Physical adsorption (physisorption) is the study of atoms or molecules weakly bound to material surfaces. Physisorption-related investigations raise critical questions concerning phase transitions, fractals, wetting transitions, two-dimensional superfluidity, and Van der Waals interactions. This chapter focuses on adsorption of gases (e.g. Ar, Kr, H2, CO2, and CH4) in nanomaterials, and in particular the authors describe equilibrium properties of the gases adsorbed in carbon nanotubes, graphene and Metal Organic Frameworks (MOFs). The adsorption potential used for developing the theoretical model for studying physisorption involves the summing of two-body interactions, and several important properties of adsorbates can be obtained via simulations, namely equilibrium properties, thermal characteristics, selectivity, wetting features, and structure and phase of the adsorbed monolayer. Applications of physisorption include the separation of cryogenic gases, their storage and their use as a surface characterization tool.

Nanobubbles have been found to form at the interface of water and solid surfaces. We examine the conditions for such bubbles to form and estimate the pressure inside the bubble based on thermodynamic considerations. Using a simple model we calculate the contact angle for a wide range of temperatures and hypothetical substrates possessing a continuous range of strengths. We show that as the temperature increases the shape of a bubble changes continuously from a spherical cap with low curvature to a complete sphere. An equivalent effect results from either increasing the strength of the solid or decreasing the surface tension. A model of a substrate formed by layers of materials is proposed to obtain a nanobub- ble with a particular contact angle.

Nanotubes and buckyballs represent novel substrates for gas adsorption. This situation has attracted significant experimental and theoretical attention, resulting in a wide variety of intriguing behaviors, including phases of unconventional effective dimensionality. This article reviews this field. Many of the unusual predictions have yet to be tested. In some cases, heterogeneity plays a significant role in actual experiments. This research area therefore presents many unanswered questions of fundamental significance.

Low-energy electron diffraction (LEED) experiments and grand canonical Monte Carlo simulations were carried out to study the adsorption of Xe on a substrate composed of a monolayer of C(60) molecules on a Ag(111) surface. LEED adsorption isobars indicated that the adsorption occurs in steps, with the Xe initially adopting a structure having the same unit cell as the C(60). Isosteric heats corresponding to the first two steps were measured to be 234 +/- 8 and 204 +/- 14 meV, respectively. For the simulations, the interaction potential of Xe with the composite substrate was modeled as the sum of two parts: the Xe-Ag part was computed using an ab initio van der Waals potential that varies as an inverse-distance cubed and the Xe-C(60) part was computed using a spherically averaged C(60) potential [E. S. Hernandez , J. Low Temp. Phys. 134, 309 (2004)]. The resulting adsorption potential is highly corrugated, with the most attractive sites located in the threefold hollows between the C(60) molecules, forming a honeycomb array. The simulations (at temperatures ranging from 55 to 90 K) show that these attractive sites are filled first, followed by adsorption in two types of secondary sites, where a competition exists due to steric hindrance. The thermodynamic properties of film growth obtained in the simulation are in good agreement with the experiment.

We employ canonical Monte Carlo simulations to explore the properties of an Ar film adsorbed on the external surface of a bundle of carbon nanotubes. The study is concerned primarily with three properties: specific heat $c(T)$, differential heat of adsorption $q_d$, and Ar-Ar correlation functions $g(\mathbf{r})$. These measurable functions exhibit information about the dependence of film structure on coverage and temperature.

Recent experiments have found unusual behavior of the specific heat of 3He-4He mixtures within the regular porous material FSM-16. We analyze this problem with quantum density functional calculations of 4He, followed by ideal gas calculations of 3He in the resulting potential. The results are in semiquantitative agreement with the experimental data.

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.

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.

A wetting transition occurs when the contact angle of a liquid drop on a surface changes from a nonzero value to zero. Such a transition has never been observed for water on any solid surface. This paper discusses the value of the temperature T_w at which the transition should occur for water on graphite. A simple model, previously used for nonpolar fluids, predicts the value of T_w as a function of the well-depth D of the adsorption potential. While D is not well known for the case of water/graphite, the model implies that T_w is likely to fall in the range 350 to 500 K. Experimental search for this transition is warranted. Water wetting transition temperatures on other surfaces are also discussed.

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.

Helium atoms and hydrogen molecules can be strongly bound inside interstitial channels within bundles of carbon nanotubes. An exploration of the low energy and low temperature properties of 3He atoms is presented here. Recent study of the analogous 4He system has shown that the effect of heterogeneity is to yield a density of states N(E) that is qualitatively different from the one-dimensional (1D) form of N(E) that would occur for an ideal set of identical channels. In particular, the functional form of N(E) is that of a 4D gas near the very lowest energies and a 2D gas at somewhat higher energies. Similar behavior is found here for 3He. The resulting thermodynamic behavior of this fermi system is computed, yielding an anomalous form of the heat capacity and its dependence on coverage.

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.

The three-body (triple dipole) interaction of Axilrod, Teller, and Muto (ATM) contributes 5--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.

We evaluate the equation of state of the quasi-one-dimensional (1D) phase of C-60 molecules in small carbon nanotubes, nicknamed peapods. 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.

We perform a systematic investigation of the structure, elementary, and phonon excitations of quantum fluid He-4 adsorbed in the interior of carbon nanotubes. We show that the helium fluid inside the cylinder behaves exactly as in planar films on a graphite substrate, presenting the same kind of layering transition. This tendency is confirmed by the behavior of a single He-3 impurity diluted into adsorbed He-4. We also present a simple description of the lowest excitation modes of the adsorbed fluid and compute the low-temperature contribution of the phonon spectrum to the specific heat, which displays the dimensionality characteristics reported in previous works.

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.

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 the cluster 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.

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.

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.