The Behavior of Benzene Confined in Single Wall Carbon Nanotube
aa r X i v : . [ c ond - m a t . m e s - h a ll ] N ov The Behavior of Benzene Confined in Single WallCarbon Nanotube
Yu. D. Fomin(1,2), E.N. Tsiok(1) and V.N. Ryzhov(1,2) ∗ July 26, 2018
Abstract
We present the molecular dynamics study of benzene molecules confined into thesingle wall carbon nanotube. The local structure and orientational ordering of benzenemolecules are investigated. It is found that the molecules mostly group in the middledistance from the axe of the tube to the wall. The molecules located in the vicinity ofthe wall demonstrate some deviation from planar shape. There is a tilted orientationalordering of the molecules which depends on the location of the molecule. It is shownthat the diffusion coefficient of the benzene molecules is very small at the conditionswe report here.
Keywords:
Benzene, carbon nanotubes, orientational order, structure. ∗ (1)Institute for High Pressure Physics Russian Academy of Sciences, (2) Moscow Institute of Physicsand Technology (State University) UMMARY
It is well known that confining a liquid into a pore strongly alters the liquid behavior.Investigations of the effect of confinement are of great importance for many scientific andtechnological applications. Here we present a study of the behavior of benzene moleculesconfined in the single wall carbon nanotubes. We find that the molecules of benzene mostlygroup in the middle distance from the axe of the tube to the wall. The molecules locatedin the vicinity of the wall demonstrate some deviation from planar shape. There is noany strong ordering in the system, however, there is a tilted orientation of molecules whichdepends on the location of the molecule.
INTRODUCTION
It is well known that materials confined in nanoscale dimensions have properties that stronglydiffer from the properties of bulk systems. This is due to the reducing the dimensionalityof the system and interface effects. Confining boundaries bias the spatial distribution of theconstituent molecules and the ways by which those molecules can dynamically rearrange.These effects play important roles in the thermodynamics of the confined systems and in-fluence the topology of the phase diagram . The confinement can drastically change thethermodynamic parameters of phase transitions and even form the new phases due to in-teraction with the boundaries. For example, the melting temperature of confined benzenedepends on the form and size of the nanopores. In most cases the melting point of the solidin the pore decreases with decreasing pore diameter . In Ref. the melting behavior of theconfined benzene was discussed for different types of porous confinement. It was shown thatno crystallization is observed in the cylindrical pores below the pore size about 4 . nm . Thisvalue corresponds approximately to 10 molecular diameters. It was shown that benzenedoes crystallize in 4 . nm pores but vitrifies in narrower pores . On the other hand, as itwas shown in Refs. , experimental freezing of tetrachloromethane was observed in acti-vated carbon fibers for the pore widths up to 0 . nm (less than two molecular diameters),whereas cylindrical pores of several molecular sizes are necessary to have crystallization of2etrachloromethane molecules.The general motivation for the study of different nanoconfined systems follows from thefact that there are a lot of real physical and biological phenomena and processes that dependon the properties of such systems and play an important role in the different fields of mod-ern technology. However, nanoconfinement is considerably interesting also due to the newphysics observed in these systems. For example, fluids confined in carbon nanotube exhibitformation of layers, crystallization of the contact layer and a superflow which depends onthe confinement .In this paper, we present a systematic molecular dynamics study of single wall carbonnanotubes (SWCN) doped with benzene ( C H ) molecules. Carbon nanotubes are widelyinvestigated first of all because of their potential applications in material science, biotechnol-ogy and medicine . Introducing molecules into carbon nanotubes can drastically changethe electronic properties of nanotubes. Benzene molecules are widely used for study theinfluence of doping on the properties of carbon nanotubes because of their small size whichpermits them to be encapsulated easily inside carbon nanotubes of different diameters. Theorientation and the position of the benzene molecules inside the carbon nanotubes determinethe optical, magnetic and electrical transport properties of the whole system .In Ref. a semi-analytical model for the interaction of a benzene molecule and a car-bon nanotube was proposed. It was shown that the orientation of the molecule drasticallydepends on the radius of the nanotube. The authors found that horizontal, tilted and per-pendicular equilibrium configurations are possible for the benzene molecule on the axis of thecarbon nanotube when the radius of it is less than 5 . A . However, when the radius of thenanotube is larger than 5 . A , the equilibrium configurations occur at an offset horizontalorientation.The results of Ref. were obtained for one molecule. The main goal of this article isto study the positional, orientational and dynamic behavior of the ensemble of benzenemolecules in the single wall carbon nanotube.3 ETHODOLOGY
In the present article we study benzene molecules in carbon single wall nanotube by meansof the molecular dynamics simulation. The benzene molecule consists of a ring of 6 carbonatoms. Each carbon is also bonded with a hydrogen atom out of the ring. The radius ofbenzene ring is about 2 . A . If one takes into account the length of the hydrogen bonds thenthe size of benzene molecule is approximately 5˚ A . The radius of the nanotube is 6 . A andthe length is equal to 250 . A . It means that the radius of the nanotube is just a bit largerthen the size of the molecule. We choose this radius because it corresponds to the situationwhen, as proposed in Ref. , one can expect to find the offset horizontal orientation of thebenzene molecules. The tube is oriented parallel to the z axe. The system has periodicboundary conditions in z direction while it is confined in x and y ones. Three systemswere studied: 150 ,
200 and 250 benzene molecules in the nanotube described above. Thelater system corresponds to the density 0 . g/cm which is the density of bulk benzene atambient conditions. All systems were simulated at three temperatures: 300 K , 400 K and500 K . Doing this way we could check the influence of both density and temperature on thebehavior of benzene in nanotubes.We simulate the system in canonical ensemble (constant number of particles N , volume V and temperature T ). The temperature is kept constant by applying Nose-Hoover thermostat.The carbon atoms of the nanotube are held rigid in order to stabilize the system while thebenzene molecules are moved in molecular dynamics runs. The timestep is 0 . f s . So smalltimestep was necessary in order to correctly take into account the motion of hydrogens inthe benzene molecules.All interactions in the system were described by AIREBO interatomic potential . Thispotential is specially developed for simulation of the systems containing carbon and hydrogenatoms, and it allows to consider all interactions in the system in framework of the same model.All simulations were made in lammps simulation package .4 ESULTS AND DISCUSSIONS
The qualitative ideas on the structure of benzene inside nanotube can be obtained from thesnapshots on the system. Fig. 1 (a) shows a part of the nanotube. In order to make theview of the molecules clearer we do not show the tube itself. One can see that the systemdoes not demonstrate pronounced order. Another important conclusion from the snapshotsis that if one looks at a cross section of the tube (Fig. 1 (b)) one can see that the centersof mass of the molecule do not approach both the central axe and the walls and prefer tobe somewhere in the middle. In Ref. a simple model of benzene in carbon nanotube wasproposed. Basing on this model, the authors studied possible locations and orientations ofbenzene molecules inside the nanotube. It was found that for the tube radius R < . A the equilibrium position of the molecule belongs to the central axe while for higher radiusesthe position moves apart. Our calculations are made at R = 6 . A in order to compare ourresults with this publication.The described features can be easily seen from the density profiles of different species.Fig. 2 shows the profiles of number density of carbon and hydrogen species and of the centersof mass of the molecules. The largest peak of the carbon density distribution corresponds tothe distance 5 . A from the central axe of the tube. After that the curve rapidly vanish. Sothe closest approach of carbon atoms to the wall of the tube is approximately 1 . A .However, the main peak of the centers of mass of the molecules is closer to the center(Fig. 2). It corresponds to the distance r cm = 3 . A . The second peak of the centers ofmass density is almost of the same height and located at r cm = 5 . A .One can see that the closest peak to the wall is the one of hydrogen distribution. Themaximum is located at 5 . A , i.e. approximately 1˚ A from the wall. So close approach ofhydrogens to the nanotube can mean that some kind of effective hydrogen bonds appear inthe system.Importantly, all distributions vanish at r = 0 which means that at this density theparticles try to avoid the central axe of the tube.Fig. 3 (a) and (b) demonstrate the influence of the total density N/V on the local densitiesdistribution of carbon and centers of mass of the molecules. As one expects from general5igure 1: (a) Snapshot of benzene molecules in the SWCN. The nanotube itself is not shown.(b) Cross section of the system. N = 250, T = 300 K .6 C H CM ( r ) r,A N=250 T=300K
Figure 2: Radial distribution of number densities of carbon, hydrogen and centers of massof the molecules for N = 250 and T = 300 K . C r,A N=250
N=200
N=150 (a) (b)
N=250
N=200
N=150 C M r,A Figure 3: Radial distributions of number densities of (a) carbon and (b) centers of mass ofthe molecules for different densities of benzene at T = 300 K .7 T=300K
T=400K
T=500K C r,A (a) (b) C M r,A T=300K
T=400K
T=500K
Figure 4: Radial distributions of number densities of (a) carbon and (b) centers of mass ofthe molecules for different temperatures. The number of benzene molecules inside the tubeis N = 150.point of view, as the density increases the peaks become more pronounced. In the case ofthe local density of carbon one can see that at the lower number of molecules ( N = 150 and200) the peaks are almost of the same height. However, as the number of particles increasethe peaks next to the wall rapidly increase while the increase of the second peak is rathermodest.In the case of the distribution of the centers of mass the situation is more complex. Atthe smallest number of molecules ( N = 150) the main peak is located at 3 . A . As thenumber of molecules increases to N = 200 this peak rises up. However, further densificationof the system leads to placing the molecules closer to the wall and the second peak ( ≈ A )starts to increase while the first one even decreases with respect to the previous values.Figs. 4 (a) and (b) demonstrate the influence of temperature on the density profiles ofcarbon and centers of mass of the molecules. As one can expect, the peaks become higheras the temperature decreases.In our previous work we studied benzene in graphite and amorphous carbon slit pores .It was shown that in the case of graphite walls and relatively small pore sizes (the dis-tance between the walls below approximately 14 . A ) benzene molecules form graphite-like8heets. This phenomenon was related to the close match of the carbon-carbon bond lengthin graphite and in benzene ring. Basing on this observation one can ask a question whetherbenzene molecules located in the vicinity of the nanotube mimic the shape of the wall. Ifso, the molecules loose theirs planar shape and become scrolled.In order to estimate the degree of deviation from planar shape of the benzene ring weemploy the following procedure. Denote all carbon atoms in a ring by numbers from 1 to 6and define the vectors connecting them: 1 −
2, 2 −
3, ..., 6 −
1. Now we take three neighboringatoms, say, 1 , ,
3. Since they do not belong to the same straight line there is a unique planecontaining these points. The normal vector of this plane can be identified as a vector productof the vectors 1 − −
3. If we repeat this procedure for all six carbons of the ring weobtain 6 vectors perpendicular to the ring. If the molecule is ideally planar then all thesevectors should be parallel. One can check if these vectors are parallel by taking theirs scalarproduct. One can construct 15 different pairs. We compute all 15 scalar products and sumup the absolute values of the resulting products. In the case of ideal plane the result shouldbe equal to 15, so we divide the final result over 15. We denote the final quantity as P .It measures the ”planarity” of the ring. By definition the planarity can be less or equal tounity. The deviation of P from unity can characterize the deviation of benzene moleculefrom planar shape.In order to check the validity of the P parameter we calculate its value for pure bulkbenzene at ambient conditions. We find it to be P = 0 .
97 which corresponds to the case ofalmost planar rings. In our previous publication we described the structure of benzene ingraphite slit pore . For the case of the pore size 12 . A we find P = 0 .
95 which is veryclose to the pure benzene result. Fig. 5 shows the P parameter for the case of N = 200 atthree different temperatures. One can see that up to the distance r = 4˚ A the value of P is0 .
87 which is lower then in the bulk case. Closer to the walls of the tube the planes becomeeven more distorted. The minimum value of P is reached at r = 4 . A which correspondsto one of the peaks of the center of mass density distribution. The magnitude of P at thisdistance is P min = 0 .
53. One can conclude that close to the walls of the tube the rings bendfrom planar shape but the effect is rather weak. The temperature effect on this planarityparameter is negligible and mostly appears in low r limit. The curves at different densities9 P r,A T=300 K
T=400 K
T=500 K
Figure 5: P parameter which characterizes the deviation of the benzene ring from planarshape for N = 200 and different temperatures.also look qualitatively very similar. For this reason we do not show these curves for othernumbers of particles studied in our work.Although the deviation of the rings from planar shape can be quite large one can de-fine the orientational order parameter via second order Legender polynomial P ( cos ( θ )) =1 . cos ( θ ) − . θ is the angle between the normal vector to the plane of a ring and z direction. If the benzene ring is perpendicular to the axe of the tube, P = 1 while if themolecule is parallel to the axe of the tube P = − .
5. The normal vector to the benzene ringwas defined as an arithmetic average of six vectors described above for planarity calculations.Fig. 6 shows the radial distribution of P for N = 250 and T = 300 K , i.e. the highestdensity and the lowest temperature studied. One can see that although there is a small peakat origin the distribution does not demonstrate strong ordering. It means that unlike thecase of graphite slit pores benzene does not have strong orientational order being confinedin cylindrical geometry. In Ref. it was obtained that for the nanotube radius above 5 . A the equilibrium position of a benzene molecule is the one parallel to the tube axe apartfrom the central line. In our simulation we do not find strong orientational order, however,there is a tilted orientation which depends on the location of the molecule. Comparison ofFig. 6 with Fig. 2 shows that inside the layers where the local density is higher, the benzene10 P ( c o s ()) r, A Figure 6: Legender polynomial P ( cos ( θ )) for N = 250 and T = 300 K .molecules are oriented more perpendicular than between the layers. Mean field calculationsin Ref. do not take into account the heterogenous structure of the system and present onlyqualitative tendency in orientations of the benzene molecules.Finally we discuss the dynamic properties of benzene in carbon nanotube. Correct cal-culation of diffusion coefficient requires simulation in microcanonical ensemble. Our calcu-lations are done in canonical one. Although such calculations do not give completely correctnumerical value of diffusion coefficient they allow to get the correct qualitative picture.The radius of the nanotube we simulate is 6 . A which is just above the size of benzenemolecule. It means that the molecules are confined in a very narrow channel. In such anarrow channel the system can be roughly considered as one dimensional. In the case of1 D system one does not expect large diffusion. The particles are strongly caged by theirsnearest neighbors. This is what we observe in our simulation. Fig. 7 shows the mean squaredisplacement in the radial directions and in the direction of the axe of the tube at the lowestdensity ( N = 150) and highest temperature T = 500 K studied. One can see that the meansquare displacement in both directions grows very slowly which means strong confinementof the molecules. The diffusion coefficient in both directions is very small in the limits of theerrors of calculations. 11 .1 1 10 1000.010.11 x +y z r (t) , A t, ps Figure 7: Mean square displacement of centers of mass of the molecules in radial directionand in the direction of the axe of the tube. N = 150, T = 500 K Conclusions
This paper reports simulation study of benzene molecules confined into the single wall carbonnanotube. We study the structure and dynamics of benzene for three densities and threetemperatures. We find that the molecules of benzene mostly group in the middle distancefrom the axe of the tube to the wall. The molecules located in the vicinity of the walldemonstrate some deviation from planar shape. There is no strong ordering in the system incontrast to the semianalytical model, proposed in Ref. , however, there is a tilted orientationof the molecules which depends on the location of the molecule. Comparison of Fig. 6 withFig. 2 shows that inside the layers where the local density is higher, the benzene molecules areoriented more perpendicular than between the layers. Last, we find that benzene moleculesare almost immobile at the conditions we report here. ACKNOWLEDGMENTS
Y.F. also thanks the Joint Supercomputing Center of the Russian Academy of Sciences forcomputational power and the Russian Scientific Center Kurchatov Institute for computa-tional facilities. The work was supported by the Russian Science Foundation (Grant No14-12-00820). 12 eferences
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