Energy and mass balances related to climate change and remediation.

The goal of this paper is to provide a forum for a broad interdisciplinary group of scientists and engineers to see how concepts of climate change, energy, and carbon remediation strategies are related to quite basic scientific principles. A secondary goal is to show relationships between general concepts in traditional science and engineering fields and to show how they are relevant to broader environmental concepts. This paper revisits Fourier's early mathematical derivation of the average temperature of the Earth from first principles, i.e. an energy balance common to chemical and environmental engineering. The work then uses the concept of mass balance to critically discuss various carbon remediation strategies. The work is of interest to traditional scientists/engineers, but also it is potentially useful as an educational document in advanced undergraduate science or engineering classes.

Adsorption-induced shape transitions in bistable nanopores with atomically thin walls.

Atomically thin cylindrical nanopores can change shape in response to physically adsorbed gas inside. Coupled to a gas reservoir, an initially collapsed pore can expand to allow the adsorbed gas to form concentric shells on the inner part of the pore, driven by adsorption energetics, not gas pressure. A lattice gas model describes the evolution of the nanotube pore shape and absorbed gas as a function of gas chemical potential at zero temperature. We found that narrow-enough tubes are always expanded and gas inside adsorbs in sequences of concentric shells as the gas chemical potential increases. Wider tubes, which are collapsed without gas, can expand with one or more concentric shells adsorbed on the inner surface of the expanded region.

Corresponding states interpretation of adsorption in gate-opening metal-organic framework Cu(dhbc)2(4,4'-bpy).

The "universal adsorption theory" (UAT) extends the principle of corresponding states for gas compressibility to describe the excess density of an adsorbed phase at comparable reduced conditions. The UAT helps to describe experimental trends and provide predictive capacity for extrapolation from one adsorption isotherm to that of a different adsorbate. Here, we extend the UAT to a flexible metal-organic framework (MOF) as a function of adsorbate, temperature, and pressure. When considered via the UAT, the adsorption capacity and GO pressure of multiple gases to Cu(dhbc)2(4,4'-bpy) [H2dhbc=2,5-dihydroxybenzoic acid, bpy=bipyridine] show quantifiable trends over a considerable temperature and pressure range, despite the chemical and structural heterogeneity of the adsorbent. Exceptions include quantum gases (such as H2) and prediction of maximum capacity for large and/or polar adsorbates. A method to derive the heat of gate opening and heat of expansion from experimental trends is also presented, and the parameters can be treated as separable and independent over the temperature and pressure range studied. We demonstrate the relationship between the UAT and the common Dubinin analysis, which was not previously noted.

Wetting transitions of water on graphite and graphene.

Water has been predicted theoretically and observed experimentally to exhibit a wetting transition on graphite. Previous study of this problem was based on quite uncertain water-graphite interaction potentials. This paper computes the wetting temperature on graphite using recent, more realistic, interactions. Similar calculations are presented for the case of water on a suspended (free-standing) graphene sheet.

Theory of electrocaloric effect in a shape-changing container: gas in a nanotube.

Driven by applied voltage or Ohmic heating, bistable nanotubes filled with gas can transform between expanded and collapsed configurations and by doing so convert energy between mechanical, electrical, and thermal forms. The electrocaloric response, a reversible change of temperature in response to applied voltage, combines the advantages of a working fluid with the lack of internal interfaces characteristic of robust solid-state thermoelectric devices. Such devices could be constructed from any conductive two-dimensional atomically thin material wrapped into an appropriate geometry.

Novel behavior of monolayer quantum gases on graphene, graphane and fluorographene.

This article discusses the behavior of submonolayer quantum films (He and H2) on graphene and newly discovered surfaces that are derived from graphene. Among these substrates are graphane (abbreviated GH), which has an H atom bonded to each C atom, and fluorographene (GF). The subject is introduced by describing the related problem of monolayer films on graphite. For that case, extensive experimental and theoretical investigations have revealed that the phase diagrams of the Bose gases (4)He and para-H2 are qualitatively similar, differing primarily in a higher characteristic temperature scale for H2 than for He. The phase behavior of these films on one side of pristine graphene, or both sides of free-standing graphene, is expected to be similar to that on graphite. We point out the possibility of novel phenomena in adsorption on graphene related to the large flexibility of the graphene sheet, to the non-negligible interaction between atoms adsorbed on opposite sides of the sheet and to the perturbation effect of the adsorbed layer on the Dirac electrons. In contrast, the behavior predicted on GF and GH surfaces is very different from that on graphite, a result of the different corrugation, i.e., the lateral variation of the potential experienced by these gases. This arises because on GF, for example, half of the F atoms are located above the C plane while the other half are below this plane. Hence, the He and H2 gases experience very different potentials from those on graphite or graphene. As a result of this novel geometry and potential, distinct properties are observed. For example, the (4)He film's ground state on graphite is a two-dimensional (2D) crystal commensurate with the substrate, the famous [Formula: see text] phase; on GF and GH, instead, it is predicted to be an anisotropic superfluid. On GF the anisotropy is so extreme that the roton excitations are very anisotropic, as if the bosons are moving in a multiconnected space along the bonds of a honeycomb lattice. Such a novel phase has not been predicted or observed previously on any substrate. Also, in the case of (3)He the film's ground state is a fluid, thus offering the possibility of studying an anisotropic Fermi fluid with a tunable density. The exotic properties expected for these films are discussed along with proposed experimental tests.

Experimental and theoretical comparison of gas desorption energies on metallic and semiconducting single-walled carbon nanotubes.

Single-walled carbon nanotubes (SWNTs) exhibit high surface areas and precisely defined pores, making them potentially useful materials for gas adsorption and purification. A thorough understanding of the interactions between adsorbates and SWNTs is therefore critical to predicting adsorption isotherms and selectivities. Metallic (M-) and semiconducting (S-) SWNTs have extremely different polarizabilities that might be expected to significantly affect the adsorption energies of molecules. We experimentally and theoretically show that this expectation is contradicted, for both a long chain molecule (n-heptane) and atoms (Ar, Kr, and Xe). Temperature-programmed desorption experiments are combined with van der Waals corrected density functional theory, examining adsorption on interior and exterior sites of the SWNTs. Our calculations show a clear dependence of the adsorption energy on nanotube diameter but not on whether the tubes are conducting or insulating. We find no significant experimental or theoretical difference in adsorption energies for molecules adsorbed on M- and S-SWNTs having the same diameter. Hence, we conclude that the differences in polarizabilities between M- and S-SWNTs have a negligible influence on gas adsorption for spherical molecules as well as for highly anisotropic molecules such as n-heptane. We expect this conclusion to apply to all types of adsorbed molecules where van der Waals interactions govern the molecular interaction with the SWNT.

Is there a difference in van der Waals interactions between rare gas atoms adsorbed on metallic and semiconducting single-walled carbon nanotubes?

The differences in the polarizabilities of metallic (M) and semiconducting (S) single-walled carbon nanotubes (SWNTs) might give rise to differences in adsorption potentials. We show from experiments and van der Waals--corrected density functional theory that the binding energies of Xe adsorbed on M- and S-SWNTs are nearly identical. Temperature programed desorption experiments of Xe on purified M- and S-SWNTs give similar peak temperatures, indicating that desorption kinetics and binding energies are independent of the type of SWNT. Binding energies computed from vdW-corrected density functional theory are in good agreement with experiments.

Van der Waals interactions: accuracy of pair potential approximations.

Van der Waals interactions between single atoms and solids are discussed for the regime of large separation. A commonly employed approximation is to evaluate this interaction as a sum of two-body interactions between the adatom and the constituent atoms of the solid. The resulting potentials are here compared with known results in various geometries. Analogous comparisons are made for diatomic molecules near either single atoms or semi-infinite surfaces and for triatomic molecules' interactions with single atoms.

Frictional temperature rise in a sliding physisorbed monolayer of Kr/graphene.

A quartz crystal microbalance (QCM) with a graphene/Ni(111) electrode has been used to probe frictional heating effects in Kr monolayers sliding on the microbalance electrode in response to its oscillatory motion. The temperatures of the sliding Kr monolayers are observed to rise approximately 13 K higher than their static counterparts, but show surprisingly little dependence on oscillation amplitude. Although counterintuitive, the observation can be explained by noting that the Kr surface residence times are limited, which effectively caps how much the temperature can rise.

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).

Structural, electronic, optical and vibrational properties of nanoscale carbons and nanowires: a colloquial review.

This review addresses the field of nanoscience as viewed through the lens of the scientific career of Peter Eklund, thus with a special focus on nanocarbons and nanowires. Peter brought to his research an intense focus, imagination, tenacity, breadth and ingenuity rarely seen in modern science. His goal was to capture the essential physics of natural phenomena. This attitude also guides our writing: we focus on basic principles, without sacrificing accuracy, while hoping to convey an enthusiasm for the science commensurate with Peter's. The term 'colloquial review' is intended to capture this style of presentation. The diverse phenomena of condensed matter physics involve electrons, phonons and the structures within which excitations reside. The 'nano' regime presents particularly interesting and challenging science. Finite size effects play a key role, exemplified by the discrete electronic and phonon spectra of C(60) and other fullerenes. The beauty of such molecules (as well as nanotubes and graphene) is reflected by the theoretical principles that govern their behavior. As to the challenge, 'nano' requires special care in materials preparation and treatment, since the surface-to-volume ratio is so high; they also often present difficulties of acquiring an experimental signal, since the samples can be quite small. All of the atoms participate in the various phenomena, without any genuinely 'bulk' properties. Peter was a master of overcoming such challenges. The primary activity of Eklund's research was to measure and understand the vibrations of atoms in carbon materials. Raman spectroscopy was very dear to Peter. He published several papers on the theory of phonons (Eklund et al 1995a Carbon 33 959-72, Eklund et al 1995b Thin Solid Films 257 211-32, Eklund et al 1992 J. Phys. Chem. Solids 53 1391-413, Dresselhaus and Eklund 2000 Adv. Phys. 49 705-814) and many more papers on measuring phonons (Pimenta et al 1998b Phys. Rev. B 58 16016-9, Rao et al 1997a Nature 338 257-9, Rao et al 1997b Phys. Rev. B 55 4766-73, Rao et al 1997c Science 275 187-91, Rao et al 1998 Thin Solid Films 331 141-7). His careful sample treatment and detailed Raman analysis contributed greatly to the elucidation of photochemical polymerization of solid C(60) (Rao et al 1993b Science 259 955-7). He developed Raman spectroscopy as a standard tool for gauging the diameter of a single-walled carbon nanotube (Bandow et al 1998 Phys. Rev. Lett. 80 3779-82), distinguishing metallic versus semiconducting single-walled carbon nanotubes, (Pimenta et al 1998a J. Mater. Res. 13 2396-404) and measuring the number of graphene layers in a peeled flake of graphite (Gupta et al 2006 Nano Lett. 6 2667-73). For these and other ground breaking contributions to carbon science he received the Graffin Lecture award from the American Carbon Society in 2005, and the Japan Carbon Prize in 2008. As a material, graphite has come full circle. The 1970s renaissance in the science of graphite intercalation compounds paved the way for a later explosion in nanocarbon research by illuminating many beautiful fundamental phenomena, subsequently rediscovered in other forms of nanocarbon. In 1985, Smalley, Kroto, Curl, Heath and O'Brien discovered carbon cage molecules called fullerenes in the soot ablated from a rotating graphite target (Kroto et al 1985 Nature 318 162-3). At that time, Peter's research was focused mainly on the oxide-based high-temperature superconductors. He switched to fullerene research soon after the discovery that an electric arc can prepare fullerenes in bulk quantities (Haufler et al 1990 J. Phys. Chem. 94 8634-6). Later fullerene research spawned nanotubes, and nanotubes spawned a newly exploding research effort on single-layer graphene. Graphene has hence evolved from an oversimplified model of graphite (Wallace 1947 Phys. Rev. 71 622-34) to a new member of the nanocarbon family exhibiting extraordinary electronic properties. Eklund's career spans this 35-year odyssey.

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.

Transitions of gases physisorbed on graphene.

The behavior of gases physically adsorbed on graphene might be expected to be similar to that of ones adsorbed on graphite. Here, three kinds of phase transitions are examined for gases adsorbed on suspended, free-standing graphene. In one case, the quasi-two-dimensional condensation of a van der Waals fluid is evaluated, using perturbation theory. In a second case, changes are discussed for contributions to the ground state energies of monolayer solid and liquid phases of quantum adsorbates (especially He) on graphene. This includes a determination of the leading perturbation terms in the adsorption-mediated (McLachlan) dispersion energy for two adatoms on a graphene sheet. The third problem is the wetting transition of water and other fluids on graphene. In each case, the relevant energies are somewhat different from those for adsorption on graphite.

Adsorption of ammonia on graphene.

We report on experimental studies of NH3 adsorption/desorption on graphene surfaces. The study employs bottom-gated graphene field effect transistors supported on Si/SiO2 substrates. Detection of NH3 occurs through the shift of the source-drain resistance maximum ('Dirac peak') with the gate voltage. The observed shift of the Dirac peak toward negative gate voltages in response to NH3 exposure is consistent with a small charge transfer (f approximately 0.068 +/- 0.004 electrons per molecule at pristine sites) from NH3 to graphene. The desorption kinetics involves a very rapid loss of NH3 from the top surface and a much slower removal from the bottom surface at the interface with the SiO2 that we identify with a Fickian diffusion process.

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.

Van der Waals dispersion forces between dielectric nanoclusters.

Various methods are evaluated for their ability to calculate accurate van der Waals (VDW) dispersion forces between nanoclusters. We compare results for spheres using several methods: the simple Hamaker two-body method, the Lifshitz (DLP) theory with the Derjaguin approximation, the Langbein result for spheres, and our "coupled dipole method" (CDM). The assumptions and shortcomings of each method are discussed. The CDM accounts for all n-body forces, does not assume a continuous and homogeneous dielectric function in each material, accounts for the discreteness of atoms in the particles, can be used for particles of arbitrary shape, and can exactly include the effects of various media. At present, the CDM does not account for retardation. It is shown that even for spheres, methods other than the CDM often give errors of 20% or more for VDW dispersion forces between typical dielectric materials. A related calculation for metals reveals an error in the Hamaker two-body result of nearly a factor of 2.

Fully retarded van der Waals interaction between dielectric nanoclusters.

The van der Waals (dispersion) interaction between an atom and a cluster or between two clusters at large separation is calculated by considering each cluster as a point particle, characterized by a polarizability tensor. For the extreme limit of very large separation, the fully retarded regime, one needs to know just the static polarizability in order to determine the interaction. This polarizability is evaluated by including all many-body (MB) intracluster atomic interactions self-consistently. The results of these calculations are compared with those obtained from various alternative methods. One is to consider each cluster as a collection of many atoms and evaluate the sum of two-body interatomic interactions, a common assumption. An alternative method is to include three-body atomic interactions as a MB correction term in the total energy. A comparison of these results reveals that the contribution of the higher-than-three-body MB interactions is always attractive and non-negligible even at such a large separation, in contrast to common assumptions. The procedure employed is quite general and is applicable, in principle, to any shape or size of dielectric cluster. We present numerical results for clusters composed of atoms with polarizability consistent with silica, for which the higher-than-three-body MB correction term can be as high as 42% of the atomic pairwise sum. This result is quite sensitive to the anisotropy and orientation of the cluster, in contrast to the result found in the additive case. We also present a power law expansion of the total van der Waals interaction as a series of n-body interaction terms.

van der Waals forces between nanoclusters: importance of many-body effects.

van der Waals interactions between nanoclusters have been calculated with a self-consistent, coupled dipole method. The method accounts for all many-body (MB) effects. Comparison is made between the exact potential energy, V, and the values obtained with two alternative methods: the sum of two-body interactions and the sum of two-body and three-body interactions. For all cases considered, the three-body term alone does not accurately represent the MB contributions to V. MB contributions are especially large for shape-anisotropic clusters.