Langmuir 2007, 23, 7451-7455
7451
Selective Intercalation of Polymers in Carbon Nanotubes
Alexander V. Bazilevsky, Kexia Sun, Alexander L. Yarin,* and Constantine M. Megaridis
Department of Mechanical and Industrial Engineering, UniVersity of Illinois at Chicago,
Chicago, Illinois 60607-7022
ReceiVed January 17, 2007. In Final Form: April 30, 2007
A room-temperature, open-air method is devised to selectively intercalate relatively low-molecular-weight polymers
(∼10-100 kDa) from dilute, volatile solutions into open-end, as-grown, wettable carbon nanotubes with 50-100 nm
diameters. The method relies on a novel self-sustained diffusion mechanism driving polymers from dilute volatile
solutions into carbon nanotubes and concentrating them there. Relatively low-molecular-weight polymers, such as
poly(ethylene oxide) (PEO, 600 kDa) and poly(caprolactone) (PCL, 80 kDa), were encapsulated in graphitic nanotubes
as confirmed by transmission electron microscopy, which revealed morphologies characteristic of mixtures in
nanoconfinements affected by intermolecular forces. Whereas relatively small, flexible polymer molecules can conform
to enter these nanotubes, larger macromolecules (∼1000 kDa) remain outside. The selective nature of this process
is useful for filling nanotubes with polymers and could also be valuable in capping nanotubes.
Introduction
Carbon nanotubes (CNT) not only are promising for future
technological applications but also offer an intriguing platform
for fundamental research.1 Filling carbon nanotubes with lowmolecular-weight fluids or particles is a challenge faced in
numerous applications of nanofluidics, including lab-on-a-chip
devices, molecular separation (including DNA), drug delivery,
dialysis, and so forth.2-7 Early successes in this area involved
the encapsulation of molten materials (liquid metals, salts, and
oxides).8,9 More recent studies reported the filling of CNTs with
aqueous fluids10-13 and organic dopants.14 Advancements in the
capillary filling of nanotubes have, in turn, facilitated the
successful entrainment of nanoparticles in CNT channels.15,16
CNT channels represent themselves as a particular example of
nanopores. Recent work in this area includes pressure-induced
and thermally induced infiltration by water.17,18 These developments inspired efforts to trap polymer macromolecules into
nanotube channels. The first successful experiments on filling
carbon nanotubes with polymers were reported by Liu et al.,19
who employed supercritical CO2, an excellent solvent, to
* Corresponding author. E-mail: [email protected]. Tel: (312) 996-3472.
Fax: (312) 413-0447.
(1) Coleman, J. N.; Khan, U.; Blau, W. J.; Gun’ko, Y. K. Carbon 2006, 44,
1624-1652.
(2) Darhuber, A. A.; Troian, S. M. Annu. ReV. Fluid Mech. 2005, 37, 425455.
(3) Prins, M. W. J.; Welters, W. J. J.; Weekamp, J. W. Science 2001, 291,
277-280.
(4) Squires, T. M.; Quake, S. R. ReV. Mod. Phys. 2005, 77, 977-1026.
(5) Stone, H. A.; Stroock, A. D.; Ajdari, A. Annu.ReV. Fluid Mech. 2004, 36,
381-411.
(6) Thompson, P. A.; Troian, S. M. Nature 1997, 389, 360-362.
(7) Thorsen, T.; Maerkl, S. J.; Quake, S. R. Science 2002, 298, 580-584.
(8) Ajayan, P. M.; Iijima, S. Nature 1993, 361, 333-334.
(9) Ugarte, D.; Chatelain, A.; de Heer, W. A. Science 1996, 274, 1897-1899.
(10) Gogotsi, Y.; Libera, J.; Yazicioglu, A. G.; Megaridis, C. M. Appl. Phys.
Lett. 2001, 79, 1021-1023.
(11) Megaridis, C. M.; Yazicioglu, A. G.; Libera, J. A.; Gogotsi, Y. Phys.
Fluids 2002, 14, L5-L8.
(12) Naguib, N.; Ye, H. H.; Gogotsi, Y.; Yazicioglu, A. G.; Megaridis, C. M.;
Yoshimura, M. Nano Lett. 2004, 4, 2237-2243.
(13) Yarin, A. L.; Yazicioglu, A. G.; Megaridis, C. M.; Rossi, M. P.; Gogotsi,
Y. J. Appl. Phys. 2005, 97, 124309.
(14) Takenobu, T.; Takano, T.; Shiraishi, M.; Murakami, Y.; Ata, M.; Kataura,
H.; Achiba, Y.; Iwasa, Y. Nat. Mater. 2003, 2, 683-688.
(15) Kim, B. M.; Qian, S.; Bau, H. H. Nano Lett. 2005, 5, 873-878.
(16) Korneva, G.; Ye, H. H.; Gogotsi, Y.; Halverson, D.; Friedman, G.; Bradley,
J. C.; Kornev, K. G. Nano Lett. 2005, 5, 879-884.
(17) Han, A.; Kong, X.; Qiao, Y. J. Appl. Phys. 2006, 100, 014308.
(18) Qiao, Y.; Punyamurtula, V. K.; Han, A. Appl. Phys. Lett. 2006, 89, 251905.
encapsulate polystyrene into multiwalled CNTs with outer
diameters of 40-50 nm and lengths of 2-3 µm. The energetics
and electronic structure of a polyacetylene chain inside a carbon
nanotube were examined theoretically.20 Preliminary experiments
on the polyacetylene/CNT system have also been carried out.21
Steinmetz et al.22 reported the preparation of poly(N-vinyl
carbazole) or polypyrrole in multiwalled CNTs using supercritical
fluid impregnation. The above-mentioned studies have shown
that polymer encapsulation in CNT channels is feasible using a
two-step process. In the first step,19 supercritical CO2 carries the
monomer/initiator components into the CNT cavities. After the
removal of CO2, the monomers are then polymerized at a suitable
temperature, resulting in polymer/CNT composites. Whereas in
principle the supercritical fluid method can be adapted for many
other polymers, the procedure involves elevated pressures (∼100
bar), thus posing significant challenges.
This letter describes and demonstrates a transport-based, roomtemperature, open-air method of filling untreated (as-grown)
hydrophilic CNTs with different flexible polymers. Depending
on the size of the polymer macromolecules, the procedure can
be used for selective intercalation, wherein high-molecular-weight
polymers do not enter the CNT channel but lower-molecularweight polymers do. In addition to the experimental methods,
a theoretical model is also presented to describe the physical
transport mechanism believed to be responsible for the selective
filling of CNTs with different polymers.
Experimental Methods and Results
Consider a wettable carbon nanotube submerged in dilute polymer
solution (Figure 1). The nanotube initially is void of any polymer.
Through capillary filling, the polymer molecules (if small enough)
will be entrained in the cavity by the wettability-driven flow of the
solvent. For linear flexible polymer molecules, their radius of gyration
Rg varies approximately in the range of 10-100 nm for molecular
weights in the range of 1-1000 kDa.23 Consequently, for 100-nm(19) Liu, Z. M.; Dai, X. H.; Xu, J.; Han, B. X.; Zhang, J. L.; Wang, Y.; Huang,
Y.; Yang, G. Y. Carbon 2004, 42, 458-460.
(20) McIntosh, G. C.; Tomanek, D.; Park, Y. W. Phys. ReV. B 2003, 67,
125419.
(21) Steinmetz, J.; Lee, H.-J.; Kwon, S.; Lee, D.-S.; Goze-Bac, C.; AbouHamad, E.; Kim, H.; Park, Y. W. Curr. Appl.Phys. 2007, 7, 39-41.
(22) Steinmetz, J.; Kwon, S.; Lee, H. J.; Abou-Hamad, E.; Almairac, R.; GozeBac, C.; Kim, H.; Park, Y. W. Chem. Phys. Lett. 2006, 431, 139-144.
(23) Pluen, A.; Netti, P. A.; Jain, R. K.; Berk, D. A. Biophys. J. 1999, 77,
542-552.
10.1021/la070140n CCC: $37.00 © 2007 American Chemical Society
Published on Web 06/08/2007
7452 Langmuir, Vol. 23, No. 14, 2007
Letters
Figure 1. Carbon nanotube immersed in dilute polymer solution.
The polymer macromolecular coils are indicated as dark dots
dispersed in a liquid solvent (gray medium).
diameter nanotubes (2a ) 100 nm, 2L is on the order of several
micrometers), flexible macromolecules with molecular weights of
10-100 kDa should fit in the cavity, whereas those with weight on
the order of 1000 kDa should be incapable of entering. In the case
of an evaporating solvent, the concentration of polymer molecules
around the CNT would gradually increase as the solvent evaporates.
In turn, the resulting concentration gradients would drive (by
diffusion) polymer molecules toward the CNT interior. In principle,
these polymer concentration gradients can be sustained throughout
the entire process until all of the solvent has been removed from the
CNT surroundings. Diffusion coefficients of polymer macromolecules with molecular weight M vary as Dp ∝ M-1/2 in dilute solution
at the θ temperature (where polymer macromolecules behave almost
as ideal chains), or Dp ∝ M-3/5 for dilute solutions with excluded
volume, or Dp ∝ M-2 in the concentrated reptational regime.24,25 In
all cases, the diffusion-driven supply of smaller molecules is faster.
To this end, it seems feasible that during the transient stages, diffusion
can be used to enrich the CNT interior in low-molecular-mass
polymers dissolved in volatile solvents. Moreover, because the
polymer concentration gradients are self-sustained as a result of
solvent evaporation, the polymer content inside CNTs could reach
almost 100%, even though the initial solution is dilute or semidilute.
It is emphasized that in the symmetric situation depicted in Figure
1 with both CNT ends submerged in polymer solution, no polymer
entrainment in the CNT can occur by wettability-driven flow (which
occurs only in the beginning of the process) or by the flow caused
via evaporation near a triple contact line26 because during most of
the filling process the CNT is fully filled by solution. The abovementioned diffusion-driven mechanism is demonstrated experimentally below.
Commercial, as-grown, highly graphitic (multiwalled) carbon
nanotubes (PR-24, Pyrograph III) were employed in this study. The
CNTs, which also had some amorphous carbon on their surface,
contained some iron (<14 000 ppm) and less than 5% moisture.
These open-end carbon nanotubes had inner diameters of 50-100
nm, a wall thickness of ∼O(10 nm), and lengths in the range of
10-100 µm. In selected experiments, CNTs were dispersed in
deionized water at ∼0.5 wt %. The suspension was sonicated for
1 h to eliminate aggregates. Nanotubes after sonication probably
contained some water and are referred to as prewetted CNTs. This
term is conditional because it is not possible to determine with
certainty that water had not evaporated before these nanotubes were
submerged in polymer solution. In other experiments, as-received
nanotube powders were submerged in polymer solution. Therefore,
initially these nanotubes were empty and are referred to as dry CNTs.
Five dilute or semidilute polymer solutions were prepared: (iiii) 0.01 wt % aqueous solutions of PEO with three different average
molecular weights 600, 2000, and 4000 kDa; (iv, v) 0.1 and 1 wt
% solutions of PCL (80 kDa, insoluble in water) in methylene
chloride, MC.
Specimens were prepared using lacey carbon electron microscope
(TEM) grids placed on top of a porous substrate (Figure 2). The
porous substrates consisted of absorbing paper or lint-free paper
cloth. The results were very similar for both substrates. The
experimental procedure was as follows. In the case of prewetted
(24) Doi, M.; Edwards, S. F. The Theory of Polymer Dynamics; Clarendon
Press: Oxford, U.K., 1986.
(25) De Gennes, P. G. Scaling Concepts in Polymer Physics; Cornell University
Press: Ithaca, NY, 1979.
(26) Deegan, R. D.; Bakajin, O.; Dupont, T. F.; Huber, G.; Nagel, S. R.;
Witten, T. A. Nature 1997, 389, 827-829.
Figure 2. Sketch of the experimental procedure used to intercalate
low-molecular-weight polymers in open-ended carbon nanotubes.
The polymer is introduced into the gently deposited droplet (gray
circle on center top), whereas the layer of nanotubes rests on top
of the lacey carbon TEM grid (3 mm diameter). The small vertical
arrows indicate the absorbance of polymer solution by the porous
substrate, which creates a thin film rapidly depleted of solvent as
a result of evaporation.
tubes, a small drop of the CNT suspension in water was dispensed
onto the grid. The rapidly absorbing substrate under the grid
immediately converted the drop to a thin film. Water evaporation
ensued and continued until the surface of the TEM grid lost its shiny
texture (3-5 s at room temperature). At this moment, some CNTs
could probably still contain water inside. With dry CNTs, this step
was absent, and CNT powder was directly deposited onto the TEM
grid. Dispersion of the CNT water suspension resulted in a more
uniform nanotube layer on the grid than in the case of dry CNT
powder. A few seconds after the deposition of prewetted CNTs or
any time after the deposition of dry CNTs, a drop of polymer solution
was dispensed over the CNTs. Dilute and semidilute polymer
solutions yielded a very thin (below 100 nm) dried polymer film on
the TEM grid, thus making it possible to obtain TEM images of the
nanotube interiors after the removal of the grids from the substrates.
The presence of the porous substrate underneath the TEM grids was
critical to the polymer filling process. The substrate porosity facilitated
rapid imbibition27 of the solvent/polymer solution into the substrate
pores, thus creating a thin fluid film over the TEM grid with CNTs.
This thin film evaporated rapidly, causing rising polymer concentrations around the CNTs. These concentrations supported polymer
diffusion into the CNTs, in turn enriching polymer content in the
CNT interior.
A JEOL-3010 transmission electron microscope operating at 300
kV was employed to visualize the CNT interiors at high resolution.
The thin layer of dried polymer covering the CNTs allowed an
examination by electron microscopy, which was used to evaluate
the effectiveness of the polymer filling process.
The effect of polymer molecular weight on the intercalation process
was investigated first using dry CNTs. The experiments showed that
nanotubes submerged into dilute solutions of relatively lowmolecular-weight PEO (600 kDa in water) or PCL (80 kDa in MC)
were filled with polymer deposits by the end of the drying process.
This outcome is consistent with the fact that the radii of gyration
of these polymer macromolecules are smaller than the CNT radii.
Being supplied by diffusion to the open ends of the CNTs, these
molecules proceeded into the CNTs and accumulated there. Various
morphologies of the encapsulated polymer deposits are shown in the
TEM micrographs of Figure 3a-c. In the tight confinement of the
CNTs in Figure 3, polymer molecules are experiencing strong
intermolecular interactions in the bulk, as well as with the CNT
walls. These interactions tend to condense the polymer material,
whereas the entropy-related diffusion process tends to make the
material homogeneous. As a result of the competition between these
two mechanisms, the dissolved polymer can experience an internal
instability with characteristic scales on the order of 10 nm, similar
to spinodal decomposition.13 The instability should result in
characteristic deposit patterns with length scales on the order of the
CNT inner diameter. The presence of this instability was confirmed
(27) Bazilevsky, A. V.; Kornev, K. G.; Rozhkov, A. N.; Neimark, A. V. J.
Colloid Interface Sci. 2003, 262, 16-24.
Letters
Langmuir, Vol. 23, No. 14, 2007 7453
Figure 3. Relatively low-molecular-weight PEO deposits inside CNTs. They were obtained by dispensing 0.01 wt % PEO (600 kDa) in
deionized water over dry CNTs. Three different dried polymer patterns are displayed in the TEM micrographs: (a) pea pod, (b) foam, and
(c) dispersed bubbles.
Figure 5. Transmission electron micrographs of PCL deposits inside
CNTs. They were obtained by dispensing PCL (80 kDa) in MC over
prewetted CNTs: (a) 0.1 wt % solution and (b) 1 wt % solution.
Figure 4. Transmission electron micrographs of higher-molecularweight PEO deposits inside CNTs. They were obtained by dispensing
0.01 wt % PEO in deionized water over dry CNTs. (a) PEO, Mw )
2000 kDa and (b-d) PEO, Mw ) 4000 kDa. The detail in d is an
enlargement of the marked area in c.
by the dried polymer patterns seen in Figure 3a-c. However, this
instability and the associated cellular dried polymer patterns were
absent outside the CNTs, where the dried polymer deposit appeared
uniform when observed in the TEM. The morphological differences
of the polymer deposits across the CNT walls facilitated the distinction
between the polymer masses inside and outside the CNT. It is noted
that the encased PEO patterns seen in Figure 3 closely resemble
those observed in the polystyrene/CNT system of Liu et al.19 However,
the filling in the latter study was done by means of supercritical fluid
processing (elevated pressure) and subsequent polymerization
(elevated temperature), whereas in the present study, the filling was
done by diffusion at room temperature and pressure.
At higher PEO molecular weight (2000 and 4000 kDa), where
the polymer molecule radii of gyration become comparable to the
CNT diameter, polymer macromolecules are continuously supplied
to the open ends of the CNTs by diffusion (albeit slower than those
with lower molecular weight) but have difficulty penetrating the
CNT cavity. As a result, in the case of 2000 kDa PEO, much less
polymer could be found deposited inside the CNTs (Figure 4a). At
yet higher PEO molecular weight (4000 kDa), even less polymer
was found inside the CNTs (Figure 4b). The PEO volumes found
deep in the CNT channels in the 2000 and 4000 kDa cases were
attributed to lower-molecular-weight fractions present in polydisperse
polymers. These lighter molecules with a radius of gyration smaller
than the channel radius, Rg < a, were able to penetrate the CNTs,
whereas the higher-molecular-weight components with Rg > a were
deposited near the CNT ends (Figure 4c,d) or mostly remained
outside. The polymer plugs formed near the CNT ends (Figure 4c,d)
could effectively seal the CNTs. In this context, the CNTs acted as
selective macromolecule separators allowing the lower-molecularweight fractions into their cavity while keeping the higher-molecularweight components outside.
Prewetted CNTs that were brought into contact with PCL solutions
in MC, which is miscible with water, were also filled with polymer
along their full length (Figure 5a,b). In this case, the filling process
should initially involve the rapid diffusion of water molecules (much
smaller than PCL molecules) from the prewetted nanotube cavity
(if still not evaporated) and the rapid diffusion of MC molecules
(also much smaller than PCL molecules) into the CNT. Later on,
the diffusion of relatively larger PCL macromolecules (but small
enough to enter the CNT channel) brings them without hindrance
into the CNTs, which are already filled with MC.
The reported results are significant because polymer-filled
nanotubes could have numerous applications in composites, flat
panel displays, sensors, and so forth. In addition, the selective nature
of the filling may be used to cap (cork)28 CNTs with large
macromolecules that cannot enter the CNT cavity and deposit at the
tube end, thus blocking access to its interior. Capping of CNTs filled
with a liquid has applications in drug delivery. The unique advantages
of this technique (room temperature, open-air processing, singlestep, low cost) are very attractive for DNA (e.g., lambda bacteriophage
(28) Hillebrenner, H.; Buyukserin, F.; Kang, M.; Mota, M. O.; Stewart, J. D.;
Martin, C. R. J. Am. Chem. Soc. 2006, 128, 4236-4237.
7454 Langmuir, Vol. 23, No. 14, 2007
Letters
DNA typically used in microfluidic experiments),29,30 protein and
virus segregation by molecular weight, and encapsulation in CNTs,
with potential applications in nanobiotechnology.31,32
Theoretical Analysis and Results
A theoretical analysis was performed to examine the feasibility
of the diffusion-based transport mechanism believed to be
responsible for the selective filling of CNTs with different
polymers. For the system shown in Figure 1 (CNT length 2L,
diameter 2a) and because the characteristic size 2A of the spread
out droplet (Figure 2) is much larger than 2L, the diffusion process
in the vicinity of the nanotube open end can be approximately
considered to be spherically symmetric. Then, the polymer
concentration Cp,d in the spread out droplet is governed by the
following quasi-steady-state diffusion equation
(
)
1 d 2 dCp,d
r
)0
dr
r2 dr
r ) ∞, Cp,d ) Cp,d∞
r ) L, Cp,d ) Cp,t
(1)
where r is the radial spherical coordinate centered at the nanotube
midpoint, Cp,d∞ is the polymer concentration in the droplet far
from the nanotube, and Cp,t is the polymer concentration inside
the nanotube. Note that in the first approximation we assume the
polymer concentration inside the nanotube to be uniform. This
assumption is valid because possible polymer diffusion inside
a CNT is not in the Knudsen regime. Indeed, the mean free path
in concentrated polymer solutions inside a CNT is on the order
of Rg. For those macromolecules that can enter a CNT, Rg < a
and obviously Rg, L, which is equivalent to a small Knudsen
number and thus ordinary diffusion. The formation of the cellular
nanostructures seen inside CNTs in Figures 3 and 5 is attributed
to the action of intermolecular forces13 in addition to diffusion
and could be the result of a subsequent spinodal decomposition
step after a uniform deposit has filled the tube.
If the nanotube is initially empty, then it will be almost
immediately filled with the solvent. Then, the diffusion of the
high-molecular-weight polymers can bring them inside the
nanotube. Given the concentration distribution following from
eq 1, the corresponding polymer flux into the nanotube is given
by J ) 2πa2Dp(Cp,d∞ - Cp,t)/L, where Dp is the polymer diffusion
coefficient in the solvent. Then, the lump mass balance for the
nanotube yields the following equation for Cp,t:
Dp
dCp,t
) 2 2 (Cp,d∞ - Cp,t)
dt
L
liquid is given by Ms ≈ Ms0 - KADvcst, where Ms0 is the initial
solvent mass and K ) 2π(0.1) ) 0.628. However, when the
polymer solution is considered to be a thin, uniform film, js,n ≈
Dvcs/l, where the diffusion length scale is l ≈ nA (n > 1) and
K ) π/n. The corresponding polymer concentration in the drop
Cp,d∞ is given by
Cp,d∞ )
Polymer concentration Cp,d∞ in eq 2 varies with time as a
result of solvent evaporation only because polymer losses into
the CNT are negligibly small. The surface distribution of the
evaporation rate of a sessile droplet shaped as a spherical segment
with base radius A is given33 as js,n ≈ 0.1Dvcs/A, where js,n and
cs are the normal component of the solvent vapor flux and the
saturated vapor concentration at the spread out liquid surface,
respectively, and Dv is the diffusion coefficient of solvent vapor
in air. Then, at any instant t, the solvent mass in the spread out
(29) Perkins, T. T.; Smith, D. E.; Chu, S. Science 1997, 276, 2016-2021.
(30) Chan, E. Y.; Goncalves, N. M.; Haeusler, R. A.; Hatch, A. J.; Larson,
J. W.; Maletta, A. M.; Yantz, G. R.; Carstea, E. D.; Fuchs, M.; Wong, G. G.;
Gullans, S. R.; Gilmanshin, R. Genome Res. 2004, 14, 1137-1146.
(31) Cui, D.; Ozkan, C. S.; Ravindran, S.; Kong, Y.; Gao, H. Mech. Chem.
Biosyst. 2004, 1, 113-121.
(32) Salalha, W.; Kuhn, J.; Dror, Y.; Zussman, E. Nanotechnology 2006, 17,
4675-4681.
(33) Yarin, A. L.; Szczech, J. B.; Megaridis, C. M.; Zhang, J.; Gamota, D. R.
J. Colloid Interface Sci. 2006, 294, 343-354.
(3)
where Mp is the polymer mass in the entire liquid volume; Mp
does not change in time because the losses into the CNT are
negligibly small. It is important to note that polymer solution
absorption by the porous substrate is assumed to be over at this
stage and polymer concentration in the spread out drop is growing
only because of evaporation from the free surface. Nonetheless,
ongoing infiltration into the porous substrate could be easily
incorporated into the model without affecting the result qualitatively.
By substituting eq 3 into eq 2, we deduce the following problem
for Cp,t
C′p,d0
dCp,t
2
2
+ Cp,t )
dt
τdif
τdif C′p,d0 + 1 - (t/τev)
t ) 0, Cp,t ) 0
(4)
where C′p,d0 ) Mp/Ms0 [the initial polymer concentration Cp,d0)
C′p,d0/(1 + C′p,d0)] and the characteristic diffusion and evaporation times are given by
τdif )
L2
,
Dp
τev )
Ms0
KADvcs
(5)
The exact solution of eq 4 is
Cp,t )
2C′p,d0
exp(-2t/τdif)
τdif
exp(2t/τdif)
∫0t 1 + C′
p,d0
- (t/τev)
dt (6)
For L ≈ 1 µm and Dp ≈ 10-5 cm2/s, the characteristic diffusion
time is τdif ≈ 10-3 s. However, in the experiment τev ≈ 1 min;
therefore, τdif , τev. Then, for t e τdif, the third term in the
denominator inside the integral in eq 6 can be neglected, yielding
Cp,t )
(2)
Mp
Mp + Ms0 - KADvcst
C′p,d0
[1 - exp(-2t/τdif)] )
1 + C′p,d0
Cp,d0[1 - exp(-2t/τdif)] (7)
In other words, at short times t < τdif, liquid evaporation has no
effect while the tube is being filled via diffusion to the level
approximately corresponding to the ambient low polymer
concentration.
However, at long times τdif , t e τev the integral in eq 6 can
be evaluated using the asymptotic Laplace method,34 and the
resulting expression for the polymer concentration in the nanotube
becomes
Cp,t ) C′p,d0
1
1 + C′p,d0 - (t/τev)
(8)
A comparison of eq 8 with eq 3 reveals that at this stage the
polymer concentration in the CNT resembles that in the drying
droplet.
(34) Naifeh, A. H. Introduction to Perturbation Techniques; Wiley: New
York, 1981.
Letters
The evaporation process continues until t ) τev when the solvent
is fully evaporated. Therefore, the maximum value of the polymer
concentration inside the nanotube can reach Cp,tmax) 1 (i.e., the
diffusion process, which is permanently sustained by the growing
concentration of the polymer in the solution, as a result of solvent
evaporation, can raise the polymer concentration in the nanotube
to almost 100%). In reality, complete filling is not attained, with
foamlike cellular structures eventually forming inside the CNT
(Figures 3 and 5). These patterns are consistent with the results
reported in a separate study13 where the condensation of vapor
molecules inside carbon nanotubes led to the emergence of similar
structures formed by the competition of Brownian diffusion and
intermolecular forces (Figures 12 and 13 in ref 13).
It is emphasized that because of the dependence of the polymer
diffusion coefficient Dp on the molecular weight of the polymer
(or, in other words, on the radius of gyration Rg), in the case of
polydisperse polymer solutions, the CNT content will not resemble
that in the drying droplet at intermediate stages but rather will
be enriched in the lighter fraction. However, in the case of τdif
, τev at the end of the long intercalation process, all of the
polymer fractions whose radii of gyration are less than the CNT
channel radius (i.e., Rg < a) will eventually diffuse into the CNT
cavity according to the diffusion mechanism described in this
section. Only those fractions with Rg > a will settle outside the
CNT or, at the very best, reach the CNT entrance. Therefore,
Langmuir, Vol. 23, No. 14, 2007 7455
selective intercalation in the present case (τdif , τev) is not the
outcome of the diffusion mechanism itself but is rather due to
the physical smallness of the CNT channels as compared to the
higher-molecular-weight polymers. Finally, it should be mentioned that for the case of very rapid evaporation (i.e., τdif ≈ τev)
the possibility still exists to enrich the CNT content with the
lighter polymer fraction because the heavier components would
not have adequate time to enter the cavity.
Conclusions
We have demonstrated a room-temperature, open-air method
to selectively intercalate low-molecular-weight polymers from
a volatile solvent solution into wettable graphitic nanotubes of
50-100 nm diameter. Low-molecular-weight polymers, such as
PEO and PCL, were encapsulated in CNTs as confirmed by
transmission electron microscopy, which revealed foam and peapod-like patterns of the dried polymer in the CNT channels.
Acknowledgment. This material is based upon work supported in part by the Volkswagen Foundation and the National
Science Foundation under grants NIRT CTS-0609062 and
CBET-0543538.
LA070140N