Effect of the molecular structure on the hierarchical self-assembly of semifluorinated alkanes at the air/water interface

Semifluorinated alkanes (C(n)F(2n+1)C(m)H(2m+1)), short FnHm display local phase separation of mutually incompatible hydrocarbon and fluorocarbon chain moieties, which has been utilized as a structure-forming motif in supramolecular architectures. The packing of semifluorinated alkanes, nominally based on dodecyl subunits, such as perfluoro(dodecyl)dodecane (F12H12) and perfluoro(dodecyl)eicosane (F12H20), as well as a core extended analogue, 1,4-dibromo-2-((perfluoroundecyl)methoxy)-5-(dodecyloxy)benzene) (F11H1-core-H12), was studied at the air/water interface. Langmuir monolayers were investigated by means of neutron reflectivity directly at the air/water interface and scanning force microscopy after transfer to silicon wafers. Narrowly disperse surface micelles formed in all three cases; however, they were found to bear different morphologies with respect to molecular orientation and assembly dimensionality, which gives rise to different hierarchical aggregate topologies. For F12H12, micelles of ca. 30 nm in diameter, composed of several circular or "spherical cap" substructures, were observed and a monolayer model with the fluorocarbon block oriented toward air is proposed. F12H20 molecules formed larger (ca. 50 nm diameter) hexagonally shaped surface micelles that were hexagonally, densely packed, besides more elongated but tightly interlocked wormlike structures. Conversely, F11H1-core-H12 films organized into linear rows of elongated surface micelles with comparable width, but an average length of ca. 400 nm, apparently formed by antiparallel molecular packing.     

Characterization of Co-blockers for Simple Perfect Matchings in a Convex Geometric Graph

Consider the complete convex geometric graph on $2m$ 2 m vertices, CGG $(2m)$ ( 2 m ) , i.e., the set of all boundary edges and diagonals of a planar convex $2m$ 2 m -gon P. In (Keller and Perles, Israel J Math 187:465–484, 2012), the smallest sets of edges that meet all the simple perfect matchings (SPMs) in CGG $(2m)$ ( 2 m ) (called “blockers”) are characterized, and it is shown that all these sets are caterpillar graphs with a special structure, and that their total number is $m \cdot 2^{m-1}$ m · 2 m ? 1 . In this paper we characterize the co-blockers for SPMs in CGG $(2m)$ ( 2 m ) , that is, the smallest sets of edges that meet all the blockers. We show that the co-blockers are exactly those perfect matchings M in CGG $(2m)$ ( 2 m ) where all edges are of odd order, and two edges of M that emanate from two adjacent vertices of P never cross. In particular, while the number of SPMs and the number of blockers grow exponentially with m, the number of co-blockers grows super-exponentially.     

Experiments on the location of chain ends in monolayer single crystals of polyethylene

The location of vinyl end groups in monolayer polyethylene crystals (specially prepared to have surfaces highly accessible to gaseous reactants) has been investigated by exposing the crystals to ozone and determining the extent of reaction by infrared spectroscopy. It was found that, for the type of crystals used, about nine-tenths of the chain ends reacted very rapidly and it is deduced that these are excluded from the crystal lattice and should lie on the crystal surfaces. The remaining fraction of ends were, by comparison, highly resistant to oxidation.

The consequences of this deduction are discussed; it is suggested that the chain segment ejected together with the chain ends could account for a large part of the amorphous content associated with this type of crystal. In addition, the results imply that the crystal lattice is inaccessible to ozone even when it contains defects such as those caused by end groups, which is of consequence for work on oxidative degradation both for its own sake and in aid of morphological studies.     

Transport equations for waves in a half Space

We derive boundary conditions for the phase space energy density of acoustic waves in a half space, in the high frequency limit. These boundary conditions generalize the usual reflection—transmission relations for plane waves and are well suited for the study of wave propagation in bounded randed random media in the radiative transport approximation[15]. The high frequency analysis is based on direct calculations with Fourier integrals in the case of constant coefficients and Wigner measures in general, and it is presented in detail     

On the Potential of Tomographic Methods when Applied to Compacted Crushed Rock Salt

Compacted crushed rock salt is considered as potential backfill material in repositories for nuclear waste. To evaluate the sealing properties of this material knowledge concerning the nature of the pore space is of eminent interest. Here, the pore microstructures of crushed rock salt samples with different compaction states were investigated by X-ray (XCT) computed tomography and Focused Ion Beam nanotomography (FIB-nt). Based on these methods the pore microstructures were reconstructed and quantitatively analyzed with respect to porosity, connectivity and percolation properties. Regarding pores with radii \(> 4\,\upmu \hbox {m}\) , porosity differs substantially in the two analyzed samples ( \(\phi = 0.01\) and 0.10). The pore microstructures are considered isotropic in connectivity and percolation threshold. Using two finite-scaling schemes we found percolation thresholds with critical porosities \(\phi _{c} > 0.05\) . Based on statistical considerations, the millimeter size samples that can be analyzed by XCT are large enough to provide a meaningful picture of the pore geometry related to macroporosity. The samples contain also a small fraction (i.e. \(< 0.01\) ) of pores with radii \(< 1\,\upmu \hbox {m}\) , which were resolved by FIB-nt. Often these pores can be found along grain boundaries. These pores are granular shaped and are not connected to each other. Typical samples size that can be analyzed by FIB-nt is on the order of tens of microns, which turned out to be too small to provide representative geometric information unless an effort is made that involves several FIB-nt realizations per sample.     

A Note on Chow Stability of the Projectivization of Gieseker Stable Bundles

We investigate Chow stability of projective bundles ?(E), where E is a strictly Gieseker stable bundle over a base manifold that has constant scalar curvature. We show that, for suitable polarizations \(\mathcal{L}\) , the pair \((\mathbb{P}(E),\mathcal{L})\) is Chow stable and give examples for which it is not asymptotically Chow stable.     

Improved synthesis of oligomeric phthalonitriles and studies designed for low temperature cure

An improved synthetic method has been developed for oligomeric aromatic ether ketone‐based phthalonitrile (PN) resins. A new curing additive was studied that lowers the cure temperature of the PN resin to around 150 °C and compared to the traditional high‐temperature aromatic diamine. Mechanical and thermo‐oxidative analyses of polymeric samples from both systems were determined and compared under various curing conditions. The PN polymer exhibited low water absorption regardless of the chosen cure system. Published 2014. This article is a U.S. Government work and is in the public domain in the USA. J. Polym. Sci., Part A: Polym. Chem. 2014 , 52, 1662–1668     

Experimentally verified pulse formation model for high-power femtosecond VECSELs

Optically pumped vertical-external-cavity surface-emitting lasers (OP-VECSELs), passively modelocked with a semiconductor saturable absorber mirror (SESAM), have generated the highest average output power from any sub-picosecond semiconductor laser. Many applications, including frequency comb synthesis and coherent supercontinuum generation, require pulses in the sub-300-fs regime. A quantitative understanding of the pulse formation mechanism is required in order to reach this regime while maintaining stable, high-average-power performance. We present a numerical model with which we have obtained excellent quantitative agreement with two recent experiments in the femtosecond regime, and we have been able to correctly predict both the observed pulse duration and the output power for the first time. Our numerical model not only confirms the soliton-like pulse formation in the femtosecond regime, but also allows us to develop several clear guidelines to scale the performance toward shorter pulses and higher average output power. In particular, we show that a key VECSEL design parameter is a high gain saturation fluence. By optimizing this parameter, 200-fs pulses with an average output power of more than 1 W should be possible.     

Permutation entropy: One concept, two approaches

Since C. Bandt and B. Pompe introduced permutation entropy in 2002 for piecewise strictly monotonous self-maps of one-dimensional intervals, this concept has been generalized to ever more general settings by means of two similar, though not equivalent, approaches. The first one keeps the original spirit in that it uses “sharp” dynamics and the corresponding ordinal partitions. The second uses symbolic (or “coarse-grained” dynamics with respect to arbitrary finite partitions, as in the conventional approach to the Kolmogorov-Sinai entropy of dynamical systems. Precisely, one of the main questions along these two avenues refers to the relation between permutation entropy and Kolmogorov-Sinai entropy. In this paper the authors will explain the underpinnings of both approaches and the latest theoretical results on permutation entropy. The authors also discuss some remaining open questions.