Stability of droplets and channels on homogeneous and structured surfaces

Wetting of structured or imprinted surfaces which leads to a variety of different morphologies such as droplets, channels or thin films is studied theoretically using the general framework of surface or interface thermodynamics. The first variation of the interfacial free energy leads to the well-known Laplace equation and a generalized Young equation which involves spatially dependent interfacial tensions. Furthermore, we perform the second variation of the free energy for arbitrary surface patterns and arbitrary shape of the wetting morphology in order to derive a new and general stability criterion. The latter criterion is then applied to cylindrical segments or channels on homogeneous and structured surfaces. Received 4 August 1999     

An optical study of phase transitions of poly (ethylene terephthalate-co-p-hydroxybenzoic acid) liquid crystal

The copolyester containing 40 mol % ethylene terephthalate (PET) and 60 mol % p-hydroxybenzoate (HB) units has been reported by several investigators to be biphasic in the solid and the liquid states. The reported thermal transitions in the two phases, however, are in part contradictory, perhaps partly due to different polymerization conditions. The present work is a study of the transitions in each of the two phases of this copolyester by polarized light microscopy and by light transmission measurements. By light transmission measurements, the two phases were found to have two different glass transition temperatures for the onset of segmental motion, consistent with two assignable temperatures (T.). Cold crystallization and melting in each of the two different phases was also detected. The results help clarify the nature of transitions and agree with the results of dynamic mechanical analysis on the same thermotropic liquid crystalline copolyester.     

Advances in pulsed-laser atom probe: instrument and specimen design for optimum performance.

The performance of the pulsed-laser atom probe can be limited by both instrument and specimen factors. The experiments described in this article were designed to identify these factors so as to provide direction for further instrument and specimen development. Good agreement between voltage-pulsed and laser-pulsed data is found when the effective pulse fraction is less than 0.2 for pulsed-laser mode. Under the conditions reported in this article, the thermal tails of the peaks in the mass spectra did not show any significant change when produced with either a 10-ps or a 120-fs pulsed-laser source. Mass resolving power generally improves as the laser spot size and laser wavelength are decreased and as the specimen tip radius, specimen taper angle, and thermal diffusivity of the specimen material are increased. However, it is shown that two of the materials used in this study, aluminum and stainless steel, depend on these factors differently. A one-dimensional heat flow model is explored to explain these differences. The model correctly predicts the behavior of the aluminum samples, but breaks down for the stainless steel samples when the tip radius is large. A more accurate three-dimensional model is needed to overcome these discrepancies.     

X-ray diffraction by thermotropic main-chain polymers with side groups. II. semiflexible polyesters

Semiflexible thermotropic aromatic polyesters with lateral groups were aligned magnetically and mechanically in monodomains after separation into high-molecular-weight (polymer) and low-molecular-weight (oligomer) fractions. Based on the x-ray intensity distributions recorded for a series of seven different substituents in the arylsulfonyl substituted group, a novel smectic structure was determined for H, F, Cl, OCH₃, and CH₃ in the para position while a normal nematic alignment prevailed when it contained Br or NO₂.     

PS-b-PEO block copolymer thin films as structured reservoirs for nanoscale precipitation reactions

Thin films of PS-b-PEO block copolymers were utilized as structured reservoirs for localized nanoscale precipitation reactions. By consecutively immersing the film into solutions of thioacetamide and cadmium chloride, we were able to obtain a monolayer of cadmium sulfide nanostructures on top of the block copolymer film. AFM and grazing incidence small angle X-ray scattering revealed spherical nanostructures (d = 15 nm) corresponding to the dimensions given by the block copolymer film. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 1569–1573, 2010     

Multicolor Ramsey Numbers For Complete Bipartite Versus Complete Graphs

Let be graphs. The multicolor Ramsey number is the minimum integer r such that in every edge‐coloring of by k colors, there is a monochromatic copy of in color i for some . In this paper, we investigate the multicolor Ramsey number , determining the asymptotic behavior up to a polylogarithmic factor for almost all ranges of t and m. Several different constructions are used for the lower bounds, including the random graph and explicit graphs built from finite fields. A technique of Alon and Rödl using the probabilistic method and spectral arguments is employed to supply tight lower bounds. A sample result is for any t and m, where c₁ and c₂ are absolute constants.     

Cationic polymerization of p-substituted α-methylstyrenes. III. Effect of polymerization conditions on tacticity and molecular weight for p-chloro-α-methylstyrene

The cationic polymerization of p-chloro-α-methylstyrene was investigated for the effect of initiator and solvent on polymer tacticity, molecular weight, and molecular weight distribution. The products were generally crystalline polymers of 80–90% syndiotactic content with fairly high molecular weights and broad molecular weight distributions. Tacticities and molecular weight distributions followed similar patterns suggesting that the effect of reaction conditions on ionpair end-group structures was the dominant factor.     

Uniform existence of the integrated density of states for models on $${\mathbb{Z}}^d$$

We provide an ergodic theorem for certain Banach-space valued functions on structures over , which allow for existence of frequencies of finite patterns. As an application we obtain existence of the integrated density of states for associated discrete finite-range operators in the sense of convergence of the distributions with respect to the supremum norm. These results apply to various examples including periodic operators, percolation models and nearest-neighbour hopping on the set of visible points. Our method gives explicit bounds on the speed of convergence in terms of the speed of convergence of the underlying frequencies. It uses neither von Neumann algebras nor a framework of random operators on a probability space.      

Structure of neutron-rich Be and C isotopes

The structure of neutron-rich beryllium isotopes has been investigated using different heavy-ion-induced transfer reactions. In neutron transfer reactions, the population of final states shows a strong sensitivity to the chosen core nucleus, i.e., the target nuclei ⁹Be or ¹⁰Be, respectively. Molecular rotational bands up to high excitation energies are observed with ⁹Be as the core due to its pronounced 2α-cluster structure, whereas only a few states at low excitation energies are populated with ¹⁰Be as the core. For ¹¹Be, a detailed investigation has been performed for the three states at 3.41, 3.89, and 3.96 MeV, which resulted in the most probable spin-parity assignments 3/2⁺, 5/2^?, and 3/2^?, respectively. Furthermore, we have studied particle-hole states of ¹⁶C using the ¹³C(¹²C, ⁹C)¹⁶C reaction and found 14 previously unknown states. Using the ¹²C(¹²C, ⁹C)¹⁵C reaction, five new states were observed for ¹⁵C.     

Algebras of Random Operators Associated to Delone Dynamical Systems

We carry out a careful study of operator algebras associated with Delone dynamical systems. A von Neumann algebra is defined using noncommutative integration theory. Features of these algebras and the operators they contain are discussed. We restrict our attention to a certain C ^*-subalgebra to discuss a Shubin trace formula.