The effective dielectric constant of a dispersion of clustering spheres

If one measures the dielectric constant of a water in oil microemulsion the large increase of this dielectric constant both as function of the temperature as well as a function of the volume fraction of water suggests that the water droplets will bind together in clusters. In order to analyse this suggestion in more detail we derive a systematic expansion of the Clausius-Mossotti function in terms of integrals over products of excess cluster polarizabilities and correlation functions. It is found that the excess polarizability of a cluster of spherical droplets is zero except when the spheres almost touch each other. Crucial for this property is the fact that the water spheres are conducting or if they are not conducting have a dielectric constant much larger than the dielectric constant of oil. The large increase of the dielectric constant is a consequence of the increase of the number of bound clusters. An explicit formula is given for the resulting temperature and volume fraction dependence of the dielectric constant.Dedicated to Professor Harry Thomas on the occasion of his 60th birthday     

Optical properties of thin films on rough surfaces

A general theory, of second order in the film thickness and surface roughness over the wavelength, is developed of the optical properties of a thin film. These properties are described by a small number of electromagnetic constitutive coefficients. Formulae for these coefficients are derived in terms of the height-height correlation functions of the upper and lower surfaces of the film, and its average thickness. The reflectance, transmittance and ellipsometric coefficient are expressed in terms of the constitutive coefficients, for arbituary angles of incidence.     

Sensitivity-enhanced phase-corrected ultra-slow magic angle turning using multiple-echo data acquisition

The increase in the sensitivity of the phase-corrected magic angle turning (PHORMAT) experiment at ultra-slow spinning rates by means of multiple-echo data acquisition (ME-PHORMAT) is evaluated. This is achieved by replacing the acquisition dimension in the original experiment with a train of equally spaced pi-pulses. It is shown that the echoes following the odd and even pi-pulses in the CPMG train must be processed differently in order to avoid spectral distortions. The method is illustrated for 13C CP-ME-PHORMAT on solid 1,2,3-trimethoxybenzene and for 1H ME-PHORMAT on excised rat liver tissue, both at a sample-spinning rate of 1.3 Hz. Sensitivity enhancements of a factor 4 for the solid and 2.3 for the liver were obtained. Finally, it is shown that with ME-PHORMAT one of the two RF pulse sequences, in standard PHORMAT used to obtain a pure absorption mode 2D spectrum, can be eliminated, thus reducing the usually long measuring time by a factor 2.     

Structural relaxation of polymers at the glass transition: conformational memory in poly(n-alkylmethacrylates)

Conformational memory is introduced as a new aspect of structural relaxation of polymers. In poly(n-alkylmethacrylates) extended backbone chain conformations are identified by advanced NMR techniques as the molecular units involved in structural relaxation. They retain conformational memory over many steps of restricted axial chain motion. Randomization of conformation and isotropization of backbone orientation occur on the same time scale, yet much slower than the slowest relaxation process identified so far. Behavior typical of fragile glass formers is found for this new process of chain relaxation.     

H DNP at 1.4 T of Water Doped with a Triarylmethyl-Based Radical

Recently a triarylmethyl-based (TAM) radical has been developed for research in biological and other aqueous systems, and in low magnetic fields, 10 mT or less, large ¹H dynamic nuclear polarization (DNP) enhancements have been reported. In this paper the DNP properties of this radical have been investigated in a considerably larger field of 1.4 T, corresponding to proton and electron Larmor frequencies of 60 MHz and 40 GHz, respectively. To avoid excessive microwave heating of the sample, an existing DNP NMR probe was modified with a screening coil, wound around the sample capillary and with its axis perpendicular to the electric component of the microwave field. It was found that with this probe the temperature increase in the sample after 4 s of microwave irradiation with an incident power of 10 W was only 16°C. For the investigations, 10 mM of the TAM radical was dissolved in deionized, but not degassed, water and put into a 1-mm i.d. and 6-mm long capillary tube. At 26°C the following results were obtained: (I) The relaxivity of the radical is 0.07 (mMs)⁻¹, in accordance with the value extrapolated from low-field results; (II) The leakage factor is 0.63, the saturation factor at maximum power is 0.85, and the coupling factor is −0.0187. It is shown that these results agree very well with an analysis where the electron–dipolar interactions are the dominant DNP mechanism, and where the relaxation transitions resulting from these interactions are governed by translational diffusion of the water molecules. Finally, the possibilities of combining DNP with magnetic resonance microscopy (MRM) are discussed. It is shown that at 26°C the overall DNP-enhanced proton polarization should become maximal in an external field of 0.3 T and become comparable to the thermal equilibrium polarization in a field of 30 T, considerably larger than the largest high-resolution magnet available to date. It is concluded that DNP MRM in this field, which corresponds to a standard microwave frequency of 9 GHz, has the potential to significantly increase the sensitivity in NMR and MRI experiments of small aqueous samples doped with the TAM radical.     

Second-order Møller–Plesset perturbation theory with terms linear in the interelectronic coordinates and exact evaluation of three-electron integrals

 The second-order correlation energy of M?ller–Plesset perturbation theory is computed for the neon atom using a wave function that depends explicitly on the interelectronic coordinates (MP2-R12). The resolution-of-identity (RI) approximation, which is invoked in the standard formulation of MP2-R12 theory, is largely avoided by rigorously computing the necessary three-electron integrals. The basis-set limit for the second-order correlation energy is reached to within 0.1 mE _h. A comparison with the conventional RI-based MP2-R12 method shows that only three-electron integrals over s and p orbitals need to be computed exactly, indicating that the RI approximation can be safely used for integrals involving orbitals of higher angular momentum. Received: 9 May 2001 / Accepted: 31 October 2001 / Published online: 9 January 2002     

Vortex lattice transitions in YNi2B2C

We have performed extensive small-angle neutron scattering (SANS) diffraction studies of the vortex lattice in single crystal YNi₂B₂C for B‖c. High-resolution SANS, combined with a field-oscillation vortex lattice preparation technique, allows us to separate Bragg scattered intensities from two orthogonal domains and accurately determine the unit cell angle, β. The data suggest that upon increasing field there is a finite transition width where both low- and high-field distorted hexagonal vortex lattice phases, mutually rotated by 45°, coexist. The smooth variation of diffracted intensity from each phase through the transition corresponds to a redistribution of populations between the two types of domains.     

Centred TVD schemes for hyperbolic conservation laws

New first- and high-order centred methods for conservation lawsare presented. Convenient TVD conditions for constructing centredTVD schemes are then formulated and some useful results areproved. Two families of centred TVD schemes are constructedand extended to nonlinear systems. Some numerical results arealso presented.