Factors affecting propagating fronts of addition polymerization: Velocity,front curvature,temperatue profile,conversion, and molecular weight distribution

Several properties of propagating fronts of addition polymerization were studied. A power function could be fit to the velocity dependence on initiator concentration, but not with the exponents predicted by current models or in agreement with other published work. Bubbles from the volatile by-products of initiator decomposition were found to affect the front velocity and curvature. The front velocity for triethylene glycol dimethacrylate polymerization was found to depend linearly on temperature over a moderate range. The conversion of methacrylic acid in fronts varied greatly with initiator type and concentration. Benzoyl peroxide produced much lower conversion than t-butyl peroxide, but fronts with tBPO propagated slower. A dual initiator system of BPO and tBPO produced rapidly propagating fronts with good conversion but the contribution of each initiator to the velocity was not additive. The possibility of chain branching was considered. The apparent molecular weight distributions were very broad, often trimodal, and found to depend on initiator type and concentration as well as the tube diameter. The temperature profiles were measured and found to be very sharp for BPO and broader for tBPO but both had front temperatures in excess of 200°C, indicating a high ceiling temperature. © 1995 John Wiley & Sons, Inc.     

Recent advances in catalytic asymmetric epoxidation using the environmentally benign oxidant hydrogen peroxide and its derivatives

There has been a recent drive to develop asymmetric catalytic methods to produce epoxides using environmentally benign oxidants, especially hydrogen peroxide. This critical review discusses the advances that have been made using both metal-based and organocatalytic homogeneous catalysts (142 references).     

Numerical modeling of self-propagating polymerization fronts: The role of kinetics on front stability

Frontal propagation of a highly exothermic polymerization reaction in a liquid is studied with the goal of developing a mathematical model of the process. As a model case we consider monomers such as methacrylic acid and n-butyl acrylate with peroxide initiators, although the model is not limited to these reactants and can be applied to any system with the similar basic polymerization mechanism. A three-step reaction mechanism, including initiation, propagation and termination steps, as well as a more simple one-step mechanism, were considered. For the one-step mechanism the loss of stability of propagating front was observed as a sequence of period doubling bifurcations of the front velocity. It was shown that the one-step model cannot account for less than 100% conversion and product inhomogeneities as a result of front instability, therefore the three-step mechanism was exploited. The phenomenon of superadiabatic combustion temperature was observed beyond the Hopf bifurcation point for both kinetic schemes and supported by the experimental measurements. One- and two-dimensional numerical simulations were performed to observe various planar and nonplanar periodic modes, and the results for different kinetic schemes were compared. It was found that stability of the frontal mode for a one-step reaction mechanism does not differ for 1-D and 2-D cases. For the three-step reaction mechanism 2-D solutions turned out to be more stable with respect to the appearance of nonplanar periodic modes than corresponding 1-D solutions. Higher Zeldovich numbers (i.e., higher effective activation energies or lower initial temperatures) are necessary for the existence of planar and nonplanar periodic modes in the 2-D reactor with walls than in the 1-D case. (c) 1997 American Institute of Physics.     

Asymmetric synthesis of oxindoles containing a quaternary stereogenic centre by catalytic O/C-carboxyl rearrangement

A catalysed O/C-carboxyl rearrangement generates the all-carbon stereogenic centre in phenyl 1,3-dimethyl-5-methoxy-2-oxoindoline-3-carboxylate (up to 57% ee). Crystallisation and removal of racemic crystals enhance the ee to 95%. The X-ray crystal structure of the cobalt metallocene-pyrrolidinopyridine nucleophilic catalyst employed is reported.     

Shannon entropy in the research on stationary regimes and the evolution of complexity

The questions of the identification of complex biological systems (complexity) as special self-organizing systems or systems of the third type first defined by W. Weaver in 1948 continue to be of interest. No reports on the evaluation of entropy for systems of the third type were found among the publications currently available to the authors. The present study addresses the parameters of muscle biopotentials recorded using surface interference electromyography and presents the results of calculation of the Shannon entropy, autocorrelation functions, and statistical distribution functions for electromyograms of subjects in different physiological states (rest and tension of muscles). The results do not allow for statistically reliable discrimination between the functional states of muscles. However, the data obtained by calculating electromyogram quasiatttractor parameters and matrices of paired comparisons of electromyogram samples (calculation of the number k of “coinciding” pairs among the electromyogram samples) provide an integral characteristic that allows the identification of substantial differences between the state of rest and the different states of functional activity. Modifications and implementation of new methods in combination with the novel methods of the theory of chaos and self-organization are obviously essential. The stochastic approach paradigm is not applicable to systems of the third type due to continuous and chaotic changes of the parameters of the state vector x(t) of an organism or the contrasting constancy of these parameters (in the case of entropy).     

Cascades of <Emphasis Type="Italic">ε</Emphasis>-invisibility

We consider statistical attractors of locally typical dynamical systems and their “ε-invisible” subsets: parts of the attractors whose neighborhoods are visited by orbits with an average frequency of less than e << 1{\varepsilon \ll 1}. For extraordinarily small values of ε (say, smaller than 2^-106{{2^{-10}}^6}), an observer virtually never sees these parts when following a generic orbit.     

Enantioselective Synthesis and Application to the Allylic Imidate Rearrangement of Amine‐Coordinated Palladacycle Catalysts of Cobalt Sandwich Complexes

The reaction of (η⁵‐(N,N‐dimethylaminomethyl)cyclopentadien‐yl)(η⁴‐tetraphenylcyclobutadiene)cobalt with sodium tetrachloropalladate and (R)‐N‐acetylphenylalanine gave planar chiral palladacycle di‐μ‐chloridebis[(η⁵‐(S_p)‐2‐(N,N‐dimethylaminomethyl)cyclopentadienyl,1‐C,3′‐N)(η⁴‐tetraphenylcyclobutadiene)cobalt]dipalladium [(S_p)‐Me₂‐CAP‐Cl] in 92 % ee and 64 % yield. Enantiopurity (>98 % ee) was achieved by purification of the monomeric (R)‐proline adducts and conversion back to the chloride dimer. Treatment with AgOAc gave (S_p)‐Me₂‐CAP‐OAc which was applied to asymmetric transcyclopalladation (up to 78 % ee). The (R)‐N‐acetylphenylalanine mediated palladation methodology was applicable also to the corresponding N,N‐diethyl (82 % ee, 39 % yield) and pyrrolidinyl (>98 % ee, 43 % yield) cobalt sandwich complexes. A combination of 5 mol % of the latter [(S_p)‐Pyrr‐CAP‐Cl] and AgNO₃ (3.8 equiv) is a catalyst for the allylic imidate rearrangement of an (E)‐N‐aryltrifluoroacetimidate (up to 83 % ee), and this catalyst system is also applicable to the rearrangement of a range of (E)‐trichloroacetimidates (up to 99 % ee). This asymmetric efficiency combined with the simplicity of catalyst synthesis provides accessible solutions to the generation of non‐racemic allylic amine derivatives.     

Diffeomorphisms with intermingled attracting basins

We construct a diffeomorphism F of a manifold with boundary into itself with the following property. The attractor of F has two components, and the attracting basins of these components are dense in the phase space and have positive measure. We prove that the class of examples constructed in the paper has codimension infinity in the space of all diffeomorphisms of the same manifold.     

Kupka-Smale theorem for polynomial automorphisms of ?2 and persistence of heteroclinic intersections

A map is Kupka-Smale if all periodic points are hyperbolic and the stable and unstable manifolds of any two saddle points are transverse. Here we prove that Kupka-Smale maps form a residual set of full Lebesgue measure in the space of polynomial automorphisms of ² of fixed dynamical degree d2. We also prove that a heteroclinic point of two saddle periodic orbits may be continued over (almost) the entire parameter space for this set of maps. This is one of the first persistence theorems proved in holomorphic dynamics in several variables.