Molecular diffusion on a time scale between nano- and milliseconds probed by field-cycling NMR relaxometry of intermolecular dipolar interactions: application to polymer melts

A formalism is presented permitting the evaluation of the relative mean-squared displacement of molecules from the intermolecular contribution to spin-lattice relaxation dispersion of dipolar coupled spins. The only condition for the applicability is the subdiffusive power law character of the time dependence of the mean-squared displacement as it is typical for the chain mode regime in polymer liquids. Using field-cycling NMR relaxometry, an effective diffusion time range from nano- to almost milliseconds can be probed. The intermolecular spin-lattice relaxation contribution can be determined with the aid of isotopic dilution, that is, mixtures of undeuterated and deuterated molecules. Experiments have been performed with melts of polyethyleneoxide and polybutadiene. The mean-squared segment displacements have been evaluated as a function of time over five decades. The data can be described by a power law. The extrapolation to the much longer time scale of ordinary field-gradient NMR diffusometry gives good coincidence with literature data. The total time range thus covers nine decades.     

Higher-order integrable evolution equation and its soliton solutions

We consider an extended nonlinear Schrödinger equation with higher-order odd and even terms with independent variable coefficients. We demonstrate its integrability, provide its Lax pair, and, applying the Darboux transformation, present its first and second order soliton solutions. The equation and its solutions have two free parameters. Setting one of these parameters to zero admits two limiting cases: the Hirota equation on the one hand and the Lakshmanan–Porsezian–Daniel (LPD) equation on the other hand. When both parameters are zero, the limit is the nonlinear Schrödinger equation.     

Boundary closures for fourth-order energy stable weighted essentially non-oscillatory finite-difference schemes

A general strategy was presented in 2009 by Yamaleev and Carpenter for constructing energy stable weighted essentially non-oscillatory (ESWENO) finite-difference schemes on periodic domains. ESWENO schemes up to eighth order were developed that are stable in the energy norm for systems of linear hyperbolic equations. Herein, boundary closures are developed for the fourth-order ESWENO scheme that maintain, wherever possible, the WENO stencil biasing properties and satisfy the summation-by-parts (SBP) operator convention, thereby ensuring stability in an L₂ norm. Second-order and third-order boundary closures are developed that are stable in diagonal and block norms, respectively, and achieve third- and fourth-order global accuracy for hyperbolic systems. A novel set of nonuniform flux interpolation points is necessary near the boundaries to simultaneously achieve (1) accuracy, (2) the SBP convention, and (3) WENO stencil biasing mechanics.     

DITHIOPHOSPHORIC ACIDS AND TETRAPHOSPHORUS DECASULFIDE IN THE SYNTHESIS OF BORON DITHIOPHOSPHATES

Abstract

The reactions of O,O-dialkyl dithiophosphoric acids with triisobutyl borate, ammonium O,O-diisobutyl dithiophosphate with fluorodiisobutyl borate, and tetraphosphorus decasulfide with triisobutyl borate were studied. On the basis of these studies, new boron derivatives of dithiophosphoric acids were obtained. Low frequency ultrasonic irradiation (22 kHz, power 130 W) leads to reduction in reaction temperature and time in the reactions studied.     

The role of intermolecular interactions in the viscoelastic properties of polymer melts

The exact microscopic expression for the stress tensor in polymer liquids contains a tensor product of the the segment position vector with the total, intra- plus inter-chain, force acting on the segment. On the other hand, the widely accepted theory of viscoelasticity of polymer melts¹⁾ is based on the assumption, that contributions from interchain interactions to the viscosity of polymer melts is negligible relative to the effectively intrachain entropic interactions. Starting from the exact Green-Kubo formula for the viscosity, the Rouse dynamic correlation functions, and Newton's second law, we show that the intrachain assumption is inadequate. Rather, the intrachain and interchain forces acting on polymer segments cancel each other largely. The intrachain contribution therefore cannot be dominant as anticipated in the usual treatment¹⁾, or, in other words, the interchain contribution cannot be ignored. The main contribution to viscoelastic properties of polymer melts can only arise from a part of the total stress tensor as already suggested by M. Fixman based on a different argument²⁾. It is concluded that the viscosity is of a purely interchain nature, and is determined by the tensor product of the vector connecting the centers-of-mass of neighboring macromolecules on the one hand, and the total force by which macromolecules interact, on the other, just in the case of simple liquids.     

Boron derivatives of dithiophosphoric acids

The reactions of tetraphosphorus decasulfide 1 with trialkyl borates 2a,b and O‐isobutyl diphenylborate 2c were studied. On the basis of these studies, a novel method of synthesizing S‐boron derivatives of dithiophosphoric acids was developed. The use of low frequency ultrasonic irradiation (22 kHz, power 130 W) leads to a reduction in reaction temperature and time required for completion of the reactions studied. © 2000 John Wiley & Sons, Inc. Heteroatom Chem 11:102–106, 2000