Chemical Physics Letters 496 (2010) 50–55

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Chemical Physics Letters

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Filling carbon nanotubes with liquid acetonitrile

Vitaly ChabanSchool of Chemistry, V.N. Karazin Kharkiv National University, Svoboda Square 4, 61077 Kharkiv, Ukraine

a r t i c l e i n f o a b s t r a c t

Article history:Received 4 June 2010In final form 3 July 2010Available online 8 July 2010

0009-2614/$ - see front matter � 2010 Elsevier B.V. Adoi:10.1016/j.cplett.2010.07.003

E-mail addresses: vvchaban@gmail.com, chaban@u

Carbon nanotubes and acetonitrile are of interest for modern electrochemistry since they are used tomake supercapacitors more efficient. In order to assess the feasibility of this setup, molecular dynamicssimulations were performed to investigate the hydrophobic degasified single-walled nanotubes fillingwith liquid acetonitrile. The simulation shows that nanotubes with 10 nm of length can be completelyfilled with acetonitrile during less than 100 ps. Surprisingly, the filling process is not significantly affectedby nanotube diameter and ambient conditions. In general, the ability of small hydrophobic carbon nano-tubes to be completely filled with acetonitrile is an important feature for supercapacitors.

� 2010 Elsevier B.V. All rights reserved.

1. Introduction

The static and dynamic behavior of fluids inside the nanosizedconfinements is now an important and broad field [1–7] of inves-tigation generally called nanofluidics. With a widespread availabil-ity of carbon nanotubes, interest in nanofluidics has greatlyincreased mainly due to the revolutionary possibilities of exploringthe fluids inside the extremely narrow channels of about 1 nm oreven less. The use of nanotubes to study the confined fluids alsoraises the interest to the specific atomic interactions betweennanotube and confined particles of different chemical nature thatbasically defines the nature of the confined liquid flow [1,2,7,8].The recent studies of nanofluidics comprise various aspects: boththe fluids entering the tube and the overall flow inside the tube.By now, experimental studies dealt with very different nanotubediameters (from 1 to 100 nm) and lengths [9–15], whereas com-puter simulations were concentrated only on the rather smallerCNTs (with diameters of a few nanometers) [1,5,16–19]. Varioussubstances were recently used to fill the hollow carbon nanotubesincluding molten metals, salts [9,20], oxides, aqueous and non-aqueous solutions [35] through metal evaporation [10], capillaryfilling [21] and other techniques. These works raised the produc-tion of a large number of hybrid materials [22,23]. An empiricallaw for single-walled CNTs filling was suggested by Dujardinet al. [11] stating that no liquid with a surface tension of more than180–200 mN/m could enter the tube inner cavity. This law workswell for the nanotubes with diameters of up to 4 nm. Althoughthe surface tension of many polar liquids, including water(72 mN/m), is significantly below the threshold, they are generallybelieved not to wet pristine carbon nanotubes (in analogy with ba-sal planes of graphite).

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The present work focuses on acetonitrile (ACN), an important or-ganic dipolar liquid both for science and chemical technology,which is also often used as a solvent for modern supercapacitors[24–29]. Among various possible setups, such devices are often de-signed with their electrodes containing carbon nanotubes or porouscarbon to increase the electrolyte adsorption. Obviously, the perfor-mance of supercapacitors critically depends on the ability of theparticular electrolyte solution to enter, and subsequently fill, theCNTs of the certain sizes. Since the transport properties of electro-lyte solutions tightly depend on a particular solvent, direct investi-gation of the latter is important. Moreover, the pristine carbonnanotube can be considered as an ideal model of a porous carbonwith nanosized channels. The another important question arisingin this context is how far the solvent and its solution can go insidecarbon nanotube. In spite of the considerable interest to superca-pacitors in modern electrochemistry and general nanofluidics, thementioned questions still remain open. For this kind of investiga-tions, computer simulation appears to be the most productive toolbecause of the principal experimental limitations on the nanoscale.

Here, the molecular dynamics (MD) study of filling CNTs withacetonitrile was carried out with a series of narrow armchairsingle-walled nanotubes ranging from (5, 5) to (11, 11) and theconstant length of 10 nm for all species. The influence of the differ-ent ambient conditions, temperature and elevated pressure, hasbeen considered. The adsorption processes of ACN molecules onthe internal and external surfaces of the CNTs were separated intime by means of the specific consequent MD setups.

2. Simulation details

2.1. Force fields

The GROMACS [30] program package was used to perform MDsimulations on several systems containing a few carbon nanotubes

V. Chaban / Chemical Physics Letters 496 (2010) 50–55 51

and liquid acetonitrile. The exact composition of all MD systems ispresented in Table 1. To represent all bonded and non-bondedinteractions within the carbon nanotubes, AMBER force field [31]was applied. All simulated nanotubes were treated as flexiblenon-polarizable (hydrophobic) particles with 1–4 carbon–carboninteractions switched on. The acetonitrile molecule was repre-sented using the six-site model of Nikitin et al. [32] which appearsto be the best force field for this liquid by now. It reproduces ther-modynamics and structure properties of bulk ACN very well andalso gives a pretty good viscosity (0.4 cP at 298 K and under1 bar, according to our own calculations). Surprisingly, the self-dif-fusion constant is a bit lower than experimental value (3.5 vs4.3 � 10-9 m2/s at 298 K and 1 bar). Unfortunately, no other aceto-nitrile force field gives better result for diffusion. The electrostaticswas treated by means of the Ewald summation (rcut = 1.4 nm) andLennard–Jones (12, 6) interactions were accounted with shiftedforce method (switch region between 1.2 nm and 1.3 nm). Thecross-term Lennard–Jones (12, 6) parameters between carbonnanotubes and ACN were obtained using the standard Lorenz–Berthelot combination rules. The molecular dynamics time-stepwas 0.001 ps in conjunction with a leap-frog integration algorithm.The linear velocity of the nanotube, initially centered in the box,was gradually removed to simplify the subsequent analysis.

2.2. Simulation setup

The multi-stage MD simulations were carried out to investigatedifferent aspects of the dynamic behavior of the CNT-ACN systems.Five narrow single-walled armchair carbon nanotubes were con-sidered: (5, 5), (6, 6), (7, 7), (9, 9) and (11, 11) with the constantlength of about 10 nm.

The study of the system dynamics was started with the CNTcentered in the box and surrounded by 0.6 nm of vacuum. Initially,no solvent molecules were present in the inner cavity of the nano-tube corresponding to the degasified case. The liquid acetonitrile(see Table 1 for details) was located as far as 0.6 nm from the outernanotube wall and filled all the available volume in the5 � 5 � 14 nm parallelepipedic MD box. Because of this somewhatexotic setup, the initial densities of the simulated systems were20–30% lower than equilibrium ones (Table 1). Firstly, in order to

Table 1Diameters of CNTs, dCNT, numbers of acetonitrile molecules in the MD system,numbers of confined solvent molecules, times of adsorption on the external surfacesof CNTs, times of filling and system densities, d.

CNT dCNT

(nm)N(ACN)

Nconfined

(ACN)texter.ads,(ps)

tfilling

(ps)d(kg/m3)

(5, 5) 0.68 2463 0 20 – 828(6, 6) 0.82 2397 19 20 50 841(7, 7) 0.95 2292 28 15 55 854(9, 9) 1.22 2217 69 20 60 878(11, 11) 1.49 2137 130 20 100 904

Fig. 1. The simulated system containing centered CNT (

study the adsorption of ACN on the external surface of the nano-tubes only, the tubes were capped preventing the solvent to pene-trate inside. Secondly, when the systems were equilibrated in theirprevious configurations, the caps were removed and the solventwas allowed to enter the open-ended tubes (Fig. 1). The rate ofthe filling process was investigated at temperatures of 278, 298and 323 K and pressures of 1, 100 and 2000 bar (T = 323 K). Finally,equilibrium MD runs were performed to explore the structure pat-terns of acetonitrile in confinements and estimate its dielectricconstant in the specific single-file chains. All MD simulations werecarried out in the constant temperature and constant pressure(NPT) ensemble. V-rescale thermostat [33] with a time constantof 0.5 ps and Parrinello–Rahman barostat [34] with a time constantof 1.0 ps were applied to maintain the temperature and pressurevalues, respectively. Importantly, the pressure coupling was ap-plied only in the radial direction of the CNT to minimize its possi-ble artificial effect on the filling process of acetonitrile.

2.3. Data analysis

The rate of carbon nanotubes filling was determined by theinteraction energy between nanotube and ACN. The correspondingenergy values were dumped every 2 ps (2000 time-steps) and plot-ted vs simulation time. The structure patterns of acetonitrile con-fined inside CNTs were analyzed in terms of atomic densities inaxial and radial directions of the nanotubes separately. The nitro-gen atom of ACN was selected for that as the heaviest one in thesolvent molecule. The dielectric constants of the confined liquidwere estimated from the fluctuations of the molecule dipolemoment.

3. Results and discussion

3.1. Effect of CNT diameter

Fig. 2 illustrates the evolution of interaction energy between thenanotube and acetonitrile for CNT (5, 5), CNT (6, 6), CNT (7, 7),CNT (9, 9) and CNT (11, 11). Interestingly, both internal and exter-nal surfaces of these CNTs are wetted unexpectedly rapidly (duringless than 100 ps). For external surface, the equilibration time is notmore than 20 ps (Table 1). It does not also depend on the particulartube diameter. The general shape of the curves is also very similarindicating that the solvent approaches the tube external walls veryrapidly and wets them within 20 ps.

The penetration of ACN into the internal cavity of the nanotubeis more complicated. While CNT (6, 6), CNT (7, 7) and CNT (9, 9) arefilled rapidly and similarly during 50–70 ps (Table 1), the filling ofCNT (11, 11) is longer and exhibits somewhat different mecha-nism. The first stage occurs during the first 50 ps and correspondsto the intense penetration of solvent molecules into the nanotube.The second stage (50 ps) can be understood as repacking of ACN in-side the spatial confinements tending to the minimal potential en-

11, 11) surrounded by 2137 acetonitrile molecules.

Fig. 2. The evolution of the interaction energy between CNT and (a) inside ACN, (b)outside ACN derived from MD simulations at 298 K and 1 bar. Horizontal solid linesof the same color show the respective equilibrium energies. (For interpretation ofthe references to color in this figure legend, the reader is referred to the web versionof this article.)

Fig. 3. The evolution of the interaction energy per one carbon atom between CNTand (a) inside ACN, (b) outside ACN derived from MD simulations at 298 K and1 bar: CNT (6, 6), red solid line; CNT (7, 7), green dash-dotted line; CNT (9, 9), bluedashed line; CNT (11, 11), pink dash-dot-dotted line. (For interpretation of thereferences to color in this figure legend, the reader is referred to the web version ofthis article.)

52 V. Chaban / Chemical Physics Letters 496 (2010) 50–55

ergy of the simulated system. This repacking stage is absent forsmaller nanotubes because their diameters allow only one molec-ular layer to be located near each sidewall. Thus, subsequentrepacking is not further necessary.

Rapid filling of nanotubes was recently demonstrated for thecase of water [35] which is attributed to the tight hydrogen bonds.Although acetonitrile is even more polar (l = 3.9 D), it is known asrather unstructured liquid with low maxima on radial distributionfunctions [32] and high diffusion constant (4.3 � 10�9 m2/s). Thereis also no hydrogen bonds in liquid ACN as opposed to water [35].In spite of no tight intermolecular bonding, the filling process isunexpectedly fast and complete, even at atmospheric pressureand low temperature.

Importantly, the internal cavity of the CNT (5, 5) can not befilled with acetonitrile probably because of its too small diameter(0.68 nm). The van der Waals radius of carbon atom is 0.17 nmdecreasing the available space to 0.34 nm. As current MD studyshows, this value is too little for methyl group (the largest groupof ACN) to enter the CNT (5, 5).

The independency of the nanotube filling rate from its diameteris rather curious provided that recently self-diffusion of the con-fined ACN was shown to correlate well with CNT diameter [36].It proves that the equilibrium diffusion constants of the confinedliquid cannot be directly used to predict the dynamics of filling.The main reason for this is a considerable difference between dif-fusion in the bulk phase and at the liquid–vapor interface. Forsmall nanotubes, this effect is pronounced even more than at theordinary liquid–vapor interface because the tube geometry drasti-cally limits the number of acetonitrile molecule neighbors. In fact,during the first filling stage (Fig. 2) we observe quasi–gas phase ofthe confined acetonitrile. The molecular mobility in such a phase isfound to be high and weakly dependent on the nanotube size.

To compare the interaction energies with ACN for differentnanotubes, the corresponding energy values were divided by the

number of carbon atoms in each CNT (Fig. 3). The energy of about3 kJ/mol per one carbon atom corresponds to the interaction of theCNTs with the outside solvent molecules. The total interaction en-ergy slightly increases as the tube curvature increases. Filling theinner surface of the CNT corresponds to 1.2–2 kJ/mol per one car-bon atom of the nanotube. The energy value also correlates wellwith a tube diameter. This is rather trivial since bigger tubes areable to encapsulate a larger number of solvent molecules (Table1). All these molecules interact with CNT sidewalls directlythrough van der Waals forces. The ability of liquid acetonitrile tofill carbon nanotubes of sub-molecular sizes favors its use as a sol-vent in supercapacitors together with carbon nanotubes [24–29].The simulation results suggest that the geometric size of the prop-er carbon pore size can be as small as 0.82 nm.

3.2. Effect of temperature

Three temperatures (278, 298, 323 K) at which ACN is a liquidwere considered in this study. Their influence on the filling dynam-ics is depicted in Fig. 4. The role of temperature is not crucial,although some insignificant differences can be observed forCNT (11, 11) whereas the filling rate for CNT (6, 6) is not affectedat all. The first stage of the overall filling process becomes shorterwith the system temperature increase (at 298 and 323 K) but therepacking stage remains nevertheless rather long. At 278 K, thefirst stage is a bit longer but the second one disappears. Overall,the system simulated at 278 K comes to equilibrium faster (within70 ps). This is not correlated with the self-diffusion constants ofbulk ACN which are 2.3, 3.4, 4.3 (10�9 m2/s) at 278, 298 and323 K, respectively. The difference in the equilibrium interactionenergies can be attributed to the density decrease when tempera-

Fig. 4. The evolution of the interaction energy between CNTs and confined ACN,derived from MD simulations at 278 K (red solid line), 298 K (green dash-dottedline), 323 K (blue dashed line) and 1 bar: (a) CNT (6, 6); (b) CNT (11, 11). Horizontalsolid lines of the same color show the respective equilibrium energies. (Forinterpretation of the references to color in this figure legend, the reader is referredto the web version of this article.)

Fig. 5. The evolution of the interaction energy between CNTs and confined ACNderived from MD simulations at 1 bar (red solid line), 100 bar (green dash-dottedline) and 2000 bar (blue dashed line) and 323 K: (a) CNT (6, 6); (b) CNT (11, 11).Horizontal solid lines of the same color show the respective equilibrium energies.(For interpretation of the references to color in this figure legend, the reader isreferred to the web version of this article.)

V. Chaban / Chemical Physics Letters 496 (2010) 50–55 53

ture rises. Bigger system density always corresponds to more com-pact molecular packing resulting in larger potential energies. Gen-erally, the weak effect of temperature suggests that ACN flowinside the partially filled small hydrophobic CNTs is even fasterthan in its bulk phase. One can conclude that the filling rate is lim-ited only by geometry of confinements and does not considerablydepend on media temperature.

3.3. Effect of pressure

Three pressures (1, 100, 2000 bar) at T = 323 K were consideredto investigate their influence on the nanotube filling process.CNT (6, 6) and CNT (11, 11), as the biggest and the smallest ones,were selected for this investigation (Fig. 5). The influence of highand very high pressures is more pronounced than that of temper-ature and affects both nanotubes similarly. The increase of pres-sure to 2000 bar leads to the increase of the equilibriuminteraction energy between nanotube and solvent by about 20%.Also the filling process becomes somewhat faster as the pressuregrows. Note, the degasified nanotubes are very readily filled withACN both at atmospheric and elevated pressure. Thus, the elevatedpressure is not necessary for practical applications (supercapaci-tors, nanofluidic devices) where the carbon nanotube filling isrequired.

3.4. Confined acetonitrile structure

In order to understand the above specificity of CNT filling withacetonitrile, the partial atomic densities along axial and radial

Fig. 6. Partial atomic (nitrogen, ACN) densities along (a) radial and (b) axialdirections of the nanotubes derived from the equilibrium MD simulations at 298 Kand 1 bar. The straight vertical lines correspond to the CNT sidewalls. The showncoordinates are the absolute coordinates of the respective nitrogen atoms in the MDbox.

Fig. 7. The instantaneous configurations of acetonitrile confined by (a) CNT (6, 6), (b) CNT (7, 7), (c) CNT (11, 11) derived from the equilibrium MD simulations at 298 K and1 bar.

54 V. Chaban / Chemical Physics Letters 496 (2010) 50–55

directions of the nanotube were calculated (Fig. 6). The number ofmaxima on Fig. 6a corresponds to the number of ACN molecules lo-cated along the radial direction inside the CNT. So, CNT (6, 6) isable to encapsulate only one solvent layer, CNT (7, 7) andCNT (9, 9) – two layers each and CNT (11, 11) – three layers. InsideCNT (6, 6), the confined acetonitrile molecules are quite free tomove because of this nanotube diameter (0.82 nm). The effective(available to solvent) CNT (6, 6) diameter is 0.48 nm which is about1.4 times bigger than the van der Waals diameter of the ACN car-bon atom. This is bigger than intermolecular distances in bulk li-quid ACN leading to the anomalous mobility of the confinedsolvent molecules. The same conclusion is derived from Fig. 6bwhich demonstrates almost no oscillations of acetonitrile mole-cules along the nanotube axial direction. The effect is well pro-nounced for the CNT filling process resulting in extremely fastslipping of the ACN molecules from bulk liquid into confinement.Analyzing other systems, we get the following relations betweenthe diameters of the carbon atom and the nanotube: forCNT (7, 7) – 1.8, for CNT (9, 9) – 2.6, for CNT (11, 11) – 3.4.

It is interesting that Fig. 6a indicates two maxima for ACN insideCNT (7, 7) although two full-grown layers of solvent cannot existinside this tube, since the CNT diameter is evidently smaller thantwo diameters of the solvent molecule. This fact is also confirmedby the total number of ACN molecules inside the CNT (7, 7) – 28. Iftwo full-grown solvent layers existed in CNT (7,7), the number ofthe confined solvent molecules should have been two times morethan inside CNT (6, 6), e.g. 38. The answer is given by the instanta-neous configurations of the confined ACN inside CNT (6, 6) andCNT (7, 7) (Fig. 7). Inside CNT (6, 6), ACN molecules are aligned,so that their dipole moments coincide with the nanotube axis. Inturn, inside CNT (7, 7), the solvent dipole moments are perpendic-ular to the CNT axis. Such configuration of the confined acetonitrileallows a bigger number of molecules to be encapsulated inside thetube of the same size. Thus, two maxima for the nitrogen atoms(Fig. 6a) correspond to the neighboring ACN molecules locatedalong the nanotube axial direction. Their antiparallel dipole mo-ments are oriented towards the CNT sidewall. Both CNT (6, 6)and CNT (7, 7) show single-file chains of liquid but with differentorientations in reference to the nanotube sidewalls. Importantly,Fig. 6b proves that for all nanotubes the complete filling with ace-tonitrile (10 nm) occurs. For all investigated nanotubes it is per-formed within the first 100 ps of run.

The repacking stage for the CNT (11, 11) (Fig. 7) case is presum-ably connected with the central solvent layer which can be formedonly after the two parietal layers of the confined liquid are equili-brated. For smaller tubes this stage (Fig. 2) is not observed since

they have no central liquid layer due to their particular sizes(Fig. 6a).

3.5. Dielectric constant of confined acetonitrile

The molecular single-file patterns of the confined polar liquidshould result in a specific dielectric constant as was recentlyshown for liquid water [37]. For acetonitrile, the dielectric con-stants, e, of 1.01, 1.02, 1.08 and 1.22 were obtained for CNT (6, 6),CNT (7, 7), CNT (9, 9) and CNT (11, 11), respectively. These valuesare in good agreement with [37] for the same narrow tube lengthsexhibiting single-file liquid structures. Note, the experimental bulkvalues for water and acetonitrile are e = 80 and e = 36, respectively.The present ACN force field model slightly underestimates e giving26 instead of 36 for pure bulk liquid [32]. According to [37], atmuch bigger nanotube lengths (hundreds of lm), the dielectricconstants of the confined dielectric media is expected to grow sig-nificantly (up to 10 000). This fact favors using narrow carbonnanotubes to make supercapacitors even more efficient providedthat the penetration of the electrolyte solution is complete.

4. Conclusions

Molecular dynamics simulations were performed to investigatethe filling process of the degasified narrow single-walled carbonnanotubes with liquid acetonitrile at different temperatures andpressures. It is found that the filling rates are unexpectedly fastand weakly dependent from the nanotube diameter. Moreover,the changes of ambient temperature and pressure do not signifi-cantly affect the filling rate. This is unexpected since the diffusionof the bulk ACN increases significantly as temperature grows. Theability of small hydrophobic carbon nanotubes to be completelyfilled with acetonitrile is an important feature for efficient superca-pacitors [24–29]. It can be also found useful for the modern nano-fluidic devices that are actively developed nowadays.

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