Correct procedures for the calculation of heats of adsorption for heterogeneous adsorbents from molecular simulation

Several procedures for calculating the heat of adsorption from Monte Carlo simulations for a heterogeneous adsorbent are presented. Simulations have been performed to generate isotherms for nitrogen at 77 K and methane at 273.15 K in graphitic slit pores of various widths. The procedures were then applied to calculate the heat of adsorption of an activated carbon with an arbitrary pore size distribution. The consistency of the different procedures shows them to be correct in calculating interaction energy contributions to the heat of adsorption. The currently favored procedure for this type of calculation, from the literature, is shown to be incorrect and in serious error when calculating the heat of adsorption of activated carbon.     

Synthesis and redox properties of triarylmethane dye cation salts of anions [M6O19]2- (M = Mo, W)

Four salts have been isolated combining the triarylmethane dye cations pararosaniline (PR(+)) and crystal violet (CV(+)) with the hexametalates [M(6)O(19)](2-) (M = Mo, W). A new hexatungstic acid H(2)[W(6)O(19)]·4dma (dma = dimethylacetamide) was isolated and is a useful synthon for hexatungstate salts. Single-crystal X-ray diffraction confirmed the presence of PR(+) and [Mo(6)O(19)](2-) ions in [PR](2)[Mo(6)O(19)]·6dmf (dmf = dimethylformamide). A number of charge-assisted hydrogen bonds N-H···O exist between the cation -NH(2) functions and the anion oxygen atoms. Comparative cyclic voltammetry of salts [A]Cl (A = PR, CV), [Bu(4)N](2)[M(6)O(19)](2-) and A(2)[M(6)O(19)] was established in MeCN and Me(2)SO solutions and of solids in contact with the ionic liquid 1-ethyl-3-methylimidazolium bis(trifluoromethanesulfonyl)amide [emim][tfsa]. In the molecular solvents, the reversible potential for the process [Mo(6)O(19)](2-/3-) is less negative than the first reduction processes of the dye cations. In contrast, that for [W(6)O(19)](2-/3-) is more negative. Spectro-electrochemistry and bulk electrolysis experiments reveal significantly different pathways in the two cases. In contrast, in the [emim][tfsa] medium, a positive shift in reduction potential of at least 400 mV is seen for the anion processes but relatively little change for the dye cation processes. This means that initial reduction of the anions always precedes that of the dyes, providing significant simplification of the complex voltammetric data. Chemically modified electrodes can be used in the ionic liquid because of slow dissolution kinetics. However, reduced anion salts dissolve rapidly, allowing dissolved phase electrochemistry to be examined. The electrochemistries of the oxidized salts A(2)[M(6)O(19)] are essentially those of the individual ions, although low level interaction of A(+) with reduced anions [M(6)O(19)](3-,4-) is evident. The work establishes protocols for synthesis and handling of intensely absorbing and relatively insoluble salts which can now be applied to systems containing more complex polyoxometalate anions.     

Polyhedral end games for polynomial continuation

Bernshtein’s theorem provides a generically exact upper bound on the number of isolated solutions a sparse polynomial system can have in (ℂ^*)ⁿ, with ℂ^* = ℂ\{0}. When a sparse polynomial system has fewer than this number of isolated solutions some face system must have solutions in (ℂ^*)ⁿ. In this paper we address the process of recovering a certificate of deficiency from a diverging solution path. This certificate takes the form of a face system along with approximations of its solutions. We apply extrapolation to estimate the cycle number and the face normal. Applications illustrate the practical usefulness of our approach. This revised version was published online in August 2006 with corrections to the Cover Date.     

Characteristic heats of adsorption for slit pore and defected pore models

The characteristics of the heat of adsorption from a slit pore model of carbon are presented. This is shown to have a few key features that are always present, regardless of the pore size distribution used, as long as there is a reasonable range of pore sizes considered. The adsorption in a slit pore model is compared against the adsorption for a defected pore model. The isotherms of the defected pore model are qualitatively different from those of the slit pore and similar to those of amorphous carbon models presented in the literature. The heat of adsorption of the defected pore model is qualitatively different from the slit pore model, and its behavior falls between those of the slit pore model and the amorphous carbon models in the literature.     

The Cayley Trick, lifting subdivisions and the Bohne-Dress theorem on zonotopal tilings

In 1994, Sturmfels gave a polyhedral version of the Cayley Trick of elimination theory: he established an order-preserving bijection between the posets of coherent mixed subdivisions of a Minkowski sum ?₁+...+? _r of point configurations and of coherent polyhedral subdivisions of the associated Cayley embedding ?(?₁,...,? _r ). In this paper we extend this correspondence in a natural way to cover also non-coherent subdivisions. As an application, we show that the Cayley Trick combined with results of Santos on subdivisions of Lawrence polytopes provides a new independent proof of the Bohne-Dress theorem on zonotopal tilings. This application uses a combinatorial characterization of lifting subdivisions, also originally proved by Santos. Received February 18, 1999 / final version received January 25, 2000?Published online May 22, 2000     

Antioxidant capacity of novel amine derivatives of buckminsterfullerene: Determination of inhibition rate constants in a model oxidation system

The radical scavenging efficiency of fullerenes can be significantly activated by means of a connection with hydrogen donating groups of antioxidants such as phenolic, amine and sulfhydryl. The developed system of conjugated σ–π bonds arranged in the fullerene molecule in a closed shape can promote a strong resonance effect on the grafted units and increase the hydrogen atom abstraction efficiency. In this case the known ability of fullerene to trap alkyl radicals might be combined with the strong chain breaking functionality to afford a new class of antioxidants with bimodal action. Explorations in the field of fullerene derivatives on their antioxidant performance provide novel information on the potential stabilization properties of this type of molecular structure. A series of amine derivatives of buckminsterfullerene (C₆₀) with tethered aliphatic chain, cycloaliphatic and aromatic fragments were synthesized and their antioxidant activity was determined. The antioxidant activity of the investigated derivatives was studied by measuring the inhibition rate constants for their reaction with alkyl and peroxy radicals in a model cumene initiated (2,2′-azobisisobutyronitrile, AIBN) oxidation experiments and compared to that recorded under identical experiments for buckminsterfullerene itself and commercial primary aromatic amine stabilizers. The results indicate that linking the amine moieties groups directly to the fullerene core gives rise to a new chain breaking antioxidant mode for the buckminsterfullerene while cyclic fragments containing the same but distant amine group do not reveal this ability. The inhibition rate constants for trapping of peroxy radicals by the amine derivatives were found to be higher than that of known aromatic amine antioxidants Neozone-D and Naugard 445. In addition the C₆₀ part of these molecules acts synergistically by trapping alkyl radicals with inhibition rate constants which exceed that of underivatised fullerene. The amine derivative containing sterically hindered piperidine and pyrrolidine fragments also heighten the inherent rate constant of buckminsterfullerene for scavenging alkyl radicals due to the additional antioxidant contribution promoted by the radical-quenching ability of the formed nitroxyl intermediates. These novel C₆₀–amine conjugates may be considered as promising molecules for broad-spectrum radical scavenging antioxidants.