Global Dynamics of Some Periodically Forced,Monotone Difference Equations ∗

We study a class of periodically forced, monotone difference equations motivated by applications from population dynamics. We give conditions under which there exists a globally attracting cycle and conditions under which the attracting cycle is attenuant     

Dichlorocarbene Addition to

In contrast to the terminal phosphinidene complex PhPW(CO)(5) (2), which adds to [5]metacyclophane (1) in a 1,4-fashion, dichlorocarbene preferentially adds in a 1,2-fashion to the formal "anti-Bredt" type double bond of the aromatic ring of 1 to afford the norcaradiene 11b, which immediately rearranges to the bridged cycloheptatriene 12b and further by a [1,5] sigmatropic chlorine migration to the isomeric 13b as the first observable product. More slowly, the latter isomerizes via a dissociative mechanism to give 15b. A computational study supports the notion that the [1,5] chlorine migration in the rearrangement 12b --> 13b, for which an activation barrier of 70.2 kJ mol(-)(1) was calculated, is essentially concerted with minor charge separation. In contrast, the analogous [1,5] chlorine migration in the flat model compound 7,7-dichlorocycloheptatriene (12a) displays features of a dissociative pathway.     

Pyridalthiadiazole-based narrow band gap chromophores

π-Conjugated materials containing pyridal[2,1,3]thiadiazole (PT) units have recently achieved record power conversion efficiencies of 6.7% in solution-processed, molecular bulk-heterojunction (BHJ) organic photovoltaics. Recognizing the importance of this new class of molecular systems and with the aim of establishing a more concrete path forward to predict improvements in desirable solid-state properties, we set out to systematically alter the molecular framework and evaluate structure-property relationships. Thus, the synthesis and properties of 13 structurally related D(1)-PT-D(2)-PT-D(1) compounds, where D represents a relatively electron-rich aromatic segment compared to PT, are provided. Physical properties were examined using a combination of absorption spectroscopy, cyclic voltammetry, thermal gravimetric analysis, differential scanning calorimetry, and solubility analysis. Changes to end-capping D(1) units allowed for fine control over electronic energy levels both in solution and in the bulk. Substitution of different alkyl chains on D(2) gives rise to controllable melting and crystallization temperatures and tailored solubility. Alterations to the core donor D(2) lead to readily identifiable changes in all properties studied. Finally, the regiochemistry of the pyridal N-atom in the PT heterocycle was investigated. The tailoring of structures via subtle structural modifications in the presented molecular series highlights the simplicity of accessing this chromophore architecture. Examination of the resulting materials properties relevant for device fabrication sets forth which can be readily predicted by consideration of molecular structure and which lack a systematic understanding. Guidelines can be proposed for the design of new molecular frameworks with the possibility of outperforming the current state of the art OPV performance.