Infrared spectroscopy of competitive interactions between liquid crystals, metal salts, and dimethyl methylphosphonate at surfaces

We report the use of Fourier transform polarization modulation infrared reflection-absorption spectroscopy (PM-IRRAS) to characterize the influence of dimethyl methylphosphonate (DMMP) on the molecular interactions occurring within thin films of nitrile-containing liquid crystals supported on surfaces presenting metal perchlorate salts. Infrared spectra obtained using thin films of 4'-octyl-4-biphenylcarbonitrile (8CB) supported on copper(II) perchlorate salts reveal the nitrile groups of 8CB to be coordinated to the copper(II) on these surfaces, and subsequent exposure of the system to DMMP to result in the elimination of these coordinated nitrile groups. Concurrently, evidence of coordination of the phosphoryl group of DMMP with copper(II) is provided by measurement of a shift of the phosphoryl stretch from 1246 to 1198 cm(-1). In contrast, surfaces presenting nickel(II) perchlorate salts only weakly coordinate with DMMP [the phosphoryl peak shifts from 1246 to 1213 cm(-1) in the presence of nickel(II)], and exposure of 8CB to DMMP results in only partial loss of coordination of the nitrile groups of 8CB with nickel(II). These PM-IRRAS measurements and others reported in this article provide insights into the molecular origins of macroscopic ordering transitions that are observed when micrometer-thick films of nitrile-containing liquid crystals supported on copper(II) or nickel(II) perchlorate are exposed to DMMP: Upon exposure to DMMP, nematic phases of 4'-pentyl-4-biphenylcarbonitrile (5CB) supported on copper(II) perchlorate salts undergo ordering transitions, whereas 5CB supported on nickel(II) perchlorate salts do not. Our IR results support the hypothesis that these ordering transitions reflect the relative strengths of coordination interactions occurring between the 5CB, DMMP, and the metal salts at these interfaces.     

Approximate nucleolus-based revenue sharing in airline alliances

Alliances allow the airlines to extend their networks and increase the number of destinations they can access. Different from the traditional single airline approach, in an alliance, partner airlines may sell tickets for the same itinerary. In addition, one itinerary may consist of several flight legs, each of which may be operated by a different airline. A major issue that needs to be addressed is how to share the revenue generated from selling a ticket for a product among the individual airlines in a fair way. The fair allocation of the revenue has a critical importance for the long-term stability of the alliance. We model the problem as a cooperative game and show that the core of the game is non-empty. We propose to use a revenue proration scheme based on the concept of the nucleolus. The numerical studies reveal that the revenue shares can effectively be computed even for large alliance networks.     

A second-quantization framework for the unified treatment of relativistic and nonrelativistic molecular perturbations by response theory

A formalism is presented for the calculation of relativistic corrections to molecular electronic energies and properties. After a discussion of the Dirac and Breit equations and their first-order Foldy-Wouthuysen [Phys. Rev. 78, 29 (1950)] transformation, we construct a second-quantization electronic Hamiltonian, valid for all values of the fine-structure constant alpha. The resulting alpha-dependent Hamiltonian is then used to set up a perturbation theory in orders of alpha(2), using the general framework of time-independent response theory, in the same manner as for geometrical and magnetic perturbations. Explicit expressions are given to second order in alpha(2) for the Hartree-Fock model. However, since all relativistic considerations are contained in the alpha-dependent Hamiltonian operator rather than in the wave function, the same approach may be used for other wave-function models, following the general procedure of response theory. In particular, by constructing a variational Lagrangian using the alpha-dependent electronic Hamiltonian, relativistic corrections can be calculated for nonvariational methods as well.     

Construction and properties of quasi-linear functionals

Quasi-linear functionals are shown to be uniformly continuous and decomposable into a difference of two quasi-integrals. A predual space for the quasi-linear functionals inducing the weak*-topology is given. General constructions of quasi-linear functionals by solid set-functions and q-functions are given.

     

Kinetic and thermodynamic stability of naphthalene oxide and related compounds. A comparative microcalorimetric and computational (DFT) study

The kinetics of the acid-catalyzed ring opening of naphthalene 1,2-oxide (5) in highly aqueous media to give naphthols has been measured by heat-flow microcalorimetry. The reaction enthalpy of this aromatization reaction was measured as DeltaH = -51.3 +/- 1.7 kcal mol(-)(1). The unexpectedly low reactivity of naphthalene oxide is suggested to be due to an unusually large thermodynamic stability. A crude estimate of the stabilization effect, approximately 1 kcal mol(-)(1)(not a significant stabilization), is obtained by using the measured reaction enthalpies of structurally related substrates as references. A larger value (2.7 kcal mol(-)(1)) was obtained by calculation using the B3LYP hybrid functional corrected with solvation energies derived from semiempirical AM1/SM2 calculations. The origin of this effect is discussed in terms of homoconjugative stabilization and homoaromaticity. There is a good linear correlation (with slope = 0.63) between the experimentally measured free energy of activation and the calculated enthalpy of carbocation formation in water.     

A trace theorem for the Dirichlet form on the Sierpinski gasket

In connection with the theory for Brownian motion on fractals, a corresponding Dirichlet form has been defined. We consider here the fractal known as the Sierpinski gasket, and characterize the trace of the domain of the Dirichlet form to the boundary of the gasket, boundary in this context meaning the triangle which confines the gasket.