Invariant barriers to reactive front propagation in fluid flows

We present theory and experiments on the dynamics of reaction fronts in two-dimensional, vortex-dominated flows, for both time-independent and periodically driven cases. We find that the front propagation process is controlled by one-sided barriers that are either fixed in the laboratory frame (time-independent flows) or oscillate periodically (periodically driven flows). We call these barriers burning invariant manifolds (BIMs), since their role in front propagation is analogous to that of invariant manifolds in the transport and mixing of passive impurities under advection. Theoretically, the BIMs emerge from a dynamical systems approach when the advection-reaction-diffusion dynamics is recast as an ODE for front element dynamics. Experimentally, we measure the location of BIMs for several laboratory flows and confirm their role as barriers to front propagation.

Barriers to front propagation in ordered and disordered vortex flows

We present experiments on reactive front propagation in a two-dimensional (2D) vortex chain flow (both time-independent and time-periodic) and a 2D spatially disordered (time-independent) vortex-dominated flow. The flows are generated using magnetohydrodynamic forcing techniques, and the fronts are produced using the excitable, ferroin-catalyzed Belousov-Zhabotinsky chemical reaction. In both of these flows, front propagation is dominated by the presence of burning invariant manifolds (BIMs) that act as barriers, similar to invariant manifolds that dominate the transport of passive impurities. Convergence of the fronts onto these BIMs is shown experimentally for all of the flows studied. The BIMs are also shown to collapse onto the invariant manifolds for passive transport in the limit of large flow velocities. For the disordered flow, the measured BIMs are compared to those predicted using a measured velocity field and a three-dimensional set of ordinary differential equations that describe the dynamics of front propagation in advection-reaction-diffusion systems.

Polymerization of Styrene and Cyclization to Macrocyclic Polystyrene in a One-Pot, Two-Step Sequence

Dibrominated polystyrene (BrPStBr) was produced by atom transfer radical polymerization (ATRP) at 80 degrees C, using the bifunctional initiator benzal bromide to afford the telechelic precursor. The ATRP reaction was stopped around 40% monomer conversion and directly converted into an radical trap-assisted atom transfer radical coupling (RTA-ATRC) reaction by lowering the temperature to 50 degrees C, and adding the radical trap 2-methyl-2-nitrosopropane (MNP) along with additional catalyst, reducing agent, and ligand to match ATRC-type reaction conditions. In an attempt to induce intramolecular coupling, rather than solely intermolecular coupling and elongation, the total reaction volume was increased by the addition of varying amounts of THF. Cyclization, along with intermolecular coupling and elongation, occurred in all cases, with the extent of ring closure a function of the total reaction volume. The cyclic portion of the coupled product was found to have a (G) value around 0.8 by GPC analysis, consistent with the reduction in hydrodynamic volume of a cyclic polymer compared to its linear analog. Analysis of the sequence by H-1 NMR confirmed that propagation was suppressed nearly completely during the RTA-ATRC phase, with percent monomer conversion remaining constant after the ATRP phase. (C) 2013 Elsevier Ltd. All rights reserved.