OSCILLATIONS OF NONLINEAR DELAY DIFFERENTIAL EQUATIONS——GENERAL LINEARIZED OSCILLA TIONS RESULTS

It is shown that for a wide class of the scalar and vector functional equations of the delay and the neutral type a positive solution exists if and only if the linearized approximating equations are non-oscillatory or, equivalently, the characteristic equations of these linear equations have a real root.     

Hydrophilic and hydrophobic adsorption on Y zeolites

The uniform large micropores of hydrothermally stable Y zeolites are used widely to confine both polar and non-polar molecules. This paper compares the physisorption of water, methanol, cyclohexane, benzene and other adsorbates over various Y zeolites. These adsorbents are commercial products with reproducibly controllable physical and chemical characteristics. Results indicate that the type I isotherms typical for micropore adsorption can turn into type II or type III isotherms depending on either or both the hydrophobicity of the adsorbent and the polarity of the adsorbate. Methanol produced a rare type V isotherm not reported over zeolites before. Canonical and grand canonical Monte Carlo molecular simulations with Metropolis importance sampling reproduced the experimental isotherms and showed characteristic geometric patterns for molecules confined in Na-X, Na-Y, dealuminated Y, and ZSM5 structures. Adsorbate—adsorbate interactions seem to determine the micropore condensation of both polar and non-polar molecules. Exchanged ions and lattice defects play a secondary role in shaping the adsorption isotherms. The force field of hydrophobic Y appears to exert an as yet unexplored sieving effect on adsorbates having different dipole moments and partial charge distributions. This mechanism is apparently different from both the monolayer formation controlled adsorption on hydrophobic mesopores and macropores and the polarizability and small-pore opening controlled micropore confinement in hydrophobic ZSM5.     

BSSE-free second order intermolecular perturbation theory II. Sample calculations on hydrogen-bonded complexes

The second order BSSE-free intermolecular perturbation theory based on the ‘Chemical Hamiltonian Approach’ (CHA), which was developed in the first part of this paper is applied to several hydrogen bonded systems using a variety of different basis sets. The results show that the second order BSSE-free interaction energy is remarkably close to that obtained by the conventional MP2 interaction energy if the latter is properly CP corrected. This shows that these two independent and conceptually different approaches–the classical Boys-Bernardi scheme and the CHA method–strongly corroborate each other.