Environ. Sci. Technol. 2008, 42, 2931–2936
Efficient Adsorption of Super
Greenhouse Gas
(Tetrafluoromethane) in Carbon
Nanotubes
P I O T R K O W A L C Z Y K * ,† A N D
ROBERT HOLYST‡
Applied Physics, RMIT University, GPO Box 2476V,
Victoria 3001, Australia, and Department III, Institute of
Physical Chemistry, Polish Academy of Sciences, Kasprzaka
Street 44/52, 01-224 Warsaw
Received June 2, 2007. Revised manuscript received
January 21, 2008. Accepted January 28, 2008.
Light membranes composed of single-walled carbon nanotubes
(SWNTs) can serve as efficient nanoscale vessels for
encapsulation of tetrafluoromethane at 300 K and operating
external pressure of 1 bar. We use grand canonical Monte Carlo
simulation for modeling of CF4 encapsulation at 300 K and
pressures up to 2 bar. We find that the amount of adsorbed
CF4 strongly depends on the pore size in nanotubes; at 1 bar the
most efficient nanotubes for volumetric storage have size R
) 0.68 nm. This size corresponds to the (10,10) armchair nanotubes
produced nowadays in large quantities. For mass storage
(i.e., weight %) the most efficient nanotubes have size R )
1.02 nm corresponding to (15,15) armchair nanotubes. They are
better adsorbents than currently used activated carbons and
zeolites, reaching ≈2.4 mol kg-1 of CF4, whereas, the best activated
carbon Carbosieve G molecular sieve can adsorb 1.7 mol
kg-1 of CF4 at 300 K and 1 bar. We demonstrate that the high
enthalpy of adsorption cannot be used as an only measure
of storage efficiency. The optimal balance between the binding
energy (i.e., enthalpy of adsorption) and space available for
the accommodation of molecules (i.e., presence of inaccessible
pore volume) is a key for encapsulation of van der Walls
molecules. Our systematic computational study gives the clear
direction in the timely problem of control emission of CF4 and
other perfluorocarbons into atmosphere.
Introduction
The potential for global warming has spurred the development of various strategies to decrease the concentration of
greenhouse gases in the atmosphere (1–5). Among these gases
there are perfluorocarbons (PFCs), which are extensively used
as etching/cleaning gases in microelectronic and semiconductor manufacturing processes as well as in the aluminum
production (6–8). Tetrafluoromethane (CF4), a compound
belonging to PFC, is an extremely stable molecule whose
lifetime in the atmosphere is 50 000 years (9). Moreover CF4
is much more efficient absorber of infrared radiation than
CO2; its global warming potential is 6500 per 100 years, while
for CO2 it is 1 per 100 years (9). Nowadays, the concentration
* Corresponding author phone: +61 (03) 9925271; fax: +61 (03)
99255290; e-mail: [email protected].
†
RMIT University.
‡
Polish Academy of Sciences.
10.1021/es071306+ CCC: $40.75
Published on Web 03/07/2008
 2008 American Chemical Society
of CF4 in the troposphere is several orders of magnitude lower
than that of CO2; however, CF4 emission grows in time (7–9).
Promising and cost efficient methods for elimination of CF4
emission to the atmosphere are the encapsulation/recycle
processes. One of them is the pressure swing adsorption
method operating at ambient conditions (10, 11). The
principle of this approach is based on the physical adsorption
due to the nonspecific van der Walls interactions between
adsorbate and adsorbent. Due to the low enthalpy of
adsorption ≈5–40 kJ mol-1 the adsorption equilibrium is
reversible and rapidly attained (12). Among currently used
adsorbents, activated carbons and zeolites are the most
widespread and cost efficient (13). However, these two classes
of materials have important drawbacks. Due to a disordered
structure, activated carbons are inevitably characterized by
broad pore size distribution. (i.e., heterogeneity of internal
porous structure), and consequently, the structural and
energetic heterogeneity of these materials reduces the
efficiency of CF4 adsorption in carbon nanospaces (14, 15).
In contrast, zeolites are crystalline solids (16). Their pore
sizes are fixed by the crystallographic group. However, they
are usually small, which also reduces their efficiency as
adsorbent of large molecules such as tetrafluorocarbon. Here
we demonstrate that carbon nanotubes (currently produced
in large quantities) are optimal for CF4 adsorption and do
not suffer from the aforementioned drawbacks.
In a recent paper (9), a similar study has been performed
for the adsorption of CF4 in graphite slits. It has already been
observed that for selected slit sizes, the adsorption of the gas
reaches a maximum. There are, however, several practical
drawbacks of using slit geometry of carbon material for the
adsorption. First of all there is a wide distribution of pore
sizes in the slit geometry as already noted in refs 13–15.
Carbon nanotubes do not suffer from such drawbacks and
can have a very narrow distribution of pore sizes, which is
particularly important in view of the results predicting a
maximum adsorption at some pore sizes. In carbon nanotubes we can highly compress the gas reaching the density
of a solid phase (17, 18). Furthermore the interaction potential
is enhanced in curved geometries in comparison to slit
geometry and, therefore, leads to higher adsorption. We also
point out that optimal structure of carbon nanotubes for
volumetric storage capacity is different from the structure
for the optimal mass storage capacity, thus it is important
whether we consider optimal adsorbent for mass or for
volumetric storage. Finally we show that in the search for
optimal adsorbents we have to take into account two
elements: heat of adsorption and pore sizes, since it is not
true as is commonly believed that high adsorption enthalpy
is the sole condition for high adsorption capacity (13, 19).
Materials and Methods
Fluid-Fluid Interaction Potential. We have modeled the
CF4-CF4 interactions by the effective truncated central
Lennard-Jones potential (i.e., due to high thermal motion of
CF4 molecules we assumed that the details of atomic structure
can be approximated by effective spherical potential) (9),
[( ) ( ) ]
Vff(r) ) 4ff
σff
r
12
-
σff
r
6
Θ(rcut - r)
(1)
where r is the distance between two interacting fluid
molecules, σff denotes Lennard-Jones collision diameter, ff
is the Lennard-Jones well depth, rcut ) 5σff is the cutoff
distance, and Θ stands for the Heaviside function. The
Lennard-Jones parameters for CF4 interactions, σff ) 4.7 Å
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FIGURE 1. Idealized model of SWNTs bundle composed of infinitely long cylindrical nanotubes arranged into hexagonal lattice. The
incorrect construction of the simulation model of hexagonally assembled SWNTs is displayed on panels A-D. Panel E shows
correct construction of an idealized hexagonal SWNTs assembly used in the current theoretical study.
and ff/kb ) 152.27 K (with kb Boltzmann’s constant), were
taken from the previous studies (9). Müller showed that this
potential with parameters given above correctly described
the adsorption properties of tetrafluoromethane near ambient temperatures (9). We want to point out that at the high
temperature considered here tetrafluoromethane possess
high kinetic energy, i.e. the frequency of CF4 rotations are
very high. Moreover, under this thermodynamics conditions
the adsorbed CF4 molecules do not form dense, twodimensional layers. As a result, we are not expecting the
breaking of the rotational symmetry of adsorbed CF4
molecules due to the confinement (i.e., adsorbed molecules
rotate freely). That is why interacted CF4 molecules can be
treated as effective Lennard-Jones spheres. Obviously, for
temperatures below critical point of tetrafluoromethane we
suggest modeling of the fluid-fluid interactions by the fivecenter Lennard-Jones potential.
Solid-Fluid Interaction Potential. Single-walled carbon
nanotubes (SWNTs) are naturally arrange in the bundle
assembly that are stabilized by the van der Walls forces
between the individual single carbon nanotubes. We modeled
this ordered carbon nanomaterial by infinitely long idealized
hexagonal bundle of SWNTs because length to radius ratio
of nanotubes is ≈1000 (20), as displayed in Figure 1. As shown
by Kowalczyk et al. (20, 21) the total solid-fluid potential
between the spherical Lennard-Jones molecule and infinitely
long structureless cylindrical worm-like/straight tube is given
by,
zw+ML
Vsf(R) ) 4sfFs
∫
R
zw-ML
1 + (b2πL ) cos (z 2πL )[I σ
2
2
p
12
1 sf 6
I2σsf
]dzp (2)
Where
I1 )
π
×
16(a + b)5√a2 - b2
45
945 105 a + b
+
+
120
24 a - b
12
105 a + b 4 945
... +
+
24 a - b
120
[
]
( aa -+ bb ) + 1245 ( aa -+ bb ) + ... (3)
( ) ( aa -+ bb )
π
I )
[ 23 + ( aa -+ bb ) + 23 ( aa -+ bb ) ] (4)
2(a + b) √a - b
2
(
)
2
3
5
2
2
2
2
In the above equations, the surface density of carbon atoms
smeared on the wall of carbon tube is Fs ) 38.2 nm-2 (i.e.,
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ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 42, NO. 8, 2008
FIGURE 2. The excess amount of adsorbed CF4 is shown as a
function of the internal pore radii of cylindrical tube at 300 K.
The open circles are the simulation results, and the solid line
is a guide for the eyes. The maximum for 0.1 bar corresponds to
the internal pore radius characteristic for the armchair (8,8)
nanotubes, and at 2 bar corresponds to the armchair (15,15)
nanotubes.
the same as in the graphite), (xc, yc, zc) denotes the coordinates
of the individual structureless carbon tube center, R ) a +
b sin (2π · zp/L) is the internal radius of nanotubes, a > b are
parameters (i.e., for infinitely long straight structureless
cylinder b ) 0), (xw,yw,zw) denotes the coordinates of the
fluid Lennard-Jones molecule, (xp,yp,zp) defines the coordinates of the point on the carbon surface, L ) 10σff (σff is taken
for tetrafluoromethane) denotes the length of the basic
periodic unit, whereas M is the number of the periodic units
used for the calculations of the solid-fluid interaction
potential. We have found that M ) 10 is a sufficient number
of units for a calculation of the total solid-fluid interaction
potential in the infinitely long structureless single-walled
nanotubes due to the fast decrease of the dispersion
interactions with distance (20, 21). The parameters of the
solid-fluid potential (i.e., Lennard-Jones solid-fluid collision
diameter, and well-depth) were calculated from the Lorentz–
Berthelot mixing rule: σsf ) (σff + σss)/2, sf ) [(ff/kb)(ss/kb)]1/2.
For carbon we assumed σss ) 3.4 Å and ss/kb ) 28 K (12). The
structureless model of the individual nanotube is realistic
for high temperatures due to the high thermal energy of CF4
molecules. Moreover, this approximation is appropriate since
FIGURE 3. Equilibrium snapshot of encapsulated CF4 at 300 K. Left panel: idealized bundle of (8,8) SWNTs and external pressure 0.1
bar; right panel: idealized bundle of (10,10) SWNTs and external pressure 0.5 bar.
the fluid molecules are large relative to the spacing between
the surface atoms (d1/σff ) 0.3, where d1 ) 1.42 Å denotes
C-C distance in the graphite) (12). We observe that this model
predicts the enhancement of the solid-fluid intermolecular
potential between the tetrafluoromethane and carbon nanotube due to curvature effect. The effect that is not taken into
account in the present paper is the change of the set of
Lennard-Jones parameters due to the polarization of confined
tetrafluoromethane. It should also lead to the additional
enhancement of solid-fluid interactions. Therefore we
predict that our results for the amount of CF4 adsorption are
a lower boundary for the adsorption in the real bundle of
SWNTs.
Simulation Details. In the present work, we performed
the simulation of tetrafluoromethane adsorption at 300 K
for bulk pressure up to 2.2 bar. We computed the excess part
of the chemical potential and pressures of CF4 in the standard
canonical ensemble (22). In the simulation of CF4 in the
idealized bundle of SWNTs, we used a grand canonical
ensemble Monte Carlo simulation (i.e., fixed system volume,
temperature, and the chemical potential of the bulk fluid
mixture) (22, 23). Equal probabilities are used for trial moves,
creation, and destruction of the selected molecule, and the
acceptance decision follows the Metropolis sampling scheme
(22, 23). In the cubic simulation box we placed an idealized
hexagonal bundle of investigated SWNTs consisting of 11
rigid tubes, as displayed in Figure 1. Following the previous
studies and experimental reports, we used a van der Waals
gap of 4 Å between the individual SWNTs (24). A cubic
simulation box of size m · n · 10σff (σff ) 4.7Å, n and m box
sizes were adjusted to keep the intratube distance) with
periodic boundary conditions in all directions was used, with
the minimum image convention used for the computation
of molecular interactions (22, 23). We generated 8 ×
107configurations, of which the first 5 × 107 were discarded
to guarantee proper equilibration of the system. The stability
of the results was confirmed by additional longer runs. In
the longer runs with the number of configurations larger
than 108, the amount of adsorbed CF4 did not change.
The absolute value of adsorption is given by the following
(12):
Γabs ) 〈N〉 ⁄ V
(5)
where 〈N〉 is the ensemble average of the number of CF4
molecules in the simulation box of volume, V. The Gibbs
excess value of adsorption is computed from the following
equation (12):
Γexc ) 〈N〉 - FbV
(6)
Here, Fb denotes the bulk density of tetrafluoromethane. For
the considered high temperatures and pressures up to 3 bar
the Γexc ≈ Γabs since the bulk contribution is small and can
be neglected. We calculate the enthalpy of adsorption from
the fluctuation theory (12),
q ) kbT +
〈U〉〈N〉 - 〈UN〉
(7)
〈N 2 〉 - 〈N〉2
where 〈. . .〉 denotes the ensemble average, N is the number
of particles, and U denotes the configuration energy of the
system. The enthalpy of adsorption is proportional to the
strength of the biding energy between adsorbed molecules
and the adsorbent. This thermodynamics function is more
sensitive to the details of the adsorption process than the
Gibbs absolute and excess value of adsorption.
Results
The key for optimizing the amount of CF4 trapped in the
nanotubes upon assumed operating external conditions is
the size of the internal cylindrical pores and interstitials
channels of an idealized bundle of SWNTs. Due to a large
molecular size of CF4, the internal pores play predominant
role in the process of encapsulation of CF4 via the physical
adsorption mechanism, as displayed in Figures 3 and 4. The
clear maxima are observed for both volumetric and mass of
adsorbed CF4 in the investigated carbon nanostructures, as
shown in Figures 2 and 5. The position of the maxima depends
on the operating external pressure. At 0.1 bar, the optimal
size is R ) 0.54 nm. This size corresponds to the size of (8,8)
armchair carbon SWNTs (25). Table 1 shows the size of the
internal cylinders for the class of nanotubes known as
armchair (n,n) nanotubes (25). Here individual cylindrical
carbon nanotubes strongly interact with CF4 giving the high
enthalpy of adsorption of ≈34 kJ mol-1 (extrapolated to zero
coverage), as presented in Figure 6. In the interior space of
the carbon nanotubes high cohesive forces cause strong
compression of CF4 molecules leading to the quasi onedimensional solid-like structure. The encapsulated molecules
arrange in a one-dimensional dense structure even at a high
temperature of 300 K (see molecular rod of CF4 displayed on
Figures 3 and 4). The strong confinement stabilizes the
strongly packed structure of adsorbed/compressed molecules, although it is not a one-dimensional crystal because,
strictly speaking, strong fluctuations destroy ideal order in
one dimension (26). Due to the large molecular size, the CF4
molecules do not penetrate the interstitial channels for the
idealized bundle of (8,8) SWNTs, and consequently, their
high adsorption follows solely from the high adsorption
enthalpy. Increasing the external pressure causes a gradual
shift of the efficiency of volumetric amount of trapped CF4
due to a competition between the binding energy in the
nanotubes and the space available for densification/
compression of molecules, as displayed in Figures 2, 3, and
4. At the common operating external pressure of 1 bar, the
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FIGURE 4. Equilibrium snapshot of encapsulated CF4 at 300 K. Left panel: idealized bundle of (11,11) SWNTs and external pressure 1
bar; right panel: idealized bundle of (15,15) SWNTs and external pressure 2 bar.
FIGURE 5. Absolute value of adsorption of CF4 is shown as a
function of the pore radius for different types of (n,n) armchair
nanotubes, for the external pressure of 1 bar and 300 K. The
dashed lines correspond to the experimental values of CF4
mass storage for selected activated carbons and zeolites at the
same external conditions (27, 28). The solid line is a guide for
the eyes only.
TABLE 1. Chiral Vectors and Equivalent Internal Pore Radii of
Nanotubes Used in the Current Study (25)
chiral vector
pore radius, nm
(6,6)
(8,8)
(9,9)
(10,10)
(11,11)
(12,12)
(14,14)
(15,15)
(18,18)
(20,20)
0.41
0.54
0.61
0.68
0.75
0.81
0.95
1.02
1.22
1.36
idealized bundles of size R ) 0.75 and R ) 0.68 nm are the
most efficient for the densification of CF4, even though
interstitial channels are still too small for accommodation of
these molecules. These sizes correspond to the size of the
(11,11) and (10,10) armchair nanotubes (Table 1). The larger
internal pore diameter of these nanotubes allows further
adsorption and compression of CF4 into plastic structures.
Finally, we observe that volumetric and mass capacities of
the adsorbents differ, since we obtain that for R ) 1.02 nm
(corresponding to armchair (15,15) carbon nanotubes) we
get the highest mass of CF4 encapsulated per mass of
the adsorbent at 1 bar and 300 K (displayed in Figure 5). In
the (15,15) armchair nanotubes the adsorption reaches the
highest value of ≈2.4 mol kg-1. We expect that this mass of
encapsulated CF4 is a lower boundary for the real materials
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ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 42, NO. 8, 2008
FIGURE 6. The variation of the enthalpy of CF4 adsorption in
investigated idealized bundles of SWNTs versus absolute value
of adsorption at 300 K. The dashed lines correspond to the
experimental values of CF4 enthalpy at zero coverage for
selected activated carbons and zeolites at the same external
conditions (27, 28).
since the interactions between the curved cylindrical carbon
surfaces and CF4 molecules should be enhanced in comparison to the flat graphite. We expect that the LennardJones well-depth is increased due to the polarization of CF4
near curved cylindrical carbon surface. The high mass of CF4
trapped in this idealized bundle of SWNTs follows from the
delicate balance between the enthalpy of adsorption and
available space for accommodation of the molecules. As
shown in Figure 6, the enthalpy of adsorption extrapolated
to zero coverage for the idealized bundle of (15,15) SWNTs
is ≈20.7 kJ mol-1. CF4 molecules can be adsorbed and further
compressed in both internal pores and interstitial channels
of SWNTs bundle. Interestingly, the CF4 molecules compressed in the interstitial channels of the (15,15) SWNTs
bundle also form a dense structure as similarly occurs in the
internal nanopores (see molecular rod nanostructure in
Figure 4 and the movies in the Supporting Information). The
question of primary importance is this: Is the idealized SWNTs
better for encapsulation of CF4 than the currently used
activated carbon and zeolites? Figures 5 and 6 present the
comparison between different adsorbents and demonstrates
the superiority of the nanotubes over the traditional materials
(27, 28). According to the traditional viewpoint of physical
adsorption in porous materials, the higher enthalpy of
adsorption leads to the larger amount of adsorbed material
(13, 19). This hypothesis explains the high amount of CF4
adsorbed in carbon Carbosieve G (Suppleco) molecular sieve,
as presented in Figures 5 and 6 (19, 27). The highest enthalpy
of adsorption for Carbosieve G is connected with the presence
of small pores of sizes comparable to the CF4 molecular
diameter. As commonly known in such pores, the adsorption
potential is strongly enhanced. However, our computer
simulations revealed that such traditional concepts of an
optimal porous body for encapsulation is incorrect. As one
can see from Figure 6, the idealized bundles of (6,6) (size R
) 0.41 nm), (8,8) (size R ) 0.54 nm), and (9,9) (size R ) 0.61
nm) SWNTs are characterized by very high enthalpy of CF4
adsorption ≈12–15 kbT(kbT ) 2.5 kJ mol-1 at T ) 300 K). At
the same time both mass and volumetric amount of
encapsulated CF4 are lower in comparison to optimal (10,10),
(11,11), and (15,15) idealized bundles of SWNTs, as shown
in Figure 5. In the nanoscale, the geometrical pore volume
and the volume accessible for adsorbed molecules are
different. Consequently, the knowledge obtained from XRD,
high-resolution TEM, and other experimental techniques
should be supplemented by the molecular simulations to
optimize the structure of nanomaterials. The optimized
structure of SWNTs bundles seem to be very promising for
the encapsulation of CF4 and superior in comparison to the
currently used activated carbons and zeolites. The efficiency
of encapsulation in nanotubes can be explained by their
intermediate properties in comparison to currently used
materials mentioned above. As zeolites they are homogeneous materials, however, similar to activated carbons, they
have the advantage over zeolites of larger pore sizes. The
recent progress in production of high quality tubular carbonaceous materials reduced their cost which seems to be
particularly important for the application of these materials
on the industrial scale (29). In practice, CF4 exists as a gas
mixture (for example, a mixture with nitrogen that can mimic
the air mixture). So the question arises about the transferability of the current results to the selective adsorption of
CF4 from the gas mixture. As showed by Müller (9) slit-shaped
carbonaceous pores preferentially adsorbed CF4 for all pore
widths with the exception of the smaller pore widths, for
which it is sterically hindered. Moreover, the highest CF4/N2
equilibrium selectivity corresponds to silt-shaped carbon
pore width of 0.8–1.5 nm (see Figure 6 in ref 9). At the same
time, these slit-shaped pore sizes maximized the excess value
of CF4 adsorption from the CF4-N2 mixture (see Figure 7 in
ref 9). Following Müller’s study (9), we expect that the
maximum excess of CF4 adsorption corresponds to maximum
CF4/N2 equilibrium selectivity. This key observation suggested
that the current simulation results of CF4 adsorption in carbon
nanotubes are transferable for the problem of CF4-N2 mixture
adsorption. Our results as well as the results of Müller (9)
show that optimal adsorption is achieved only when the
distribution of pore sizes is sharp.
Summary
We have found that the amount of the encapsulated CF4
under the ambient external conditions (1 bar, 300 K) is
maximized for well defined pore sizes of SWNTs. These pore
sizes change as we change the external pressure. Our work
demonstrate that clear maxima exists of the volumetric/mass
amount of trapped CF4 associated with the type of the
nanotube bundle (i.e., size of internal cylindrical pores and
interstitial channels), as similarly obtained for slit geometry
by Müller (9). At the common operating external pressure of
1 bar the idealized bundles of (11,11) (size R ) 0.75 nm) and
(10,10) (size R ) 0.68 nm) SWNTs are the most efficient for
the volumetric storage of CF4, even though the interstitial
channels are too small for accommodation of these molecules. The bundle of (15,15) SWNTs (size R ) 1.02 nm) is
the most efficient for the mass adsorption (i.e., weight %).
The comparison of the efficiency of CF4 mass storage favors
the idealized bundle of (15,15) SWNTs over currently used
activated carbons and zeolites. In this idealized bundle of
SWNTs, one can reach the high amount of adsorbed CF4
approximately equal to 2.4 mol kg-1, whereas the best
activated carbon Carbosieve G molecular sieve can adsorb
1.7 mol kg-1 at 300 K and 1 bar. Interestingly, we have
observed the formation of a quasi-one-dimensional crystal
structure of confined CF4 molecules in the interior space of
the idealized bundle of (8,8) (size R ) 0.54 nm) SWNTs.
Moreover, this long-range arrangement of CF4 molecules is
also found in the interstitial channels of (15,15) SWNTs. We
showed that the high enthalpy of adsorption cannot be used
as a measure of storage efficiently. The optimal balance
between the binding energy (i.e., enthalpy of adsorption)
and space available for the accommodation of molecules
(i.e., presence of inaccessible pore volume) is the key for
encapsulation of molecules interacting via the Lennard-Jones
potential. Our systematic computational study gives the clear
direction in the timely problem of purification and control
emission of CF4 and other perfluorocarbons into atmosphere.
Experimental investigations of the capture/storage of CF4 in
the real bundle of SWNTs are needed for employing these
nanomaterials as nanoscale vessels on the industrial scale.
Acknowledgments
Dr Piotrek Kowalczyk acknowledges the University of Queensland for postdoctoral fellowship (academic level A, 2007–2009)
and Dr Piotrek Gauden (Physicochemistry of Carbon Materials Research Group, Nicolaus Copernicus University,
Torun, Poland) for fruitful comments. This work was partially
supported from the budget of the Ministry of Science and
Higher Education as a scientific project 2007–2009.
Supporting Information Available
Additional information is shown in two movies and two
figures. This material is available free of charge via the Internet
at http://pubs.acs.org. R.H. acknowledges support from the
Foundation for Polish Science (grant “Mistriz”).
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