The discovery of two kinds of ion pairs

The discovery and implications of the existence of two kinds of ion pairs in solutions of carbanion salts is described. Also discussed are the factors controlling tight–loose ion pair equilibrium: the nature of the carbanion and its counterion, temperature, pressure, solvent, and cation‐complexing additives. A few examples are presented of the effect of these ionic species on the mechanisms of anionic polymerization and proton transfer. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 3655–3667, 2004     

Complexes of polyacids with poly(vinylbenzocrown ether)s and polyvinylbenzoglymes in water

Insoluble complexes are formed in acidic aqueous media when poly(acrylic acid) (PAA) and poly-(vinylbenzo-18-crown-6) (P18C6) or polyvinylbenzoglymes are mixed. Complex formation results from hydrogen bonding between carboxyl groups and crown ether- or glyme–oxygen atoms as well as from hydrophobic interactions. The precipitation is pH dependent and was determined as a function of the ratio PAA to P18C6 or to polyglyme at different HCl concentrations in 10^?4M solutions of polycrown or polyglyme. Precipitation is nearly quantitative in 0.01N HCl. The compositions of PAA/P18C6 precipitates were determined as a function of the initial PAA/P18C6 ratio in solution. The complexes with P18C6 can be solubilized in acidic media when crown-complexable cations (K⁺, Cs⁺, Ba²⁺) are added, but the charged P18C6 reprecipitates in basic solution as a polysalt complex with the PAA–polyanion. More stable PAA–P18C6 complexes in the form of fibers can be obtained by interfacial complex formation. Poly(methacrylic acid) is less effective as a complex former.     

Anion dependence of crown ether selectivities for alkali picrates and sulfonates in dioxane and toluene. A synergistic effect

The binding constants,K _N, of sodium and potassium 8-anilinonaphthalene-1-sulfonate (ANS) and of sodium 5-dimethylamino-1-naphthalenesulfonate (DNS) to benzo-18-crown-6 bound to a 2% cross-linked polystyrene network (RN18C6) were measured spectrophotometrically in dioxane and the results compared with those obtained for picrate salts. The network RN18C6 was then used to measure in dioxane and toluene by a competition method the equilibrium constant,K, of the reaction A^–M⁺N+CrA^–M⁺Cr+N.A^–M⁺N denotes the ionic solute (ANS, DNS, methyl orange or picrate salt) bound to the network RN18C6 (N) and A^–M⁺Cr is the solute bound to a soluble ligand Cr, where Cr represents a series of 18-crown-6 and 15-crown-5 compounds. Combining theK _N andK values the formation constants,K _L, of the crown ether complexes of the respective salts were obtained in dioxane. The data show a reversal in the complexation strength of the 18-crown-6 compounds in dioxane when sodium picrate is replaced by sodium ANS. The results were rationalized in terms of a synergistic effect exerted by dioxane, with dioxane forming a 1:1 dioxanate with the crown ion pair complex. This effect is especially strong with ANS and with a rigid planar crown ether like dibenzo-18-crown-6. The binding constants,K _N, of NaANS and NaDNS to RN18C6 in dioxane are nearly three times larger than for sodium picrate, and the same holds for the potassium salts. Differences in anion interactions with the network appear to be a plausible cause for the anion dependence ofK _N.     

Historical perspectives on living anionic polymerization

A brief overview of the role that Dr. Michael Szwarc has played in unraveling the mechanism of living anionic polymerization is presented. Emphasis is placed on the different ionic species that control the propagation reaction in ether-type solvents. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 40: 2101–2107, 2002     

Eine Axiomatik der Kreisgeometrie und der Laguerregeometrie

Ohne Zusammenfassung     

Approximating geometric bottleneck shortest paths

In a geometric bottleneck shortest path problem, we are given a set S of n points in the plane, and want to answer queries of the following type: given two points p and q of S and a real number L, compute (or approximate) a shortest path between p and q in the subgraph of the complete graph on S consisting of all edges whose lengths are less than or equal to L. We present efficient algorithms for answering several query problems of this type. Our solutions are based on Euclidean minimum spanning trees, spanners, and the Delaunay triangulation. A result of independent interest is the following. For any two points p and q of S, there is a path between p and q in the Delaunay triangulation, whose length is less than or equal to 2π/(3cos(π/6)) times the Euclidean distance |pq| between p and q, and all of whose edges have length at most |pq|.     

Sparse geometric graphs with small dilation

Given a set S of n points in , and an integer k such that 0k<n, we show that a geometric graph with vertex set S, at most n−1+k edges, maximum degree five, and dilation O(n/(k+1)) can be computed in time O(nlogn). For any k, we also construct planar n-point sets for which any geometric graph with n−1+k edges has dilation Ω(n/(k+1)); a slightly weaker statement holds if the points of S are required to be in convex position.     

Algorithms for generalized halfspace range searching and other intersection searching problems

In a generalized intersection searching problem, a set S of colored geometric objects is to be preprocessed so that, given a query object q, the distinct colors of the objects of S that are intersected by q can be reported or counted efficiently. These problems generalize the well-studied standard intersection searching problems and have many applications. Unfortunately, the solutions known for the standard problems do not yield efficient solutions to the generalized problems. Recently, efficient solutions have been given for generalized problems where the input and query objects are iso-oriented (i.e., axes-parallel) or where the color classes satisfy additional properties (e.g., connectedness). In this paper, efficient algorithms are given for several generalized problems involving objects that are not necessarily iso-oriented. These problems include: generalized halfspace range searching in , for any fixed d ≥ 2, and segment intersection searching, triangle stabbing, and triangle range searching in for certain classes of line segments and triangles. The techniques used include: computing suitable sparse representations of the input, persistent data structures, and filtering search.