The effect of surface dipoles and of the field generated by a polarization gradient on the repulsive force

Double-layer and hydration interactions have been coupled into a single set of equations because both are dependent on the polarization of the water molecules. The coupled equations involve the electric fields generated by the surface charge and surface dipoles, as well as the field due to the neighboring dipoles in water. The dipoles on the surface are generated through the counterions' binding to sites of opposite charge. The equations obtained were employed to explain the restabilization observed experimentally at large ionic strengths for colloidal particles on which protein molecules were adsorbed. Polar molecules adsorbed on a charged surface of colloidal particle can generate a field either in the same direction as that generated by the charge or in the opposite direction. The effect of the sign of the dipole of the adsorbed polar molecules on the interaction between surfaces was also examined.     

Harmonic theory of thermal two-photon absorption in benzene

A correlation function formalism is applied to compute the two-photon absorption spectrum of benzene. Using harmonic Hamiltonians for the ground and excited electronic states, we find that the theory agrees qualitatively with the experimentally observed sparsity of the thermal two-photon absorption spectrum as compared with the single-photon absorption spectrum. An expression for the average vibrational energy in the excited state is derived. We find that cooling of the nascent vibrational energy in the electronically excited state is not as extensive in the two-photon absorption process as compared to the single-photon case.     

Thermally reversible linking of halide-containing polymers by potassium dicyclopentadienedicarboxylate

A novel crosslinker for thermally reversible covalent (TRC) linking of halide-containing polymers is suggested. Chlorine-containing polymers such as chloromethylstyrene copolymers, chlorinated polypropylene, polyvinylchloride, chlorinated polyisoprene, and polyepichlorohydrin were crosslinked with potassium dicyclopentadienedicarboxylate (KDCPDCA). The crosslinker was prepared by reacting potassium ethoxide with dicyclopentadienedicarboxylic acid. Because of the low solubility of KDCPDCA in organic solvents, a phase transfer catalyst, benzyltrimethyl-ammonium bromide, was employed for the crosslinking reaction. The crosslinking reaction occurred at a higher rate in a polar solvent, such as dimethylformamide, than in a nonpolar one, such as toluene, and was affected by the nature of the chlorine-containing polymer. Some of the polymers crosslinked even at room temperature. The chain-extending reaction between KDCPDCA and a α,ω-dihalide compound such as α,α′-dichloro-p-xylene, 1,4-dichlorobutane, or 1,4-dibromobutane also was carried out to obtain linear oligomers. The IR spectra indicated that the crosslinking and chain-extending reactions were based on the esterification between the halide carbon bonds of the polymer and the COOK groups of KDCPDCA. The flowability at 195 °C and solubility on heating in a dichlorobenzen-maleic compound mixture of the crosslinked polymers indicated that the TRC crosslinking occurred via the reversible Diels–Alder cyclopentadiene/dicyclopentadiene conversion as long as the polymer was thermally stable and did not contain olefinic CC bonds. The TRC linking also was confirmed by the rapid decrease of the specific viscosity of the obtained linear oligomers on heating. © 1999 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 37: 4390–4401, 1999     

Group graded <Emphasis Type=Italic>PI</Emphasis>-algebras and their codimension growth

Let W be an associative PI — algebra over a field F of characteristic zero. Suppose W is G-graded where G is a finite group. Let exp(W) and exp(W _e ) denote the codimension growth of W and of the identity component W _e , respectively. The following inequality had been conjectured by Bahturin and Zaicev: exp(W) ≤ |G|² exp(W _e ). The inequality is known in case the algebra W is affine (i.e., finitely generated). Here we prove the conjecture in general.     

Quasifactors of ergodic systems with positive entropy

The relation between the two notions, quasifactors and joinings, is investigated and the notion of a joining quasifactor is introduced. We clarify the close connection between quasifactors and symmetric infinite selfjoinings which arises from de Finetti-Hewitt-Savage theorem. Unlike the zero-entropy case where quasifactors seems to preserve some properties of their parent system, it is shown that any ergodic system of positive entropy admits all ergodic systems of positive entropy as quasifactors. A restricted version of this result is obtained for joining quasifactors.     

Acylphosphonamidates and α-hydroxyiminophosphonamidates. Synthesis of N-acylphosphordiamidates by Beckmann rearrangement. Crystal structure of (E)-α-hydroxyiminobenzyl-1-pyrrolidinylphosphinate

Reaction of methyl benzoylphosphonochloridate (3) with a secondary or primary series of amines yielded methyl benzoylphosphonamidates, 4a-e. The latter compounds reacted with hydroxylamine to yield a-hydroxyiminobenzylphosphonamidates (5a-e), largely as (E)-isomers. The structure of methyl (E)-a-hydroxyimino-benzyl-1-pyrrolidinylphosphinate (5b) was determined by single-crystal X-ray crystallography. Heating oximes 5a-e in boiling toluene caused them to undergo Beckmann rearrangement to N-benzoylphosphordiamidates 6a-e. © 1996 John Wiley & Sons, Inc.