Layer structure estimation of three‐dimensional crystal and two‐dimensional molecular film for fluorinated comb copolymers

Comb copolymers containing both hydrogenated and fluorinated side‐chains were prepared by copolymerization using acrylic or methacrylic monomers in several ratios. The crystal structures of these copolymers and layer structures of their organized molecular films were investigated by wide‐angle X‐ray diffraction (WAXD), small‐angle X‐ray scattering (SAXS), and out‐of plane X‐ray diffraction. Further, to selectively estimate the regularity of shorter fluorocarbon side‐chains, organized molecular films of copolymers were investigated by polarized near‐edge X‐ray adsorption fine structure (NEXAFS) spectroscopy. From the results of these measurements, it was inferred that these copolymers formed highly ordered layer structures, and a long spacing was predominantly determined by the arrangement of hydrogenated side‐chains, except in copolymers having extremely high fluorocarbon contents. In the case of the organized molecular films, the fluorinated side‐chains of methacrylate copolymers cannot form a highly ordered arrangement, whereas those of acrylate copolymers were oriented on monolayers. However, in both cases, the hydrogenated side‐chains predominantly formed layer structures in the organized films, and the fluorinated side‐chains did not contribute to the formation of the layer structures. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 534–546, 2008     

Magnetic circular dichroism study of directly fused porphyrins.

The magnetic circular dichroism (MCD) spectra of doubly and triply linked fused bisporphyrins (2MD and 2MT, M = Ni, Zn, Cu, Pd, and H2) and triply linked higher oligomers (3ZnT and 4ZnT) have been measured, and their Q-bands assigned based on the results of INDO/s calculations. In contrast to the Faraday A term observed for the Q(0,0) band of Ni(II) tetraphenylporphyrin, a single positive Faraday B term was observed for the lowest energy transition of the fused systems. The calculations indicated that the molecular orbitals (MOs) of the directly fused porphyrins consist of linear combinations of the constituent monomeric MOs, and that the effect of lowering the symmetry is always larger on the lowest unoccupied molecular orbital (LUMO) than on the highest occupied molecular orbital (HOMO). On the basis of Michl's perimeter model, these features can be correlated with the observed positive MCD signs in the near infrared region. A weak absorption band at 600-700 nm for the fused dimers can be assigned to a short-axis polarized Q transition.     

Triangulations on Closed Surfaces Covered by Vertices of Given Degree

A triangulation of a closed surface is said to be d-covered if all of its edges are covered by vertices of degree d. We shall give constructive characterizations of 5- and 6-covered triangulations. Received: July 17, 1998?Final version received: January 12, 2000     

Large Porphyrin Squares from the Self‐Assembly of meso‐Triazole‐Appended L‐Shaped meso–meso‐Linked ZnII–Triporphyrins: Synthesis and Efficient Energy Transfer

meso‐Triazolyl‐appended Zn^II–porphyrins were readily prepared by Cu^I‐catalyzed 1,3‐dipolar cycloaddition of benzyl azide to meso‐ethynylated Zn^II–porphyrin (click chemistry). In noncoordinating CHCl₃ solvent, spontaneous assembly occurred to form tetrameric array ( 3 )₂ from meso–meso‐linked diporphyrins 3 , and dodecameric porphyrin squares ( 4 )₄ and ( 5 )₄ from the L ‐shaped meso–meso‐linked triporphyrins 4 and 5 . The structures of these assemblies were examined by ¹H NMR spectra, absorption spectra, and their gel permeation chromatography (GPC) retention time. Furthermore, the structures of the dodecameric porphyrin squares ( 4 )₄ and ( 5 )₄ were probed by small‐ and wide‐angle X‐ray scattering (SAXS/WAXS) measurements in solution using a synchrotron source. Excitation‐energy migration processes in these assemblies were also investigated in detail by using both steady‐state and time‐resolved spectroscopic methods, which revealed efficient excited‐energy transfer (EET) between the meso–meso‐linked Zn^II–porphyrin units that occurred with time constants of 1.5 ps^?1 for ( 3 )₂ and 8.8 ps^?1 for ( 5 )₄.     

Quadrangulations on 3-Colored Point Sets with Steiner Points and Their Winding Numbers

Let P be a point set on the plane, and consider whether P is quadrangulatable, that is, whether there exists a 2-connected plane graph G with each edge a straight segment such that V(G) = P, that the outer cycle of G coincides with the convex hull Conv(P) of P, and that each finite face of G is quadrilateral. It is easy to see that it is possible if and only if an even number of points of P lie on Conv(P). Hence we give a k-coloring to P, and consider the same problem, avoiding edges joining two vertices of P with the same color. In this case, we always assume that the number of points of P lying on Conv(P) is even and that any two consecutive points on Conv(P) have distinct colors. However, for every k ≥ 2, there is a k-colored non-quadrangulatable point set P. So we introduce Steiner points, which can be put in any position of the interior of Conv(P) and each of which may be colored by any of the k colors. When k = 2, Alvarez et al. proved that if a point set P on the plane consists of \({\frac{n}{2}}\) red and \({\frac{n}{2}}\) blue points in general position, then adding Steiner points Q with \({|Q| \leq \lfloor \frac{n-2}{6} \rfloor + \lfloor \frac{n}{4} \rfloor +1}\) , P ∪ Q is quadrangulatable, but there exists a non-quadrangulatable 3-colored point set for which no matter how many Steiner points are added. In this paper, we define the winding number for a 3-colored point set P, and prove that a 3-colored point set P in general position with a finite set Q of Steiner points added is quadrangulatable if and only if the winding number of P is zero. When P ∪ Q is quadrangulatable, we prove \({|Q| \leq \frac{7n+34m-48}{18}}\) , where |P| = n and the number of points of P in Conv(P) is 2m.