Negatively curved graphite and triply periodic minimal surfaces

The Weierstrass representation has been used to construct negatively curved graphite in which atoms rest no a perfect triply periodic minimal surface. By applying the Bonnet transformation on a patch of the D surface decorated with graphite we have been able to construct the Gyroid and P minimal surfaces. Curvatures, densities and lattice parameters have been calculated. It has been found that the maximum Gaussian curvature for our negatively curved structures is less in magnitude than the Gaussian curvature ofC ₆₀. In addition, a new periodic graphitic set with the same topology as the I-WP minimal surface has been obtained by introducing pentagonal and octagonal rings.     

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.     

Microemulsion microstructure and interfacial curvature

The typical phase behavior of microemulsion systems undergoing phase inversion is briefly reviewed. As a model system H₂O-n-octane-C₁₂E₅ is studied with various experimental techniques. The occurring microstructures are visualized by freeze fracture electron microscopy and the corresponding domain sizes are quantified by small-angle neutron scattering. From the variations of the domain sizes the mean and Gaussian curvatures of the interfacial film with temperature are determined. It is found that the mean interfacial curvatureH changes gradually and nearly linearly with temperature from positive (Winsor I) to negative (Winsor II), passing through zero for bicontinuous microemulsions where these contain exactly equal volume fractions of water and oil. There the interfacial tension between bulk water-and oil-rich phases passes through an extreme minimum. Quantitative knowledge of the curvatures permits the measurements of interfacial tensions between the bulk phases to be discussed in terms of the relative contributions of bending energy and entropy of dispersion.     

Multifunctional Tricarbazolo Triazolophane Macrocycles: One‐Pot Preparation,Anion Binding,and Hierarchical Self‐Organization of Multilayers

Programming the synthesis and self‐assembly of molecules is a compelling strategy for the bottom‐up fabrication of ordered materials. To this end, shape‐persistent macrocycles were designed with alternating carbazoles and triazoles to program a one‐pot synthesis and to bind large anions. The macrocycles bind anions that were once considered too weak to be coordinated, such as PF₆^?, with surprisingly high affinities (β₂=10¹¹ M ^?2 in 80:20 chloroform/methanol) and positive cooperativity, α=(4 K₂/K₁)=1200. We also discovered that the macrocycles assemble into ultrathin films of hierarchically ordered tubes on graphite surfaces. The remarkable surface‐templated self‐assembly properties, as was observed by using scanning tunneling microscopy, are attributed to the complementary pairing of alternating triazoles and carbazoles inscribed into both the co‐facial and edge‐sharing seams that exist between shape‐persistent macrocycles. The multilayer assembly is also consistent with the high degree of molecular self‐association observed in solution, with self‐association constants of K=300 000 M ^?1 (chloroform/methanol 80:20). Scanning tunneling microscopy data also showed that surface assemblies readily sequester iodide anions from solution, modulating their assembly. This multifunctional macrocycle provides a foundation for materials composed of hierarchically organized and nanotubular self‐assemblies.     

Calculation and analysis of the structure and vibrational spectra of uracil tautomers

The structure and vibrational spectra of twelve tautomers are calculated in the B3LYP/6-311+G(d,p) approximation and analyzed. Spectral manifestations of isomeric uracil transformations into one out of the twelve tautomeric forms and cis— trans- isomeric transformations of the tautomers themselves are considered. All tautomeric transformations are shown to be characterized by the presence of at least one vibration, whose frequency is different by ~ 100-200 cm^-1 from a similar vibrational frequency of the precursor and also by a pronounced change in the intensity of bending vibrations of OH hydroxyl groups and stretching vibrations of CO bonds.     

Diarylethene Self‐Assembled Monolayers: Cocrystallization and Mixing‐Induced Cooperativity Highlighted by Scanning Tunneling Microscopy at the Liquid/Solid Interface

Stimulus control over 2D multicomponent molecular ordering on surfaces is a key technique for realizing advanced materials with stimuli‐responsive surface properties. The formation of 2D molecular ordering along with photoisomerization was monitored by scanning tunneling microscopy at the octanoic acid/highly oriented pyrolytic graphite interface for a synthesized amide‐containing diarylethene, which underwent photoisomerization between the open‐ and closed‐ring isomers and also a side‐reaction to give the annulated isomer. The nucleation (K_n) and elongation (K_e) equilibrium constants were determined by analysis of the concentration dependence of the surface coverage by using a cooperative model at the liquid/solid interface. It was found that the annulated isomer has a very large equilibrium constant, which explains the predominantly observed ordering of the annulated isomer. It was also found that the presence of the closed‐ring isomer induces cooperativity into the formation of molecular ordering composed of the open‐ring isomer. A quantitative analysis of the formation of ordering by using the cooperative model has provided a new view of the formation of 2D multicomponent molecular ordering.     

Understanding High-Rate K+-Solvent Co-Intercalation in Natural Graphite for Potassium-Ion Batteries

Graphite shows great potential as an anode material for rechargeable metal-ion batteries because of its high abundance and low cost. However, the electrochemical performance of graphite anode materials for rechargeable potassium-ion batteries needs to be further improved. Reported herein is a natural graphite with superior rate performance and cycling stability obtained through a unique K⁺-solvent co-intercalation mechanism in a 1 m KCF₃SO₃ diethylene glycol dimethyl ether electrolyte. The co-intercalation mechanism was demonstrated by ex situ Fourier transform infrared spectroscopy and in situ X-ray diffraction. Moreover, the structure of the [K-solvent]⁺ complexes intercalated with the graphite and the conditions for reversible K⁺-solvent co-intercalation into graphite are proposed based on the experimental results and first-principles calculations. This work provides important insights into the design of natural graphite for high-performance rechargeable potassium-ion batteries.     

Gaussian basis sets for first‐, third‐, and fourth‐row positive and negative ions

An improved generator coordinate Hartree–Fock (HF) method is used to generate accurate triple‐optimized Gaussian basis sets for the cations from He⁺ (Z=2) through Ne⁺ (Z=10) and from K⁺ (Z=19) through Xe⁺ (Z=54), and for the anions from H⁻ (Z=1) through F⁻ (Z=9) and from K⁻ (Z=19) through I⁻ (Z=53). For all ions here studied, our ground‐state HF total energies are better than those calculated with the generator coordinate HF method, using optimized Gaussian basis sets of the same size. For all ions studied, the largest difference between our total energy values and the corresponding results obtained with a numerical HF method is equal to 3.434 mhartrees for Te⁺. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 82: 126–130, 2001     

Synthesis of catalytic filamentous carbon on a nickel/graphite catalyst and a study of the resulting carbon-carbon composite materials in microbial fuel cells

The carbon-carbon composite materials obtained via the synthesis of catalytic filamentous carbon (CFC) on a Ni/graphite supported catalyst in the process of the pyrolysis of C₃–C₄ alkanes in the presence of hydrogen were systematically studied. The effects of the following conditions on the catalytic activity expressed as the yield of carbon (g CFC)/(g Ni) and on the character of CFC synthesis on graphite rods were studied: procedures for supporting Ni(II) compounds (impregnation and homogeneous precipitation), the concentrations of impregnating compouds (nickel nitrate, urea, and ethyl alcohol) in solution, graphite treatment (oxidation) conditions before supporting Ni(II) compounds, and the pyrolysis temperature of C₃–C₄ alkanes in the range of 400–600°C. Optimum conditions for preparing CFC/graphite composite materials, which are promising for use as electrodes in microbial fuel cells (MFCs), were chosen. The electrochemical characteristics of an MFC designed with the use of a CFC/graphite electrode (anode) and Gluconobacter oxydans glycerol-oxidizing bacteria were studied. The morphology of the surfaces of graphite, synthesized CFC, and also bacterial cells adhered to the anode was studied by scanning electron microscopy.     

Weibull analysis of the mechanical strength of silica gels

Since gels are typically brittle materials, reliable analyses are essential to determine the strength distribution. The mechanical strength of silica gels has been measured by the three point bending technique. Based on the Weibull function, the statistical analysis allows determination of the Weibull modulus (m), which characterizes the strength distribution and the flaw size effect.Two kinds of gels, alcogels and aerogels, have been investigated with respect to their different mechanical behaviour owing to the transformations occurring during the supercritical drying (SD). The toughness of the two materials has been also measured by the SENB technique. It appears that the strength increases by a factor greater than two during SD, the K_IC increases slightly. However, m is not greatly affected which would suggest that SD does not induce significant flaws or defects change in the network.     

Understanding High‐Rate K+‐Solvent Co‐Intercalation in Natural Graphite for Potassium‐Ion Batteries

Graphite shows great potential as an anode material for rechargeable metal‐ion batteries because of its high abundance and low cost. However, the electrochemical performance of graphite anode materials for rechargeable potassium‐ion batteries needs to be further improved. Reported herein is a natural graphite with superior rate performance and cycling stability obtained through a unique K⁺‐solvent co‐intercalation mechanism in a 1 m KCF₃SO₃ diethylene glycol dimethyl ether electrolyte. The co‐intercalation mechanism was demonstrated by ex situ Fourier transform infrared spectroscopy and in situ X‐ray diffraction. Moreover, the structure of the [K‐solvent]⁺ complexes intercalated with the graphite and the conditions for reversible K⁺‐solvent co‐intercalation into graphite are proposed based on the experimental results and first‐principles calculations. This work provides important insights into the design of natural graphite for high‐performance rechargeable potassium‐ion batteries.     

Generalized graphs and the Sinanoğlu graphical rules

A comparison of Sinano?lu's VIF (Ref. 1) and generalized graph is presented. Generalized graphs have vertex and edge weights. An abridged history of generalized graphs in theoretical chemistry is given. VIF 's are generalized graphs and therefore have adjacency matrices. The “graphical” rules of Sinano?lu can be represented by congruent transformations on the adjacency matrix. Thus the method of Sinano?lu is incorporated into the broad scheme of graph spectral theory. If the signature of a graph is defined as the collection of the number of positive, zero, and negative eigenvalues of the graph's adjacency matrix, then it is identical to the all-important {n₊, n₀, n_?}, the {number of positive, zero, and negative loops of a reduced graph} or the {number of bonding, nonbonding, and antibonding MO s}. A special case of the Sinano?lu rules is the “multiplication of a vertex” by (?1). In matrix language, this multiplication is an orthogonal transformation of the adjacency matrix. Thus, one can multiply any vertex of a generalized graph by ?1 without changing its eigenvalues.     

Assignment of the Absolute-Handedness Chirality of Single-Walled Carbon Nanotubes by Using Organic Molecule Supramolecular Structures

Supramolecular structures of organic molecules on planar nanocarbon surfaces, such as highly oriented pyrolytic graphite (HOPG), have been extensively studied and the factors that control them are generally well-established. In contrast, the properties of supramolecular structures on curved nanocarbon surfaces like carbon nanotubes remain challenging to predict and/or to understand. This paper reports an investigation into the first study of the supramolecular structures of 5,15-bisdodecylporphyrin (C12P) on chiral, concentrated single-walled carbon nanotubes (SWNTs; with right-handed helix P- and left-handed helix M-) surfaces using STM. Furthermore, the study is the first of its kind to experimentally assign the absolute-handedness chirality of SWNTs, as well as to understand their effect on the supramolecular structures of organic molecules on their surfaces. Interestingly, these SWNT enantiomers resulted in supramolecular structures of opposite chirality based on the handedness chirality. With molecular modelling, we predicted the absolute-handedness chirality of SWNTs, before demonstrating this experimentally.     

Maxwell–Cartesian spherical harmonics in multipole potentials and atomic orbitals

 The nature of the Maxwell–Cartesian spherical harmonics S ⁽ⁿ⁾ _K and their relation to tesseral harmonics Y _nm is examined with the help of “tricorn arrays” that display the components of a totally symmetric Cartesian tensor of any rank in a systematic way. The arrays show the symmetries of the Maxwell–Cartesian harmonic tensors with respect to permutation of axes, the traceless properties of the tensors, the linearly independent subsets, the nonorthogonal subsets, and the subsets whose linear combinations produce the tesseral harmonics. The two families of harmonics are related by their connection with the gradients of 1/r, and explicit formulas for the transformation coefficients are derived. The rotational transformation of S ⁽ⁿ⁾ _K functions is described by a relatively simple Cartesian tensor method. The utility of the Maxwell–Cartesian harmonics in the theory of multipole potentials, where these functions originated in the work of Maxwell, is illustrated with some newer applications which employ a detracer exchange theorem and make use of the partial linear independence of the functions. The properties of atomic orbitals whose angular part is described by Maxwell–Cartesian harmonics are explored, including their angular momenta, adherence to an Uns?ld-type spherical symmetry relation, and potential for eliminating an angular momentum “contamination” problem in Cartesian Gaussian basis sets. Received: 9 July 2001 / Accepted: 7 September 2001 / Published online: 19 December 2001     

Infrared spectra of some isotopomers of isopropylamine: A theoretical study

The normal‐mode frequencies and the corresponding vibrational assignments of some isotopomers of isopropylamine are examined theoretically using the Gaussian 94 set of quantum chemistry codes at the MP2 level of theory using a 6‐311g** basis set. In particular deuteration of the NH₂ hydrogen atoms as well as the deuteration of the CH₃ hydrogen atoms, the α‐CH hydrogen atom, and various combinations of deuteration of isopropylamine are examined. Correction factors for predominant vibrational motions are reported and compared for a number of isotopomers of s‐trans‐ and gauche‐isopropylamine. Comparison of theoretically predicted infrared spectra with experimental spectra is made for isotopomers for which experimental data exist. Enthalpy, entropy, and Gibbs free energy changes are considered for the trans→gauche transformation. An amino torsional potential is deduced and barrier heights are calculated for the trans→gauche, gauche→trans, and gauche→gauche transformations. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 72: 109–126, 1999     

Acid-base and complexing properties of 10-carboxymethyl-9-acridone

Acid-base and complexing properties of 10-carboxymethyl-9-acridone in a multicomponent solvent H₂O-methanol-acetonitrile-dioxane were studied at 22°C, ionic strength I = 0.1 (NaClO₄), and different water-organic component ratios. The concentration protonation constants (logK _HL = 3.11), dissociation constants (pK _HL = 4.14), and stability constants of complexes (logK _MgL = 2.18, logK _CaL = 2.09, and logK _SrL = 1.96) were determined by extrapolation to zero content of organic solvent.     

Mathematical modeling of a tubular spectrochemical cell using the finite Hankel transformation

The analytical expression of the concentration of the species, in the electrochemical cell, with tubular electrode and optical fibres inserted into it, from its two ends is derived using the finite Hankel transformation. A series form of an analytical expression for current and absorbance responses of the spectroelec-trochemical cell has been derived. The analytical expressions of current and absorbance in terms of parameters K _f , K _b , ε _A and ε _B for chronoamperometry are given. Available numerical results are compared with our analytical results and are found to be in good agreement.     

Effects of Alkyl Chain Length and Hydrogen Bonds on the Cooperative Self‐Assembly of 2‐Thienyl‐Type Diarylethenes at a Liquid/Highly Oriented Pyrolytic Graphite (HOPG) Interface

An appropriate understanding of the process of self‐assembly is of critical importance to tailor nanostructured order on 2D surfaces with functional molecules. Photochromic compounds are promising candidates for building blocks of advanced photoresponsive surfaces. To investigate the relationship between molecular structure and the mechanism of ordering formation, 2‐thienyl‐type diarylethenes with various lengths of alkyl side chains linked through an amide or ester group were synthesized. Their self‐assemblies at a liquid/solid interface were investigated by scanning tunneling microscopy (STM). The concentration dependence of the surface coverage was analyzed by using a cooperative model for a 2D surface based on two characteristic parameters: the nucleation equilibrium constant (K_n) and the elongation equilibrium constant (K_e). The following conclusions can be drawn. 1) The concentration at which a stable 2D molecular ordering is observed by STM exponentially decreases with increasing length of the alkyl chain. 2) Compounds bearing amide groups have higher degrees of cooperativity in self‐assembly on 2D surfaces (i.e., σ, which is defined as K_n/K_e) than compounds with ester groups. 3) The self‐assembly process of the open‐ring isomer of an ester derivative is close to isodesmic, whereas that of the closed‐ring isomer is cooperative because of the difference in equilibrium constants for the nucleation step (i.e., K_n) between the two isomers.     

Adsorption of Ions on the Surface of Tin Dioxide and Its Electrokinetic Characteristics in 1 : 1 Electrolyte Solutions

Adsorption and electrokinetic characteristics of tin dioxide (cassiterite) are studied as a function of pH in aqueous NaCl and KCl solutions. The dissociation constants of surface groups, formation constants of ion pairs, and the adsorption potentials of ions are calculated in terms of the 2-pK model; capacities and potentials of the electrical double layer are determined; the dissociation degree of surface groups in the point of zero charge and in the isoelectric point are also estimated. It is shown that the 2-pK model in combination with the Graham model can be applied in the studied systems for describing the experimental results.     

Direct electron transfer reactions between human ceruloplasmin and electrodes

In an effort to find conditions favouring bioelectrocatalytic reduction of oxygen by surface-immobilised human ceruloplasmin (Cp), direct electron transfer (DET) reactions between Cp and an extended range of surfaces were considered. Exploiting advances in surface nanotechnology, bare and carbon-nanotube-modified spectrographic graphite electrodes as well as bare, thiol- and gold-nanoparticle-modified gold electrodes were considered, and ellipsometry provided clues as to the amount and form of adsorbed Cp. DET was studied under different conditions by cyclic voltammetry and chronoamperometry. Two Faradaic processes with midpoint potentials of about 400 mV and 700 mV vs. NHE, corresponding to the redox transformation of copper sites of Cp, were clearly observed. In spite of the significant amount of Cp adsorbed on the electrode surfaces, as well as the quite fast DET reactions between the redox enzyme and electrodes, bioelectrocatalytic reduction of oxygen by immobilised Cp was never registered. The bioelectrocatalytic inertness of this complex multi-functional redox enzyme interacting with a variety of surfaces might be associated with a very complex mechanism of intramolecular electron transfer involving a kinetic trapping behaviour.