Trapping of random walks on the line

Several features of the trapping of random walks on a one-dimensional lattice are analyzed. The results of this investigation are as follows: (1) The correction term to the known asymptotic form for the survival probability ton steps is O(( ₂n)^–1/3), where =–ln(1–c), andc is the trap concentration. (2) The short time form for the survival probability is found to be exp[–a(c)n ^1/2], wherea(c) is given in Eq. (21). (3) The mean-square displacement of a surviving random walker is found to go liken ^2/3for largen. (4) When the distribution of trap-free regions is changed so that very large regions are much rarer than for ideally random trap placement the asymptotic survival probability changes its dependence onn. One such model is studied.     

Structures of the Intermediate Complexes in Friedel-Crafts Acylations

Addition compounds of Lewis acids MX_n and acyl halides R? COX occur as intermediates in Friedel-Crafts acylations. IR and NMR studies on these intermediates have indicated the probable existence of structural isomers. In X-ray structural analysis, it is possible to distinguish two forms, i.e. the molecular form, in which the compounds are present as donor-acceptor complexes R? CXO→MX_n, and the ionic form, in which they can be formulated as oxocarbenium salts [R? CO]⁺[MX_n+1]^?. The compounds of the donor-acceptor type R? CXO→MX_n are characterized by the formation of a coordinate oxygen-metal bond; the transfer of electrons from the oxygen to the metal of the acceptor is always due to a weak donor-acceptor interaction. The positive charge of the aryloxocarbenium ions is partly delocalized over the aromatic nucleus. The positive charge in alkyloxocarbenium ions, on the other hand, is essentially localized on the carbon atom of the carbonyl group, as is confirmed by electron density distribution calculations.     

Die Glykoside der Samen von Dregea volubilis (L.) BENTH. ex HOOK. 2. Mitt. Isolierung weiterer Drevogenine Glykoside und Aglykone, 277. Mitteilung

A total of fifteen substances were identified through thin-layer chromatography, after mild acid hydrolysis of the chloroform extract from the seeds of Dregea volubilis (L.) BENTH . ex HOOK . Of these fifteen substances, eight (B, D, P, O; U, V, H and T) were isolated in crystalline form. Two of these were identical with the known genins drevogenin B (B) and drevogenin D (D). Drevogenin P (P) and the unknown substance O (probably a genin) were isolated for the first time. U proved to be identical with D -cymarose, V with the biose U1 obtained from Asclepias lilacina, and H with (+)-methyl-pachybioside. T was not investigated (probably a sugar derivative).     

Über metall-alkyl- und -aryl-verbindungen: XVII. Die kristallstruktur des kaliumhydridotrimethylaluminats,K[AlH(CH3)3]

K[AlH(CH₃)₃] is formed by decomposition of K[Al(CH₃)₃SiH₃] in diethyl ether. The compound crystallizes in the orthorhombic space group Cmca with the lattice parameters a = 9.647, b = 17.332, c = 7.711 Å. There are eight formula units in the unit cell. Analogously to K[Al(CH₃)₄] the hydrido compound contains isolated anions with a tetrahedral coordination of aluminium by hydrogen and three methyl groups.     

A Titration Microcalorimetric Study of the Effects of Halide Counterions on Vesicle-Forming Aggregation in Aqueous Solution of Branched-Chain Alkylpyridinium Surfactants

Titration microcalorimetry is used to study the influences of iodide, bromide, and chloride counterions on the aggregation of vesicle-forming 1-methyl-4-(2-pentylheptyl)pyridinium halide surfactants. Formation of vesicles by these surfactants was characterised using transmission electron microscopy. When the counterion is changed at 303 K through the series iodide, bromide, to chloride, the critical vesicular concentration (cvc) increases and the enthalpy of vesicle formation changes from exo- to endothermic. With increase in temperature to 333 K, vesicle formation becomes strongly exothermic. Increasing the temperature leads to a decrease in enthalpy and entropy of vesicle formation for all three surfactants. However the standard Gibbs energy for vesicle formation is, perhaps surprisingly, largely unaffected by an increase in temperature, as a consequence of a compensating change in both standard entropy and standard enthalpy of vesicle formation. Interestingly, standard isobaric heat capacities of vesicle formation are negative, large in magnitude but not strikingly dependent on the counterion. We conclude that the driving force for vesicle formation can be understood in terms of overlap of the thermally labile hydrophobic hydration shells of the alkyl chains. Copyright 2000 Academic Press.     

Preparation of Neutral Ionophores for Alkali and Alkaline Earth Metal Cations and their application in ion selective membrane electrodes

The preparation of a series of non-cyclic, uncharged ligands able to selectively complex alkali and alkaline earth metal cations is described. These molecules are designed to be used as carriers for cations through membranes. Some of the compounds show high Ca²⁺ and Na⁺ selectivity, respectively, in liquid membrane electrodes.     

Alkyl and aryl substituted corroles. 1. Synthesis and characterization of free base and cobalt containing derivatives. x-ray structure of (Me(4)Ph(5)Cor)Co(py)(2)

The synthesis, spectroscopic properties, and electrochemistry of six different alkyl- and aryl-substituted Co(III) corroles are presented. The investigated compounds contain methyl, ethyl, phenyl, or substituted phenyl groups at the eight beta-positions of the corrole macrocycle and four derivatives also contain a phenyl group at the 10-meso position of the macrocycle. Each cobalt corrole undergoes four reversible oxidations in CH(2)Cl(2) containing 0.1 M tetra-n-butylammonium perchlorate and exists as a dimer in its singly and doubly oxidized forms. The difference in potential between the first two oxidations is associated with the degree of interaction between the two corrole units of the dimer and ranges from an upper value of 0.62 V, in the case of (Me(6)Et(2)Cor)Co, to a lower value of about 0.17 V, in the case of four compounds which have a phenyl group located at the 10-meso position of the macrocycle. These Co(III) corroles strongly coordinate two pyridine molecules or one carbon monoxide molecule in CH(2)Cl(2) media, and ligand binding constants were evaluated using spectroscopic and electrochemical methods. The structure of (Me(4)Ph(5)Cor)Co(py)(2) was also determined by X-ray diffraction. Crystal data: (Me(4)Ph(5)Cor)Co(py)(2).3CH(2)Cl(2).H(2)O, orthorhombic, a = 19.5690(4) A, b = 17.1070(6) A, c = 15.9160(6) A, V = 5328.2(5) A(3), space group Pna2(1), Z = 2, 35 460 observations, R(F) = 0.069.     

Mapping the influence of molecular structure on rates of electron transfer using direct measurements of the electron spin-spin exchange interaction

The spin-spin exchange interaction, 2J, in a radical ion pair produced by a photoinduced electron transfer reaction can provide a direct measure of the electronic coupling matrix element, V, for the subsequent charge recombination reaction. We have developed a series of dyad and triad donor-acceptor molecules in which 2J is measured directly as a function of incremental changes in their structures. In the dyads the chromophoric electron donors 4-(N-pyrrolidinyl)- and 4-(N-piperidinyl)naphthalene-1,8-dicarboximide, 5ANI and 6ANI, respectively, and a naphthalene-1,8:4,5-bis(dicarboximide) (NI) acceptor are linked to the meta positions of a phenyl spacer to yield 5ANI-Ph-NI and 6ANI-Ph-NI. In the triads the same structure is used, except that the piperidine in 6ANI is replaced by a piperazine in which a para-X-phenyl, where X = H, F, Cl, MeO, and Me(2)N, is attached to the N' nitrogen to form a para-X-aniline (XAn) donor to give XAn-6ANI-Ph-NI. Photoexcitation yields the respective 5ANI(+)-Ph-NI(-), 6ANI(+)-Ph-NI(-), and XAn(+)-6ANI-Ph-NI(-) singlet radical ion pair states, which undergo subsequent radical pair intersystem crossing followed by charge recombination to yield (3)NI. The radical ion pair distances within the dyads are about 11-12 A, whereas those in the triads are about approximately 16-19 A. The degree of delocalization of charge (and spin) density onto the aniline, and therefore the average distance between the radical ion pairs, is modulated by the para substituent. The (3)NI yields monitored spectroscopically exhibit resonances as a function of magnetic field, which directly yield 2J for the radical ion pairs. A plot of ln 2J versus r(DA), the distance between the centroids of the spin distributions of the two radicals that comprise the pair, yields a slope of -0.5 +/- 0.1. Since both 2J and k(CR), the rate of radical ion pair recombination, are directly proportional to V(2), the observed distance dependence of 2J shows directly that the recombination rates in these molecules obey an exponential distance dependence with beta = 0.5 +/- 0.1 A(-)(1). This technique is very sensitive to small changes in the electronic interaction between the two radicals and can be used to probe subtle structural differences between radical ion pairs produced from photoinduced electron transfer reactions.     

Liquid-vapor interface of square-well fluids of variable interaction range

Properties of the liquid-vapor interface of square-well fluids with ranges of interaction lambda=1.5, 2.0, and 3.0 are obtained by Monte Carlo simulations and from square-gradient theories that combine the Carnahan-Starling equation of state for hard spheres with the second and third virial coefficients. The predicted surface tensions show good agreement with the simulation results for lambda=2 and for lambda=3 in a temperature range reasonably close to the critical point, 0.8相似文献   

Structures of Organo Alkali Metal Complexes and Related Compounds

The investigation of the reactivity and structure of organometallic compounds of alkali metals has experienced a blustering development in the last decades. This class includes compounds that are especially important for our understanding of chemical bonding and also quite simple, for example methyl alkali metal complexes, whose structures have been unequivocally determined. Organometallic compounds of alkali metals (and also magnesium) generally exist as ion aggregates whose properties can be significantly modified through solvation by, for example, ether or amines. Important advances in the synthesis of new compounds, especially those of the heavier alkali metals, have been based on these results. It was long believed that the alkali metals had little tendency to undergo coordination and that their coordination chemistry would offer few surprises. This picture has now changed completely. Results from crystal structure investigations have revealed a variety of often surprising structure types (rings, heterocubanes, chains, layers, etc.) not only with the organometallic compounds but also with the amides, imides, alkoxides, phenoxides, enolates, and even halides. A comparison reveals interesting similarities between compounds that appear to be so different and leads to a general classification of the structure types possible with C, N, O, and halo ligands.