On the affine heat equation for non-convex curves

In this paper, we extend to the non-convex case the affine invariant geometric heat equation studied by Sapiro and Tannenbaum for convex plane curves. We prove that a smooth embedded plane curve will converge to a point when evolving according to this flow. This result extends the analogy between the affine heat equation and the well-known Euclidean geometric heat equation.

     

Synthesis of arylenealkyne conjugated macrocycles containing a long alkylene bridge

The synthesis of the first two arylenealkyne conjugated macrocycles containing a long alkylene bridge via Glaser coupling of template-directed tetraacetylenes was reported. Tetraacetylene intermediates with complex structures were constructed rapidly via quadruple Hagihara coupling of monoprotected bisacetylenes to appropriate tetraiodides and subsequent desilylation. The characterization of such compounds was carried out by NMR, GPC and UV-Vis spectra. Unfortunately, the two compounds were not liquid crystals and had no biaxial nematic mesophase character as expected. __________ Translated from Chemical Journal of Chinese Universities, 2007, 28(1): 65–70 [译自: 高等学校化学学报]     

Infrared analysis of CO ice particles in the aerosol phase

Fourier transform infrared extinction spectra of a variety of CO ice aerosols, generated at low temperatures in a liquid helium cooled collisional-cooling cell, have been analyzed. Different operation modes of the cooling system were used for the generation of spherical and nonspherical CO nanoparticles at temperatures between 5 and 35 K and with diameters between 10 and 1000 nm. In contrast to the predominantly amorphous CO films described in the literature the presented CO particles are (poly)crystalline. A Mie inversion iterative scheme is presented and used to infer the optical constants of CO ice for the cases compact particles have been produced. The spectra of nonspherical CO aerosol particles are interpreted by modeling the extinction using the discrete dipole approximation procedure combined with the retrieved optical constants. A global positive matrix factorization scheme allows us to infer the dominant shapes in the observed particle distribution and can be used as a guide for further experiments. Near 25 K a pronounced shape evolution of smaller particles from spherical toward longish structures was observed at low buffer-gas pressure over 400 s.     

Synthesis and Dynamics of Nanosized Phenylene–Ethynylene–Butadiynylene Rotaxanes and the Role of Shape Persistence

Phenylacetylene‐based [2]rotaxanes were synthesized by a covalent‐template approach by aminolysis of the corresponding prerotaxanes. The wheel and the bulky stoppers are made of phenylene–ethynylene–butadiynylene macrocycles of the same size. The stoppers are large enough to enable the synthesis and purification of the rotaxane. However, the wheel unthreads from the axle at elevated temperatures. The deslipping kinetics and the activation parameters were determined. We described theoretically the unthreading by state‐of‐the‐art DFT‐based molecular‐mechanics models and a string method for the simulation of rare events. This approach enabled us to characterize in detail the unthreading mechanism, which involves the folding of the stopper during its passage through the wheel opening, a process that defies intuitive geometrical considerations. The conformational and energetic features of the transition allowed us to infer the molecular residues controlling the disassembly timescale.     

Synthesis and adsorption of shape-persistent macrocycles containing polycyclic aromatic hydrocarbons in the rigid framework

Shape-persistent macrocycles with interiors in the nanometer regime were prepared by the oxidative cyclization of the appropriate bisacetylene precursors under high-dilution conditions. These compounds contain polycyclic aromatic hydrocarbons in the ring backbone and are decorated with extra annular oligoalkyl or silyl side groups. Interestingly, after depositing them on different surfaces and investigating the self-assembled structures by means of scanning tunneling microscopy (STM) and atomic force microscopy (AFM), various nanostructures were observed. STM showed that these macrocycles are organized in two-dimensional (2D) layers, whereas AFM showed, in addition, the formation of 2D crystallites and one-dimensional fibrils. These results reveal the importance of the extra annular substitution of the macrocycles in creating patterned surfaces and nanoscale objects.