Cross-polarization with magic-angle spinning kinetics and impedance spectroscopy study of proton mobility,local disorder,and thermal equilibration in hydrogen-bonded poly(methacrylic acid)

The ¹H–¹³C cross-polarization with magic-angle spinning (CP MAS) kinetics was studied in poly(methacrylic acid) (PMAA) having the purpose to track the links between the local order in the main chain and the proton dynamics in peripheral hydrogen bond networks. The experimental CP MAS kinetic curves were analyzed applying the models of isotropic and anisotropic spin-diffusion with thermal equilibration. The fractal dimension D_p ≈ 3 was deduced that indicates that PMAA behaves as an isotropic 3D-system. No proton conductivity in the neat PMAA was deduced from the impedance spectroscopy data analyzing the frequency dependences of the complex dielectric permittivity. The value of local order parameter S = 0.70 for CH₂ in PMAA occupies an intermediate position between 0.63 and 0.85 deduced for CH₂ sites in the main chains of poly(vinyl phosphonic acid) and poly(2-hydroxyethyl methacrylate), that is, the true proton conductor and the polymer that contains the H-bond network, however, no proton conductivity, respectively.     

Separation and kinetic analysis of the thermo-oxidative reactions of polyacrylonitrile upon heat treatment

A polyacrylonitrile (PAN) homopolymer and a copolymer with methyl acrylate were analyzed by differential scanning calorimetry (DSC) in order to establish a method for the kinetic analysis of the stabilization reaction steps during heat treatment. The application of a program rarely used for the study of the chemical transformation of PAN and its copolymers resulted in five separate steps, which can be assigned with large probability to various cyclization and oxidation reactions. A more exact identification of the reactions needs further measurements and considerations. Overlapping peaks appearing in the DSC traces were deconvoluted and then quantitatively analyzed to obtain kinetic parameters. The kinetics of the processes were described by the Kissinger model. The model could be fitted well to four of the five processes that may indicate that these belong to individual reactions of the first order. The parameters obtained agree well with the few values of similar investigations published in the literature up to now. The results have large practical relevance, since the kinetic parameters obtained can be used in the preparation of intermediates and for the optimization of the stabilization process.     

Moments of an exponential functional of random walks and permutations with given descent sets

The exponential functional of simple, symmetric random walks with negative drift is an infinite polynomial Y = 1 + ξ₁ + ξ₁ξ₂ + ξ₁ξ₂ξ₃ + ⋯ of independent and identically distributed non-negative random variables. It has moments that are rational functions of the variables μ _k = E(ξ ^k ) < 1 with universal coefficients. It turns out that such a coefficient is equal to the number of permutations with descent set defined by the multiindex of the coefficient. A recursion enumerates all numbers of permutations with given descent sets in the form of a Pascal-type triangle. This revised version was published online in August 2006 with corrections to the Cover Date.     

Random Partial Orders Defined by Angular Domains

The d-dimensional random partial order is the intersection of d independently and uniformly chosen (with replacement) linear orders on the set [n] = {1, 2, . . . , n}. This is equivalent to picking n points uniformly at random in the d-dimensional unit cube Q_d=[0,1]^dQ_d=[0,1]^d with the coordinate-wise ordering. If d = 2, then this can be rephrased by declaring that for any pair P ₁, P ₂ ∈ Q ₂ we have P ₁ ≺ P ₂ if and only if P ₂ lies in the positive upper quadrant defined by the two axis-parallel lines crossing at P ₁. In this paper we study the random partial order with parameter α (0 ≤ α ≤ π) which is generated by picking n points uniformly at random from Q ₂ equipped with the same partial order as above but with the quadrant replaced by an angular domain of angle α.     

Space-time discontinuous Galerkin method for the solution of fluid-structure interaction

The paper is concerned with the application of the space-time discontinuous Galerkin method (STDGM) to the numerical solution of the interaction of a compressible flow and an elastic structure. The flow is described by the system of compressible Navier-Stokes equations written in the conservative form. They are coupled with the dynamic elasticity system of equations describing the deformation of the elastic body, induced by the aerodynamical force on the interface between the gas and the elastic structure. The domain occupied by the fluid depends on time. It is taken into account in the Navier-Stokes equations rewritten with the aid of the arbitrary Lagrangian-Eulerian (ALE) method. The resulting coupled system is discretized by the STDGM using piecewise polynomial approximations of the sought solution both in space and time. The developed method can be applied to the solution of the compressible flow for a wide range of Mach numbers and Reynolds numbers. For the simulation of elastic deformations two models are used: the linear elasticity model and the nonlinear neo-Hookean model. The main goal is to show the robustness and applicability of the method to the simulation of the air flow in a simplified model of human vocal tract and the flow induced vocal folds vibrations. It will also be shown that in this case the linear elasticity model is not adequate and it is necessary to apply the nonlinear model.     

Large antipodal families

A family {A _i | i ∈ I} of sets in ℝ ^d is antipodal if for any distinct i, j ∈ I and any p ∈ A _i , q ∈ A _j , there is a linear functional ϕ:ℝ ^d → ℝ such that ϕ(p) ≠ ϕ(q) and ϕ(p) ≤ ϕ(r) ≤ ϕ(q) for all r ∈ ∪ _i∈I A _i . We study the existence of antipodal families of large finite or infinite sets in ℝ³. The research was supported by the Hungarian-South African Intergovernmental Scientific and Technological Cooperation Programme, NKTH Grant no. ZA-21/2006 and South African National Research Foundation Grant no. UID 61853, as well as Hungarian National Foundation for Scientific Research Grants no. NK 67867, no. T47102, and no. K72537.     

Binding,Release and Functionalization of Intact Pnictogen Tetrahedra Coordinated to Dicopper Complexes

The bridging MeCN ligand in the dicopper(I) complexes [(DPFN)Cu₂(μ,η¹ : η¹-MeCN)][X]₂ (X=weakly coordinating anion, NTf₂ ( 1 a ), FAl[OC₆F₁₀(C₆F₅)]₃ ( 1 b ), Al[OC(CF₃)₃]₄ ( 1 c )) was replaced by white phosphorus (P₄) or yellow arsenic (As₄) to yield [(DPFN)Cu₂(μ,η² : η²-E₄)][X]₂ (E=P ( 2 a – c ), As ( 3 a – c )). The molecular structures in the solid state reveal novel coordination modes for E₄ tetrahedra bonded to coinage metal ions. Experimental data and quantum chemical computations provide information concerning perturbations to the bonding in coordinated E₄ tetrahedra. Reactions with N-heterocyclic carbenes (NHCs) led to replacement of the E₄ tetrahedra with release of P₄ or As₄ and formation of [(DPFN)Cu₂(μ,η¹ : η¹-^MeNHC)][X]₂ ( 4 a,b ) or to an opening of one E−E bond leading to an unusual E₄ butterfly structural motif in [(DPFN)Cu₂(μ,η¹ : η¹-E₄^DippNHC)][X]₂ (E=P ( 5 a,b ), E=As ( 6 )). With a cyclic alkyl amino carbene (^EtCAAC), cleavage of two As−As bonds was observed to give two isomers of [(DPFN)Cu₂(μ,η² : η²-As₄^EtCAAC)][X]₂ ( 7 a,b ) with an unusual As₄-triangle+1 unit.