Curved graphite and its mathematical transformations

Mathematical transformations for graphite with positive, negative and zero Gaussian curvatures are presented. When the Gaussian curvatureK is zero, we analyse a bending transformation from a planar sheet into a cone. The Bonnet, the Goursat and a mixed transformation are studied for graphitic structures with the same topologies as triply periodic minimal surfaces (K < 0). We have found that using the Kenmotsu equations for surfaces of constant mean curvature it is possible to invert spherical and cylindrical graphite. A bending transformation for surfaces of revolution is also studied; during this transformation the helical arrangement of cylinders changes. All these transformations can give an insight into kinematic processes of curved graphite and into new shapes.     

Energy-band structure and charge distribution for BaC6

An ab initio self-consistent calculation has been carried out for the electronic properties of BaC₆. Energy bands and charge densities are presented for BaC₆ and compared with those of LiC₆. The results show that the band originating from Ba states has a mixture of s and d character and the d component hybridizes appreciably with the π bands of graphite. The Fermi level intersects this band as well as the graphite π bands, giving rise to a complicated Fermi surface with several types of carriers. Depending on the type of volumetric partitioning, the charge transfer from Ba to graphite layers is determined to be between 0.7 and 1.0 electron per Ba atom. The calculated results are consistent with available transport and optical measurements.     

SCF calculations for H 2 + , Li 2 + and LiH+ with atomic basis sets enlarged by bond functions

To simulate the charge distortion in the formation of a molecule from the separated atoms, a set of concentrics-type Gaussian functions is placed on the internuclear axis in addition to thes-type atomic basis functions to construct the molecular orbital for the one valence-electron systems H ₂ ⁺ , Li ₂ ⁺ and LiH⁺. This simple model gives 90.1%, 75.2% and 61.7%, respectively, of the improvement over minimal basis relative to Hartree-Fock energies.Supported in part by a research grant to Rice University from the Robert A. Welch Foundation.     

Some aspects of the symmetry and topology of possible carbon allotrope structures

Elemental carbon has recently been shown to form molecular polyhedral allotropes known as fullerenes in addition to the familiar graphite and diamond known since antiquity. Such fullerenes contain polyhedral carbon cages in which all vertices have degree 3 and all faces are either pentagons or hexagons. All known fullerenes are found to satisfy the isolated pentagon rule (IPR) in which all pentagonal faces are completely surrounded by hexagons so that no two pentagonal faces share an edge. The smallest fullerene structures satisfying the IPR are the known truncated icosahedral C₆₀ of I _h symmetry and ellipsoidal C₇₀ of D _5h symmetry. The multiple IPR isomers of families of larger fullerenes such as C₇₆, C₇₈, C₈₂ and C₈₄ can be classified into families related by the so-called pyracylene transformation based on the motion of two carbon atoms in a pyracylene unit containing two linked pentagons separated by two hexagons. Larger fullerenes with 3ν vertices can be generated from smaller fullerenes with ν vertices through a so‐called leapfrog transformation consisting of omnicapping followed by dualization. The energy levels of the bonding molecular orbitals of fullerenes having icosahedral symmetry and 60n ² carbon atoms can be approximated by spherical harmonics. If fullerenes are regarded as constructed from carbon networks of positive curvature, the corresponding carbon allotropes constructed from carbon networks of negative curvature are the polymeric schwarzites. The negative curvature in schwarzites is introduced through heptagons or octagons of carbon atoms and the schwarzites are constructed by placing such carbon networks on minimal surfaces with negative Gaussian curvature, particularly the so-called P and D surfaces with local cubic symmetry. The smallest unit cell of a viable schwarzite structure having only hexagons and heptagons contains 168 carbon atoms and is constructed by applying a leapfrog transformation to a genus 3 figure containing 24 heptagons and 56 vertices described by the German mathematician Klein in the 19th century analogous to the construction of the C₆₀ fullerene truncated icosahedron by applying a leapfrog transformation to the regular dodecahedron. Although this C₁₆₈ schwarzite unit cell has local O _h point group symmetry based on the cubic lattice of the D or P surface, its larger permutational symmetry group is the PSL(2,7) group of order 168 analogous to the icosahedral pure rotation group, I, of order 60 of the C₆₀ fullerene considered as the isomorphous PSL(2,5) group. The schwarzites, which are still unknown experimentally, are predicted to be unusually low density forms of elemental carbon because of the pores generated by the infinite periodicity in three dimensions of the underlying minimal surfaces. This revised version was published online in July 2006 with corrections to the Cover Date.     

Molecular modeling study on surface,thermal, mechanical and gas diffusion properties of chitosan

The motivation of this work is to provide reliable and accurate modeling studies of the physical (surface, thermal, mechanical and gas diffusion) properties of chitosan (CS) polymer. Our computational efforts have been devoted to make a comparison of the structural bulk properties of CS with similar type of polymers such as chitin and cellulose through cohesive energy density, solubility parameter, hydrogen bonding, and free volume distribution calculations. Atomistic modeling on CS polymer using molecular mechanics (MM) and molecular dynamics (MD) simulations has been carried out in three dimensionally periodic and effective two dimensionally periodic condensed phases. From the equilibrated structures, surface energies were computed. The equilibrium structure of the films shows an interior region of mass density close to the value in the bulk state. Various components of energetic interactions have been examined in detail to acquire a better insight into the interactions between bulk structure and the film surface. MD simulation (NPT ensemble) has also been used to obtain polymer specific volume as a function of temperature. It is demonstrated that these V–T curves can be used to locate the volumetric glass transition temperature (T_g) reliably. The mechanical properties of CS have been obtained using the strain deformation method. Diffusion coefficients of O₂, N₂, and CO₂ gas molecules at 300 K in CS have been estimated. The calculated properties of CS are comparable with the experimental values reported in the literature. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 1260–1270, 2007     

Effect of Annulation Mode of Twistarene on the Physical Property and Self-Assembly Behavior of Functionalized Curved Aromatic Molecules

Four novel curved polycyclic aromatic hydrocarbons 3 a , 5 , 8 , 15 a have been synthesized and characterized, where molecules 3 a and 15 a bear [5]carbohelicene units. X-ray single crystal analyses indicate that compound 3 a shows offset packing arrangements of (P₅)- and (M₅)-isomers, and 15 a has a symmetrical plane and looks like a butterfly. In comparison, 8 exhibits a slightly curved structure, in which the significant convex-to-convex π-overlap with the shortest distance of 3.42 Å occurs. In addition, the effect of annulation mode of twistarenes on the physical properties, self-assembly behaviors, and switchable photoconductivity of the as-prepared curved aromatic compounds were further examined in a comparative manner.     

A Hybrid of Corannulene and Azacorannulene: Synthesis of a Highly Curved Nitrogen‐Containing Buckybowl

A highly curved nitrogen‐containing buckybowl, which can be considered as a corannulene/azacorannulene hybrid, was synthesized and characterized. This molecule has a polycyclic aromatic C₄₀N core, corresponding to a partial azafullerene structure C_80−xN_x (x=1,2,3…), and exhibits interesting properties that arise from its large and highly curved π surface and the embedded nitrogen atom, which include association with C₆₀, a lower LUMO level relative to azapentabenzocorannulene, and the formation of a radical cationic species upon oxidation.     

Derivatization and characterization of functionalized carbon powder via diazonium salt reduction

Chemical reduction of 4-chloro-2-nitrobenzenediazonium chloride salt in the presence of hypophosphorous acid and carbon powder results in functionalized carbon powder with chloronitrophenyl groups attached on carbon particle surface. This type of bulk derivatization protocol is very useful and most inexpensive compared to widely used electrochemically assisted derivatization protocol. The derivatized carbon powder has been characterized by studying its Fourier transform infrared spectroscopy (FTIR) and cyclic voltammetric studies. The surface functionalized moieties have been examined electrochemically by immobilizing them onto the surface of basal plane pyrolytic graphite electrode and studying its cyclic voltammetry. The effect of pH, scan rate (v), and the peak potentials (E _p) as a function of pH has revealed that the species are surface bound in nature and covalently attached on the carbon surface. The FTIR studies of the derivatized carbon powder have revealed that the modifying molecule is covalently attached on the carbon particle surface.     

Negatively Curved Octagon-Incorporated Aza-nanographene and its Assembly with Fullerenes

A negatively curved aza-nanographene (NG) containing two octagons was synthesized by a regioselective and stepwise cyclodehydrogenation procedure, in which a double aza[7]helicene was simultaneously formed as an intermediate. Their saddle-shaped structures with negative curvature were unambiguously confirmed by X-ray crystallography, thereby enabling the exploration of the structure–property relationship by photophysical, electrochemical and conformational studies. Moreover, the assembly of the octagon-embedded aza-NG with fullerenes was probed by fluorescence spectral titration, with record-high binding constants (K_a=9.5×10³ M⁻¹ with C₆₀, K_a=3.7×10⁴ M⁻¹ with C₇₀) found among reported negatively curved polycyclic aromatic compounds. The tight association of aza-NG with C₆₀ was further elucidated by X-ray diffraction analysis of their co-crystal, which showed the formation of a 1 : 1 complex with substantial concave-convex interactions.     

Quantum-chemical calculation of a spillover model on a graphite support

The simplest quantum-chemical models of hydrogen spillover over a graphite-like surface as a proton or radical have been considered. The condensed planar C₂₄H₁₂ molecule was used as a model surface. Theab initio calculations of the interaction of hydrogen with the model surface were carried out by the restricted Hartree-Fock (HF) method in the STO-3G and 6-31 G^* basis sets. The radical hydrogen can not bind to such a surface, whereas the proton binds to it with an energy release of 186 kcal mol⁻¹. The activation energy of the transfer of the proton between two neighboring carbon atoms (10 kcal mol⁻¹) has been determined. The simplest model of the hydrogen migration as a proton over the model surface can be used for describing the spillover of hydrogen over the graphite surface. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 3, pp. 428–430, March, 1997.     

Synthesis of nanostructured carbon on graphite electrodes with a supported Co catalyst for preparing anodes for microbial fuel cells

The synthesis of nanostructured carbon (NSC) on graphite electrodes with a supported Co catalyst by C₃ and C₄ alkane pyrolysis in the presence of hydrogen has been investigated. Co(II) hydroxo compounds have been deposited onto graphite, and a Co/graphite catalyst has been prepared by the homogeneous precipitation of divalent cobalt from cobalt nitrate solutions in the presence of urea and compounds containing OH groups, namely, lower alcohols (ethanol, n-propanol, and n-butanol) and polyols (ethylene glycol, glycerol, and sorbitol). The effect of Co catalyst preparation conditions on the pyrolytic activity of the catalyst and on the morphology of the synthesized NSC has been investigated. An active Co/graphite catalyst forms in the presence of an alcohol containing 1-3 OH groups. A fairly uniform NSC layer on the graphite surface is obtained at Co(II) nitrate concentrations of 0.05–0.1 mol/L, a urea concentration of 1 mol/L, and glycerol concentrations of 5–20 vol %. The electrochemical characteristics of the electrodes prepared and those of a microbial fuel cell (MFC) involving an NSC/graphite anode and an activated-sludge microbial consortium have been determined. The maximum power of the MFC under the conditions examined is 4.8 mW per square meter of the anode’s geometric surface area.     

Determination of the depth profiles of ion-implanted impurities by electron probe x-ray microanalysis

The aim of this paper is to demonstrate the suitability of electron probe x-ray microanalysis (EPMA) for nondestructive determination of the depth profiles of ion-implanted impurities. The intensities of the characteristic x-ray emission of impurity atoms (P and As) were measured (on a WDX spectrometer) on the implanted specimens and references (GaP and GaAs) at three values of primary electron energy E_P. The range distribution of the implanted impurity as a first approximation is given by a Gaussian distribution. A two-parameter fitting has been developed for the determination of Gaussian parameters R_P and ΔR_P of the profiles, which give a minimal difference between the experimental and calculated x-ray intensities at different E_P. The dose of the implanted impurity is a third parameter that can be obtained here. The results were compared with those of depth profiles from AES (for P) and SIMS (for As) and good agreement is observed. A new method for the determination of the depth distribution of x-ray production for the characteristic x-rays of impurity atoms is also presented.     

Minimal basis sets in calculations of intermolecular interaction energies

Several minimal (7, 3/3) Gaussian basis sets have been used to calculate the energies and some other properties of CH₄ and H₂O. Improved basis sets developed for these molecules have been extended to NH₃ and HF and employed to H₂CO and CH₃OH. Interaction energies between XH_n molecules have been calculated using the old and the new minimal basis sets. The results obtained with the new basis sets are comparable in accuracy to those calculated with significantly more extended basis sets involving polarization functions. Binding energies calculated using the counterpoise method are not much different for the new and the old minimal basis sets, and are likely to be more accurate than the results of much more extended calculations.     

Mass Distribution and Diffusion of [1‐Butyl‐3‐methylimidazolium][Y] Ionic Liquids Adsorbed on the Graphite Surface at 300–800 K

The structure and diffusion behavior of 1‐butyl‐3‐methylimidazolium ([bmim]⁺) ionic liquids with [Cl]^?, [PF₆]^?, and [Tf₂N]^? counterions near a hydrophobic graphite surface are investigated by molecular dynamics simulation over the temperature range of 300–800 K. Near the graphite surface the structure of the ionic liquid differs from that in the bulk and it forms a well‐ordered region extending over 30 Å from the surface. The bottom layer of the ionic liquid is stable over the investigated temperature range due to the inherent slow dynamics of the ionic liquid and the strong Coulombic interactions between cation and anion. In the bottom layer, diffusion is strongly anisotropic and predominantly occurs along the graphite surface. Diffusion perpendicular to the interface (interfacial mass transfer rate k_t) is very slow due to strong ion–substrate interaction. The diffusion behaviors of the three ionic liquids in the two directions all follow an Arrhenius relation, and the activation barrier increases with decreasing anion size. Such an Arrhenius relation is applied to surface‐adsorbed ionic liquids for the first time. The ion size and the surface electrical charge density of the anions are the major factors determining the diffusion behavior of the ionic liquid adjacent to the graphite surface.     

PtPd-nanoparticles supported by new carbon materials

Nanocomposites based on PtPd nanoparticles with chemical ordering like disordered solid solution on surface of multilayer graphene have been prepared through thermal shock of mechanically obtained mixture of double complex salt [Pd(NH₃)₄][PtCl₆] and different carbon materials–exfoliated graphite, graphite oxide and graphite fluoride. An effect of original carbon precursors on formation of PtPd bimetallic nanoparticles was studied using X-ray absorption spectroscopy (XAFS), transmission electron microscopy (TEM) and X-ray photoelectron spectroscopy (XPS). It was shown that the distribution of bimetallic nanoparticles over the multilayer graphene surface as well as the particles size distribution is controlled by the graphene precursors. For all nanocomposites, the surface of the nanoparticles was found to be Pd-enriched. In case when the thermal exfoliated graphite and graphite oxide were used as the graphene precursors a thin graphitized layer covered the nanoparticles surface. Such a graphitized layer was not observed in the nanocomposite, which used the fluorinated graphite as the precursor.     

Electrochemical chlorine sensor with multi-walled carbon nanotubes as electrocatalysts

It has been reported for the first time that an electrochemical gas sensor modified with multi-walled carbon nanotubes (MWNTs) film as electrocatalyst was fabricated for the determination of chlorine (Cl₂).Here, MWNTs and graphite were compared with each other in terms of their electrochemical properties using cyclic voltammetry. Cl₂ gas was allowed through the cathode surface of the sensor and the resulting galvanic effects were monitored. Results indicated that both of the MWNTs and graphite have the electrocatalytic activity for the reduction of Cl₂ while the MWNTs-modified electrode exhibited a higher accessible surface area in electrochemical reactions, excellent sensitivity, stable response, reproducibility and recovery for the determination of Cl₂.     

Palladium Nanoparticles Embedded into Graphene Nanosheets: Preparation,Characterization, and Nonenzymatic Electrochemical Detection of H2O2

A novel nonenzymatic H₂O₂ sensor based on a palladium nanoparticles/graphene (Pd‐NPs/GN) hybrid nanostructures composite film modified glassy carbon electrode (GCE) was reported. The composites of graphene (GN) decorated with Pd nanoparticles have been prepared by simultaneously reducing graphite oxide (GO) and K₂PdCl₄ in one pot. The Pd‐NPs were intended to enlarge the interplanar spacing of graphene nanosheets and were well dispersed on the surface or completely embedded into few‐layer GN, which maintain their high surface area and prevent GN from aggregating. XPS analysis indicated that the surface Pd atoms are negatively charged, favoring the reduction process of H₂O₂. Moreover, the Pd‐NPs/GN/GCE could remarkably decrease the overpotential and enhance the electron‐transfer rate due to the good contact between Pd‐NPs and GN sheets, and Pd‐NPs have high catalytical effect for H₂O₂ reduction. Amperometric measurements allow observation of the electrochemical reduction of H₂O₂ at 0.5 V (vs. Ag/AgCl). The H₂O₂ reduction current is linear to its concentration in the range from 1×10^?9 to 2×10^?3 M, and the detection limit was found to be 2×10^?10 M (S/N=3). The as‐prepared nonenzymatic H₂O₂ sensor exhibits excellent repeatability, selectivity and long‐term stability.     

A thermal analysis investigation of new insulator compositions based on EPDM and phenolic resin

New rocket insulator compositions have been studied by adding various types and amounts of fillers, such as graphite and asbestos fibres, Al₂O₃, MgZrO₂, Cr₂O₃, SiC, carbon powders and phenolic resin to the base EPDM gum and graphite, kevlar,E type glass fibres to the base phenolic resin in order to improve thermal and ablative efficiency. The degradation of the insulators has been investigated by thermogravimetry (TG) analysis to 900°C and DSC analysis to 500°C. Conversion curves of the insulators at different heating rates were performed and maximum degradation temperatures were found as 646 and 661°C for EPDM P and phenolic resin, respectively. The kinetic parameters for degradation have been evaluated and the lifetime of the rocket insulators has been estimated. Thermal analysis has been conducted on the insulators and the indepth temperature distribution was evaluated in order to find optimum insulation thickness.