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As part of a systematic study on the kinetic compensation effect, we use kinetic Monte Carlo simulations to observe the effects of substrate topology on the transient variations in the Arrhenius parameters - effective activation energy $E_{a}$, and preexponential factor $\nu$ - during thermal desorption, with a particular focus on differences between ordered and disordered surfaces at a fixed global coordination number. The rates of desorption depend on surface configuration due to the inherent differences in the local environments of adsorbing sites in the two cases. While the compensation effect persists for the disordered substrate, the change in topology introduces an element that produces variations in $\nu$ that are independent of variations in $E_{a}$, which implies that the parameters cannot be fully characterized as functions of each other. We expect our results to provide a deeper insight into the microscopic events that originate compensation effects in our system of study but also in other fields where these effects have been reported., Comment: 13 pages, 20 figures

The kinetic compensation effect (KCE), observed in many fields of science, is the systematic variation in the apparent magnitudes of the Arrhenius parameters $E_a$, the energy of activation, and $\nu$, the preexponential factor, as a response to perturbations. If, in a series of closely related activated processes, these parameters exhibit a strong linear correlation, it is expected that an isokinetic relation will occur, then the rates $k$ become the same at a common compensation temperature $T_c$. The reality of these two phenomena continues to be debated as they have not been explicitly demonstrated and their physical origins remain poorly understood. Using kinetic Monte Carlo simulations on a model interface, we explore how site and adsorbate interactions influence the Arrhenius parameters during a typical desorption process. We find that their transient variations result in a net partial compensation, due to the variations in the prefactor not being large enough to completely offset those in $E_a$, both in plots that exhibit a high degree of linearity and in curved non-Arrhenius plots. In addition, the observed isokinetic relation arises due to a transition to a non-interacting regime, and not due to compensation between $E_a$ and $\ln{\nu}$. We expect our results to provide a deeper insight into the microscopic events that originate compensation effects and isokinetic relations in our system, and in other fields where these effects have been reported., Comment: 11 pages, 17 figures, 3 tables

Fluids confined within narrow channels exhibit a variety of phases and phase transitions associated with their reduced dimensionality. In this review paper, we illustrate the crossover from quasi-one dimensional to higher effective dimensionality behavior of fluids adsorbed within different carbon nanotubes geometries. In the single nanotube geometry, no phase transitions can occur at finite temperature. Instead, we identify a crossover from a quasi-one dimensional to a two dimensional behavior of the adsorbate. In bundles of nanotubes, phase transitions at finite temperature arise from the transverse coupling of interactions between channels., Comment: 8 pages, 5 figures, presented at CMT33

We analyze the relationship between our group's results and those of three recent papers about gases in interstitial channels within nanotube bundles. In particular, we explain the relation between our prediction about bundle dilation upon interstitial adsorption (questioned in some way in these works) and their results.

Helium atoms or hydrogen molecules are believed to be strongly bound within the interstitial channels (between three carbon nanotubes) within a bundle of many nanotubes. The effects on adsorption of a nonuniform distribution of tubes are evaluated. The energy of a single particle state is the sum of a discrete transverse energy Et (that depends on the radii of neighboring tubes) and a quasicontinuous energy Ez of relatively free motion parallel to the axis of the tubes. At low temperature, the particles occupy the lowest energy states, the focus of this study. The transverse energy attains a global minimum value (Et=Emin) for radii near Rmin=9.95 Ang. for H2 and 8.48 Ang.for He-4. The density of states N(E) near the lowest energy is found to vary linearly above this threshold value, i.e. N(E) is proportional to (E-Emin). As a result, there occurs a Bose-Einstein condensation of the molecules into the channel with the lowest transverse energy. The transition is characterized approximately as that of a four dimensional gas, neglecting the interactions between the adsorbed particles. The phenomenon is observable, in principle, from a singular heat capacity. The existence of this transition depends on the sample having a relatively broad distribution of radii values that include some near Rmin., Comment: 21 pages, 9 figures

Three problems are considered in which inhomogeneous broadening can yield unusual consequences. One problem involves the energy levels of atoms moving within nanopores of nearly cylindrical cross section. A second involves atomic or molecular motion in a quasi-one dimensional interstitial channel within a bundle of carbon nanotubes. The third problem involves motion within a groove between two nanotubes at the surface of such a bundle. In each case, the density of states at low energy is qualitatively different from that occurring in the perfectly homogeneous case., Comment: 15 pages, 5 figures

A lattice gas model of adsorption inside cylindrical pores is evaluated with Monte Carlo simulations. The model incorporates two kinds of site: (a line of) ``axial'' sites and surrounding ``cylindrical shell'' sites, in ratio 1:7. The adsorption isotherms are calculated in either the grand canonical or canonical ensembles. At low temperature, there occur quasi-transitions that would be genuine thermodynamic transitions in mean-field theory. Comparison between the exact and mean-field theory results for the heat capacity and adsorption isotherms are provided.

We explore the ground state of a single hydrogen molecule within an interstitial channel (IC) of a bundle of carbon nanotubes. A previous (variational) study found that when many molecules are present, comprising a dense fluid, the nanotube lattice is slightly dilated, with a 1% relative increase of lattice constant. Although small, that dilation doubled the binding energy per molecule inside the ICs. Here, in the case of a single particle, the result is an even smaller dilation, localized near the particle, and a much smaller increase of the binding energy.

Gases adsorbed within bundles of carbon nanotubes (inside of the nanotubes or in the interstitial channels between the tubes) exhibit a variety of phase transitions with the help of interactions between molecules in neighboring channels or tubes. Because the channels/tubes are widely separated, these transverse interactions are weaker than the (longitudinal) interactions within the same channel. The transition temperatures that result are therefore lower than those of typical two- or three-dimensional transitions of the same species of molecules. We discuss here the condensation transition of such a gas to form a liquid, expressing the transition behavior in universal form, where the reduced critical temperature T_c* is a universal function of the reduced transverse interaction.

We evaluate the effects of heterogeneity on the density of states of H$_2$ molecules inside interstitial channels within bundles of carbon nanotubes. As temperature (T) falls, the density increases within those tubes having the greatest binding energy. At T ~ 10 mK, the molecules undergo Bose-Einstein condensation, exhibiting a singular heat capacity.

The three body (triple dipole) interaction of Axilrod, Teller and Muto (ATM) contributes 5 to 10 % of the total energy of condensed phases of inert elements. It is shown in this paper for clusters and films that a much larger or smaller ATM contribution can arise for other geometries or other atomic species. The ratio R of the three body interaction energy to the two body energy is evaluated for a wide variety of configurations. This ratio varies considerably with the geometry. For highly polarizable atoms in certain geometries, the magnitude of the three body energy is comparable to that of the two body energy and can be either attractive or repulsive. Systematic trends are established and explained., Comment: Changed format to include figures in same file

We evaluate the equation of state of the quasi-one-dimensional (1D) phase of C60 molecules in small carbon nanotubes, nicknamed ``peas in a pod''. The chemical potential and 1D pressure are evaluated as functions of the temperature and density, initially with the approximation of nearest neighbor interactions and classical statistical mechanics. Quantum corrections and long-range interaction corrections are discussed, as are the effects of interactions with neighboring peapods. Transition phenomena involving the 3D coupling are evaluated.

In some respects, a cluster consisting of many atoms may be regarded as a single large atom. Knowing the dielectric properties of such a cluster permits one to evaluate the form of the van der Waals (dispersion) interactions between two clusters or between one cluster and a surface. In this paper, we derive these interactions in two extreme opposite regimes of separation: fully retarded and nonretarded. In the fully retarded regime (very large separation), the magnitude of the interaction is determined by just the static polarizability of the cluster(s). In the nonretarded regime (small separation), we employ a single resonant frequency model of thecluster polarizability to derive expressions for the interactions' coefficients. Numerical examples are presented to demonstrate that many-body screening of these interactions can be significant. The results represent the corrections to the commonly used approximation of pairwise additivity of interatomic interactions.

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., Comment: 6 pages, 12 figures

Adsorption properties of several gases (Ne, CH4, Ar, Xe) on the external surface of a carbon nanotube bundle are investigated. Calculations are performed at low coverage and variable temperature, and for some temperatures as a function of coverage. Within a simple model (in the limit of very low coverage) we are able to study the evolution of the film's thermal properties from those of a one dimensional (1D) fluid to those of a 2D film. In addition, grand canonical Monte Carlo simulations are performed in order to identify a second layer groove phase, which occurs once a monolayer of atoms covers the external surface. We derive from the simulations the isosteric heat, compresibility and specific heat as a function of coverage. We evaluate alternative models in order to derive quantum corrections to the classical results. We compare our findings with those of recent adsorption experiments., Comment: 24 pages, 13 figure

We employ a simple model to describe the phase behavior of 4He and Ar in a hypothetical porous material consisting of a regular array of infinitely long, solid, parallel cylinders. We find that high porosity geometries exhibit two transitions: from vapor to film and from film to capillary condensed liquid. At low porosity, the film is replaced by a ``necking'' configuration, and for a range of intermediate porosity there are three transitions: from vapor to film, from film to necking and from necking to a capillary condensed phase., Comment: 14 pages, 7 figures

We explore the thermodynamic behavior of gases adsorbed within a nanopore. The theoretical description employs a simple lattice gas model, with two species of site, expected to describe various regimes of adsorption and condensation behavior. The model includes four hypothetical phases: a cylindrical shell phase (S), in which the sites close to the cylindrical wall are occupied, an axial phase (A), in which sites along the cylinder's axis are occupied, a full phase (F), in which all sites are occupied, and an empty phase (E). We obtain exact results at T=0 for the phase behavior, which is a function of the interactions present in any specific problem. We obtain the corresponding results at finite T from mean field theory. Finally, we examine the model's predicted phase behavior of some real gases adsorbed in nanopores.

We explore the behavior of neon, xenon, and methane filmas adsorbed on the external surface of a bundle of carbon nanotubes. The methods used are classical: a ground state calculation, by grand potential energy minimization, and the grand canonical Monte Carlo (GCMC) method of simulation. Our results are similar to those found recently in a GCMC study of Ar and Kr. At low chemical potential (pressure) the particles form a quasi-one dimensional phase within the groove formed by two contiguous tubes. At higher chemical potential, there occurs a "three-stripe" phase aligned parallel to the groove (except for xenon). This is followed by monolayer and bilayer phases. The low temperature monolayer phase is striped; the number of stripes per nanotube is a quantized function of the adatom size. In the neon case, the bilayer regime also includes a second layer groove phase. Our results are compared with recent thermal and diffraction experiments. We find no evidence of a zig-zag phase reported recently.

An overview is presented of the various phases predicted to occur when gases are absorbed within a bundle of carbon nanotubes. The behavior may be characterized by an effective dimensionality, which depends on the species and the temperature. Small molecules are strongly attracted to the interstitial channels between tubes. There, they undergo transitions between ordered and disordered quasi-one dimensional (1D) phases. Both small and large molecules display 1D and /or 2D phase behavior when adsorbed within the nanotubes, depending on the species and thermodynamic conditions. Finally, molecules adsorbed on the external surface of the bundle exhibit 1D behavior (striped phases), which crosses over to 2D behavior (monolayer film) and eventually 3D behavior (thick film) as the coverage is increased. The various phases exhibit a wide variety of thermal and other properties that we discuss here., Comment: 12 fig., submitted to Review of Modern Physics Colloquia

A study is presented of the effects of gas (especially H2) absorption within the interstitial channels of a bundle of carbon nanotubes. The ground state of the system is determined by minimizing the total energy, which includes the molecules' interaction with the tubes, the inter-tube interaction, and the molecules' mutual interaction (which is screened by the tubes). The consequences of swelling include a significant increase in the gas uptake and a 3 per cent increase in the tubes' breathing mode frecuency., Comment: 4 pages

We explore the equations of state and other properties of various quantum fluids (3He, 4He, their mixtures, and H_2) confined within individual carbon nanotubes. Above a threshold number of particles, N_a, the fluid density near the axis begins to grow above a negligibly small value. The properties of this axial fluid phase are sensitive to the tube size and hence to the transverse compression in the case of a bundle of nanotubes. We consider He at zero temperature and H_2 at low temperatures., Comment: 19 pages, 17 figures, submitted to J. Low Temp. Phys