Adsorption and Gas Separation of Molecules by Carbon Nanohorns.

In this paper, we report the results of Monte Carlo simulations of the adsorption of neon, argon, methane and carbon dioxide in carbon nanohorns. We model the nanohorns as an array of carbon cones and obtained adsorption isotherms and isosteric heats. The main sites of adsorption are inside the cones and in the interstices between three cones. We also calculated the selectivity of carbon dioxide/methane, finding that nanohorns are a suitable substrate for gas separation. Our simulations are compared to available experimental data.

Phase behavior of Ar and Kr films on carbon nanotubes.

Recent experiments (Wang et al., 2010) have found evidence of phase transitions of gases adsorbed on a single carbon nanotube. In order to understand the observations, we have carried out classical grand canonical Monte Carlo simulations of this system, for the cases of Ar and Kr on zigzag and armchair nanotubes with radius R > 0.7 nm. The calculated behavior resembles the experimental results in the case of Ar. However, the prominent, ordered phase found for Kr in both simulations and (classical) energy minimization calculations differs from that deduced from the experimental data. A tentative explanation of the apparent discrepancy is that the experiments involve a nanotube of rather large radius (>1.5 nm).

Anomalous effective dimensionality of quantum gas adsorption near nanopores.

Three problems involving quasi-one-dimensional (1D) ideal gases are discussed. The simplest problem involves quantum particles localized within the 'groove', a quasi-1D region created by two adjacent, identical and parallel nanotubes. At low temperature (T), the transverse motion of the adsorbed gas, in the plane perpendicular to the axes of the tubes, is frozen out. Then, the low T heat capacity C(T) of N particles is that of a 1D classical gas: C(*)(T) = C(T)/(Nk(B)) --> 1/2. The dimensionless heat capacity C(*) increases when T ≥ 0.1T(x, y) (transverse excitation temperatures), asymptoting at C(*) = 2.5. The second problem involves a gas localized between two nearly parallel, co-planar nanotubes, with small divergence half-angle γ. In this case, too, the transverse motion does not contribute to C(T) at low T, leaving a problem of a gas of particles in a 1D harmonic potential (along the z axis, midway between the tubes). Setting ω(z) as the angular frequency of this motion, for T ≥ τ(z) ≡ ω(z)h/k(B), the behavior approaches that of a 2D classical gas, C(*) = 1; one might have expected instead C(*) = 1/2, as in the groove problem, since the limit γ ≡ 0 is 1D. For T << τ(z), the thermal behavior is exponentially activated, C(*) ∼ (τ(z)/T)(2)e(-τ(z)/T). At higher T (T ≈ ε(y)/k(B) ≡ τ(y) >> τ(z)), motion is excited in the y direction, perpendicular to the plane of nanotubes, resulting in thermal behavior (C(*) = 7/4) corresponding to a gas in 7/2 dimensions, while at very high T (T > hω(x)/k(B) ≡ τ(x) >> τ(y)), the behavior becomes that of a D = 11/2 system. The third problem is that of a gas of particles, e.g. (4)He, confined in the interstitial region between four square parallel pores. The low T behavior found in this case is again surprising--that of a 5D gas.

Interaction thresholds for adsorption of quantum gases on surfaces and within pores of various shapes.

Adsorption within pores and on surfaces occurs because of the attractive potential provided by the adsorbent. If the attraction is too weak, however, adsorption does not occur to any significant extent. This paper evaluates the criterion for such adsorption, at zero temperature, of the quantum gases 4He and H2. This criterion is expressed as a relationship between a threshold value of the well-depth (D) of the adsorption potential (on a semi-infinite planar surface) and the hard-core diameter (sigma) of the gas-surface pair potential. Six geometries are considered, of which two result in two-dimensional (2D) adsorbed phases, two result in one-dimensional (1D) phases, and two result in zero-dimensional phases. These are monolayer films on semi-infinite substrates or within a slit pore, linear or axial phases within cylindrical pores (within bulk solids) or cylindrical tubes, and single-particle adsorption within spherical pores or hollow spherical cavities, respectively. The criteria for film adsorption are consistent with analogous criteria for film wetting to occur, evaluated with a simple thermodynamic model.

Capillary condensation in cylindrical nanopores.

Using grand canonical Monte Carlo simulations, we have explored the phenomenon of capillary condensation (CC) of Ar at the triple temperature inside infinitely long, cylindrical pores. Pores of radius R = 1 nm, 1.7 nm, and 2.5 nm have been investigated using a gas-surface interaction potential parametrized by the well depth D of the gas on a planar surface made of the same material as that comprising the porous host. For strongly attractive situations--i.e., large D--one or more (depending on R) Ar layers adsorb successively before liquid fills the pore. For very small values of D, in contrast, negligible adsorption occurs at any pressure P below saturated vapor pressure P0; above saturation, there eventually occurs a threshold value of P at which the coverage jumps from empty to full, nearly discontinuously. Hysteresis is found to occur in the simulation data whenever abrupt CC occurs--i.e., for R > or = 1.7 nm--and for small D when R = 1 nm. Then, the pore-emptying branch of the adsorption isotherm exhibits larger coverage than the pore-filling branch, as is known from many experiments and simulation studies. The relation between CC and wetting on planar surfaces is discussed in terms of a threshold value of D, which is about one-half of the value found for the wetting threshold on a planar surface. This finding is consistent with a simple thermodynamic model of the wetting transition developed previously.

Possible one-dimensional 3He quantum fluid formed in nanopores.

Heat capacity measurements have been made down to 5 mK for 3He fluid films adsorbed in one-dimensional (1D) nanometer-scale pores, 28 A in diameter, preplated with 4He of 1.47 atomic layers. At low 3He density, the heat capacity shows a density-dependent, Schottky-like peak near 150 mK asymptoting to the value corresponding to a 2D Boltzmann gas at high temperatures. The peak behavior is attributed to the crossover from a 2D gas to a 1D state at low temperatures. The degenerate state of the 1D 3He fluid is indicated by a predominantly linear temperature dependence below about 30 mK.

Designing van der Waals Forces between Nanocolloids.

van der Waals (VDW) dispersion forces are often calculated between colloidal particles by combining the Dzyaloshinskii-Lifshitz-Pitaevskii (DLP) theory with the Derjaguin approximation; however, several limitations prevent using this method for nanocolloids. Here we use the Axilrod-Teller-Muto 3-body formulation to predict VDW forces between spherical, cubic, and core-shell nanoparticles in a vacuum. Results suggest heuristics for "designing" nanocolloids to have improved stability.

Ground state and thermal properties of a lattice gas on a cylindrical surface.

Adsorbed gases within, or outside of, carbon nanotubes may be analyzed with an approximate model of adsorption on lattice sites situated on a cylindrical surface. Using this model, the ground state energies of alternative lattice structures are calculated, assuming Lennard-Jones pair interactions between the particles. The resulting energy and equilibrium structure are nonanalytic functions of radius (R) because of commensuration effects associated with the cylindrical geometry. Specifically, as R varies, structural transitions occur between configurations differing in the "ring number," defined as the number of atoms located at a common value of the longitudinal coordinate (z). The thermodynamic behavior of this system is evaluated at finite temperatures, using a Hamiltonian with nearest-neighbor interactions. The resulting specific heat bears a qualitative resemblance to that of the one-dimensional Ising model.