The Calculus of Moving Surfaces and Laplace Eigenvalues on an Ellipse with Low Eccentricity

Our goal is to demonstrate the utility of the calculus of moving surfaces (CMS) in boundary variation problems. We discuss the relative advantages of the CMS compared to the alternative approach of interior variations. We illustrate the technique by calculating the two leading terms of a power series for the Laplace eigenvalues on an ellipse with semi-axes 1 + a and 1 + b, where a and b are small. We compare the CMS estimates with those obtained by the conventional finite element method with Richardson extrapolation. The comparison confirms the cubic rate of convergence for the CMS estimates.     

Mean curvature flow with free boundary – Type 2 singularities

In this paper we give sufficient conditions that guarantee the mean curvature flow with free boundary on a pinched cylinder develops a Type 2 curvature singularity. We additionally prove that Type 0 singularities may only occur at infinity.     

Exploring Potential Energy Surfaces for Aggregation‐Induced Emission—From Solution to Crystal

Aggregation‐induced emission (AIE) is a phenomenon where non‐luminescent compounds in solution become strongly luminescent in aggregate and solid phase. It provides a fertile ground for luminescent applications that has rapidly developed in the last 15 years. In this review, we focus on the contributions of theory and computations to understanding the molecular mechanism behind it. Starting from initial models, such as restriction of intramolecular rotations (RIR), and the calculation of non‐radiative rates with Fermi's golden rule (FGR), we center on studies of the global excited‐state potential energy surfaces that have provided the basis for the restricted access to a conical intersection (RACI) model. In this model, which has been shown to apply for a diverse group of AIEgens, the lack of fluorescence in solution comes from radiationless decay at a CI in solution that is hindered in the aggregate state. We also highlight how intermolecular interactions modulate the photophysics in the aggregate phase, in terms of fluorescence quantum yield and emission color.     

Generalization of the Kelvin equation for arbitrarily curved surfaces

Capillary condensation, which takes place in confined geometries, is the first-order vapor-to-liquid phase transition and is explained by the Kelvin equation, but the equation's applicability for arbitrarily curved surface has been long debated and is severe problem. Recently, we have proposed generic dynamic equations for moving surfaces. Application of the equations to the vapor/fluid interfaces in chemical equilibrium conditions nearly trivially solves the generalization problem for the Kelvin equation. The equations are universally true for any surfaces: atomic, molecular, micro or macro scale, real or virtual, Riemannian or pseudo-Riemannian, active or passive.     

Versatile functional poly(3‐hexylthiophene) for hybrid particles synthesis by the grafting onto technique: Core@shell ZnO nanorods

We demonstrate an efficient strategy to anchor poly(3‐hexylthiophene) (P3HT) onto zinc oxide (ZnO) surfaces. Synthesis of a novel triethoxysilane‐terminated regioregular P3HT is herein reported and supported by thorough characterization. Three triethoxysilane‐terminated P3HTs of different molar masses were prepared via a hydrosilylation reaction from allyl‐terminated P3HT. MALDI‐TOF and ¹H NMR were performed to characterize the polymer and show that around 80% of the chains are end‐functionalized. These polymers were then grafted onto the ZnO nanorods to create a macromolecular self‐assembled monolayer. This versatile technique could be subsequently applied to different metal oxide surfaces, such as silicon, titanium, or indium‐tin oxide, and represents a new one‐pot strategy based on triethoxysilane coupling reaction. Importantly, the influence of the molar mass on the grafting density and the polymer shell thickness was studied via thermo gravimetric analysis and transmission electron microscopy. The optical properties of the hybrid materials were determined by UV–visible absorption and photoluminescence to show a quenching effect of P3HT fluorescence by ZnO when grafted. This electronic transfer associated with an improved miscibility of the ZnO@P3HT, makes these hybrid materials suitable candidates for photovoltaic applications. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2014 , 52, 30–38     

Effect of permodified β‐cyclodextrin on the photophysical properties of poly[2,7‐(9,9‐dioctylfluorene)‐alt‐(5,5′‐bithiophene)] main chain polyrotaxanes

The photophysical properties of two polyrotaxanes ( PFBTh?PSβCD and PFBTh?PMeβCD ) composed of fluorene and bithiophene encapsulated into permodified β‐cyclodextrin cavities have been investigated and compared with those of the reference PFBTh . Rotaxane formation results in improvements of the thermal stability, solubility in common organic solvents, as well as better film forming ability combined with a high transparency. As expected PFBTh and its encapsulated forms absorb at wavelengths beyond 510 nm, and time‐resolved photoluminescence (PL) in solution shows a well‐define vibronic structures with a predominance of the 0‐0 transitions and an energy difference of 0.16 eV. The fluorescence lifetimes follow a monoexponential decay with a value τ = 630 ± 30 ps. Atomic force microscopy, AFM, indicated a tendency of polyrotaxanes to organize into fibers. The advancing contact angles indicated higher surface hydrophobicity and lower surface free‐energy values for polyrotaxanes compared with their unthreaded analogues. The device based on PFBTh?PSβCD: PCBM in a 1/1 w/w ratio under simulated AM 1.5G illumination at 100 mW cm^?2 exhibited improved photovoltaic parameters of cells, resulted in high V_oc (0.68 V), J_sc (1.65 mA cm^?2), FF (31.6%), and PCE (0.35) values, compared with PFBTh or PFBTh?PMeβCD , respectively. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2014 , 52, 460–471     

Developments in antimicrobial polymers

Effective antimicrobial polymers have been attracting more interests because of the low propensity to cause drug-resistant microorganisms. The recent progresses in antimicrobial polymers are updated according to the action approaches, that is, antimicrobial polymers with free mobility or fixed on surfaces, respectively. Free antimicrobial polymers kill pathogens majorly via electrostatic interaction followed by disruption of the cell membranes; strong antimicrobial activity of primary/secondary amines, new chemical units, and peptides without facial amphiphilicity are highlighted; and the dependences on amphiphilicity, topology, and self-assembly profiles are summarized. Antimicrobial polymers fixed on surfaces kill pathogens via interaction with the cell membranes of pathogens via electrostatic or hydrophobic interaction; approaches to antimicrobial surfaces based on covalently grafting, anchoring, and bulk-mixing of polymers are summarized; and new designs of sustainable antimicrobial surfaces and hydrogels are highlighted. Deep biology understanding and development strategies of materials are suggested for the future. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2017 , 55, 632–639     

Crystallographic and computational study of a network composed of [ZnCl4]2− anions and triply protonated 4′‐functionalized terpyridine cations

We report herein the synthesis, crystallographic analysis and a study of the noncovalent interactions observed in the new 4′‐substituted terpyridine‐based derivative bis[4′‐(isoquinolin‐2‐ium‐4‐yl)‐2,2′:6′,2′′‐terpyridine‐1,1′′‐diium] tris[tetrachloridozincate(II)] monohydrate, (C₂₄H₁₉N₄)₂[ZnCl₄]₃·H₂O or (ITPH₃)₂[ZnCl₄]₃·H₂O, where (ITPH₃)³⁺ is the triply protonated cation derived from 4′‐(isoquinolin‐4‐yl)‐2,2′:6′,2′′‐terpyridine (ITP) [Granifo et al. (2016). Acta Cryst. C 72 , 932–938]. The (ITPH₃)³⁺ cation presents a number of interesting similarities and differences compared with its neutral ITP relative, mainly in the role fulfilled in the packing arrangement by the profuse set of D —H…A [D (donor) = C, N or O; A (acceptor) = O or Cl], π–π and anion…π noncovalent interactions present. We discuss these interactions in two different complementary ways, viz. using a point‐to‐point approach in the light of Bader's theory of Atoms In Molecules (AIM), analyzing the individual significance of each interaction, and in a more `global' analysis, making use of the Hirshfeld surfaces and the associated enrichment ratio (ER) approach, evaluating the surprisingly large co‐operative effect of the superabundant weaker contacts.     

Action of the Cremona group on a noncommutative ring

The Cremona group acts on the field of two independent commutative variables over complex numbers. We provide a noncommutative algebra that is an analog of a noncommutative field of two independent variables and prove that the Cremona group embeds in a group of outer automorphisms of this algebra. We give two proofs of it, the first proof is technical, the second one is conceptual and proceeds through a construction of a birational invariant of an algebraic variety from its bounded derived category of coherent sheaves.