High-dimensional Kuramoto model limited on smooth curved surfaces

In this Letter, a high-dimensional Kuramoto model limited on smooth curved surfaces is established. Some synchronization phenomena of this new model are displayed by simulations. A necessary and sufficient condition of equilibria is obtained and the linearized system around an equilibrium is derived. As the considered smooth curved surface is an ellipsoid, some dynamical properties including limit behavior and instability are obtained. Based on those results, almost global synchronization is achieved for the high-dimensional Kuramoto model limited on ellipsoids with complete or tree graphs. Moreover, numerical simulations are given to validate the obtained theoretical results.     

Electrochemical Studies of Polymeric Carbons. II. Surface Layer Formation on Glassy Carbon Electrodes in Chloride Solutions as Studied by Radiotracer Techniques

The interaction of chloride ions with glassy carbon electrodes is studied by means of ³⁶Cl as radiotracer. Chloride ions are bonded on the electrode in case of anodization depending on electrode potential and duration of the polarization. Strong interaction is observed at electrode potentials more positive than +1.3 V. A significant part of the chloride ions bonded at the glassy carbon can not be displaced neither by cathodic polarization nor by rinsing with water or non-labelled solutions. It is concluded that chloride ions are chemically bonded at the surface and the surface region of glassy carbon.     

2H‐Tetrakis(3,5‐di‐tert‐butyl)phenylporphyrin on a Cu(110) Surface: Room‐Temperature Self‐Metalation and Surface‐Reconstruction‐Facilitated Self‐Assembly

The adsorption behavior of 2H‐tetrakis(3,5‐di‐tert‐butyl)phenylporphyrin (2HTTBPP) on Cu(110) and Cu(110)–(2×1)O surfaces have been investigated by using variable‐temperature scanning tunneling microscopy (STM) under ultrahigh vacuum conditions. On the bare Cu(110) surface, individual 2HTTBPP molecules are observed. These molecules are immobilized on the surface with a particular orientation with respect to the crystallographic directions of the Cu(110) surface and do not form supramolecular aggregates up to full monolayer coverage. In contrast, a chiral supramolecular structure is formed on the Cu(110)–(2×1)O surface, which is stabilized by van der Waals interactions between the tert‐butyl groups of neighboring molecules. These findings are explained by weakened molecule–substrate interactions on the Cu(110)–(2×1)O surface relative to the bare Cu(110) surface. By comparison with the corresponding results of Cu–tetrakis(3,5‐di‐tert‐butyl)phenylporphyrin (CuTTBPP) on Cu(110) and Cu(110)–(2×1)O surfaces, we find that the 2HTTBPP molecules can self‐metalate on both surfaces with copper atoms from the substrate at room temperature (RT). The possible origins of the self‐metalation reaction at RT are discussed. Finally, peculiar irreversible temperature‐dependent switching of the intramolecular conformations of the investigated molecules on the Cu(110) surface was observed and interpreted.     

Surface engineering the cellular microenvironment via patterning and gradients

Cell organization, proliferation, and differentiation are impacted by diverse cues present in the cellular microenvironment. As a result, the surface of a material plays an important role in cellular function. Synthetic surfaces may be augmented by physical as well as chemical means. In particular, patterning and interfacial gradients may be utilized to mitigate the cellular response. Patterning is advantageous as it affords control over a range of feature sizes from several nanometers to millimeters. Gradients exist in vivo, for instance in stem cell niches, and the ability to create interfacial gradients in vitro can provide valuable insights into the influence of a series of minute surface changes on a single sample. This review focuses on fabrication methods for generating micro‐ and nanoscale surface patterns as well as interfacial gradients, the impact of these surface modifications on the cellular response, and the advantages and challenges of these surfaces in in vitro applications. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys., 2013     

Ru–bis(pyridine)pyrazolate (bpp)‐Based Water‐Oxidation Catalysts Anchored on TiO2: The Importance of the Nature and Position of the Anchoring Group

Three distinct functionalisation strategies have been applied to the in,in‐[{Ru^II(trpy)}₂(μ‐bpp)(H₂O)₂]³⁺ (trpy=2,2′:6′,2′′‐terpyridine, bpp=bis(pyridine)pyrazolate) water‐oxidation catalyst framework to form new derivatives that can adsorb onto titania substrates. Modifications included the addition of sulfonate, carboxylate, and phosphonate anchoring groups to the terpyridine and bis(pyridyl)pyrazolate ligands. The complexes were characterised in solution by using 1D NMR, 2D NMR, and UV/Vis spectroscopic analysis and electrochemical techniques. The complexes were then anchored on TiO₂‐coated fluorinated tin oxide (FTO) films, and the reactivity of these new materials as water‐oxidation catalysts was tested electrochemically through controlled‐potential electrolysis (CPE) with oxygen evolution detected by headspace analysis with a Clark electrode. The results obtained highlight the importance of the catalyst orientation with respect to the titania surface in regard to its capacity to catalytically oxidize water to dioxygen.     

Hierarchical comb brush architectures via sequential light‐mediated controlled radical polymerizations

A novel strategy for the synthesis and characterization of branched polymer brushes by sequential light‐mediated controlled radical polymerizations is described. Initially, linear brushes are prepared by surface‐initiated copolymerization of methyl methacrylate and 2‐hydroxyethyl methacrylate (HEMA). In a subsequent step, the HEMA side chains are functionalized with initiating groups for secondary graft polymerization, leading to hierarchical, branched architectures. The increased steric bulk due to the polymer side chains results in a dramatic increase in film thickness when compared to the starting linear brushes. This strategy also allows chemical gradient and complex three‐dimensional structures to be obtained by employing grayscale photomasks in combination with controlled radical polymerization. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2016 , 54, 2276–2284     

Synthesis of cationic N‐[3‐(dimethylamino)propyl]methacrylamide brushes on silicon wafer via surface‐initiated RAFT polymerization

Surface‐initiated reversible addition‐fragmentation chain transfer (SI‐RAFT) polymerization of N‐[3‐(dimethylamino)propyl]methacrylamide (DMAPMA) on the silicon wafer was conducted in attempt to create controllable cationic polymer films. The RAFT agent‐immobilized substrate was prepared by the silanization of hydroxyl groups on silicon wafer with 3‐aminopropylthriethoxysilane (APTS) and by the amide reaction of amine groups of APTS with ester groups of 4‐cyano‐4‐((thiobenzoyl) sulfanyl) pentanoic succinimide ester (CPSE); followed by the RAFT polymerization of DMAPMA using a “free” RAFT agent, that is, 4‐cyanopentanoic acid dithiobenzoate (CPAD) and an initiator, that is, 4,4′‐azobis‐4‐cyanopentanoic acid (CPA). The formation of homogeneous tethered poly(N‐[3‐(dimethylamino)propyl]methacrylamide) [poly(DMAPMA)] brushes, whose thickness can be tuned by reaction time varying, is evidenced by using the combination of grazing angle attenuated total reflectance‐Fourier transform infrared spectroscopy, X‐ray photoelectron spectroscopy, atomic force microscopy, and water contact‐angle measurements. The calculation of grafting parameters from the number‐average molecular weight, M _n (g/mol) and ellipsometric thickness, h (nm) values indicated the synthesis of densely grafted poly(DMAPMA) films and allowed us to predict a polymerization time for forming a “brush‐like” conformation for the chains. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2011     

Control of cell growth direction by direct fabrication of periodic micro‐ and submicrometer arrays on polymers

In this work, we describe a laser‐assisted microstructuring technique called Direct Laser Interference Patterning to produce topographical cues for tumor cells in a one‐step process. Line‐like patterns with spatial periods ranging from 500 nm to 10 μm are fabricated on polyimide (PI) films. The resulting structures exhibit a well‐defined shape and quality even for patterns with small periodic distances. Subsequently, the behavior of mouse mammary adenocarcinoma cells over those structures is evaluated. The results show that cell growth is well aligned to the direction of the patterns (over 60% lying within 0° to 15° to either side of the surface lines) for all evaluated structure sizes. Moreover, cells grown on patterns with 500 nm spatial period are the most narrowly aligned (up to 80% found between 0° and 15°), showing the potential of the technique. The fabrication process of the PI patterns is supported by a mathematical model of the underlying photo‐chemical ablation process. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2012     

Obstacle-type problems for minimal surfaces

We study certain obstacle-type problems involving standard and nonlocal minimal surfaces. We obtain optimal regularity of the solution and a characterization of the free boundary.