Experimental Investigations on the Thermal Diffusion Characteristics and Photoluminescence in Multiphase Micro Fluids Containing ZnO Micro Tubes and Fluorescein Dye

Optics and Spectroscopy - Scattering of light by disordered structures is normally detrimental to their applicability in many optoelectronic devices. However, some micro and nanostructures are...     

Invariant discrete flows

In this paper, we investigate the evolution of joint invariants under invariant geometric flows using the theory of equivariant moving frames and the induced invariant discrete variational complex. For certain arc length preserving planar curve flows invariant under the special Euclidean group , the special linear group , and the semidirect group , we find that the induced evolution of the discrete curvature satisfies the differential‐difference mKdV, KdV, and Burgers' equations, respectively. These three equations are completely integrable, and we show that a recursion operator can be constructed by precomposing the characteristic operator of the curvature by a certain invariant difference operator. Finally, we derive the constraint for the integrability of the discrete curvature evolution to lift to the evolution of the discrete curve itself.     

meso- and β-Pyrrole-Linked Chlorin-Bacteriochlorin Dyads for Promoting Far-Red FRET and Singlet Oxygen Production

A series of chlorin-bacteriochlorin dyads (derived from naturally occurring chlorophyll-a and bacteriochlorophyll-a), covalently connected either through the meso-aryl or β-pyrrole position (position-3) via an ester linkage have been synthesized and characterized as a new class of far-red emitting fluorescence resonance energy transfer (FRET) imaging, and heavy atom-lacking singlet oxygen-producing agents. From systematic absorption, fluorescence, electrochemical, and computational studies, the role of chlorin as an energy donor and bacteriochlorin as an energy acceptor in these wide-band-capturing dyads was established. Efficiency of FRET evaluated from spectral overlap was found to be 95 and 98 % for the meso-linked and β-pyrrole-linked dyads, respectively. Furthermore, evidence for the occurrence of FRET from singlet-excited chlorin to bacteriochlorin was secured from studies involving femtosecond transient absorption studies in toluene. The measured FRET rate constants, k_FRET, were in the order of 10¹¹ s⁻¹, suggesting the occurrence of ultrafast energy transfer in these dyads. Nanosecond transient absorption studies confirmed relaxation of the energy transfer product, ¹BChl*, to its triplet state, ³Bchl*. The ³Bchl* thus generated was capable of producing singlet oxygen with quantum yields comparable to their monomeric entities. The occurrence of efficient FRET emitting in the far-red region and the ability to produce singlet oxygen make the present series of dyads useful for photonic, imaging and therapy applications.     

Switching from linear to cyclic δ‐Polyvalerolactone synthesized via zeolitic imidazolate framework as a catalyst: A promising approach

A series of spray dried zeolitic imidazolate frameworks (ZIFs = ZIF‐8, ZIF‐67, and Zn/Co‐ZIF) are used as a catalyst for the bulk ring‐opening polymerization of δ‐valerolactone without any co‐catalyst to generate polyvalerolactone. Interestingly, using the same catalyst under the same reaction conditions could manipulate the structure of the product polymer, and thus its physical properties. Thus, using a dried substrate leads to the formation of the cyclic polymer while a linear polymer was formed on using the commercially available substrate. An activated monomer mechanism has been suggested where the propagating zinc alkoxide undergoes an intramolecular transesterification to release cyclic or linear polyvalerolactone. The ROP of δ‐VL without drying shows that the polymeric zwitterions have little tendency to cyclize in the presence of moisture. At 140 °C, ZIF‐8 shows a superior catalytic activity resulting in the production of cyclic polyvalerolactone having a high molecular weight as compared to ZIF‐67 or Zn/Co‐ZIF due to the presence of highly active sites. The catalyst could be recycled and reused without any significant loss of catalytic activity.     

Quadrupolar Ultrafast Charge Transfer in Diaminoazobenzene-Bridged Perylenediimide Triads

Strong push-pull interactions between electron donor, diaminoazobenzene (azo), and an electron acceptor, perylenediimide (PDI), entities in the newly synthesized A−D−A type triads (A=electron acceptor and D=electron donor) and the corresponding A−D dyads are shown to reveal wide-band absorption covering the entire visible spectrum. Electrochemical studies revealed the facile reduction of PDI and relatively easier oxidation of diaminoazobenzene in the dyads and triads. Charge transfer reversal using fluorescence-spectroelectrochemistry wherein the PDI fluorescence recovery upon one-electron oxidation, deterring the charge-transfer interactions, was possible to accomplish. The charge transfer state density difference and the frontier orbitals from the DFT calculations established the electron-deficient PDI to be an electron acceptor and diaminoazobenzene to be an electron donor resulting in energetically closely positioned PDI ^δ− -Azo ^δ+ -PDI ^δ− quadrupolar charge-transfer states in the case of triads and Azo ^δ+ -PDI ^δ− dipolar charge-transfer states in the case of dyads. Subsequent femtosecond transient absorption spectral studies unequivocally proved the occurrence of excited-state charge transfer in these dyads and triads in benzonitrile wherein the calculated forward charge transfer rate constants, k_f, were limited to instrument response factor, meaning >10¹² s⁻¹ revealing the occurrence of ultrafast photo-events. The charge recombination rate constant, k_r, was found to depend on the type of donor-acceptor conjugates, that is, it was possible to establish faster k_r in the case of triads (∼10¹¹ s⁻¹) compared to dyads (∼10¹⁰ s⁻¹). Modulating both ground and excited-state properties of PDI with the help of strong quadrupolar and dipolar charge transfer and witnessing ultrafast charge transfer events in the studied triads and dyads is borne out from the present study.     

Dual Functioning Thieno‐Pyrrole Fused BODIPY Dyes for NIR Optical Imaging and Photodynamic Therapy: Singlet Oxygen Generation without Heavy Halogen Atom Assistance

We discovered a rare phenomenon wherein a thieno‐pyrrole fused BODIPY dye (SBDPiR690) generates singlet oxygen without heavy halogen atom substituents. SBDPiR690 generates both singlet oxygen and fluorescence. To our knowledge, this is the first example of such a finding. To establish a structure–photophysical property relationship, we prepared SBDPiR analogs with electron‐withdrawing groups at the para‐position of the phenyl groups. The electron‐withdrawing groups increased the HOMO–LUMO energy gap and singlet oxygen generation. Among the analogs, SBDPiR688, a CF₃ analog, had an excellent dual functionality of brightness (82290 m ^?1 cm^?1) and phototoxic power (99170 m ^?1 cm^?1) comparable to those of Pc 4, due to a high extinction coefficient (211 000 m ^?1 cm^?1) and balanced decay (Φ_flu=0.39 and Φ_Δ=0.47). The dual functionality of the lead compound SBDPiR690 was successfully applied to preclinical optical imaging and for PDT to effectively control a subcutaneous tumor.     

Geometry‐Related Children's Literature Improves the Geometry Achievement and Attitudes of Second‐Grade Students

Use of mathematics‐related literature can engage students' interest and increase their understanding of mathematical concepts. A quasi‐experimental study of two second‐grade classrooms assessed whether daily inclusion of geometry‐related literature in the classroom improved attitudes toward geometry and achievement in geometry. Consistent with the hypothesis, only the students in the classroom with a strong emphasis on geometry‐related children's literature showed a significant improvement in their attitudes about geometry over time. While both classes improved their geometry performance over the 4 weeks of the study, the class with a strong emphasis on geometry‐related literature improved significantly more (51.2%) than the control class (33.47%). Children's literature can provide a useful and interesting context in which students can develop their understanding of geometry.     

Semilattice transversals of regular bands I

Every regular band can be isomorphically embedded into a regular band which has a semilattice transversal. The latter constitute the variety of regular split bands, whose subvariety lattice is isomorphic to the lattice of regular band varieties.     

<Emphasis Type="Italic">p</Emphasis>-adic valuation of exponential sums associated to trinomials and some consequences

In this paper, we compute the p-adic valuation of exponential sums associated to trinomials \(F\left( X \right) = a{X^{{d_1}}} + b{X^{{d_2}}} + c{X^{{d_3}}}\) over Fp. As a byproduct of our results, we obtain restrictions for permutation polynomials of type \(a{X^{{d_1}}} + b{X^{{d_2}}} + c{X^{{d_3}}}\) over F_p.