Journal of Colloid and Interface Science

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1 Journal of Colloid and Interface Science 391 (2013) Contents lists available at SciVerse ScienceDirect Journal of Colloid and Interface Science Detecting adsorption space in carbon nanotubes by benzene uptake Marek Wiśniewski a, Piotr A. Gauden a, Artur P. Terzyk a,, Piotr Kowalczyk b, Agnieszka Pacholczyk a, Sylwester Furmaniak a a N. Copernicus University, Department of Chemistry, Physicochemistry of Carbon Materials Research Group, Gagarin Street 7, Toruń, Poland b Nanochemistry Research Institute, Department of Chemistry, Curtin University of Technology, P.O. Box U1987, Perth, 6845 Western Australia, Australia article info abstract Article history: Received 9 August 2012 Accepted 11 September 2012 Available online 4 October 2012 Keywords: Adsorption Adsorption from solution Adsorption from gaseous phase Carbon nanotubes Benzene GCMC simulations Experimental results of benzene and nitrogen adsorption from gaseous phase and benzene adsorption and kinetics of the process from aqueous solution, measured on a series of eight commercial closed carbon nanotubes, are presented. Additionally we show the results of adsorption on compressed nanotubes. Using simple analytical approach and the analysis of adsorption and kinetics results it is concluded that in the architecture of nanotubes very important role has been played by isolated nanotubes. Ó 2012 Elsevier Inc. All rights reserved. 1. Introduction It is generally accepted that there are at least three possible types of adsorption centres on closed nanotube bundles (see Fig. 1) namely: interstitial channels, grooves and external tube walls [1]. Among those sites different defects are also distributed [1,2]. According to adsorption nomenclature external tube walls can be called primarily adsorption sites while grooves and interstitial channels can be called secondary adsorption sites. LaBrosse et al. [3] concluded that better fit to experimental data can be obtained assuming that nanotube bundles are heterogeneous, i.e. nanotubes differ in diameters. Since the contribution of different adsorption centres (we can call this architecture of bundles) depends mainly on the preparation procedure it is obvious that it is different for different nanotubes. Thus, for example Agnihotri et al. [4] concluded that the pore width of interstitial channels depends on the diameters of adjoining nanotubes but that of grooves is irrespective of the size of neighbouring nanotubes. The adsorption interstitial channel was envisioned as a partial slit pore of width equal to 0.34 nm. It is also interesting that Komarneni et al. [5] while studied benzene desorption from carbon nanotubes concluded that nanotube thickness has influence on the type of adsorption sites, due to differences in electronic structure of bundled and isolated nanotubes. Corresponding author. Fax: address: aterzyk@chem.uni.torun.pl (A.P. Terzyk). URL: (A.P. Terzyk). Wang et al. [6] studied adsorption of organics from aqueous solutions and observed the increasing maximum adsorption value (calculated from the fitting of Dubinin Radushkevich model to experimental data) with the rise of surface area of carbon nanotubes. At the same time they observed the decrease in maximum adsorption with the rise in molecular volume of a sorbate. Detailed discussion on the surface area of closed and opened nanotubes was reported [7]. We discussed different empirical correlations confirming, that during adsorption process nanotubes behave independently [7]. In the current study we try to check the contribution of all three adsorption centres to the architecture of the series of eight closed carbon nanotubes. Benzene is treated as the probe molecule. Benzene adsorption measurements from aqueous solution is often studied on nanotubes since it is important environmental problem [8 10]. Measuring adsorption from solution as well as adsorption from gaseous phase we prove that the architecture shown in Fig. 1 is observed only at the places of tube contacts, and the isolated tubes play the most important role in adsorption. 2. Experimental 2.1. Nanotubes Eight commercial, high purity, closed carbon nanobubes (provided by three producers) are investigated. The tubes of series A were single-walled (labeled as A-0) as well as multi-walled carbon nanotubes (labeled as A-1, A-2, and A-3) from Nanostructured & /$ - see front matter Ó 2012 Elsevier Inc. All rights reserved.

2 M. Wiśniewski et al. / Journal of Colloid and Interface Science 391 (2013) (H-1) does not appear to contain single-walled tubes. It contained multiwalled tubes. The so-called double walled tube sample (labeled H-2) does in fact contain some double-walled tubes, but mainly tubes with three or more layers are present. To check the influence of compression on the architecture of nanotubes we prepared the samples of A-1 and H-1 nanotubes using hydraulic press at exerting by 15 min the pressure 200, 500 and 600 atm Adsorption from aqueous solution Fig. 1. Potential adsorption centres on closed carbon nanotubes. Table 1 Characteristics of studied carbon nanotubes: diameter (D exp ) and number of walls (n w,exp ), the BET surface area (S BET ) calculated from nitrogen adsorption data, and benzene adsorption data (a) from aqueous solution (T = 303 K). Nanotube D exp (nm) n w,exp S BET (m 2 /g) a (mol/g) A a (2 b ) 1 2 a (1 b ) A-1 <8 a (6 b ) 4 7 a (6 b ) A a (11 b ) a (12 b ) A a (20 b ) a (24 b ) H a (7.7 b ) 2 4 a (3 b ) H-2 4 a (4 b ) 2 5 a (4 b ) H-3 <10 a (10 b ) a (15 b ) B 15 a (15 b ) a (20 b ) Tube diameters were published previously [12,13]. Surface areas determined using nitrogen adsorption data taken from [12,13]. a Data provided by producer. b Maximum values for the distribution of diameters. Amorphous Materials (Nanoamor, Houston, TX, USA). Second series (labeled as H) contained single-walled (H-1), double-walled (H-2) and multi-walled carbon nanotubes (H-3) produced by Helix Material Solutions (Richardson, TX, USA). Finally we also studied multi-walled carbon nanotubes from Bayer (Bay Tubes, Germany) labeled as B. Previous HRTEM studies of H series [7] revealed that the sample of so-called (by the producer) single walled nanotubes Saturated solution of benzene at 300 K was prepared. Benzene adsorption values were measured using a flow system constructed in our laboratory according to the Polish Pharmacopea requirements [11 14]. A well known mass of carbon material was placed inside the chamber and thermostated in flow water (50 ml/h). Sixway valve was used to switch water into the solution containing benzene. Flow rates (50 g/h) were controlled with a mass flow controllers with the accuracy less than 0.1 %. All measurements were performed at 303 K. Connection of flow system on-line to the UV vis spectrophotometer (JASCO V-660, Japan) was used (k = 254 nm) to guarantee the quantitative analysis of the observed phenomena. Simultaneously kinetics of the adsorption process was measured Adsorption from gaseous phase Nitrogen adsorption isotherms were measured at T = 77 K using ASAP 2010 (Micromeritics, Norcross, GA, USA) sorption apparatus. Benzene adsorption isotherms were measured (T = 298 K) using typical volumetric apparatus with Baratron pressure transducers (MKS Instruments, Germany) up to the relative pressures equal to ca. 0.7p/p s [15 18]. Before measurements all carbon nanotube samples were desorbed in vacuum at T = 453 K. Detailed experimental procedures as well as information on used calorimetric system were published previously (for example see [15 18]) Molecular simulation in Grand Canonical ensemble Simulation studies of nitrogen adsorption in multi-walled carbon ((72,0), (64,0), 56,0)) nanotubes can be performed assuming a diatomic molecule (see [7] and reference therein). Thus in this study nitrogen molecule was modelled using the double LJ (but Fig. 2. The comparison between surface areas (S BET or S theor ) of carbon nanotubes and the tube diameter (D exp or D theor ).

3 76 M. Wiśniewski et al. / Journal of Colloid and Interface Science 391 (2013) Fig. 3. The relation between the number of walls forming a nanotube and nanotube diameter (open circles the ranges of n w,exp taken from Table 1, closed circles average n w,exp values, solid line linear approximation for closed circles, diamonds theoretical relation (n w,theor ) for mutiwalled nanotubes) (a) and the dependence between the number of carbon atoms forming a nanotube (N C ) and tube diameter (D) (b). three centre) model of TraPPE type. Two of three centres located on nitrogen atoms of a molecule are the Lennard Jones centres and possess point charges, while the third centre (located at a half-distance between the mentioned two) is only a point charge. We use the cut-offs for electrostatic interactions but this is used for whole molecules i.e. if the centres of mass of two molecules are located at a distance smaller than r cut,c the sum of interactions between all pairs of charges occurring in both molecules is calculated, otherwise the electrostatic interactions are neglected. In this study this distance (r cut,c ) is assumed as equal to 1.5 nm. We performed simulations for a bundle containing three nanotubes separated at the distances dx = 0.34 nm, 2dx, 5dx, 6dx, and 8dx, respectively (see Fig. 9 for details). Nitrogen adsorption isotherms (77.3 K) were simulated using the classical Grand Canonical Monte Carlo method. The cubicoid simulation boxes with a tube placed in a box centre (along z axis) having dimensions nm were applied. Periodic boundary conditions were used in all three directions, and the internal space of a tube was assumed as inaccessible for adsorbed molecules. For each adsorption point iterations were performed during the equilibration, and next equilibrium ones, applied for the calculation of the averages (one iteration = an attempt to change the state of the system by creation, annihilation, rotation or displacement). The probability of attempts of changing a system state by creation, annihilation, and rotation and displacement (the latter one is connected with the change in angular orientation) were equal to: 1/3, 1/3, 1/6 and 1/6. 3. Results and discussion 3.1. The origin of relationship between adsorption and tube diameter Obtained experimental data of benzene adsorption from aqueous solution together with characteristics of nanotubes are collected in Table 1. In this table the experimental tube diameters (D exp ) and the number of walls (n w,exp ) detected for the analysis of the series of HRTEM images are also shown. Considering the data from Table 1 one can observe the correlation between surface area calculated from nitrogen adsorption data (S BET ) and the diameter of carbon nanotubes (D exp ). To analyse this correlation we performed theoretical calculations, assuming the d CC value as equal to nm and the mass of carbon M C = 12 g/mol. The calculations were performed for tubes with chirality (n,0) changing n value from 13 up to 260 (20 structures). Tube diameters (D theor ) were calculated using the well-known equation:

4 M. Wiśniewski et al. / Journal of Colloid and Interface Science 391 (2013) Fig. 4. The relationship between benzene adsorption from aqueous solution and tube diameter (a), the number of benzene molecules adsorbed on external surface of nanotubes plotted as the function of tube diameter (b) and the dependence between percentage contents of benzene and tube diameter (c). D cyl ¼ d CC ½3ðn 2 þ nm þ m 2 ÞŠ 1=2 =p increasing obtained D cyl values by the value of carbon atom diameter (r cc ) equal to 0.34 nm. ð1þ To calculate the value of surface area we assumed the average tube length (H cyl ) as equal to 8.52 nm (it should be noted that infinitely-long carbon nanotubes are studied). This length is chosen because it is sufficient to imitate the properties of nanotubes in

5 78 M. Wiśniewski et al. / Journal of Colloid and Interface Science 391 (2013) Fig. 5. Top panel: lines benzene vapour adsorption isotherms (T = 298 K), solid horizontal lines show the values of adsorption from aqueous solution (a) and nitrogen (T = 77 K) adsorption desorption isotherms (b). Bottom panel: the same isotherms plotted in logarithmic scale. computer simulations [13]. Moreover, it is important to point out that the assumption of different tube length does not influence on the final results of presented below considerations. Nanotube accessible geometric surface areas (S theor ) [19 21] were calculated from: S theor ¼ H cyl P cyl where P cyl is the tube perimeter, equal to: P cyl ¼ 2p½ðD cyl þ r CC þ r NN Þ=2Š In Eq. (3) r NN is the nitrogen Lennard Jones collision diameter equal to nm [15]. It should be noted that in the current studies similar procedure of calculation is considered as implemented in the VEGA ZZ package (i.e. leading to so-called accessible surface area) [19,22]. Since the BET surface area is expressed per mass unit (i.e. usually m 2 /g) one must determine the number of carbon atoms (N C ) forming a nanotube. For assumed tube length (H cyl ) it is easily to show that the linear relation (for SWNT of type (n,0)) occurs, given by: N C;SWNT;theor ¼ 80n Calculated from geometric consideration relation between S theor and D theor is compared with relation determined from experiment in Fig. 2 (S BET vs. D exp ). As one can observe from the data collected in Fig. 2 the assumption that all studied nanotubes are isolated single-walled ð2þ ð3þ ð4þ (S SWNT,theor ) does not lead to the satisfactorily recovering of experimental correlation; however, we observe similarity between shapes of the both curves. As it is shown in Table 1 only for the tubes A-0 we can assume that the number of walls approaches 1. For all remaining systems this number should be larger. In order to calculate the values of n w,theor for twenty (n, 0) MWNTs the average, experimentally determined, values of n w,exp are studied (Table 1 and Fig. 3a). In the other words, the linear approximation describing experimental n w,exp,av vs. D exp is proposed. Summing up, knowing the outer diameter of modelled nanotubes it is easy to estimate the n w,theor assuming the similarity of both, i.e. experimental and theoretical, values shown in Fig. 3a. The final results of S MWNT,theor (for the respective values of n w,theor and D theor ) are collected in Fig. 2. This plot leads to quite good overlap between theoretical and experimental results (Fig. 2). It should be noted that we obtained similar results as published by Peigney et al. [23] calculated based on the advanced mathematical calculations. However, the mentioned above authors studied, in contrast to this study, so called van der Waals surface. They also discussed the influence of the existence of bundles on the relationship S MWNT,theor vs. D theor. From the analysis of the theoretical considerations it is seen that for this architecture of the nanotubes the estimated surface area is lower in comparison with isolated ones. It can be concluded that for tubes having diameter larger than ca. D = 15 nm we do not observe remarkable influence of curvature

6 M. Wiśniewski et al. / Journal of Colloid and Interface Science 391 (2013) Fig. 6. The influence of the benzene molecule specific surface area, x (literature range: nm 2 [32], customary value: nm 2 [32], and estimated from computer simulations [19] (i.e nm 2 ) on the relationship between surface area of nanotubes calculated from benzene adsorption at the B- and C-points and from application of the BET model to low-temperature N 2 adsorption data. on surface area value. One can also note, that for the flat surface (D? 1) a reasonable value of ca m 2 /g is observed, and this is the typical value recorded for graphite (or graphitised carbon black) [24,25]. The most important conclusion of this part of the study is that taking into account experimentally determined number of carbon walls in nanotubes leads to the agreement between geometric surface area calculated for isolated tubes and the surface area calculated using the BET model. Note that agreement between both types of surface areas has been also observed for different adsorbents for example carbon nanotubes [19,26,27], ideal planar adsorbents [28] and MOFs [29], where the BET surface areas are almost the same as geometric ones. In the presented approach only ideal nanotubes are discussed and in this model well-documented presence of defects is neglected. It is important to mention that the assumption of the non-ideality of the inner tubes leads to better correlation between theoretical and experimental curves shown in Fig. 2. On the other hand, if we take into account the presence of larger number of grooves in our theoretical approach, worse correlation between theory and experiment than reported in this figure will be recorded The relationship between benzene adsorption and tube diameter One can consider the number of benzene molecules adsorbed on nanotubes, N benz. It is important especially in Molecular Dynamics simulations where before equilibration of the system it is necessary to place the correct number of molecules into simulation box. Below a simple procedure is presented showing how to calculate the number of molecules for arbitrarily chosen adsorption values. One can start from the calculation of the number of carbon atoms forming a nanotube (N C ) having diameter (D theor ). This is very simple for calculation since the tube length and the number of walls are known. The respective theoretical relationships for twenty MWNTs is proposed and the final results are collected in Fig. 3b. Because the parameters of relation between N C vs. D theor, as well as for studied nanotubes D exp are known, one can easily calculate the number of carbon atoms for theoretical systems (see Fig. 3b). Fig. 4a shows the dependence between benzene adsorption and tube diameter. Experimental data were fitted by equation (see Fig. 4a inset), and knowing the parameters and the number of

7 80 M. Wiśniewski et al. / Journal of Colloid and Interface Science 391 (2013) Fig. 7. The dependence between adsorption at selected relative pressures and tube diameters for benzene (a) and nitrogen (b) adsorption data. carbon walls forming nanotube (Table 1) one can easily estimate the number of adsorbed molecules (note that presented procedure is valid not only for benzene but also for other organic compounds). The results for zigzag tubes (changing n value from 13 up to 260) are shown also in Fig. 4a (these values are calculated on the basis of theoretical relationship related a exp and D exp ). It is interesting that as in the case of the data collected in Fig. 2, also in this case we observe realistic values for the case of flat surface (D? 1). Namely, it was shown previously [30] that the value of benzene adsorption from saturated solution, determined for adsorption on graphitised carbon black, is around ca mol/g. As one can see from Fig. 4b the number of adsorbed benzene molecules increases almost linearly with D. Finally, the dependence between percentage contents of benzene adsorbed on adsorbents and D is shown in Fig. 4c. One can see that the percentage content of benzene depends on tube diameter and varies from ca. 50 down to 20% Relationship between surface area of carbon nanotubes calculated from nitrogen and benzene vapour adsorption isotherms Fig. 5a collects benzene vapour adsorption isotherms (T = 298 K), and the values of adsorption from aqueous solution (Table 1). Using the data collected in this figure and the standard B-point and C-point methods, the values of surface areas were calculated [19,31,32]. The C-point method was tested because it was shown using molecular simulations [19] that the C-point adsorption value leads to the most realistic monolayer capacities, and obtained surface areas of nanotube bundles are almost the same as the geometric ones. Fig. 6 shows that we observe a linear relationship between surface area of nanotubes calculated from benzene adsorption (B- and C-points) and from nitrogen adsorption data. Similar relationship was recently observed for adsorption of alcohols [33] as well as for adsorption of phenols from aqueous solutions [12,13]. The best agreement between both values of surface areas for B- point method is recorded if one assumes the value of benzene specific surface equal to nm 2 [32]. In contrast, for the C- point method the best agreement is recorded using x equal to 0.25 nm 2 [32]. Fig. 7 collects adsorption data (taken from Fig. 5) plotted for selected relative pressure values, as the function of tube diameters. One can observe the progressive rise in adsorption with the rise in relative pressure; however, the most important is that the shapes of the curves are similar to this presented in Fig. 4a. The regular changes in adsorption suggest that no enhancement of adsorption potential in micropores is observed and, as a consequence, the tubes form only mesoporous interstitial channels.

8 M. Wiśniewski et al. / Journal of Colloid and Interface Science 391 (2013) Fig. 8. Nitrogen adsorption isotherms for nanotubes A-1 and H-1 under and/or without compression for 15 min. To confirm this idea we performed additional measurements, i.e. two of the studied nanotubes were compressed using hydraulic press. Fig. 8 shows the results of nitrogen adsorption isotherms measured for nanotubes of A-1 and H-1 series under compression. As one can easily observe for both series we see the progressive decrease in maximum adsorption, i.e. the decrease in total pore volume under compression, but at the same time, no remarkable changes in the adsorption for monolayer (i.e. at the B-point) are observed. The behaviour of adsorption isotherms under compression can be explained basing on the GCMC simulation results (see Fig. 9). The progressive approaching of nanotubes from the distance 6dx down to dx (i.e nm) leads to the same effect as observed on experimental isotherms for A-1 and H-1 nanotubes; the B-point remains the same and we only observe the decrease in the volume of pores and the vanishing of the phase transition. Contrary, only for the case of osculating nanotubes (dx = 0.34 nm) we observe the decrease in the B-point value on simulated isotherm since the places of the contacts of nanotubes are inaccessible for molecules. It should be pointed out that this type of study will be continued in future. However, generally obtained results demonstrate that isolated nanotubes under compression approach one to the other, and confirm our idea about the importance of isolated nanotubes in architecture of the bundle. The most important conclusion of this part of the study is that from the experimental point of view, to avoid low temperature nitrogen adsorption experiment, one can measure benzene adsorption at the ambient conditions and to obtain similar surface area values as from nitrogen adsorption. The studies of adsorption from gaseous phase for initial and compressed nanotubes confirm our idea about the importance of isolated nanotubes.

9 82 M. Wiśniewski et al. / Journal of Colloid and Interface Science 391 (2013) Fig. 9. The changes in shapes of nitrogen adsorption isotherms (77.3 K) simulated for bundles of carbon nanotubes (multi-walled nanotubes ((72,0), (64,0), (56,0)) the average diameter as for A-1 series [13]) with the progressive rise in the separations between tubes. Snapshots show the configurations of nitrogen molecules adsorbed (p/ p s = 1) we only show central part of a simulation box, molecules adsorbed in monolayer are marked in blue. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) 3.4. Kinetics of benzene adsorption from aqueous solution To describe experimental data of benzene kinetics of adsorption from aqueous solution, we used the pseudo second order (PSOE) equation [34 38]: dn dt ¼ k 2ðN e NÞ 2 in the form: t N ¼ 1 þ 1 t k 2 N 2 N e e ð5þ ð5aþ This model was applied because it leads to good fit to experimental data and contains only two the best fit parameters (therefore it is simple). As it was pointed out by Azizian [37] this equation describes experimental kinetics data if the initial concentration of a solute is not too high. On the other hand, Ho et al. [38] derived this equation assuming the presence of two types of adsorption sites on a surface. Therefore, PSOE equation was fitted to experimental data using typical linearisation procedure (Fig. 10). Fig. 10 shows kinetics of adsorption curves, the same curves but normalised (divided by the maximum adsorption value), the presentation of data in the coordinates of linear PSO equation form (Eq. (5a)), and the fit of theoretical model to experimental data for adsorption on A-0 tubes (chosen arbitrarily). As one can observe the relative rate of adsorption decreases with the rise in specific surface areas of nanotubes. This is clearly seen in Fig. 11 where the dependence between k 2 of the PSOE model (Eq. (5)), the values of tube diameters and the BET specific surface area of studied nanotubes are plotted. The existence of the relationships of this type (Fig. 11a and b) suggests the dependence between energy of benzene diffusion, tube diameter, and the surface area. However, further studies are necessary to check this relation in detail. Interesting is that we observe very good correlation between maximum adsorption obtained from fitting of Eq. (5a) to experimental data and the experimental maximum adsorption value. Thus it can be concluded that the PSO model predicts maximum adsorption correctly for the case of benzene adsorption on studied carbon nanotubes. Finally in Fig. 12 the relation between adsorption at chosen times and the tube diameter is plotted. The curves have similar shapes as plotted in Figs. 4b and 7, confirming importance of isolated nanotubes in adsorption process. 4. Conclusions Presented in this paper results lead to the following conclusions about studied closed carbon nanotubes. Benzene adsorption isotherm data measured at ambient temperature can be used for calculation of the specific surface areas of nanotubes, and one can easily obtain agreement between

10 M. Wiśniewski et al. / Journal of Colloid and Interface Science 391 (2013) Fig. 10. Kinetics of adsorption curves (maximum adsorption values are collected in Table 1) (a), the same curves but normalised (divided by the maximum adsorption value) (b), the presentation of data in the coordinates of linear PSO form (Eq. (5a)) (c), and the fit of theoretical model to experimental data for adsorption on A-0 tubes (d). Fig. 11. The dependence between k 2 of the PSOE model (Eq. (5a)) and (a) the value of tube diameter and (b) BET specific surface area of studied nanotubes. The dependence between maximum adsorption obtained from the fitting of Eq. (5a) to experimental data and the experimental maximum adsorption values (c). Note that k 0 is a constant (equal to 1 g s 1 mol 1 ) introduced for the purpose of reduction of units.

11 84 M. Wiśniewski et al. / Journal of Colloid and Interface Science 391 (2013) Fig. 12. Adsorption values plotted as the function of tube diameters from kinetic curves (Fig. 10) for different times. determined in this way areas and the areas obtained from low temperature nitrogen adsorption isotherms. In this way one can avoid more complicated low temperature measurements. Kinetics of benzene adsorption from aqueous solution is well described by the PSO equation and the constant of this model is related to the diameter of carbon nanotubes, confirming the relation between the energy of adsorption and tube curvature. Proposed in this study new approach of calculation of the number of adsorbed molecules can be applicable in molecular simulations for preparation of simulation boxes. Presented experimental results demonstrate the existence of the relationship between surface area of nanotubes and tube diameter. Using simple geometric considerations we show that this relationship can be recovered by theoretical calculations assuming that isolated nanotubes play more important role in bundle architecture as it has been assumed till now. The agreement between experiment and theory is not perfect (Fig. 2), but we consider in our approach only ideal nanotubes, neglecting the well-documented presence of defects. It is important to mention that if we take into account the presence of larger number of grooves in our theoretical approach, we observe worse correlation between theory and experiment than reported on Fig. 2. Proposed role of isolated nanotubes is confirmed by the results of low temperature nitrogen adsorption, benzene adsorption and the progressive changes in the shapes of adsorption desorption isotherms measured for the tubes under compression. Especially compression results are very important and show, that during compression there are negligibly small changes in the value characteristic to the B-point while maximum adsorption decreases. At the same time hysteresis loop becomes smaller and smaller. This is in agreement with GCMC simulation results and shows that during compression we observe approaching of nanotubes with the simultaneous decrease in secondary porosity between them. Therefore taking this into account we propose the arrangement of nanotubes shown schematically in Fig. 13. As one can see, generally accepted model of tube bundles plotted in Fig. 1 is valid only at the places where nanotubes are osculating, and in our opinion isolated nanotubes are more important in adsorption processes as it was presumed till now.

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