Encapsulation of carbon chain molecules in single-walled carbon nanotubes

The vacuum space inside carbon nanotubes offers interesting possibilities for the inclusion, transportation, and functionalization of foreign molecules. Using first-principles density functional calculations, we show that linear carbon-based chain molecules, namely, polyynes (C(m)H(2), m = 4, 6, 10) and the dehydrogenated forms C(10)H and C(10), as well as hexane (C(6)H(14)), can be spontaneously encapsulated in open-ended single-walled carbon nanotubes (SWNTs) with edges that have dangling bonds or that are terminated with hydrogen atoms, as if they were drawn into a vacuum cleaner. The energy gains when C(10)H(2), C(10)H, C(10), C(6)H(2), C(4)H(2), and C(6)H(14) are encapsulated inside a (10,0) zigzag-shaped SWNT are 1.48, 2.04, 2.18, 1.05, 0.55, and 1.48 eV, respectively. When these molecules come inside a much wider (10,10) armchair SWNT along the tube axis, they experience neither an energy gain nor an energy barrier. They experience an energy gain when they approach the tube walls inside. Three hexane molecules can be encapsulated parallel to each other (i.e., nested) inside a (10,10) SWNT, and their energy gain is 1.98 eV. Three hexane molecules can exhibit a rotary motion. One reason for the stability of carbon chain molecules inside SWNTs is the large area of weak wave function overlap. Another reason concerns molecular dependence, that is, the quadrupole-quadrupole interaction in the case of the polyynes and electron charge transfer from the SWNT in the case of the dehydrogenated forms. The very flat potential surface inside an SWNT suggests that friction is quite low, and the space inside SWNTs serves as an ideal environment for the molecular transport of carbon chain molecules. The present theoretical results are certainly consistent with recent experimental results. Moreover, the encapsulation of C(10) makes an SWNT a (purely carbon-made) p-type acceptor. Another interesting possibility associated with the present system is the direction-controlled transport of C(10)H inside an SWNT under an external field. Because C(10)H has an electric dipole moment, it is expected to move under a gradient electric field. Finally, we derive the entropies of linear chain molecules inside and outside an open-ended SWNT to discuss the stability of including linear chain molecules inside an SWNT at finite temperatures.     

A novel algorithm to model the influence of host lattice flexibility in molecular dynamics simulations: loading dependence of self-diffusion in carbon nanotubes

We describe a novel algorithm that includes the effect of host lattice flexibility into molecular dynamics simulations that use rigid lattices. It uses a Lowe-Andersen thermostat for interface-fluid collisions to take the most important aspects of flexibility into account. The same diffusivities and other properties of the flexible framework system are reproduced at a small fraction of the computational cost of an explicit simulation. We study the influence of flexibility on the self-diffusion of simple gases inside single walled carbon nanotubes. Results are shown for different guest molecules (methane, helium, and sulfur hexafluoride), temperatures, and types of carbon nanotubes. We show, surprisingly, that at low loadings flexibility is always relevant. Notably, it has a crucial influence on the diffusive dynamics of the guest molecules.     

Rapid diffusion of CH4/H2 mixtures in single-walled carbon nanotubes

Equilibrium molecular dynamics (EMD) are used to examine the self-diffusion and macroscopic diffusion of CH4/H2 mixtures adsorbed inside a (10,10) single-walled carbon nanotube. EMD can be used to determine the macroscopic diffusion coefficients of adsorbed mixtures by evaluating the matrix of Onsager transport coefficients. Earlier studies have indicated the diffusion of light gases adsorbed as single components in carbon nanotubes is extremely rapid compared to that in other known nanoporous materials. The results presented here indicate that extremely rapid diffusion can also occur for mixtures of adsorbed molecules. The rapid diffusion of adsorbed molecules and the strong coupling between the fluxes of the adsorbed species in a mixture have interesting implications for uses of carbon nanotubes in membrane-based applications.     

Conformational flexibility in open chain molecules: chiral and achiral alkanes

Conformational partition functions of chiral and achiral alkanes have been computed by using a continuum approach (instead of rotational isomeric state approximations). The accessible conformational space per bond depends upon the structure of the compound and is only in the range of 5–13% of the maximum accessible range. In order to partly overcome the intrinsic ambiguity of the term “conformational flexibility”, the distinction between number flexibility (a measure of the number of accessible energy minima) and space flexibility (a measure of the total allotted space) is proposed. Further, the conformational versatility of each bond of a molecule is evaluated in terms of the a priori probability density function of that bond, and it is shown that the use of this function permits a comparison of the relative conformational flexibilities of the individual bonds, which is particularly useful for molecules having more than two rotation angles (where the conventional energy maps cannot be used). Optical rotations are calculated for a series of chiral alkanes by combining the continuum approach for conformational analysis and a recent optical activity calculation scheme. Contributions of single bonds to the molar optical rotation are evaluated and discussed. The influence of temperature upon conformational and chiral properties is evaluated.     

Li-insertion into carbon nanotubes: Experiment and theory

Lithium-insertion during the arc discharge growth process is investigated by using resonance Raman spectroscopy combined with ab initio calculations. The measurements were performed using two pairs of single-wall carbon nanotubes, one of the members being prepared employing a lithium-contained catalyst and the other its lacking lithium counterpart. The lowest wave number lines were observed as selective resonances for the first pair for which a line occurs at 142.3 cm⁻¹ from the Li-catalyst prepared sample and at 162.2 cm⁻¹ for the non-lithium case. The remaining lines are seen in both samples. For the second pair the first two lower-lying lines are selectively seen for the non-lithium sample while for the lithium-contained catalyst case the two highest wave number lines are selectively observed. These different resonance conditions lead us to perform electronic property calculations. The results show that this effect can be tracked to the charge transfer occurring from lithium atoms inserted into the bundles. Calculation shows that the transfer is limited to a Li-insertion rate of Li₆C₆₈.     

Viscosity of liquid mixtures: the Vesovic-Wakeham method for chain molecules

New expressions for the viscosity of liquid mixtures, consisting of chain-like molecules, are derived by means of Enskog-type analysis. The molecules of the fluid are modelled as chains of equally sized, tangentially joined, and rigid spheres. It is assumed that the collision dynamics in such a fluid can be approximated by instantaneous collisions. We determine the molecular size parameters from the viscosity of each pure species and show how the different effective parameters can be evaluated by extending the Vesovic-Wakeham (VW) method. We propose and implement a number of thermodynamically consistent mixing rules, taking advantage of SAFT-type analysis, in order to develop the VW method for chain molecules. The predictions of the VW-chain model have been compared in the first instance with experimental viscosity data for octane-dodecane and methane-decane mixtures, thus, illustrating that the resulting VW-chain model is capable of accurately representing the viscosity of real liquid mixtures.     

Self‐diffusion of small molecules into rubbery polymers: A lattice free‐volume theory

In the framework of the free‐volume (FV) theory, a new equation was derived for the evaluation of self‐diffusion coefficients of small molecules in polymers above the mixture glass transition temperature. The derivation of the equation turned out to be straightforward once the equivalence between the free volume and the unoccupied volume given by thermodynamic lattice theories is assumed. A parameter evaluation scheme is proposed, which is substantially simpler compared with the conventional Vrentas–Duda approach, even without losing generality. The key assumption is discussed, and its consistency is verified from a numerical viewpoint. A comparison with experimental solvent self‐diffusion coefficients for several solvent/polymer binary systems confirmed that the proposed theory presents good correlative ability over wide temperature and composition ranges. Moreover, the introduced thermodynamic foundation allows one to easily include the pressure effect too. In the frame of the proposed lattice free volume theory, the sizes of the polymer jumping units decrease with temperature and increase with pressure. Such behavior converges with theoretical expectations and opens the way for a predictive FV theory. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 529–540, 2010     

Diffusion theory of the thermal decomposition of diatomic molecules

A quasi-stationary solution of the Fokker—Planck equation for definite limiting conditions, describing the process of thermal decomposition of diatomic molecules in a light inert gas, has been considered. The rate of thermal dissociation of Morse oscillators has been calculated for a relatively arbitrary intermolecular interaction potential.     

Dispersion of single-walled carbon nanotubes in alcohol-cholic acid mixtures

A procedure for dispersing single-walled carbon nanotubes (SWNTs) for the preparation of suspensions with high concentrations of individual nanotubes in various solvents was described. The most stable suspensions were obtained from a mixture of ethanol with cholic acid at an acid concentration of 0.018 mol/kg.     

Temperature and size effects on diffusion in carbon nanotubes

We study the self-diffusion of simple gases inside single-walled carbon nanotubes at the zero-loading limit by molecular dynamics simulations. The host-framework flexibility influence is taken into account. In particular, we study the influences of nanotube size and temperature. For the carbon-nanotube radius-dependent self-diffusivities, a maximum is observed, which resembles the so-called levitation effect. This occurs for pores having a radius comparable to the position of the interaction-energy minimum. Surprisingly, the temperature influence is not uniform throughout different pore sizes. Diffusivities are expected to increase with temperature. This effect is observed for carbon nanotubes distinctly larger than the guest molecules. Remarkably, for smaller pores, the self-diffusivities decrease with increasing temperature or exhibit a maximum in the temperature dependence. This effect is caused by competing influences of collision frequency and temperature.     

Molecular and thermal diffusion coefficients of alkane-alkane and alkane-aromatic binary mixtures: effect of shape and size of molecules

New molecular and thermal diffusion coefficients of binary mixtures of normal decane-normal alkanes and methylnaphthalene-normal alkanes are measured at atmospheric pressure and T = 25 degrees C. The normal alkanes used in this work include nC5-nC20. Thermal diffusion coefficients were measured in a thermogravitational column. Molecular diffusion coefficients were measured using an open-ended capillary tube technique. Results show a significant effect of molecular shape and size on thermal and molecular diffusion coefficients. Molecular diffusion coefficients show a monotonic behavior in both aromatic-normal alkane and normal decane-normal alkane mixtures. Thermal diffusion coefficients reveal a nonmonotonic trend with molecular size in the normal decane-normal alkane mixtures. This is the first report of the nonmonotonic behavior in the literature. The data presented in this paper provide an accurate self-molecular diffusion coefficient for nC10 from binary data.     

Equilibrium and kinetics: water confined in carbon nanotubes as one-dimensional lattice gas

We present a simple one-dimensional lattice gas model, which describes very well the equilibrium and kinetic behaviors of water confined in a thin carbon nanotube found in an atomistic molecular dynamics simulation [G. Hummer, J. C. Rasaiah, and J. P. Noworyta, Nature (London), 414, 188 (2001)]. The model parameters correspond to various physical interactions and can be calculated or estimated by using statistical mechanics. Then, the roles of all interactions in the water filling, emptying, and transporting processes are clearly understood. Our results indicate that the interaction from the water molecules outside the nanotube plays a key role in these processes and the interaction can be simply treated as an average effect of the bulk water.     

Thermal diffusion measurements and simulations of binary mixtures of spherical molecules

Thermal diffusion forced Rayleigh scattering measurements on binary mixtures of carbon tetrabromide (CBr(4)), tetraethylsilane, and di-tert-butylsilane in carbon tetrachloride (CCl(4)) are reported at different temperatures and concentrations. The Soret coefficient of CBr(4) in CCl(4) is positive and S(T) of both silanes in CCl(4) is negative, which implies that the heavier component always moves to the cold side. This is the expected behavior for unpolar simple molecules. Both silanes have the same mass so the influence of the difference in shape and moment of inertia could be studied. For all three systems, S(T) decreases with decreasing CCl(4) concentration. The results are discussed in the framework of thermodynamic theories and the Hildebrand parameter concept. Additionally, the Soret coefficients for both silaneCCl(4) systems were determined by nonequilibrium molecular-dynamics calculations. The simulations predict the correct direction of the thermophoretic motion and reflect the stronger drive toward the warm side for di-tert-butylsilane compared to the more symmetric tetraethylsilane. The values deviate systematically between 9% and 18% from the experimental values.     

Strong correlations and Fickian water diffusion in narrow carbon nanotubes

The authors have used atomistic molecular dynamics (MD) simulations to study the structure and dynamics of water molecules inside an open ended carbon nanotube placed in a bath of water molecules. The size of the nanotube allows only a single file of water molecules inside the nanotube. The water molecules inside the nanotube show solidlike ordering at room temperature, which they quantify by calculating the pair correlation function. It is shown that even for the longest observation times, the mode of diffusion of the water molecules inside the nanotube is Fickian and not subdiffusive. They also propose a one-dimensional random walk model for the diffusion of the water molecules inside the nanotube. They find good agreement between the mean-square displacements calculated from the random walk model and from MD simulations, thereby confirming that the water molecules undergo normal mode diffusion inside the nanotube. They attribute this behavior to strong positional correlations that cause all the water molecules inside the nanotube to move collectively as a single object. The average residence time of the water molecules inside the nanotube is shown to scale quadratically with the nanotube length.     

Water diffusion inside carbon nanotubes: mutual effects of surface and confinement

The mutual effects of two crucial features of carbon nanotubes (CNTs) (surface and confinement) on the temperature-dependent water diffusion are studied through molecular dynamics simulations. A two-stage diffusion mechanism is detected in the CNTs of diameter smaller than 12.2 ?, which becomes obscure as the temperature increases. This peculiar phenomenon can be ascribed to the cooperation of the small confinement and the periodic surface. The diffusion coefficient of the confined water exhibits a nonmonotonic dependence on the confinement size and an unexpected increase inside the large CNTs (compared to that of bulk water). These anomalous behaviors can be attributed to the competition of the smooth surface and the small confinement. Considering the mutual effects, an empirical formula is proposed on the basis of two groups of numerical examples, whose results indicate that the confinement effect will dominate over the surface effect until the CNT diameter increases up to ~16 ?, whereas thereafter the surface effect becomes dominant and finally both of them vanish gradually.     

Adsorption and diffusion of molecular nitrogen in single wall carbon nanotubes

Using molecular simulation, the adsorption and self-diffusion of diatomic nitrogen molecules inside a single wall carbon nanotube have been studied over a range of nanotube diameters (8.61-15.66 A) and loadings at temperatures of 100 and 298 K. Nitrogen adsorption energy is found to increase as the nanotube diameter is reduced toward the molecular diameter of nitrogen. A discrete organization of the nitrogen into adsorbed layers is observed at high loadings that follows a regular progression determined primarily by geometric considerations. The formation of an adsorbate core at the center of the nanotube is found to increase the self-diffusion of nitrogen. A "wormlike" phase is found for the adsorbed nitrogen in the (15, 0) carbon nanotube at high loadings and at 100 K.     

Transport diffusion of gases is rapid in flexible carbon nanotubes

Molecular dynamics simulations of rigid, defect-free single-walled carbon nanotubes have previously suggested that the transport diffusivity of gases adsorbed in these materials can be orders of magnitude higher than any other nanoporous material (A. I. Skoulidas et al., Phys. Rev. Lett. 2002, 89, 185901). These simulations must overestimate the molecular diffusion coefficients because they neglect energy exchange between the diffusing molecules and the nanotube. Recently, Jakobtorweihen et al. have reported careful simulations of molecular self-diffusion that allow nanotube flexibility (Phys. Rev. Lett. 2005, 95, 044501). We have used the efficient thermostat developed by Jakobtorweihen et al. to examine the influence of nanotube flexibility on the transport diffusion of CH4 in (20,0) and (15,0) nanotubes. The inclusion of nanotube flexibility reduces the transport diffusion relative to the rigid nanotube by roughly an order of magnitude close to zero pressure, but at pressures above about 1 bar the transport diffusivities for flexible and rigid nanotubes are very similar, differing by less than a factor or two on average. Hence, the transport diffusivities are still extremely large compared to other known materials when flexibility is taken into account.