Vinyl Polymerization Initiated by Ceric Ion–Ethyl Cellosolve Redox System in Aqueous Nitric Acid

Abstract

Polymerizations of methyl methacrylate (MMA) and acrylonitrile (AN) were carried out in aqueous nitric acid at 30°C with the redox initiator system ammonium ceric nitrate-ethyl cellosolve (EC). A short induction period was observed as well as the attainment of a limiting conversion for polymerization reactions. The consumption of ceric ion was first order with respect to Ce(IV) concentration in the concentration range (0.2–0.4) × 10^?2 M, and the points at higher and lower concentrations show deviations from a linear fit. The plots of the inverse of pseudo-first-order rate constant for ceric ion consumption, (k ¹)^?1 vs [EC]^?1, gave straight lines for both the monomer systems with nonzero intercepts supporting complex formation between Ce(IV) and EC. The rate of polymerization increases regularly with [Ce(IV)] up to 0.003 M, yielding an order of 0.41, then falls to 0.0055 M and again shows a rise at 0.00645 M for MMA polymerization. For AN polymerization, R _p shows a steep rise with [Ce(IV)] up to 0.001 M, and beyond this concentration R _p shows a regular increase with [Ce(IV)], yielding an order of 0.48. In the presence of constant [NO^? ₃], MMA and AN polymerizations yield orders of 0.36 and 0.58 for [Ce(IV)] variation, respectively. The rates of polymerization increased with an increase in EC and monomer concentrations: only at a higher concentration of EC (0.5 M) was a steep fall in R _p observed for both monomer systems. The orders with respect to EC and monomer for MMA polymerization were 0.19 and 1.6, respectively. The orders with respect to EC and monomer for AN polymerization were 0.2 and 1.5, respectively. A kinetic scheme involving oxidation of EC by Ce(IV) via complex formation, whose decomposition gives rise to a primary radical, initiation, propagation, and termination of the polymeric radicals by biomolecular interaction is proposed. An oxidative termination of primary radicals by Ce(IV) is also included.     

Vibration of rectangular plates with time-dependent boundary conditions

A general method of solution for the vibration of rectangular plates with any type of time-dependent boundary conditions is developed by an extension of the method of Mindlin and Goodman [1]. For illustration, the problems of a plate with different time-dependent boundary conditions are solved and the closed form solutions for the transverse deflections of the plate are obtained. The non-dimensionalized transverse deflections, ($\text{w}\text{a}$) at the middle of the plate are evaluated numerically for different dimensions of the plate and different forcing functions. These are presented graphically against the non-dimensionalized time, T, for three cases and tabulated for other cases.     

Finitely generated profinitely dense free groups in higher rank semi-simple groups

We prove that if is an arithmetic subgroup of a non-compact linear semi-simple groupG such that the associated simply connected algebraic group over has the so-called congruence subgroup property, then contains a finitely generated profinitely dense free subgroup. As a corollary we obtain af·g·p·d·f subgroup of SL _n () (n 3. More generally, we prove that if is an irreducible arithmetic non-cocompact lattice in a higher rank group, then containsf·g·p·d·f groups.Partially supported by GIF grant No. G-454-213.06/95     

On Cycles on Compact Locally Symmetric Varieties

 We give a criterion to determine when the cycle class of a locally symmetric subvariety of a compact locally symmetric variety generates a non-trivial module under the action of Hecke operators, and give several examples where this criterion is satisfied. We also exhibit examples of subvarieties which do generate the trivial module under the action of Hecke operators. We show that all Hodge classes (in degree ) on the locally symmetric variety associated to certain arithmetric subgroups Γ of are algebraic (provided that ). Received 16 January 2001; in revised form 18 October 2001     

Erratum to: Several Articles in JETP Letters Published Online First

JETP Letters - An Erratum to this paper has been published: https://doi.org/10.1134/S0021364022330013     

Versatile soluble oligomeric styrene supports for peptide synthesis

Soluble oligomeric styrene supports are reported here with high loading capacities of 1.5–1.6 mmol/g similar to resins used in solid phase peptide synthesis. Oligoether and alkyl chains are incorporated into the scaffold to improve the support solubility and act as spacers between the attachment sites. Amino acids have been attached to the support in 59–85% yields and 0.87–1.3 mmol/g loading. The supports have been used to synthesize tri‐ to hexapeptides in 38–64% yields using only 2 equivalents of coupling reagents, which is much lower than the amount of reagents typically used in solid phase synthesis. A modular synthetic approach is used to obtain the supports so that any efficient styrene‐based attachment site can be readily incorporated into our soluble support scaffold. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2015 , 53, 2501–2509     

Discrete components of some complementary series representations

We show that the restriction of the complementary series representations of SO(n, 1) to SO(m, 1) (m < n) contains complementary series representations of SO(m, 1) discretely, provided that the continuous parameter is sufficiently close to the first point of reducibility and the representation of M — the compact part of the Levi- is a sufficiently small fundamental representation.