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We determined experimentally the complex transient optical dielectric function of a well-characterized polyelectrolyte/gold-nanoparticle composite system over a broad spectral range upon short pulse laser excitation by simultaneously measuring the time-dependent reflectance and transmittance of white light pulses with femtosecond pump-probe spectroscopy. We extracted directly the ultrafast changes in the real and imaginary parts of the effective dielectric function, epsilon(eff)(r) (omega,t)and epsilon(eff)(i) (omega,t), from the experiment. This complete experimental set of information on the time-dependent complex dielectric function challenges theories modeling the transient dielectric function of gold particles and the effective medium.
Derivatization of fullerene (C-60) with branched aliphatic chains softens C-60-based materials and enables the formation of thermotropic liquid crystals and room temperature nonvolatile liquids. This work demonstrates that by carefully tuning parameters such as type, number and substituent position of the branched chains, liquid crystalline C-60 materials with mesophase temperatures suited for photovoltaic cell fabrication and room temperature nonvolatile liquid fullerenes with tunable viscosity can be obtained. In particular, compound 1, with branched chains, exhibits a smectic liquid crystalline phase extending from 84 degrees C to room temperature. Analysis of bulk heterojunction (BHJ) organic solar cells with a ca. 100 nm active layer of compound 1 and poly(3-hexylthiophene) (P3HT) as an electron acceptor and an electron donor, respectively, reveals an improved performance (power conversion efficiency, PCE: 1.6 + 0.1%) in comparison with another compound, 10 (PCE: 0.5 + 0.1%). The latter, in contrast to 1, carries linear aliphatic chains and thus forms a highly ordered solid lamellar phase at room temperature. The solar cell performance of 1 blended with P3HT approaches that of PCBM/P3HT for the same active layer thickness. This indicates that C-60 derivatives bearing branched tails are a promising class of electron acceptors in soft (flexible) photovoltaic devices.
We show a Lefschetz fixed point formula for holomorphic functions in a bounded domain D with smooth boundary in the complex plane. To introduce the Lefschetz number for a holomorphic map of D, we make use of the Bergman kernel of this domain. The Lefschetz number is proved to be the sum of the usual contributions of fixed points of the map in D and contributions of boundary fixed points, these latter being different for attracting and repulsing fixed points