Extended Wiener-Khinchin theorem for quantum spectral analysis

The classical Wiener-Khinchin theorem (WKT), which can extract spectral information by classical interferometers through Fourier transform, is a fundamental theorem used in many disciplines. However, there is still need for a quantum version of WKT, which could connect correlated biphoton spectral information by quantum interferometers. Here, we extend the classical WKT to its quantum counterpart, i.e., extended WKT (e-WKT), which is based on two-photon quantum interferometry. According to the e-WKT, the difference-frequency distribution of the biphoton wavefunctions can be extracted by applying a Fourier transform on the time-domain Hong-Ou-Mandel interference (HOMI) patterns, while the sum-frequency distribution can be extracted by applying a Fourier transform on the time-domain NOON state interference (NOONI) patterns. We also experimentally verified the WKT and e-WKT in a Mach-Zehnder interference (MZI), a HOMI and a NOONI. This theorem can be directly applied to quantum spectroscopy, where the spectral correlation information of biphotons can be obtained from time-domain quantum interferences by Fourier transform. This may open a new pathway for the study of light-matter interaction at the single photon level.Comment: 13 pages, 5 figure

Oxygen Vacancies Enriched Hollow Bi₂MoO₆ Microspheres for Efficient Photocatalytic Oxidation of Hydrocarbons

Photocatalytic aerobic oxidation of hydrocarbons to ketones is an attractive route for synthesizing high-value-added chemicals. However, the main challenge of photocatalytic oxidation reactions is their low activity. Herein, hollow Bi2MoO6 microspheres were synthesized by a facile two-step synthesis route combining ethylene glycol solvothermal with postannealing treatment. In the photocatalytic aerobic oxidation of ethylbenzene to the corresponding ketones under visible light irradiation using O2 as an oxidant, the hollow Bi2MoO6 microspheres exhibit a record acetophenone production rate of 1.1 mmol g–1 h–1 with 90% selectivity. The photoactivity of oxygen vacancy-enriched Bi2MoO6 is 61 times higher than that of uncalcined Bi2MoO6, which can be attributed to the effective separation of photogenerated carriers and the abundant catalytic active sites (i.e., oxygen vacancies) on hollow Bi2MoO6 microspheres. This work provides more insights into understanding how to construct highly efficient and active visible-light-responsive photocatalysts for the aerobic oxidation of organic compounds

High Melt Strength and High Toughness PLLA/PBS Blends by Copolymerization and in Situ Reactive Compatibilization

Poly­(l-lactide)/poly­(butylene succinate) (PLLA/PBS) blends were prepared by melt mixing with a PLLA-based compatibilizer (PBS-PLLA) and a chain extender triarm block copolymer (PLLA-<i>block</i>-poly­(glycidyl methacrylates))₃ (PLLA-<i>b</i>-PGMA)₃. The tensile testing showed significant improvement in mechanical properties and remarkably maintained high strength. Rheological investigation of PLLA/PBS/PBS-PLLA/(PLLA-<i>b</i>-PGMA)₃ indicated that the viscosity and storage modulus was improved greatly compared with neat PLLA. Elongational viscosity measurements exhibited strong strain-hardening behavior. The increase of the torque indicated the occurrence of chain branching and chain extension reaction. The imperfect crystallization of PLLA/PBS/PBS-PLLA/(PLLA-<i>b</i>-PGMA)₃ blends was demonstrated by the lowered melt point of PLLA. SEM showed that the PBS-PLLA and (PLLA-<i>b</i>-PGMA)₃ significantly improved the compatibility of the PLLA/PBS blends. It was indicated that the synergistic effects of PBS-PLLA and (PLLA-<i>b</i>-PGMA)₃ in PLLA/PBS blends played a key role in properties enhancement. With copolymerization and in situ reactive compatibilization, PLLA/PBS/PBS-PLLA/(PLLA-<i>b</i>-PGMA)₃ blends not only improved the toughness but also improved the melt strength

Synthesis, Electronic and Photophysical Characterization of π‑Conjugated <i>meso</i>-Ferrocenyl-porphyrin Fluorescent Redox Switches

A series of <i>meso</i>-ferrocenyl-porphyrin dyads linked by four different π-conjugated bridging units (directly bound, vinyl, ethynyl, and phenyl) have been synthesized to investigate the influence of the conjugated linker on both the electronic and photochemical properties of the porphyrin chromophore. The basic structure consists of 5-(Fc)-15-(4-methylbenzoate)-10,20-diphenylporphyrin zinc­(II), where Fc = ferrocene, vinylferrocene, ethynylferrocene, or phenylferrocene. Upon introduction of the various electron-donating ferrocenyl moieties at the <i>meso</i>-position of the porphyrin ring, Soret and Q-band electronic transitions of the resultant dyads are red-shifted compared with those of the nonferrocenyl reference porphyrin system 15-(4-methylbenzoate)-10,20-diphenylporphyrin zinc­(II). The electronic properties of these systems have been investigated by electrochemical (cyclic voltammetry) and computational (DFT/TDDFT) methods, while UV/vis absorption and fluorescence emission spectroscopic analysis is also presented. Collectively, electronic and photophysical analysis indicate a strong electronic communication between the porphyrin macrocycle and directly bound ferrocenyl, vinylferrocenyl, and ethynylferrocenyl dyads. The presence of a phenyl spacer acts to inhibit such electronic communication due to the orthogonal geometry of the bridging phenyl ring at the <i>meso</i>-position of the porphyrin macrocycle. In addition to electronic factors, and in particular for the directly bound 5-(ferrocenyl)-15-(4-methyl­benzoate)-10,20-dipheny­lporphyrin zinc­(II) dyad, computational analysis suggests that a significant ruffling of the porphyrin macrocyle from planarity is required to facilitate the bulky ferrocene group directly at the <i>meso</i>-position. Of particular note for each of the <i>meso</i>-ferrocenyl-porphyrin dyads is how fluorescence emission derived from the porphyrin S₁ (π–π*) excited state is quantitatively quenched due to photoinduced charge-transfer from the ferrocene unit onto the excited state porphyrin. Spectroelectrochemical studies demonstrate redox off/on switching of the porphyrin fluorescence emission via ferricenium/ferrocene redox cycling. Interestingly, it was found that the S₀ ← S₁ fluorescence emission is also switched-on following titration with the metal ions Ce­(IV), Cu­(II), and Fe­(III) in acetonitrile

Development of Self-Healing d‑Gluconic Acetal-Based Supramolecular Ionogels for Potential Use as Smart Quasisolid Electrochemical Materials

Formation of supramolecular ionic liquid (IL) gels (ionogels) induced by low-molecular-mass gelators (LMMGs) is an efficient strategy to confine ILs, and the negligible influence of LMMGs on the electrochemical properties of ILs makes ionogels ideal quasisolid electrochemical materials. Furthermore, the stimuli-responsive and self-healing characters of the supramolecular gel can be utilized for the potential development of smart electrochemical materials. However, the poor mechanical properties of supramolecular ionogels reported so far limit their practical applications. Herein, we investigated a series of efficient d-gluconic acetal-based gelators (Gn, PG16, and B8) that can harden a wide variety of ILs at low concentrations. It was shown that both alkyl chain length and the number of hydrogen bonding sites of a certain gelator, as well as the nature of the IL anion, significantly influenced the gelation abilities. The resulting ionogels were thermally reversible, and most of them were stable at room temperature. Interestingly, a PG16-based supramolecular ionogel showed rapid self-healing properties upon mechanical damage. Furthermore, the PG16-based ionogel demonstrated unprecedented performances including the favorable ionic conductivity, excellent mechanical strength, and enhanced viscoelasticity, which make it a great self-healing electrochemical material. The ionogel formation mechanism was proposed based on the analysis of Fourier transform infrared, ¹HNMR, and X-ray diffraction, indicating that a combination of hydrogen bonding, π–π stacking, and interactions between alkyl chains was responsible for the self-assembly of gelators in ILs. Overall, our present studies on exploring the structure–property relationship of gelators for the formation of practically useful supramolecular ionogels shed light for future development of more functionalized ionogels

Nucleotide and protein diversity among cattle breeds.

<p>Each number in a diamond-shaped box represents the number of differences between two breeds indicated by the flanking vertical bars. Differences in nucleotides (A), coding bases (B), and non-synonymous bases (C) are shown.</p

Haplotypes frequency and association analysis.

<p>Significant p-values are in italic bold. Common Haplotypes are shown, if frequency more than 2.5%.</p>1<p>Based on 10000 permutations.</p>2<p>Corrected by Bonferroni.</p>3<p>Based on comparison of frequency distribution of all haplotypes for the combination of SNPs.</p>4<p>Haplotypes in italics are the significant ones in the study.</p

Scheme of preparing CMS microgels.

<p>Scheme of preparing CMS microgels.</p

Alternative splicing events detected in genes and significant differential alternative splicing between Holstein and Cholistani.

1<p>Alternative splicing events were classified as in Wang et al. 2008 <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0030244#pone.0030244-Wang1" target="_blank">[27]</a>.</p

(a) Numbers of starch polymer microgel particles in water vs. their size (volume weighted mean diameter in µm), for various degrees of substitution (DS); (b) Optical microscopic image of microgels with DS = 0.31 dispersed in water.

<p>Scale bar shown in graph is 50 µm.</p