Dark cure studies of cationic photopolymerizations of epoxides: Characterization of kinetic rate constants at high conversions

The effective propagation rate constant (k_p; averaged over all the propagating active centers) was characterized for solvent‐free cationic photopolymerizations of phenyl glycidyl ether over the entire range of conversions, including the high conversion regime in which mass transfer limitations become important. The profile for the k_p as a function of conversion was found to exhibit a constant plateau value at low to intermediate conversions, followed by a monotonic increase above a threshold value of conversion. To explain this trend, it is proposed that at high conversion the diffusional mobility of the photoinitiator counterion is reduced whereas the mobility of the cationic active center remains high because of reactive diffusion. Therefore, with increasing conversion, the average distance between the active centers and counterions may increase, resulting in an increase in the propagation rate constant. The profiles for the k_p values were investigated as a function of the temperature, photoinitiator anion, and photoinitiator concentration. As the photoinitiator concentration was increased, the plateau value of the effective propagation rate constant decreased whereas the threshold conversion increased. All of the experimental trends are consistent with the proposed increase in ion separation at high conversions. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 4409–4416, 2004     

Complexation thermodynamics of free and graft oligomers with complementary polymers

The dilute solution complexation equilibrium between linear macromolecules and smaller complementary oligomers is considered when: (1) the oligomers are free in solution; and (2) the oligomers are covalently attached at one end to the polymer. A general statistical mechanical framework is developed and is illustrated using a simple random walk model for polymer conformation. The statistical mechanical partition functions are formulated using a generating function technique, allowing thermodynamic averages in the complexed state to be calculated. Loops, trains, and tails of all possible length are allowed in the conformation of a complexed oligomer. Simulation results for the free oligomer case are compared with those obtained for oligomers covalently attached to the polymeric molecular. The model provides a theoretical explanation for the experimentally observed enhancement of complexation of oligomers grafted to the complementary polymers.     

Excited-state electron-transfer quenching by a series of water photoreduction mediators

Rate constants k_q for the quenching of the excited state of Ru(bipy)₃²⁺ by a series of viologen salts having different redox potential E_{$\text{1}\text{2}$} have been determined in deaerated aqueous solutions at pH = 5 by laser flash photolysis. The k_q values are found to decrease with increasing —E_{$\text{1}\text{2}$} and to correlate with the reaction free-energy change ΔG. Such a correlation is shown to be consistent with the Rehm—Weller model for electron-transfer reactions.     

The Zygmund Morse-Sard Theorem

The classical Morse-Sard Theorem says that the set of critical values off:R ^n+k →R ⁿ has Lebesgue measure zero iff ∈C ^k+1. We show theC ^k+1 smoothness requirement can be weakened toC ^k+Zygmund. This is corollary to the following theorem: For integersn >m >r > 0, lets = (n ?r)/(m ?r); iff:R ⁿ →R ^m belongs to the Lipschitz class Λ _s andE is a set of rankr forf, thenf(E) has measure zero.     

Temperature-sensitive luminescence of tris (β-diketone) europium chelates for monitoring high-speed cationic photopolymerizations

The temperature-dependent luminescence of tris (β-diketone) chelates of europium was used for in situ temperature measurements during cationic photopolymerizations of vinyl ethers. These molecular-level luminescent probes provided a real-time, noninvasive method for monitoring temperature during these high-speed polymerizations. Two specific probes, tris (benzoyl-1, 1, 1-trifluoroacetone) europium and tris (1,1,1,5,5,5,-hexafluoroacetylacetone) europium, met several stringent spectral and performance requirements for application in our system. The luminescence from these probes exhibits a reproducible temperature dependence over a wide temperature range and is not sensitive to changes in viscosity. In situ temperature profiles obtained using this novel technique verified the importance of thermal effects during these highly exothermic photopolymerizations. These studies have demonstrated the utility of the tris(β-diketone) europium chelates for characterizing the temperature during high-speed photopolymerizations that cannot be monitored using conventional techniques. © 1995 John Wiley & Sons, Inc.     

A statistical model of free-radical copolymerization/crosslinking reactions

A statistical model for network formation by the free-radical copolymerization and crosslinking reaction with small crosslinker content is used to obtain expressions for structural averages as a function of reaction parameters. The analysis accounts for reaction features that are characteristic of free-radical mechanisms and can be adapted to include cyclization, various modes of termination, and the gel effect. Profiles for structural averages such as the weight average molecular weight, the sol weight fraction, the molecular weight between crosslinks, and the number of elastically active network chains are obtained as functions of conversion.     

Complex dynamics in equilibrium asset pricing models with boundedly rational,heterogeneous agents

We study a simple model based upon the Lucas framework where heterogeneous agents behave rationally in a fully intertemporal setting but do not know other investors' personal preferences, wealth or investment portfolios. As a consequence, agents initially do not know the equilibrium asset pricing function and must make guesses, which they update via adaptive learning with constant gain. We demonstrate that even in this simple environment the economy can, depending on parameters, exhibit either stable convergence to equilibrium, or chaotic dynamical behavior of asset prices and trading volume without converging to the rational expectations equilibrium of the Lucas model. This contradicts the assertion that the Lucas model is stable in the face of modest deviations from the strong assumptions required to compute the equilibrium. © 2013 Wiley Periodicals, Inc. Complexity 19: 38–55, 2014     

Three-Component Reaction for the Synthesis of Highly Functionalized Propargyl Ethers

Multicomponent reactions provide efficient means to access molecular complexity. Herein, we report a copper-catalyzed three-component reaction of diazo compounds, alcohols and ethynyl benziodoxole (EBX) reagents for the synthesis of propargyl ethers. Extensive variations of the three partners of the reaction is possible, leading to highly functionalized and structurally diverse products under mild conditions. Alkynylation of a copper ylide intermediate is postulated as key step for this transformation.     

Kinetics of cationic photopolymerizations of divinyl ethers characterized using in situ Raman spectroscopy

In situ Raman spectroscopy experiments were used to determine effective kinetic propagation constants for a series of unsteady-state divinyl ether polymerizations at different isothermal temperatures and light intensities. Raman spectroscopy was found to be ideally suited for monitoring cationic photopolymerizations because the technique allows isothermal experiments to be performed with excellent time resolution and allows several spectral features to be observed simultaneously. In addition, the Raman experiments provided direct information about the vinyl bond concentration in situ as the reaction takes place. For these cationic photopolymerizations, the reaction rate and limiting conversion were both found to increase as the reaction temperature was increased. At all temperatures, the profile for the propagation rate constant, k_p, exhibited a dramatic increase at the start of the reaction, plateaued at a value between 10 and 40 l/mol s (depending upon temperature), and then decreased as the reaction reached a limiting conversion due to trapping of the active centers. Finally, the overall activation energy for polymerization was found to be 25.1 ± 6.1 kJ/mol. © 1996 John Wiley & Sons, Inc.     

Stereoretentive and regioselective selenium-catalyzed intermolecular propargylic C–H amination of alkynes

Herein we report an intermolecular propargylic C–H amination of alkynes. This reaction is operationally convenient and requires no transition metal catalysts or additives. Terminal, silyl, and internal alkynes bearing a wide range of functional groups can be aminated in high yields. The regioselectivity of amination for unsymmetrical internal alkynes is strongly influenced by substitution pattern (tertiary > secondary > primary) and by relatively remote heteroatomic substituents. We demonstrate that amination of alkynes bearing α-stereocenters occurs with retention of configuration at the newly-formed C–N bond. Competition experiments between alkynes, kinetic isotope effects, and DFT calculations are performed to confirm the mechanistic hypothesis that initial ene reaction of a selenium bis(imide) species is the rate- and product-determining step. This ene reaction has a transition state that results in substantial partial positive charge development at the carbon atom closer to the amination position. Inductive and/or hyperconjugative stabilization or destabilization of this positive charge explains the observed regioselectivities.

Selenium catalysis enables a general intermolecular propargylic C–H amination of alkynes. The concerted mechanism gives rise to high regioselectivity for the more electron-rich end of the alkyne and retention of the C–H propargylic stereocenter.