The discretized flow on domains of attraction: a structural stability result

It is well known that, for stepsize sufficiently small, compactattractors of ordinary differential equations persist underdiscretization. The present paper describes the structure ofthe discrete-time dynamical system obtained via discretizationon A(M_h)\M_h where M_h is the approximate attractor and A(M_h)is its domain of attraction. The existence of a smooth embeddinginto a continuous-time parallelizable flow is proved. The constructioncan be used to define sections for discretizations and can beinterpreted as a justification of the method of modified equations.     

Convenient Synthesis of 3,4-bis(Alkylthio) Thiophenes

A variety of symmetrically substituted 3,4-dithioether-thiophenes were prepared by the acid catalyzed nucleophilic substitution of 3,4-di(methoxy)thiophene with the appropriate thiol.     

Charge transfer absorption for pi-conjugated polymers and oligomers mixed with electron acceptors

Pi-conjugated polymers and oligomers show charge transfer (CT) absorption bands when mixed with electron acceptors in chloroform solution. This is attributed to the formation of (ground state) donor-acceptor complexes in solution. By varying the concentration of the donor and acceptor, the extinction coefficient for the CT absorption and the association constant of donor and acceptor are estimated. The spectral position of the CT bands correlates with the electrochemical oxidation potential of the pi-conjugated donor and the reduction potential of the acceptor.     

Separation and characterization of oligomers by reversed-phase high-performance liquid chromatography: a study on well-defined oligothiphenes

Reversed-phase high-performance liquid chromatography (RP-HPLC) was used for the separation of 3-hexylthiophene oligomers in the range of 3 to 30 monomeric units, while systematically varying stationary and mobile phases. A set of different columns was chosen, covering a broad range of silica types, pore sizes and bonding chemistry. Mobile phases of tetrahydrofuran (THF) combined with water, acetonitrile (ACN) or methanol (MeOH) were used. Although differences between columns were small, a higher selectivity correlated with a lower hydrophobicity parameter from the Galushko column test. The model of Jandera, based on the linear solvent strength model of Snyder, was used to describe the retention of the oligomers in gradient mode. This gave information about selectivities on different stationary phases similar to the hydrophobicity parameter. Contrary to the stationary phase, the mobile phase had a major influence on the selectivity. The THF-water combination gave much higher selectivities compared to THF combined with MeOH or ACN. Using the aqueous mobile phase even enabled separation of different isomers. Determination of thermodynamic parameters for the model compounds showed that retention of the different isomers was mainly determined by the orientation of the side chains at both ends of the chain. An additional repeating unit in the middle of the polymer backbone gave a similar contribution to retention, irrespective of the orientation of its side chain. Three model isomers were separated by preparative RP-HPLC and identified by proton nuclear magnetic resonance spectroscopy. The combination of subsequent preparative size-exclusion chromatography, RP-HPLC and matrix-assisted laser desorption ionization time-of-flight mass spectrometry enabled the identification of the two major oligomeric series in the sample as the regioregular product with one bromine end group and, in smaller amounts, a regioirregular product with two bromine end groups. reserved.