Influence of Ag+ on the Magnetic Response of [2.2.2]Paracyclophane: NMR Properties of a Prototypical Organic Host for Cation Binding Based on DFT Calculations

The complexation of metal cations into a host–guest situation is particularly well exemplified by [2.2.2]paracyclophane and Ag^I, which leads to a strong cation–π interaction with a specific face of the host molecule. Through this study we sought a deeper understanding of the effects the metal center has on the NMR spectroscopic properties of the prototypical organic host, generating theoretical reasons for the observed experimental results with an aim to determine the role of the cation–π interaction in a host–guest scenario. From an analysis of certain components of the induced magnetic field and the ¹³C NMR shielding tensor under its own principal axis system (PAS), the local and overall magnetic behavior can be clearly described. Interestingly, the magnetic response of such a complex exhibits a large axis-dependent behavior, which leads to an overall shielding effect for the coordinating carbon atoms and a deshielding effect for the respective uncoordinated counterparts, evidence that complements previous experimental results. This proposed approach can be useful to gain further insight into the local and overall variation of NMR shifts for host–guest pairs involving both inorganic and organic hosts.     

Semiempirical determination of the atom-surface interaction

We discuss three methods of determining V(z), the lateral average (G = 0 Fourier component) of the atom-surface interaction, from the bound state spectrum found in beam scattering. One method uses the Rydberg-Klein-Rees technique, which yields the width of the potential (i.e., separation of classical turning points) as a function of energy. This method incorporates also the known asymptotic form V ～ ?C₃z^?3, whereC₃ is derived from the polarizability and dielectric function of atom and solid, respectively. The second method uses a hybrid potential, constructed from a Morse potential with shifted zero of energy connected to the asymptotic form,?C₃z^?3, requiring continuity of V and $\text{d}\text{V}\text{d}\text{z}$. The third potential is a Lennard-Jones 3–9 interaction. Results are presented for H and He scattering from LiF and NaF.     

Stream function finite element solution of Stokes flow with penalties

A finite element method for solution of the stream function formulation of Stokes flow is developed. The method involves complete cubic non-conforming (C⁰) triangular Hermite elements. This element fails the patch test. To correct the element and produce a convergent method we employ a penalty method to weakly enforce the desired continuity constraint on the normal derivative across the inter-element boundaries. Successful use of the method is demonstrated to require reduced integration of the inter-element penalty with a 1-point Gauss rule. Error estimates relate the optimal choice of penalty parameter to mesh size and are corroborated by numerical convergence studies. The need for reduced integration is interpreted using rank relations for an associated hybrid method.     

Non-planar smoulder propagation governed by diffusion

The steady propagation of a thin smouldering front in a half-spacehas been considered. A suitable coordinate transformation hasallowed the region near the leading edge of the front to beexamined for both a maintained planar surface and with surfacecollapse due to material shrinkage. The change in the oxidizerconcentration for a small increment in the propagation speedfor large time and surface collapse has been determined. Theinfluence of two types of nonlinear diffusion on the shape ofthe smouldering front has been found; other cases can be dealtwith in a similar manner.     

Enhanced thermal conductance at a copper-liquid helium interface in the presence of acoustic streaming

In a conventional Kapitza resistance experiment involving heat transfer across a copper surface into liquid helium, an acoustic streaming velocity field (at 10 MHz) was directed transverse to the surface normal. Ultrasound had no observable effect on the heat transfer to the superfluid phase (He-II), but in the normal fluid phase (He-I) the thermal conductance increased linearly with acoustic velocity amplitude, reaching a value 2.5 times the zero sound conductance for a sound velocity amplitude of 0.8 cm s^?1.     

Use of acousto-optic techniques to detect subharmonic and cavitation activity

Observations were made of the diffraction patterns produced by the acousto-optic effect in superfluid helium and in methanol for both cylindrical and plane wave sound fields. Thresholds for the subharmonic of order $\text{1}\text{2}$ and transient cavitation were determined by observation of abrupt changes in the diffraction patterns. The onset of the subharmonic produced additional diffracted signals in a stable diffraction pattern while onset of cavitation completely disrupted the diffraction pattern.