Two New Mechanism Generators of Chemical Instability in Polymerization Reactions

Two new kinetic mechanisms of polymerization are proposed (0Re–1,2 and 0Re–1) to study the instability of the steady states by the Lyapounov method. Both mechanisms take into account a reinitiation step in the polymerization process, but they are different because 0Re–1,2 considers two kinds of termination steps: a zero‐ and a second‐order terminations. However, in the second mechanism, 0Re–1, only one of those termination steps (the zero‐order one) is presented. In both proposed mechanisms, the nondiffusive and diffusive cases are studied. The results show that they are able to display arrangements in time (limit cycle oscillations) and space (order form fluctuations).     

Kinetics and mechanisms of homogeneous catalytic reactions: Part 6. Hydroformylation of 1-hexene by use of Rh(acac)(CO)2/dppe [dppe = 1,2-bis(diphenylphosphino)ethane] as the precatalyst

A kinetic study of the homogeneous hydroformylation of 1-hexene to the corresponding aldehydes (heptanal and 2-methyl-hexanal) was carried out using a rhodium catalyst formed by addition of 1 equiv. of 1,2-bis(diphenylphosphino)ethane (dppe) to Rh(acac)(CO)₂ under mild reaction conditions (80 °C, 1–7 atm H₂ and 1–7 atm CO) in toluene; in all cases linear to branched ratios were close to 2. The reaction rate is first-order in dissolved hydrogen concentration at pressures below 3 atm, but independent of this parameter at higher pressures. In both regimes (low and high H₂ pressure), the initial rate was first-order with respect to the concentration of Rh and fractional order with respect to 1-hexene concentration. Increasing CO pressure had a positive effect on the rate up to a threshold value above which inhibition of the reaction was observed; the range of positive order on CO concentration is smaller when the total pressure is increased. The kinetic data and related coordination chemistry are consistent with a mechanism involving RhH(CO)(dppe) as the active species initiating the cycle, hydrogenolysis of the acyl intermediate as the rate-determining step of the catalytic cycle at low hydrogen pressure, and migratory insertion of the olefin into the metal-hydride bond as rate limiting at high hydrogen pressure. This catalytic cycle is similar to the one commonly accepted for RhH(CO)(PPh₃)₃ but different from previous proposals for Rh-diphosphine catalysts.     

New selective haloform-type reaction yielding 3-hydroxy-2,2-difluoroacids: theoretical study of the mechanism

Experimental results of an unprecedented haloform-type reaction in which 4-alkyl-4-hydroxy-3,3-difluoromethyl trifluoromethyl ketones undergo base-promoted selective cleavage of the CO-CF(3) bond, yielding 3-hydroxy-2,2-difluoroacids and fluoroform, are rationalized using DFT (B3LYP) calculations. The gas-phase addition of hydroxide ion to 1,1,1,3,3-pentafluoro-4-hydroxypentan-2-one (R) is found to be a barrierless process, yielding a tetrahedral intermediate (INT), involving a DeltaG(r)(298 K) of -61.4 kcal/mol. The CO-CF(3) bond cleavage in INT leads to a hydrogen-bonded [CH(3)CHOHCF(2)CO(2)H...CF(3)](-) complex by passage through a transition structure (TS1) with a DeltaG()(298 K) of 20.8 kcal/mol and a DeltaG(r)(298 K) of 9.8 kcal/mol. This complex undergoes a proton transfer between its components, yielding a hydrogen-bonded [CH(3)CHOHCF(2)CO(2)...CHF(3)](-) complex. This process has associated with it a DeltaG()(298 K) of only 3.1 kcal/mol and a DeltaG(r)(298 K) of -43.3 kcal/mol. The CO-CF(2) bond cleavage in INT leads to a hydrogen-bonded [CH(3)CHOHCF(2)...CF(3)CO(2)H](-) complex by passage through a transition structure (TS3) with a DeltaG()(298 K) of 29.2 kcal/mol and a DeltaG(r)(298 K) of 25.1 kcal/mol. The lower energy barrier found for CO-CF(3) bond cleavage in INT is ascribed to the larger number of fluorine atoms stabilizing the negative charge accumulated on the CF(3) moiety of TS1, as compared to the number of fluorine atoms stabilizing the negative charge on the CH(3)CHOHCF(2) moiety of TS3. The solvent-induced effects on the two pathways, introduced within the SCRF formalism through PCM calculations, do not reverse the predicted preference of the CO-CF(3) over the CO-CF(2) bond cleavage of R in the gas phase.     

Cyanoxyl‐mediated free‐radical polymerization of acrylic acid: Its scope and limitations

This work examines the scope and limitations of the cyanoxyl (^·OC?N)‐mediated free‐radical polymerization of acrylic acid (AA) with respect to the criteria of livingness. Cyanoxyl persistent radicals were generated in situ through the reaction between arenediazonium salts (X? C₆H₄N?N^⊕BF, where X is H, OCH₃, Cl, or NO₂) and sodium cyanate (NaOCN). This article thoroughly discusses the role played by such oxygen‐centered radicals in the polymerization process; it particularly focuses on the influence of the concentration and nature of the diazonium salt, the solvent, and the temperature on features such as the variations of ln([M]₀/[M]) versus time (where [M]₀ is the initial monomer concentration and [M] is the monomer concentration), the number‐average molar mass versus conversion, and the polydispersity versus conversion in cyanoxyl‐mediated free‐radical polymerizations of AA. Cyanoxyl‐terminated samples were used as macroinitiators for the polymerization of methyl methacrylate to generate poly(acrylic acid)‐b‐poly(methyl methacrylate) block copolymers. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 519–533, 2005     

Synthesis of Hydrophilic-Lypophilic Copolymers in Emulsion: Initiation of Vinyl Chloride by Aqueous Soluble Polymeric Radicals at the Interface

The emulsion polymerization of vinyl chloride initiated by a redox pair in the presence of acrylamide in the aqueous phase gives a product which apparently corresponds to a block copolymer of polyacrylamide and polyvinyl chloride). A reaction scheme is proposed which involves the attack of the vinyl chloride in the micelles by a growing polyacrylamide radical, thus producing the hydrophilic - lypophilic copolymer. Isopropyl alcohol is used as a transfer agent to limit the size of the PAA chains growing in the aqueous phase. The reaction product was characterized by selective solvent extraction, elemental analysis, infrared spectroscopy, and differential thermal analysis.     

The elastic sphere under arbitrary concentrated surface loads

The elastostatic problem of a sphere subject to a concentrated surface load of arbitrary direction which is equilibrated in a very simple manner by a distribution of surface tractions is solved. Particular attention is placed in the analysis of the singularity at the point of application of the concentrated load.The solution obtained provides a means for reducing problems pertaining to a sphere under arbitrary concentrated and distributed loads to a regular second boundary-value problem for the sphere. For illustration the problem of a sphere acted by two equal, opposite and collinear loads applied at two arbitrary surface points is treated.The paper also contains an exposition and an essential extension of an integration scheme developed by Almansi. Thus, an explicit integral representation of the displacements in an elastic sphere in terms of a vector valued harmonic potential which coincides on the surface with the tractions is obtained.

---

Résumé On présente la résolution du problème élastostatique d'une sphère soumise en surface à une charge ponctuelle de direction arbitraire équilibrée par une distribution trés simple de contraintes superficielles. On s'attache plus spécialement à l'analyse de la singularité au point d'application de la charge ponctuelle.La solution obtenue permet de réduire les problèmes d'une sphère soumise de manière quelconque à des charges ponctuelles et réparties, à un problème avec conditions aux limites régulières. A titre d'exemple, on traite le problème d'une sphère soumise à deux forces ponctuelles, co linéaires, égales et de sens opposé, appliquées en deux points arbitraires de la surface.L'article contient également une exposition et une extension d'un schéma d'intégration développé par Almansi. On obtient ainsi une représentation explicite, sous forme d'intégrale, des déplacements dans une sphère élastique, en termes de potentiel vecteur qui coïncide, à la surface, avec le champ de contraintes.