Generating Function of the Tilings of an Aztec Rectangle with Holes

We consider a generating function of the domino tilings of an Aztec rectangle with several unit squares removed from the boundary. Our generating function involves two statistics: the rank of the tiling and half number of vertical dominoes as in the Aztec diamond theorem by Elkies, Kuperberg, Larsen and Propp. In addition, our work deduces a combinatorial explanation for an interesting connection between the number of lozenge tilings of a semihexagon and the number of domino tilings of an Aztec rectangle.     

Air‐Stable Spirofluorene‐Containing Ladder‐Type Bis(alkynyl)borane Compounds with Readily Tunable Full Color Emission Properties

A series of air‐stable spiro‐fused ladder‐type boron(III) compounds has been designed, synthesized, and the electrochemistry and photophysical behavior have been characterized. By simply varying the substituents on the pyridine ring and extending the π‐conjugation of the spiro framework, the emission color of these compounds can be easily fine‐tuned spanning the visible spectrum from blue to red. All compounds exhibit a broad and structureless emission band across the entire visible region, assigned as an intramolecular charge‐transfer transition originating from the thiophene of the spiro framework to the pyridine‐borane moieties. In addition, these compounds demonstrate high photoluminescence quantum yields of up to 0.81 in dichloromethane solution and 0.86 in doped thin films. Some of the compounds have also been employed as emissive materials, in which solution‐processed organic light‐emitting devices (OLEDs) with tunable emission colors spanning the visible spectrum from blue, green to red have been realized, demonstrating the potential applications of these boron compounds in OLEDs.     

Phase separation dynamics of a poly(vinyl methyl ether)/polystyrene (PVME/PS) blend studied by ultrafast differential scanning calorimetry

In this work, ultrafast differential scanning calorimetry (UFDSC) is used to study the dynamics of phase separation. Taking poly(vinyl methyl ether)/polystyrene (PVME/PS) blend as the example, we firstly obtained the phase diagram that has lower critical solution temperature (LCST), together with the glass transition temperature (T_g) of the homogeneous blend with different composition. Then, the dynamics of the phase separation of the PVME/PS blend with a mass ratio of 7:3 was studied in the time range from milliseconds to hours, by the virtue of small time and spatial resolution that UFDSC offers. The time dependence of the glass transition temperature (T_g) of PVME‐rich phase, shows a distinct change when the annealing temperature (T_a) changes from below to above 385 K. This corresponds to the transition from the nucleation and growth (NG) mechanism to the spinodal decomposition (SD) mechanism, as was verified by morphological and rheometric investigations. For the SD mechanism, the temperature‐dependent composition evolution in PVME‐rich domain was found to follow the Williams–Landel–Ferry (WLF) laws. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2017 , 55, 1357–1364     

Triphenylamine derivatized phenylacetylene macrocycle with large two-photon absorption cross-section

A phenylacetylene macrocycle (PAM) derivative containing triphenylamine as the framework was synthesized in one-step Sonogashira coupling. The photophysical and electrochemical properties were investigated in details. This hexamer shows significant enhancement in two-photon absorption cross-section relative to reported PAM derivatives.     

Effect of plane-mirror installation errors on pointing errors in periscope-type satellite optical communication terminals

In a satellite optical communication system, the pointing error is an important factor that strongly influences the system performance. For periscope-type satellite optical communication terminals, installation errors of 45° plane mirrors in the coarse point apparatus (CPA) can lead to pointing errors. In this respect, we classify the installation errors of two 45° plane mirrors in the system and derive the corresponding ??transfer?? matrices to describe them. Furthermore, we establish mathematical models of the pointing error caused by installation errors of 45° plane mirrors. These models allow one to calculate and compensate the pointing errors in periscope-type satellite optical communication terminals. The results of our simulations show that the pointing errors vary with the elevation axis angle but do not depend on the azimuth axis angle. Compared to the side-angle error, the slope-angle error brings a larger pointing error. However, the mathematical model we developed allows one to compensate more than 99.9?% of the overall pointing error. The present work provides a theoretical basis for the design of periscope-type satellite optical communication terminals.     

A hidden rule in metal sulfide fullerenes: A case study of Sc2S@C88

To elucidate the structure of a compound is a necessary step for its practical applications. To study the structure and properties of metal sulfide fullerene Sc₂S@C₈₈ detected by mass spectrometry, 11 194 isomers of C₈₈ and 33 isomers of Sc₂S@C₈₈ were systematically examined by density functional theory calculations. The calculations show that the two lowest‐energy isomers are Sc₂S@C₈₈:81 738 (IPR‐35) and Sc₂S@C₈₈:81 735 (IPR‐32), followed by Sc₂S@C₈₈:81 729 (IPR‐26), Sc₂S@C_88:81 712 (IPR‐9), and Sc₂S@C_88:81 733 (IPR‐30). Structural analysis shows that the first two energetically favored isomers are bridged by the third and fifth energetically favored isomers, which can transfer into each other via direct Stone–Wales rotation. The calculations of temperature effect show that the first two favored isomers become dominant forms of Sc₂S@C₈₈ with decreasing temperature and may coexist in the soot. This structural convertibility among favored isomers of Sc₂S@C₈₈ suggest a hidden rule that birds of a feather flock together in metal sulfide fullerenes. This rule may decrease the range of candidate cages for the structural identification of a metal sulfide fullerene. IR spectra are simulated for helping the future experimental identification of Sc₂S@C₈₈.     

Morphology–luminescence correlations in europium-doped ZnO nanomaterials

In order to investigate the correlations of morphologies and optical properties, different morphologies of Eu-doped ZnO were synthesized by different methods. Specifically, the structure of SiO₂/ZnO:Eu nanoflower was synthesized for the first time and has not been reported previously. One percent was chosen as the Eu doping concentration. The relations of the morphology, diameter, and uniformity with the PL intensity were examined. The PL intensity of ZOE samples has a close relationship with the morphology. The PL intensity order of the different morphologies of ZnO:Eu is as follows: nanorod arrays > thin film > nanospheres > nanoparticles > nanoflowers > nanorods. The PL intensity of nanomaterials is larger, if the diameter of the nanomaterials is larger. However, the size of diameter is not the most important reason. It was found that the sample uniformity plays a key role on ZnO:Eu PL intensity. ZnO:Eu with small particle diameters may have strong photoluminescence intensity, if the nanoparticles are uniform.