First-order and critical wetting of alkanes on water

Ellipsometry measurements of the wetting behavior of different alkanes on water show a sequence of two wetting transitions: a first-order (discontinuous) transition followed by a critical (continuous) one. We report temperature-induced wetting transitions for different alkanes and a novel pressure-induced wetting transition for an alkane mixture. The experiments enable us to determine the global wetting phase diagram as a function of chain length and temperature which we subsequently calculate theoretically. The two transition lines are found to be approximately parallel, in accordance with basic theoretical arguments.     

On positive functions with positive derivatives

Three proofs are given for the fact that the derivative of an everywhere-positive non-constant real polynomial function must change sign. This self-contained note could find classroom use in courses on calculus or abstract algebra.     

Functions with Nonzero Wronskian form a fundamental solution set

This self-contained note could find classroom use in a course on differential equations. It is proved that if y₁(x) and y₂(x) are C ² -functions whose Wronskian is never zero for α < x < β, then y₁ and y₂ form a fundamental solution set for a uniquely determined second-order linear homogeneous ordinary differential equation, y″ + p(x)y′ + q(x)y = 0, whose coefficients, p(x) and q(x), are continuous on (α, β).     

A Generalization of Divided Domains and Its Connection to Weak Baer Going-Down Rings

Many results on going-down domains and divided domains are generalized to the context of rings with von Neumann regular total quotient rings. A (commutative unital) ring R is called regular divided if each P ∈ Spec(R)?(Max(R) ∩ Min(R)) is comparable with each principal regular ideal of R. Among rings having von Neumann regular total quotient rings, the regular divided rings are the pullbacks K× _K/P D where K is von Neumann regular, P ∈ Spec(K) and D is a divided domain. Any regular divided ring (for instance, regular comparable ring) with a von Neumann regular total quotient ring is a weak Baer going-down ring. If R is a weak Baer going-down ring and T is an extension ring with a von Neumann regular total quotient ring such that no regular element of R becomes a zero-divisor in T, then R ? T satisfies going-down. If R is a weak Baer ring and P ∈ Spec(R), then R + PR _(P) is a going-down ring if and only if R/P and R _P are going-down rings. The weak Baer going-down rings R such that Spec(R)?Min(R) has a unique maximal element are characterized in terms of the existence of suitable regular divided overrings.     

Atmospheric chemistry of linear perfluorinated aldehydes: dissociation kinetics of CnF2n+1CO radicals

Linear perfluorinated aldehydes (PFALs, CnF2n+1CHO) are important intermediate species in the atmospheric oxidation pathway of many polyfluorinated compounds. PFALs can be further oxidized in the gas phase to give perfluorinated carboxylic acids (PFCAs, CnF2n+1C(O)OH, n = 6, 12) which have been detected in animal tissues and at low parts per billion levels in human blood sera. In this paper, we report ab initio quantum chemistry calculations of the decarbonylation kinetics of CnF2n+1CO radicals. Our results show that CnF2n+1CO radicals have a strong tendency to decompose to give CnF2n+1 and CO under atmospheric conditions: the Arrhenius activation energies for decarbonylation of CF3CO, C2F5CO, and C3F7CO obtained using PMP4/6-311++G(2d,p) are 8.8, 6.6, and 5.8 kcal/mol, respectively, each of which is about 5 kcal/mol lower than the barrier for the corresponding nonfluorinated radicals. The lowering of the barrier for decarbonylation of CnF2n+1CO relative to that of CnH2n+1CO is well explained by electron withdrawal by F atoms that serve to weaken the critical C-CO bond. These results have important implications for the atmospheric fate of PFALs and the atmospheric pathways to PFCAs. The main effect of decarbonylation of CnF2n+1CO is to decrease the molar yield of CnF2n+1C(O)OH; if 100% of the CnF2n+1CO decompose, the yield of CnF2n+1C(O)OH must be zero. There is considerable scope for additional experimental and theoretical studies.     

Visible measures of maximal entropy in dimension one

A real one-dimensional analogue of Zdunik's dichotomy is proved,giving dynamical conditions for a multimodal map to have a measureof maximal entropy of dimension one.     

Rapid access to CF3-containing heterocycles

The silyl-Prins and aza-silyl-Prins reactions have been employed for the preparation of 6-CF₃-substituted dihydropyrans and 6-CF₃-substituted tetrahydropyridines. The product heterocycles have been further elaborated to a number of products, including CF₃-substituted pipecolates and hydroxylated pyrans and piperidines.     

2,6-Bis[2-(4-pentylphenyl)vinyl]anthracene: a stable and high charge mobility organic semiconductor with densely packed crystal structure

The development of new organic semiconductors with improved electrical performance and enhanced environmental stability is the focus of considerable research activity. This paper presents the design, synthesis, optical and electrochemical characterization, crystal packing, modeling and thin film morphology, and organic thin film field effect transistor (OTFT) device data analysis for a novel 2,6-bis[2-(4-pentylphenyl)vinyl]anthracene (DPPVAnt) organic semiconductor. We observed a hole mobility of up to 1.28 cm2/V.s and on/off current ratios greater than 107 for OTFTs fabricated using DPPVAnt as an active semiconductor layer. The mobility value is comparable to that of the current best p-type semiconductor pentacene-based device performance. In addition, we found a very interesting relationship between the charge mobility and molecule crystal packing in addition to the thin film orientation and morphology of the semiconductor as determined from single-crystal molecule packing study, thin film X-ray diffraction, and AFM measurements. The high performance of the semiconductor ranks among the best performing p-type organic semiconductors reported so far and will be a very good candidate for applications in organic electronic devices.