Curious Characteristics of Polar and Nonpolar Molecules Confined

Article pubs.acs.org/jced

Curious Characteristics of Polar and Nonpolar Molecules Confined within Carbon Nanotubes (CNT) of Varied Diameter: Insights from Molecular Dynamics Simulation Pooja Sahu and Sk. Musharaf Ali* Chemical Engineering Division, Bhabha Atomic Research Centre, HBNI, Mumbai, India 40085 S Supporting Information *

ABSTRACT: Carbon nanotube (CNT) has emerged as a potential candidate for desalination of salty water as well as for purification of various kinds of gaseous and liquid mixtures which is controlled by the interaction of the fluid molecules within the nanocavity of CNT. It is, therefore, worthwhile to investigate the behavior of both the polar and nonpolar fluid molecules within the nanoconfinement of CNT at the molecular level. In the present study, molecular dynamics simulations have been performed to investigate the structure and dynamics of polar and nonpolar molecules within CNTs. Results show the enhancement of confined density with increase in nanotube diameter. Single file flow of water, methanol, and methane inside CNT(6,6) was diminished with increase in nanotube diameter and converted to layered flow for larger CNTs. Surprisingly, results showed controversial effects of nanotube dimension for dynamics of polar and nonpolar fluids, which has been explained in terms of interaction forces acting between fluid particles and fluid−nanotube wall. The density of states (DOS) results have been found in line with the corresponding velocity autocorrelation function (VACF). Interestingly, the altered H bonding of methanol in the axial and radial direction of CNT(6,6) and CNT(7,7) conceded the reversal effects on rotation degree of freedom (DOF) and translation DOF respectively. However, all such effects were observed to be vanished for the larger diameter of CNTs. Overall, the present study provides an insightful view of flow transition from sub continuum to bulk fluid properties, while moving from small to large diameter CNTs, established with both the polar and nonpolar fluids, which is supposed to be very supportive for understanding of equivalent fluid channels in living cells, and the CNTs would serve as good prototypes for narrow biological channels. regard, understanding of the microscopic interaction of fluid molecules within the small cavity of nanotubes becomes important to predict the influence of CNT confinement on the fluid transport. Apart from this, such studies are supposed to be very supportive for equivalent fluid channels in the living cells.13 CNTs, being stable, simple, and small in size, serve as the best prototypes for these biological channels. Hummer et al.14 was the first one to study the water transport in CNT(6,6). Later on, numerous experimental as well as theoretical studies were devoted to the understanding of structural and dynamical aspects of fluid transport.15−19 However, most of these studies were based on water properties inside nanotube confinement. Studies by Marti and his co-workers20,21 explored the static and dynamic properties of water inside CNTs under a series of ambient and supercritical conditions. Subsequently, Koga et al.22 also focused on phase transition studies of water inside nanotubes. In addition, several researchers23 paid a particular interest in water properties outside CNTs. Hereby, special attention was given to water transport through CNTs and thus

1. INTRODUCTION Nanofluidics have been explored recently for the various fundamental and scientific applications in the diverse fields of biology,1 chemistry,2,3 and medical sciences.4,5 There has been a special curiosity for carbon nanotubes (CNTs), as fluid inside CNTs shows very extraordinary structural and transport properties compared to bulk phase,6−8 which is responsible for very selective and astonishing capacity to store or transfer fluids at nanoscale precision. The task of understanding the fluid flow in the nanoscale environment of CNTs has been a long-lasting open problem with a large set of unique fundamental questions. A significant step in this direction is to predict the transition of fluid transport from continuum to sub continuum regime inside CNTs.9,10 In continuum regime, the fluid behavior is described in terms of infinitesimal volumetric elements. Implication of these volumetric elements to Newton’s second law of fluid transport originates the Cauchy and Navier−Stokes equations, which are further applied to develop the Poiseuille and other continuum-level flow relations.11,12 On the other hand, use of volumetric elements becomes invalid for fluids having molecules of size comparable to the size of the flow domain, and therefore the applicability of continuum-based equations for such systems is doubtful. In this © 2017 American Chemical Society

Received: February 17, 2017 Accepted: June 7, 2017 Published: June 19, 2017 2307

DOI: 10.1021/acs.jced.7b00186 J. Chem. Eng. Data 2017, 62, 2307−2315

Journal of Chemical & Engineering Data

Article

Table 1. Details of the Simulated Systems CNT type

diameter (Å)

length (Å)

Nwater

CNT(3,3) CNT(4,4) CNT(5,5) CNT(6,6) CNT(7,7) CNT(8,8) CNT(9,9) CNT(10,10) CNT(12,12)

4.3 5.6 7.1 8.12 9.45 10.74 12.17 13.54 16.25

15.0 17.0 19.2 20.89 22.10 27.02 28.25 28.25 33.16

250 400 970 1346 1329 1537 1963 1990 2510

Nmethane

Nmethanol

510 496 653 704 715 1026

586 548 644 843 861 1071

box size [nm × nm × nm] 1.5 1.7 2.4 2.7 2.7 2.9 3.2 3.2 3.4

× × × × × × × × ×

1.5 1.7 2.4 2.7 2.7 2.9 3.2 3.2 3.4

× × × × × × × × ×

5.0 6.0 7.0 8.0 8.0 8.5 9.0 9.0 10.0

have been estimated using the Ewald method29 with charge parameters shown in Table S3. The CNTs were kept fixed during the complete simulation with their axis pointing toward the z direction. The systems were equilibrated for the simulation length of 50 ns, followed by 20 ns of production run. Further, the coordinates and velocities were saved after each 4 fs for calculation of dynamic parameters and ∼500 fs for structural properties. MD simulation trajectories were visualized using the VMD graphical package.30 2.2. Model and Methodology. In the present study, we investigate the structure and dynamics of polar and nonpolar fluid molecules within CNTs. The structural properties have been described in terms of density distribution and correlation functions in the axial and radial direction, whereas the dynamics of fluid molecules is explained with the help of diffusion coefficient, dynamic correlation functions such as mean square displacement and velocity auto correlation function, and density of state functions. The details of these calculation parameters are given as follows 2.2.1. Structural Properties. 2.2.1.1. Radial Density Distribution. Radial density distribution was estimated by dividing the considered CNT radial into cylindrical bins with bin width of 0.2 Å, and then finding the density of fluid in each bin. 2.2.1.2. Axial Pair Correlation Function (ACF).6 Another important structural property for the present work is axial correlation function, g(z), which describes the probability of finding the fluid molecule at a distance z from another fluid molecule. For calculation of ACFs, the neighbors around each fluid molecule were distributed into z distance bins and, further, the number of neighbors was averaged for each bin over the complete simulation length. To be noted, all these calculations were performed within the domain of nanotube confinement only. The ACF is calculated using the following expression:

the characteristic properties of water both inside and outside CNTs were reconnoitered. On the other hand, the transport of nonpolar and polar fluids other than water inside CNTs remains largely unexplored. Furthermore, it has been shown that the chemical activity of a nanotube strongly depends on its diameter and helicity.24 Therefore, one might expect an excessive variance in the behavior of fluid molecules confined in the nanotubes of different diameter and helicity, and the objective of this study is to explore these varieties. Although some scattered studies on these subjects have been already done, yet the systematic presentation of their influence is still to be scrutinized. To the best of our knowledge, we have not come across any detailed study on the impact of nanotube diameter for nonpolar fluids. Considering all these, the present work is dedicated to study the behavior of polar as well as nonpolar fluids inside nanotubes. MD simulations have been carried out for different SWCNTs with indices of (n,n) armchair, submerged in the pool of water like strong polar solvent, methanol like intermediate polar solvent, and methane like nonpolar solvent. The diameter of CNTs has been varied from 0.43 to1.66 nm, where a transition from sub continuum to continuum flow is expected with increase in CNT diameter. In addition, the present work classifies the flow transition by studying the correlation between structural properties and molecular transport of the fluids for each CNT.

2. COMPUTATIONAL METHODOLOGY 2.1. Simulation Details. In the present study, the fluid flow was studied through CNTs of diameter 0.43 nm, 0.56 nm, 0.71 nm, 0.83 nm, 0.97 nm, 1.10 nm, 1.25 nm, 1.39 nm, and 1.66 nm, corresponding to single-walled armchair CNTs, i.e., CNT(3,3) CNT(4,4), CNT(5,5), CNT(6,6), CNT(7,7), CNT(8,8), CNT(9,9), CNT(10,10), and CNT(12,12) respectively. Both ends of these CNTs were terminated with graphene sheets having x, y dimension three times the nanotube diameter. The designed CNTs were solvated in a rectangular box filled separately with water, methanol, and methane. Details of these simulated systems are given in Table 1. The LennardJones (L-J) parameters were selected for carbon atom of CNTs. Further, the bond stretching and angle bending were accounted by using harmonic potential. All the simulations were performed using GROMACS25 molecular dynamics package in the NVT ensemble26 at a temperature of 298 K for water and methanol and 136 K for methane. For water, SPC potential27 was used to model the interactions between water molecules, whereas methane and methanol were simulated with OPLS force field parameters.28 The details of all bonding and nonbonding force field parameters are shown in Tables S1 and S2 respectively. The electrostatic long-range interactions

g (z) = γ −2⟨∑ ∑ δ(z − zij)⟩ i

j≠i

(1)

where δ is the Dirac delta function, zij is the axial (z) separation between the ith and jth fluid molecules, both confined inside CNT, and γ = L/N2, where L is the length of CNT and N represents the total number of fluid molecules confined in the nanotube. 2.2.2. Dynamic Properties. During analysis, the fluid molecules confined inside the nanotube were identified and their positions and velocities were stored for all the configurations. The identities of confined fluid molecules are not fixed, but a continuous flow of these molecules through the CNTs is observed. Therefore, for calculation of dynamic correlation functions such as mean square displacement (MSD) and velocity autocorrelation (VACF) function, only those fluid 2308



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molecules were considered which remain inside CNT at least for 10 ps. In other words, only those fluid molecules were selected for dynamic correlation function which really pass through CNT or participate in fluid flow across the nanotube. Also, the correlated exit and entry events of short time interval were taken into account by registering the entry events only when the exited fluid molecules do not reenter the CNT within 5 ps. 2.2.2.1. Mean Square Displacement (MSD) and Diffusion Coefficient.31 Mean square displacement was calculated using the relation MSD = ⟨Δz 2⟩ = ⟨|z(t ) − z(0)|2 ⟩

ϕR (t ) =

i=1 k=1

⟨|z(t ) − z(0)|2 ⟩ ⟨Δz 2⟩ 1 1 = lim lim Δt 2d t →∞ Δt 2d t →∞

(9)

Iik and wik respectively represent the moment of inertia tensor and angular velocity of the ith fluid molecule in kth direction.

3. RESULTS AND DISCUSSION 3.1. Wetting of CNTs with Polar and Nonpolar Fluids. The dynamic flow of three fluids, namely, water, methanol, and methane, through CNTs with diameter of about 0.43 nm to 1.66 nm, i.e., CNT(3,3)−CNT(12,12), was considered. Results show that no fluid molecule could stay inside CNT(3,3) and CNT(4,4), while a single file of water was seen to be exist inside CNT(5,5) tube for few configurations as shown in Figure 1a. It is apparent from the results that CNT(5,5) is the

(2)

where z(t) represents the coordinate of water molecule along the CNT axis at time t. Further, the diffusion coefficient has been calculated using the well-known Einstein relation D=

3

∑ ∑ ⟨Iikwik(t′ + t ) wik(t′)⟩

(3)

where d represents the dimension of the system, and was taken as 1 for CNT confined fluids. 2.2.2.2. Velocity Autocorrelation Function.31 Furthermore, the dynamics of confined fluid molecules was estimated using velocity autocorrelation functions (VACFs). Also, for detailed revelation, the total VACF has been divided into translational VACF (CT(t))and rotational VACF (CR(t)), based on their translational and rotational velocity components, and the expression for both the VACFs is written as C T(t ) =

C R (t ) =

⟨v(t ) ·v(0)⟩ ⟨v(0) ·v(0)⟩

(4)

⟨w(t ) ·w(0)⟩ ⟨w(0) ·w(0)⟩

(5)

Figure 1. (a) Number of water molecules confined in different CNTs with respect to simulation time. (b) Number of fluid molecules in confinement vs CNT diameter, (c) Density of fluid inside CNT vs CNT diameter.

where v(t) and w(t) respectively represent the translational and rotational velocity components of fluid molecules along the CNT axis at time t. 2.2.3. Density of State Function (DOS).32 DOS(v) shows the density of state function at molecular frequency v: DOS(ν) =

2 lim kT r →∞

smallest one, whose interior could be filled with water. This is in support of studies by Mashletet al.,33 in which a similar single file water chain was observed inside CNT(5,5) with all the oxygen atoms concerted in the center of tube. However, since CNT(5,5) was seen to be only partially occupied with water for few configurations only, the remaining part of this study follows the results based on fluid flow for CNT(6,6) to CNT(12,12). Results show that all the CNTs are spontaneously filled with both the polar and nonpolar solvents. Figure 1b represents the number of fluid molecules inside CNTs. It was observed that the number of fluid molecules increases with increase in nanotube diameter. Results show that increase in the number of confined molecules is almost linear for the diameter range 11− 14 Å; beyond that, the growth is very fast for diameter higher than 15 Å and very slow for diameter less than 10 Å. Also, for a particular diameter of CNT, the number of confined fluid molecules follows the order water > methane > methanol. Furthermore, the density of fluids inside the nanotube cavity was calculated using eq 10, and corresponding results are shown in Figure 1c.

τ

∫−τ ϕ(t ) e−i2πνt dt

(6)

k and T represent the Boltzmann constant and temperature of the system respectively, and ϕ(t) is defined as velocity autocorrelation function. We estimate translational DOS, using mass weighted translational velocity autocorrelation function with ϕ(t) = ϕT(t), given by N

ϕT (t ) =

3

∑ ∑ ⟨miψik(t )⟩ i=1 k=1

(7)

where ψik(t ) = lim

τ →∞

1 2τ

τ

∫−τ vik(t′ + t )vik(t′) dt′

(8)

ρconfinement =

where mi represents the mass of the ith fluid molecule and vki(t) is the kth velocity component of ith fluid molecule at time t. Furthermore, the rotational DOS function was calculated from the inertia weighted angular velocity autocorrelation function with ϕ(t) = ϕR(t), given by eq 9.

N×m NA × VCNT

(10)

where N is the number of fluid molecules confined in the nanotube. NA is the Avogadro number, m is the mass of fluid, and V is the volume of the CNT. 2309



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Figure 2. Snapshot of water (top), methanol (middle), and methane (bottom) inside CNT(6,6), CNT(7,7), CNT(8,8), CNT(9,9), and CNT(10,10) respectively.

It is seen that, though the number of fluid molecules confined in CNTs keeps on increasing with increase in nanotube diameter, yet the density of confinement becomes almost fixed after a particular diameter of CNT (which is fluid variant), giving insights of “natural density”. Interestingly, the results show that the density of methanol is decreased from CNT(6,6) to CNT(7,7) in spite of an increase in the number of confined molecules. This is supposed to be originated from the larger increase in confinement volume, V, than the increase in number of confined molecules N while leading from CNT(6,6) to CNT(7,7) (as per eq 10). In fact, the number of fluid molecules in the CNT confinement depends on (i) the confinement volume and (ii) the arrangement of fluid molecules in the confinement. Furthermore, it was observed that the density of methanol is lower than that of water for all the CNTs except CNT(6,6). Among the three fluids, density of methane was found to be the lowest for all diameters of CNT. Results predict that, after a certain diameter of CNT, the density of confined fluids follows the order water > methanol > methane, which is in the sequence of their bulk density. 3.2. Structure of Fluids inside CNTs. Snapshots for the molecular structure of fluids inside the nanotube interior are shown in Figure 2. It has been shown that the water molecules inside the tube appear to be arranged in a very ordered fashion. Water molecules show single and double file structure respectively inside CNT(6,6) and CNT(7,7). Furthermore, a structural transformation from perfectly hydrogen bonded tetrahedral to hexagonal network was noticed for water while moving from CNT(8,8) to CNT(10,10). For most of these cases, each water molecule was observed to be hydrogen bonded in a nearly two-dimensional network, which is quite different from the original tetrahedral structure of water molecules in ice (orientation order of these confined water molecules with respect to nanotube axis is shown in Table S4). Also, water molecules exhibit some degree of spiral nature in

the CNT axis direction, which might be due to their triangular shape. Realization of such peculiar arrangements of water inside nanotubes is not new but has been proposed by many simulation studies; however, the conditions of forming such icelike structures have been found to be quite different in all these studies, depending on the simulation parameters. Furthermore, as far as methanol is concerned, they show comparatively weakly ordered arrangement inside CNTs. For example, methanol molecules exhibit exactly one column for CNT(6,6), two columns for CNT(7,7), and four columns for CNT(8,8). No obvious multicolumnar methanol structures were noticed for CNTs larger than CNT(8,8). Also, it becomes difficult to distinguish between different methanol columns for these large diameter CNTs. In addition, the methanol molecules of one column are seen to be connected with the molecules in another column via one-dimensional linear hydrogen bond network. On the other hand, methane like nonpolar fluids flow in separate fluid columns, ranging from single column in CNT(6,6) to double column in CNT(7,7) and four fluid columns in CNT(8,8). Further, five and six fluid columns were also observed for CNT(9,9) and CNT(10,10) respectively. The results show that, though the methane molecules in one column are not connected with the methane molecules in neighboring fluid columns, they keep on interchanging among the columns. 3.2.1. Radial Density Distribution Profile (RDP). Further, the detailed study of molecular structure was carried out by estimating the density distribution in the radial and the axial direction of CNTs.The radial distribution functions of fluid molecules inside nanotubes are shown in Figure 3. For each case, the origin was set at the center of the CNT. As expected, the peak intensity of RDP was decreased from CNT(6,6) to CNT(12,12) for all the fluids. The peak positions of water-RDP inside CNT(7,7), CNT(8,8), and CNT(9,9) were found to be very similar to Noon et al.,34 however, the peak shapes were 2310



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inside CNTs (shown in Figure 5). All the ACFs were calculated using the center of mass (COM) position of the considered

Figure 3. Radial density distribution profile for (a) water-oxygen, (b) methane-carbon, (c) methanol-carbon, and (d) methanol-oxygen.

slightly changed. Results show asymmetrical distribution of water density. Also, the densities were nonzero near the tube center, which is in good agreement with the results reported by Wang et al.35 as well as Marti et al.36 However, no such literature studies have been reported for methanol and methane. Further, the zero decay of RDPs prior to nanotube radius indicates the minimum space required for a fluid molecule to be confined inside a CNT. For example, water molecule cannot stay closer than ∼0.27 nm from the CNT wall. Similarly, methanol and methane cannot stay less than 0.33 and 0.3 nm respectively from the CNT wall. In other words, the minimum nanotube diameter required for water, methanol, and methane is 0.54 nm, 0.67 nm, and 0.60 nm to be wetted with the respective fluids. The same has been projected in Figure 4.

Figure 5. Pair correlation function of (a) water, (b) methanol, and (c) methane in the axial direction of CNTs.

fluid molecules. It is evident that all the fluid molecules show solid-like ACF inside CNT(6,6), in which g(z) goes to zero between the two peaks. Also, it should be noted that two humps for the first peak of methanol are due to two possible positions of methanol-COM depending on the position of side viewer as explained in section 3.2.1. As far as CNT(7,7) is considered, methanol and methane show solid-like distribution in the axial direction, whereas water shifts more toward a liquidlike phase. Further, from CNT(8,8) onward, each fluid follows liquid-like distribution in the axial direction. Surprisingly, for CNT(8,8) and beyond, methanol and methane show more than one peak in ACFs, whereas only one peak was noticed for water. ACFs show peaks at z = 2.825 Å for water, which was found to be invariant of CNT diameter. Also, the position of these peaks is akin to the first peak in the radial distribution function of bulk water. However, the same was not true for methanol and methane. In both cases, the peak positions were seen to be varied with nanotube diameter. In fact, the ACF peaks for methanol can be considered as independent of nanotube diameter except CNT(6,6) and CNT(7,7). This shows the special structuring of methanol inside CNT(6,6) and CNT(7,7) which was also visible from the snapshots shown in Figure 2. The results show that the peak position is considerably postshifted to 3.48 Å for CNT(6,6) and remarkably preshifted to 3.18 Å for CNT(7,7) compared to the larger CNTs. For intermediate CNTs of diameter 10.74− 13.54 Å, the peak position was observed at 3.37 Å and reached to bulk-like value of 3.42 Å for CNT(12,12). For methane, the peak positions were quite fluctuating. CNT(6,6) showed first peak at 3.63 Å, and a considerable preshifting was noticed for CNT(7,7) at 3.48 Å, which was then postshifted from 3.68 to 3.88 Å as the CNT diameter was increased from CNT(9,9) to CNT(12,12). It should be noted that methane could not reach the bulk peak position of 4.0 Å up to the largest considered CNT, i.e., CNT(12,12). Furthermore, the ACF pattern inside CNT(9,9) was observed to be comparable to the larger tubes for all the fluids. This suggests that the confinement-induced changes in the structure of fluid become insignificant beyond CNT(9,9). On the other hand, fluid molecules are strongly correlated in the z direction (i.e., along the CNT axis) for

Figure 4. Minimum distance of (a) water, (b) methanol, and (c) methane from the CNT wall.

This rule might illustrate the reason why CNT(3,3) and CNT(4,4) remain unoccupied with water and other fluid molecules. On the other hand, there was enough space inside CNT(10,10) to generate a second peak near to the tube center for water and inside CNT(12,12) for methanol and methane. This is indicative of layered fluid structure inside these CNTs. Furthermore, we compare the RDPs for carbon (C) and oxygen (O) atoms of methanol. Results show two peaks for O atom of methanol for all CNTs except CNT(6,6), but only one peak for C of methanol for all CNTs. This shows that there are two possible distances of methanol-O from the CNT wall, and this can be clearly realized from a 2D image of methanol inside CNT as shown in Figure 4. In fact, one can say that methanolO is at the distance of 2.67 Å or at the distance of 4.06 Å from the CNT wall, depending on the position of the viewer. This is because of the linear structure of C−O−H in methanol inside cylindrical CNT. Instead, the position of methanol-C remains fixed from all sides of the CNT wall irrespective of the viewer position. 3.2.2. Axial Pair Correlation Function (ACF). Further, we plot axial correlation function for water, methanol, and methane 2311



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that the diffusion of fluids inside the CNT is dominated by the interactive forces among the fluid molecules and fluid− nanotube wall, not by the density of confined space. Therefore, the stronger nonpolar−nonpolar interaction for CNT− methane, intermediate nonpolar−polar interaction for CNT− methanol, and weak nonpolar−polar interaction for CNT− water lead to a diffusivity order of water > methanol > methane inside nanotube confinements. Higher diffusion coefficient of water than the methanol is due to their strong H bonding capacity, which leads to enhanced correlation of water along the nanotube axis, and so enhanced motion in the same direction. In other words, water, being a stronger polar solvent compared to methanol, exhibits a higher diffusion coefficient than the methanol during nanotube confinement, whereas strong nonpolar−nonpolar interaction between CNT and methane accounts for the minimum diffusion coefficient of methane inside CNTs. 3.3.2. Velocity Autocorrelation Function (VACF). Further, the transport mechanism of fluid molecules was elaborated using velocity autocorrelation functions. To present a clear picture of all dynamic motions, we have estimated both the translational and rotational VACF named as TVACF and RVACF respectively, and the corresponding results are shown in Figure 8. For all the fluids, TVACF shows the deepest

smaller CNTs, and therefore the oscillations in the ACFs of these CNTs range for 4−10 Å from the origin. Such extended correlation among the confined fluid molecules is a distinguishing feature of the sub continuum liquid regime which cannot be observed in the bulk state of fluids. 3.3. Dynamics of Fluids inside CNTs. 3.3.1. Mean Square Displacement and Diffusion Coefficients. Further, the diffusion coefficient of fluid molecules inside CNT was estimated using mean square displacement (MSD) (shown in Figure 6) via very popular Einstein relation (eq 2). Results in

Figure 6. Mean square displacement profiles for (a) water, (b) methanol, and (c) methane inside CNTs.

Figure 7. Diffusion coefficient of water, methanol, and methane inside CNTs as a function of nanotube diameter.

Figure 7 show that the diffusivity of fluid molecules is increased from CNT(6,6) to CNT(7,7) and then reduced for CNT(8,8). Water shows a continuous increase in diffusion coefficient from CNT(8,8) to CNT(10,10), whereas methane shows a continuous decrease for the same. Also, it was shown that water reaches very near to bulk diffusion within CNT(12,12) whereas for methane it was 15 times smaller than the bulk for CNT(12,12). For methanol, the diffusion coefficient was surprisingly high for CNT(9,9) and then reached one-third of bulk value for CNT(10,10) and CNT(12,12). The pattern of these diffusion coefficient data for all the fluids has been further supported by translational velocity autocorrelation functions as discussed in section 3.3.2. Interestingly, in the bulk liquid phase, water, methanol, and methane follow the diffusion order methane > water ∼ methanol, which is in accordance with their bulk density (data not shown here), but when it comes to the nanotube confinement, water shows a much higher diffusion coefficient, followed by methanol and then methane. It seems

Figure 8. Translational velocity autocorrelation function (TVACF, left) and rotational velocity autocorrelation function (RVACF, right) for (a) water, (b) methanol, and (c) methane inside nanotube confinement. Color code for CNTs: red, CNT6; dark green, CNT7; blue, CNT8; pink, CNT9; bright green, CNT10; black, CNT12.

minima for CNT(6,6). The highest negative area for CNT(6,6) is representative of strong confinement effect inside CNT(6,6), which is in support of lowest D for CNT(6,6) confinement for all the fluids. For water, this negative area was seen to be reduced with increase in nanotube diameter afterward CNT(8,8). However, the same was not true for methanol or methane. Methanol shows very different behavior for CNT(6,6), CNT(7,7), and CNT(8,8) compared to other CNTs. In the case of CNT(9,9), a preshift was noticed with the least negative area, which supports the highest D of methanol inside CNT(9,9). Interestingly, in the case of methane, the depth of minima was seen to be increased from CNT(7,7) to 2312



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Figure 9. Translational density of state function (TDOS) and rotational density of state function (RDOS) for (a) water, (b) methanol, and (c) methane inside nanotube confinement. Color code for CNTs: red, CNT6; dark green, CNT7; blue, CNT8; pink, CNT9; bright green, CNT10; black, CNT12.

CNT(10,10) and then again reduced for CNT(12,12). This indicates that the confinement effect on methanol molecules is enhanced from CNT(7,7) to CNT(10,10) and further starts reducing from CNT(12,12), which is in accordance with the diffusion coefficient data shown in Figure 7. Also, a considerable shift in minimum position was observed with change in nanotube diameter, which indicates the change in dynamic correlation of fluid molecules inside these CNTs. Preshift in the first minimum position is indicative of decreased time period between the collisions of two fluid molecules, especially for short time interval. On the other hand, the large oscillations in VACF before they decay to zero is representative of the solid-like correlations among fluid molecules. Considering both arguments, it can be stated that inside smaller CNTs, i.e., CNT(6,6) and CNT(7,7), the fluid molecules show weak correlation of linear z-motion for the short time interval and a solid-like strong z-correlation for longer periods of time. Further, we report RVACF for water, methanol, and methane. Similar to ACF, the minimum positions in RVACF of water were seen to be invariant of CNT diameter, whereas a minor postshift was observed for methanol inside CNT(7,7) and CNT(8,8) and then become independent of nanotube diameter. Remarkably, the results of minimum position for RVACF of all the fluids were found in good correlation with the peak positions in ACFs. Furthermore, reverse to water, the depth of minima for methanol and methane was seen to be reduced from CNT(7,7) to CNT(12,12). This indicates that the rotations of methanol and methane are more restricted inside small CNTs compared to the larger CNTs. On the other hand, water has more free rotations inside small CNTs than the large CNTs. Increase in the rotational freedom of water for smaller CNTs might be related to the (i) reduced number of H bonds/water in single file and double file structure of water inside CNT(6,6) and CNT(7,7) respectively, (ii) reduced friction of water near the CNT wall due to the moderated polar−nonpolar interactions, and (iii) increased free phase

space of rotation per water molecule. Conversely, for methanol and methane the rotational freedom is reduced with increase in CNT diameter due to increased free space per fluid molecule, i.e., reduced confinement effect. 3.3.3. Density of State Function. Further, TVACF and RVACF were Fourier transformed to get translational density of state (TDOS) and rotational density of state (RDOS) respectively (shown in Figure 9). TDOS of bulk water shows a narrow peak at 50 cm−1 and a broad peak at ∼180 cm−1, corresponding to linear motion of water in the transverse (perpendicular to CNT axis) and longitudinal (parallel to CNT axis) direction, respectively. High peak intensity for the transverse direction of CNT(6,6) represents the increased translational freedom of water molecules in the radial direction f CNT(6,6) compared to the larger CNTs. Both the CNT(6,6) and CNT(7,7) show enhanced low frequency oscillations for water confinement, indicating vapor-like transverse motion of water inside these CNTs. Also, the results show that, with increase in nanotube diameter, the peak intensity of water is increased for higher frequency modes whereas it is decreased for lower frequency modes, which is indicative of reduced confinement effect inside larger CNTs. Further, methanol TDOS shows two peaks at 25 and 100 cm−1 inside CNT(6,6). On the other hand, only one broad peak at 50 cm−1 was observed for methanol inside larger CNTs. This might be because the transverse and longitudinal motion of methanol molecules could not be distinguished inside the larger CNTs, similar to the bulk state of methanol. Oppositely, smaller CNTs especially CNT(6,6) and CNT(7,7) display a different degree of linear motion for the radial and axial directions. As seen from the intensity of low frequency modes, the transverse motion of methanol seems to be more free for CNT(6,6) than the CNT(7,7). Furthermore, in the case of methane, two separate peaks at 40 and 150 cm−1 were observed for CNT(7,7) and CNT(8,8), which were combined to one broad peak at 50−140 cm−1 for CNT(9,9), 40−130 cm−1 for CNT(10,10), and 30− 2313



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90 cm−1 for CNT(12,12). This indicates that the radial and axial translations of methane molecules can be distinguished for CNT(7,7) and CNT(8,8) because of the strong columnar flow of methane inside these CNTs. On the other hand, the TDOS peaks for radial and axial translations of methane are observed to be merged for higher CNTs. It might be possible that there is large exchange of methane molecules from one column to another column for larger CNTs, leading to undistinguished linear and radial translations for these CNTs. Also, methane inside CNT(7,7) shows a moderate enhancement in low frequency oscillations with largely suppressed higher frequency modes. Reverse to it, the low frequency motions were suppressed inside CNT(6,6) and only a single peak at ∼80 cm−1 was observed, indicating the restricted translation of methane molecules for the radial direction of CNT(6,6) compared to CNT(7,7). Furthermore, we report RDOS of these systems. RDOS of water shows two peaks at ∼170 and 400 cm−1 for CNT(6,6) and CNT(7,7), but only one peak at ∼450 cm−1 for CNTs larger than CNT(8,8). The observed peak at ∼170 cm−1 is seen to be prominent in the water vapor, indicating a vapor-like phase state of water inside CNT(6,6) and CNT(7,7). This is in line with the RVACF results, where it was shown that the rotational freedom of water is increased during confinement in very small sized CNTs. The RDOS of methanol shows a peak at ∼100 cm−1 for large CNTs, which was observed to be merged with zero frequency oscillations for CNT(6,6) and postshifted for CNT(7,7). This indicates the vapor-like rotation of methanol inside CNT(6,6) but solid-like frozen rotations inside CNT(7,7). This might be due to the radial H bonding of methanol inside CNT(7,7) but axial H bonding of methanol inside CNT(6,6). In radial H bonding, a methanol molecule of one fluid layer is seen to be hydrogen bonded with a methane molecule in another fluid layer. On the other hand, two methanol molecules from the same fluid line are H bonded in axial H bonding. In reality, the axial H bonding of methanol inside CNT(6,6) restricts the translational freedom of methanol molecules in the z direction but provides more free space in the radial direction to be rotated. Instead, the radial H bonding inside CNT(7,7) leads to restricted rotation in the radial direction but free linear motion in the z direction. In other words, the rotational motion of methanol is comparatively free inside CNT(6,6) because of increased phase space in the radial direction. This might be also the reason that why methanol TDOS shows restricted radial translation of methanol molecules inside CNT(7,7) compared to CNT(6,6). Further, in the case of methane, a broad peak at ∼50 cm−1 was observed in RDOS of larger CNTs, which was seen to be merged with zero frequency oscillations inside CNT(6,6), indicating large rotational freedom of methane inside CNT(6,6). Results show the change in RDOS behavior while transmitting methanol from CNT(8,8) to CNT(12,12), which might be indicative of transition from sub continuum to continuum flow of methane for these CNTs.

nanotube diameter. The origins were investigated why CNT(3,3) and CNT(4,4) remain unoccupied with water and other fluid molecules. Further, it was shown that water could not be confined inside a tube with diameter less than 0.54 nm. Similar to this, methanol and methane cannot enter the tube having diameter less than 0.66 and 0.60 nm, respectively. Single file structure of water, methanol, and methane inside CNT(6,6) was diminished with increase in nanotube diameter. Results show the presence of two fluid layers inside larger CNTs. Further, the diffusion coefficients of fluid molecules inside CNTs were estimated. The dynamics of the considered fluid molecules was visualized with the help of velocity autocorrelation functions and density of states. It was shown that small CNTs reduce the translational mobility of confined fluid molecules, however, on the other hand, they increase their rotational freedom. In other words, results showed that the interaction forces acting between fluid particles and nanotube wall play an important role, which is reflected in the transport behavior of fluid molecules. In the case of very small CNTs, the size of fluid molecule accounts a significant role in determining the structure and mobility of confined fluid molecules.The DOS results were found in line with the corresponding VACF functions. TVACFs in small CNTs showed weak correlation of linear z-motion for the short time interval and, reverse to it, a solid-like strong correlation for long periods of time. Interestingly, the results of minimum position in RVACF were found to be in good correlation with the peak positions in ACFs. The results from RVACF show that the rotation confinement is reduced with decrease in CNT diameter in the case of water, in reverse, it is increased for methanol and methane, and the same has been established with the RDOS. Interestingly, the altered H bonding of methanol in the axial and radial direction of CNT(6,6) and CNT(7,7) attributes to reversal effects on rotation DOF (degree of freedom) and translation DOF. However, all such effects were diminished for the larger diameter of CNTs. Overall, the results show transition of fluid structures and dynamics from sub continuum to bulk fluid properties, which is supposed to be very supportive for equivalent fluid channels in living cells and would serve as good prototypes for these biological channels.13

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.7b00186. Bonded and nonbonded force field parameters, charge parameters, and bond order parameter for CNT confined water molecules (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mails: [email protected]. Tel: +91-22-25591992. ORCID

Sk. Musharaf Ali: 0000-0003-0457-0580

4. CONCLUSION The objective of the present MD simulations was to capture the sub continuum fluid dynamics inside small nanotubes. Transition from sub continuum to continuum state has been captured for water and methanol while moving from CNT(6,6) to CNT(12,12). Yet, methane could not show bulk fluid properties up to the largest simulated CNT(12,12). Results show the enhancement of confined density with increase in

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors sincerely thank Dr. Sadhna Mohan, Associate director ChEG, and Shri K. T. Shenoy, Head, ChED, for their continuous support and encouragement. The authors are also 2314



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grateful to Computer Division, BARC, for providing ANUPAM Supercomputing facility.

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