An adaptive algorithm for simulation of stochastic reaction–diffusion processes

We propose an adaptive hybrid method suitable for stochastic simulation of diffusion dominated reaction–diffusion processes. For such systems, simulation of the diffusion requires the predominant part of the computing time. In order to reduce the computational work, the diffusion in parts of the domain is treated macroscopically, in other parts with the tau-leap method and in the remaining parts with Gillespie’s stochastic simulation algorithm (SSA) as implemented in the next subvolume method (NSM). The chemical reactions are handled by SSA everywhere in the computational domain. A trajectory of the process is advanced in time by an operator splitting technique and the timesteps are chosen adaptively. The spatial adaptation is based on estimates of the errors in the tau-leap method and the macroscopic diffusion. The accuracy and efficiency of the method are demonstrated in examples from molecular biology where the domain is discretized by unstructured meshes.     

Cyclization of Propargylic Amides: Mild Access to Oxazole Derivatives

The substrate scope, the mechanistic aspects of the gold‐catalyzed oxazole synthesis, and substrates with different aliphatic, aromatic, and functional groups in the side chain were investigated. Even molecules with several propargyl amide groups could easily be converted, delivering di‐ and trioxazoles with interesting optical properties. Furthermore, the scope of the gold(I)‐catalyzed alkylidene synthesis was investigated. Further functionalizations of these isolable intermediates of the oxazole synthesis were developed and chelate ligands can be obtained. The use of Barluenga’s reagent offers a new and mild access to the synthetically valuable iodoalkylideneoxazoles from propargylic amides, this reagent being superior to other sources of halogens.     

Sulfonation of polystyrene: Toward the “ideal” polyelectrolyte

Sulfonation of narrow polydispersity polystyrene, PS, standards remains the method of choice for generating polystyrene sulfonate, PSS, samples with defined composition. Although a variety of sulfonation techniques have been described, relatively little is reported on the material obtained, which is used for so many studies on the fundamental behavior of polyelectrolytes. Here, we show that powdered polystyrene treated with concentrated sulfuric acid (96%) at 90 °C without catalyst yields fully sulfonated PSS. Extensive characterization with ¹H and ¹³C NMR as well as size exclusion chromatography coupled with static and dynamic light scattering shows no evidence of sulfone crosslinking or chain degradation under the conditions used. Though mono‐sulfonated as soon as it dissolves in the acid, the PSS contains about 6% meta substitution. Sulfonation kinetics for this heterogeneous reaction depend strongly on particle size, sulfuric acid content and temperature. For preparing perdeuterated PSS from the corresponding PS it is essential to employ D₂SO₄, as about half of the aromatic units undergo H/D exchange during sulfonation. The remaining ortho H/D may be exchanged with extended exposure to the concentrated sulfuric acid, but the meta site is deactivated. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2013, 51, 2416–2624     

Optical characterization of polycarbonate: Influence of additives on optical properties

In laser transmission welding of thermoplastics the optical properties of the joining parts determine the quality of the welding result. Especially, the scattering of laser radiation in the transparent welding part has an impact on weld seam properties. This scattering is caused by additives. For polycarbonate (PC) with different additives the transmittance, the reflectance and the collimated transmittance are measured with a UV‐VIS‐NIR spectrometer. From this data, the optical properties, such as scattering coefficient, absorption coefficient, and anisotropy factor are calculated. The calculations are made with the aid of the four‐flux model of radiation transport in the diffusive approximation. The results show that the additives have a significant influence on the scattering coefficient. For most additives under consideration the scattering is forward directed, which means that most of the radiation is transmitted into the absorbing welding part. However, the power density distribution of the transmitted radiation may differ significantly from PC without additives. So, the weld seam may also differ due to different additives. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 451–455, 2010