About crosslinking of low molecular weight ethylene‐propylene(‐diene) copolymer‐based artificial latices

Crosslinking of artificial latices based on ethylene–propylene copolymers (EPM) and/or ethylene–propylene–diene copolymers (EPDM) has not thoroughly been studied yet. Moreover, crosslinking of EPM and/or EPDM particles is a prerequisite for the formation of a shell using seeded emulsion polymerization of, for example, methyl methacrylate (MMA), as described elsewhere. Therefore, the aim of this article is to improve the general understanding of the chemistry involved in the crosslinking process. This work especially emphasizes the influence of the initiation method, that is, a peroxide or a pulsed electron‐beam, on crosslinking efficiency. All crosslinking efficiencies were obtained after extraction of the soluble polymer by tetrahydrofuran. The incorporation of the coagent, that is, divinylbenzene, into the EPM/EPDM phase was studied on a microscopic level by solid‐state ¹³C and ¹H nuclear magnetic resonance (NMR). Crosslinking of a low molecular weight EPM/EPDM latex requires the presence of a coagent, for example, divinylbenzene, 1,6‐hexanediol diacrylate, or poly(1,2‐butadiene). The efficiency of crosslinking initiated by a pulsed electron‐beam was improved to a great extent by the presence, in the aqueous phase, of potassium nitrosodisulfonate, also referred to as Fremy salt. Matrix Assisted Laser Desorption/Ionization–Time of Flight–Mass Spectrometry (MALDI‐TOF‐MS) was used to determine the influence of electron‐beam irradiation on the chemical stability of surfactants. It was demonstrated that sodium dodecyl benzene sulfonate (SDBS) is not degraded by the irradiation, and is therefore the surfactant of choice for the stabilization of EPM/EPDM‐based latices subjected to electron‐beam irradiation. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 3600–3615, 2005     

On a New Continued Fraction Expansion with Non-Decreasing Partial Quotients

We investigate metric properties of the digits occurring in a new continued fraction expansion with non-decreasing partial quotients, the so-called Engel continued fraction (ECF) expansion.     

The theta group and the continued fraction expansion with even partial quotients

F. Schweiger introduced the continued fraction with even partial quotients. We will show a relation between closed geodesics for the theta group (the subgroup of the modular group generated by z+2 and -1 / z) and the continued fraction with even partial quotients. Using thermodynamic formalism, Tauberian results and the above-mentioned relation, we obtain the asymptotic growth number of closed trajectories for the theta group. Several results for the continued fraction expansion with even partial quotients are obtained; some of these are analogous to those already known for the usual continued fraction expansion related to the modular group, but our proofs are by necessity in general technically more difficult.Supported by The Netherlands Organization for Scientific Research (NWO).     

Peptide block copolymers by N‐carboxyanhydride ring‐opening polymerization and atom transfer radical polymerization: The effect of amide macroinitiators

The synthesis of polypeptide‐containing block copolymers combining N‐carboxyanhydride (NCA) ring‐opening polymerization and atom transfer radical polymerization (ATRP) was investigated. An amide initiator comprising an amine function for the NCA polymerization and an activated bromide for ATRP was used. Well‐defined polypeptide macroinitiators were obtained from γ‐benzyl‐L ‐glutamate NCA, O‐benzyl‐serine NCA, and N‐benzyloxy‐L ‐lysine. Subsequent ATRP macroinitiation from the polypeptides resulted in higher than expected molecular weights. Analysis of the reaction products and model reactions confirmed that this is due to the high frequency of termination reactions by disproportionation in the initial phase of the ATRP, which is inherent in the amide initiator structure. In some cases selective precipitation could be applied to remove unreacted macroinitiator to yield well‐defined block copolymers. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2009     

Natural extensions for the Rosen fractions

The Rosen fractions form an infinite family which generalizes the nearest-integer continued fractions. We find planar natural extensions for the associated interval maps. This allows us to easily prove that the interval maps are weak Bernoulli, as well as to unify and generalize results of Diophantine approximation from the literature.

     

Partially renewable copolyesters prepared from acetalized d‐glucitol by solid‐state modification of poly(butylene terephthalate)

The backbone of poly(butylene terephthalate) (PBT) was modified with 2,4:3,5‐di‐O‐methylene‐D ‐glucitol (Glux) using solid‐state modification (SSM). The obtained copolyesters proved to have a non‐random overall chemical microstructure. The thermal properties of these semicrystalline, block‐like, Glux‐based materials were extraordinary, showing higher melting points, and glass transition temperatures compared with other sugar‐based copolyesters prepared by SSM. These remarkable thermal properties were a direct result of the inherently rigid structure of Glux and the relatively slow randomization of the block‐like chemical microstructure of the Glux‐based copolyesters in the melt. SSM proved to be a versatile tool for preparing partially biobased copolyesters with superior thermal properties. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2014 , 52, 164–177     

Polyamide‐6,6‐based blocky copolyamides obtained by solid‐state modification

Copolyamides based on polyamide‐6,6 (PA‐6,6) were prepared by solid‐state modification (SSM). Para‐ and meta‐xylylenediamine were successfully incorporated into the aliphatic PA‐6,6 backbone at 200 and 230 °C under an inert gas flow. In the initial stage of the SSM below the melting temperature of PA‐6,6, a decrease of the molecular weight was observed due to chain scission, followed by a built up of the molecular weight and incorporation of the comonomer by postcondensation during the next stage. When the solid‐state copolymerization was continued for a sufficiently long time, the starting PA‐6,6 molecular weight was regained. The incorporation of the comonomer into the PA‐6,6 main chain was confirmed by size exclusion chromatography (SEC) with ultraviolet detection, which showed the presence of aromatic moieties in the final high‐molecular weight SSM product. The occurrence of the transamidation reaction was also proven by ¹H nuclear magnetic resonance (NMR) spectroscopy. As the transamidation was limited to the amorphous phase, this SSM resulted in a nonrandom overall structure of the PA copolymer as shown by the degree of randomness determined using ¹³C NMR spectroscopy. The thermal properties of the SSM products were compared with melt‐synthesized copolyamides of similar chemical composition. The higher melting and higher crystallization temperatures of the solid state‐modified copolyamides confirmed their nonrandom, block‐like chemical microstructure, whereas the melt‐synthesized copolyamides were random. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2013 , 51, 5118–5129     

Modeling of the carbon dioxide solubility in imidazolium-based ionic liquids with the tPC-PSAFT equation of state

In this work, an equation of state (EoS) is developed to predict accurately the phase behavior of ionic liquid + CO2 systems based on the truncated perturbed chain polar statistical associating fluid theory (tPC-PSAFT) EoS. This EoS accounts explicitly for the dipolar interactions between ionic liquid molecules, the quadrupolar interactions between CO2 molecules, and the Lewis acid-base type of association between the ionic liquid and the CO2 molecules. Physically meaningful model pure-component parameters for ionic liquids are estimated based on literature data. All experimental vapor-liquid equilibrium data are correlated with a single linearly temperature-dependent binary interaction parameter. The ability of the model to describe accurately carbon dioxide solubility in various 1-alkyl-3-methylimidazolium-based ionic liquids with different alkyl chain lengths and different anions at pressures from 0 to 100 MPa and carbon dioxide fractions from 0 to 75 mol % is demonstrated. In all cases, good agreement with experimental data is obtained.