imaging which
solely provides height information, phase imaging allows materials with
different mechanical stiffness on the sample surface to be distinguished with
high spatial resolution. 24. Figure 2 shows a large-scale phase image taken
via tapping-mode AFM several months after synthesis. It reveals dark regions
indicating soft contaminants and light regions for graphite and gold islands.
Surface contamination becomes apparent as early as one week post-synthesis,
despite the samples having been stored in a vacuum desiccator with the
intention to deter environmental adsorbates from accumulating on the surface.
The measured height associated with contamination, as inferred from
topographical AFM imaging (see Figure S6) ranges from a few Å up to 10 Å,
which corresponds to 1–2 adsorption layers.

Manipulation of an island on a heavily contaminated sample causes a localized
change in the substance’s coverage (Figure S6a,b). However, the contamination
layer can also change over time in both coverage and morphology without
nanomanipulation (Figure S6d). Upon heating the sample to 100°C, phase-images
have no more contrast (see Figure S7) implying that the contaminant is
desorbed or has become very homogeneous, e.g., in the form of an alkane layer
with alkanes having more than $\approx 20$ carbon atoms 25, 26. According to
these characteristics, the initial contaminant layer is most plausibly a
mixture of water and hydrocarbons. As revealed by a recent study, this
combination is frequently found under ambient conditions on van der Waals
materials, such as graphite and hBN 27. More specifically, it is proposed that
the contaminant layer comprises predominantly mid-length linear alkanes
containing 20-26 carbon atoms.

Figure 2: AFM phase image of the sample system, taken 4 months after
synthesis, showing the accumulation of contaminant layers.

Although thicker lubrication layers imply a reduced resistance to sliding in
continuum mechanics and despite much knowledge about the slip of alkanes past
graphitic 28 and gold surfaces alike 29 even under high-confinement conditions
30, friction in our system appears impossible to predict from the existing
literature. This is because friction at the nanoscale often is a true system
property 23, which cannot be deduced from those of the lubricant and its two
boundaries with the confining walls. Details like the relative orientation of
the confining walls can matter 11 or confinement-induced structural
transformation of the lubricant can occur, as might be the case for alkanes
between gold 29. This motivated us to elucidate the dependence of shear stress
on coverage and other parameters for this particular system using molecular
dynamics.

The simulations reveal a highly non-monotonic dependence of friction on
coverage between the simulated island and the graphite substrate, see Figure
3. It is almost immeasurably small at zero coverage due to the absence of any
significant instabilities 31, as indicated by the blue, dashed line. The
effective shear stress, i.e., the ratio of friction force and island area, is
largest at sub-mono-layer coverages ($\Gamma$) when the gold island rests
directly on graphite but has to displace polymers in direct contact with
graphite out of the way while advancing. Thus, in this case, friction stems
predominantly from the out-of-contact rather than the contact region itself.
Friction drops discontinuously upon increasing $\Gamma$, once the island no
longer touches graphite directly, see Figure 3b. It also reveals the alkanes
to orient along graphite’s symmetry axis, thereby forming locally commensurate
domains, which explains why slip at sub-coverage occurs between gold and
adsorbate. As long as the island keeps sliding on a monolayer, friction
increases with $\Gamma$ but decreases again discontinuously as soon as a
second layer appears between gold and graphite.

Figure 3: (a) Effective shear stress ($\tau_{\textrm{eff}}$) as a function of
the nominal coverage ($\Gamma$). Black, dashed lines separate the cases where
gold slides directly on graphite at small $\Gamma$, on top of a monolayer, and
on top of a double-layer of $n$-hexadecane (HEX) molecules. The blue, dashed
line represents the mean shear stress for clean gold-graphite contacts. Solid
and hollow symbols represent results from $v=20$ and 2 m/s sliding velocity,
respectively. (b) Snapshots at different ${\Gamma}$ at $v=2$ m/s.

At $\Gamma\approx 0.62$ and $\Gamma\approx 1$, simulations were run with the
velocity reduced by a factor of ten. The resulting friction drop was by a
factor of five and two, respectively. These changes are too significant for
the friction to be labeled as Coulombic, i.e., barely dependent on velocity,
although the velocities exceed the experimental ones by nine orders of
magnitude. It is worth noting that the trailing edge of a $\Gamma=0.62$
contact drags along some polymers at $v=2$ m/s but not at $v=20$ m/s. Without
this effect, the friction-velocity relation would have moved closer to a
linear, i.e., Stokesian dependence.

Since the importance of the area below the island relative to that of the
contact line or circumference is larger in the experiments than in the
simulations (roughly by a factor of ten, because the experimental radii exceed
the simulated ones by that factor), we also simulated selected area-filling
contacts between gold and graphite (Figure 4). For this purpose, we explored
two coverages, $\Gamma=1$ and $\Gamma=6$, as well as two relative orientations
between the graphite and the Au $(111)$ surfaces so that the Au surface is
ideally aligned with graphite, i.e., $[1\bar{1}0]$ is aligned with the
graphite armchair direction, Gr${}_{\textrm{A}}$, albeit with a lattice
mismatch of roughly 17% and one time misoriented by 90∘ so that $[11\bar{2}]$
is parallel to Gr${}_{\textrm{A}}$. For both orientations, the true areal
shear stress at $\Gamma=1$ is rather small compared to the effective shear
stress of $\lesssim 6$ MPa for the island, i.e., 0.26 MPa for the
$[1\bar{1}0]$ orientation and 1.2 MPa for $[11\bar{2}]$. At $\Gamma=6$, shear
stress changes to $\tau\approx 0.87$ MPa. Results are shown in Figure 4a.

Figure 4: (a) Shear stress ($\tau$) between two area-filling graphite and gold
solids separated by either a single- (1 ML) or a six-monolayer (6-ML) HEX
film. The top and bottom ticks indicate the slab material and lattice
orientation with the armchair direction of graphite (Gr${}_{\textrm{A}}$)
being aligned with the sliding velocity $\mathbf{v}=10~{}\mathbf{e}_{x}$ m/s.
In-plane projections of (b) Au$[1\overline{1}0]$ (red squares) and (c)
Au$[11\overline{2}]$ (blue squares) on GrA (black circles). Solid and hollow
squares indicate Au atom positions in two adjacent (111) layers, respectively.

These results are interesting for a variety of reasons. First, they show that
relative orientation can matter even between (quasi-) incommensurate solids as
$\tau$ differs by a factor of almost five between the two configurations at
$\Gamma=1$. Thus, for any system, in which $\Gamma$ is small and areal
friction dominates, large scatter in the data is unavoidable. Second, the
concept of continuum mechanics is far from being applicable in our system, as
a six-fold thicker lubricant can yield a three-fold increase in friction, at
least for the misaligned surfaces, while continuum-based concepts, in
particular those based on Reynolds’ thin-film equation, would expect it to
drop with increasing $\Gamma$. Third and perhaps most importantly for our
present purposes, friction for the simulated islands is indeed dominated by
processes outside the contact, since their effective shear stress was found to
be 5.8 MPa at 20 m/s and 3.0 MPa at 2 m/s each time at $\Gamma=1$. Thus, for
islands with ten times the radius, areal friction can dominate but the
friction stemming from non-contact is not yet necessarily negligible. In fact,
when the mean areal stress decreases with contact area, as is the case for
structurally lubric contacts, the non-contact friction may well be dominant,
in particular at the small (or zero) normal loads studied in this work. Having
provided expectations from atomistic simulations, we return to the
presentation and interpretation of experimental results.

Previous studies show that a freshly prepared graphite surface becomes
completely coated with molecular contaminants in just a few minutes when
exposed to air 32. Thus, considering that our experiments are conducted under
uncontrolled, ambient conditions, some surface contamination will be present,
even if it does not reveal itself in AFM images. This is why we classify a
sample as lightly contaminated even if the contamination is not revealed by
AFM. However, when contamination is clearly visible in phase and topography
images, which typically happens $>$1 week after synthesis, we deem the sample
to be heavily contaminated. To explore the impact of the degree of
contamination on aging, rejuvenation, and friction switches, we repeated our
nanomanipulation experiments for heavily contaminated islands. Table 1 reports
the results. The numbers expressed under “frac.” (short for fraction) contain
the number of experiments in the denominator. The fractions are converted to
percentages for clearer comprehension. Remarkably, we observe that increased
levels of contamination significantly diminish the observation frequency of
all three effects (rejuvenation, aging, and friction switches), by 75% and
more.

2.5 Degree of | Rejuvenation | Aging | Switches
---|---|---|---
Contamination |  frac. |  % |  frac. |  % |  frac. |  %
light |  26/26 |  100 |  8/28 |  100 |  15/26 |  58
heavy |  20/82 |  124 |  5/22 |  123 |  16/82 |  57
2.5 |  |  |  |  |  |
Table 1: Comparative analysis of observation frequencies of the three effects
for lightly contaminated and heavily contaminated islands

While all islands in lightly contaminated samples exhibit the rejuvenation
effect and more than half the switch effect (with friction between the two
branches differing by factors from three to ten), the majority of heavily
contaminated islands show consistent friction levels across all manipulations.
The associated shear stresses align more closely with the low-friction branch
of the lightly contaminated islands, with the exception of a few data points,
as can be seen in Figure 5, which shows shear stresses as a function of
contact size $A$. Please note that Figure 5 specifically contains data for
lightly contaminated islands that exhibit the switch effect (15), and for
heavily contaminated islands that do not exhibit any of the three effects
(55). All three cases, i.e., heavy contamination as well as high and low
friction branches at light contamination, reveal the trend that larger islands
have smaller shear stresses. This observation can be a sign of structural
lubricity and/or a friction mechanism that is dominated by the contact line.
Surprisingly, the trend is most pronounced in the case of heavy contamination,
where $\tau$ evolves almost linearly with $1/A$, at least for $A\lesssim
15,000$ nm2. Such strong scaling of the shear stress does not appear plausible
outside the realm of structural lubricity.

Figure 5: Shear stress as a function of contact area recorded for lightly
contaminated and heavily contaminated islands. Black triangles represent shear
stresses associated with lightly contaminated islands that exhibit the switch
effect, separated into two branches (upward triangles for the high friction
branch, downward triangles for the low). Red circles represent shear stresses
associated with heavily contaminated islands that do not exhibit any of the
three effects.

The low friction branch shows the weakest scaling, i.e., $\tau\propto
A^{-0.4}$. Given the scatter in the data, this result is consistent with
friction that is dominated by contact line effects, i.e., the $\tau(A)$
dependence is close to a $\tau\propto 1/\sqrt{A}$ power law. The shear stress
of $\mathcal{O}(20~{}\text{kPa})$ matches previous simulation results by two
of us on gold islands sliding past perfectly clean graphite substrates 31,
after linear extrapolation to $v=0$. Thus, there is the possibility that the
the low-friction branch corresponds to the sliding of gold islands on
perfectly clean graphite. However, for this to be true, the velocity
dependence would have to be rather weak. This could be the case, because
changes in the Moiré-type patterns produced by normal displacements indicated
the friction to be driven by instabilities, which generally induces rather
weak, i.e., logarithmic-type velocity dependence of friction. 33 These
corrections cross over to a steep linear dependence at a very small velocity
33. Thus, we would expect an extrapolation of the sliding of gold cluster on a
perfectly clean substrate to produce even smaller shear stresses than those
measured experimentally. We conclude that the experimental surfaces should
still be covered by a thin, well-ordered layer of adsorbates. This additional
mono-layer (or potentially, double-layer) increases the friction compared to
clean graphite-gold contacts, albeit not to the extent that superlubricity is
destroyed.

The high-friction branch shows scaling of roughly $\tau\propto{A}^{-0.6}$,
which is again close to $\tau\propto 1/\sqrt{A}$. One possible explanation
would be that there are partial contamination layers at the early stages after
sample preparation. Moving and thus removing these partial layers costs much
energy, as has become evident from the MD simulations. For a thick
contamination layer, i.e., thicker than the correlation length of the density-
density autocorrelation function, discrete steps from one-to-two or two-to-
three monolayers no longer occur, and a sliding tip no longer removes
fractional monolayers from the surface. Another possibility for the
disappearance of the effect of fractional layers after very long waiting times
could be that fractional layers are far from thermodynamic equilibrium, which
is reached after long waiting times.

Besides molecular contamination, various other factors could contribute to the
noted friction duality within the structural lubricity regime, including the
presence of dislocations 34 and structural defects 35 in the islands. However,
shear stresses in the experiments are rather below than above those in the
simulations so that we do not see the need to introduce additional effects
into the simulations that would further increase that gap. Moreover, during
the initial stages of our simulations on this topic, i.e., before introducing
contamination, we explored gold clusters with point and line defects. Yet,
friction remained much below that observed with contamination. Potentially
more importantly, the von Mises yield strength of gold at the macroscopic
scale is on the order of 100 MPa, while expertimental shear stresses are
clearly less than 0.1 MPa at the nanoscale, at which point introducing
dislocations becomes difficult or rather impossible. Lastly, we remind the
reader of the mild, zero/negligible load condition used experimentally, which
excludes the possibility of structural defects in graphite becoming relevant.

In summary, we find that gold islands on graphite under ambient conditions and
driven under negligibly small normal load exhibit substantial increases in
friction after waiting times ranging from 30 minutes to a day, aging, dramatic
friction reduction after the first areal scan, rejuvenation, but also
spontaneous jumps between low and high friction domains during a given scan,
friction switches. The magnitude of the aging and rejuvenation was typically
on the order of three to ten, which substantially exceeds the usual 10%-30%
relative changes reported for these phenomena in both macroscopic and single-
asperity contacts. Moreover, friction changes are reversible (via switches)
and thus differ from situations like the onset of catastrophic wear or
permanent material damage. They also differ from previously reported
frictional duality 12, which was related to the difference between perfectly
clean and contaminated surfaces, rather than differing friction levels for
different degrees of contamination. All three effects are diminished and shear
stresses are small after waiting times exceeding one week, i.e., when surfaces
are heavily contaminated with air-borne molecules.

Since (1) both graphite and gold are chemically inert, (2) the gold islands
are small and driven at negligibly-small normal loads, and (3) resulting shear
stresses are well below 0.1 MPa, we can rule out dislocations, chemical
defects, bond formation or other mechanisms requiring either large stresses or
large energy densities. As such, we see contamination as the main suspect that
causes the observed phenomena. However, it is not straightforward to
understand why initial contamination after minutes to hours exposure of
graphite to ambient conditions causes high friction, while very long exposure
causes small friction, in particular in light of the rejuvenation effect,
which we believe to be caused by the removal of contaminants.

Thus, to elucidate the role of contaminants in our experiments, we simulated
gold islands on graphite with different levels of contamination. The MD
simulations reveal a highly non-monotonic dependence of the shear stress on
coverage density. Gliding over sparse mono- and double-layers show low shear
stresses, while dense ones lead to intermediate stresses. The largest shear
stresses are observed when the island is in direct contact with the substrate
but “plows” through and thus potentially removes a sub-monolayer of (highly-
ordered) adsorbed molecules. These observations can be in line with the
experimental results, if we assume that friction of a slightly contaminated
scan is high during the first areal scan, if this first scan removes partial
layers, and low during any subsequent scan as long as no new partial layer has
condensed onto the surface. However, this interpretation is admittedly
speculative in nature, given the large gap in velocity and (linear) size
between simulations and experiments, which are nine orders of magnitude and a
factor of 10 to 30, respectively. Extrapolating results are difficult for a
variety of reasons. Most importantly, friction-velocity scaling relations
generally have a limited range of validity. Typically, the response becomes
more Stokes-like as velocity decreases, in which case shear-thinning effects
are reduced at small velocity. However, even simple polymeric systems can show
the opposite trend 36. Moreover, there will not be a single dissipation
channel. The relative contribution from shear stresses caused by the motion of
the contact line or by dynamics caused outside the contact will be larger for
the small in-silico islands than the large, real islands.

Despite the difficulties of directly relating simulation to experimental
results, the simulations clearly reveal a dependence of shear stresses on the
relative orientation between the gold island and graphite at one- to two-
monolayer coverage. This does not only explain the large experimental scatter
but also reveals that superlubricity is still in effect despite the presence
of contamination and even for islands with radii as small as 3 nm. The
conclusion from the simulations that gold islands can slide in superlubric
fashion on graphite, even under lightly and heavily contaminated conditions
caused by adsorbed contaminant molecules, finally provides an answer as to why
ultra-low friction was observed experimentally for this material system under
ambient conditions 13. This is critical as the experimental observation of
structural lubricity under ambient conditions came as a surprise to the
scientific community, where, until that point, it was assumed that molecular
cleanliness was a prerequisite for the phenomenon. Our conclusions can also be
potentially extended to explain the ultra-low friction exhibited by
turbostratic graphite under ambient conditions 37, 38, due to the finding of
ultra-low shear stresses even under the presence of adsorbed alkanes and for
small contact areas a few nanometers in lateral span.

This work was supported by the National Science Foundation (NSF) via award
number 2131976 and the German Research Foundation (DFG) under grant number GA
3059/2-1. W.H.O. acknowledges support from the NSF in the form of a Graduate
Research Fellowship (GRF). The samples studied here were synthesized at the
Molecular Foundry, Lawrence Berkeley National Laboratory. Work at the
Molecular Foundry was supported by the Office of Science, Office of Basic
Energy Sciences, of the U.S. Department of Energy under Contract No. DE-
AC02-05CH11231.

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