Nuclear quantum effects in calculated NMR shieldings of benzene; a Feynman path integral study

The Feynman path integral Monte Carlo approach has been coupled to the gauge including atomic orbital formalism in order to analyse the absolute magnetic shieldings of the benzene nuclei under the conditions of thermal equilibrium. The Hamiltonian employed in the derivation of ensemble averaged NMR quantities is of the Hartree-Fock type. The basis set used is of 6–31G quality. The spatial delocalization of the atoms leads to a deshielding of both types of benzene nuclei relative to the shieldings experienced at the minimum of the potential energy surface. This deshielding has to be traced back to bond length elongations in thermal equilibrium. The influence of the nuclear fluctuations on the NMR parameters of benzene is quantum driven up to temperatures of 400 K; classical fluctuations are of minor importance in this low-temperature window.     

Rigidity of colloidal alloys as studied by reflection spectroscopy in sedimentation equilibrium

Rigidities of colloidal alloys of binary mixtures of colloidal silica spheres (CS82; 103 nm in diameter) with larger silica spheres (CS91; 110 nm, CS121; 136 nm and CS161; 184 nm) have been measured by reflection spectroscopy in sedimentation equilibrium. Substitutional-solid-solution-type alloy structures are formed for mixtures of CS82 and CS91 and for CS82 and CS121. A superlattice, probably MgCu₂ type, is formed for CS82 and CS161 mixtures. The rigidities of the colloidal crystals of the single component of the spheres increase as the sphere size increases at the same number density of spheres. The rigidities of the colloidal alloys decrease when a comparatively small number of the larger spheres are mixed with the small spheres at the same total sphere number density. Received: 14 June 2000 Accepted: 3 November 2000     

Boundary operators in the one-matrix model

The one matrix model is known to reproduce in the continuum limit the (2,2p+1)$(2,2p+1)$ minimal Liouville gravity. Recently, two of the authors have shown how to construct arbitrary critical boundary conditions within this matrix model. So far, between two such boundary conditions only one boundary operator was constructed. In this Letter, we explain how to construct all the set of boundary operators that can be inserted. As a consistency check, we reproduce the corresponding Liouville boundary 2pt function from the matrix model correlator. In addition, we remark a connection between a matrix model relation and the boundary ground ring operator insertion in the continuum theory.     

Kinetics analysis of colloidal crystallization of silica spheres modified with polymers on their surfaces in acetonitrile

 The nucleation and growth rates in the colloidal crystallization of silica spheres (136 nm in diameter) modified with polymers on their surface were measured by time-resolved reflection spectroscopy. The polymers were poly(maleic anhydride-co-styrene) [P(MA-ST)] and poly(methyl methacrylate) (PMMA). The induction period for nucleation decreased sharply when the sphere concentration increased. The crystal growth process consisted of a fast growing step leading to metastable crystals (rate v ₁) and a slow growth rate accompanied by the formation of stable crystals. The crystal size of the P(MA-ST)/SiO₂ particles decreased from 0.4 to 0.06 mm, whereas v ₁ increased from 13 to 37 μm/s, when the particle concentration increased. The slow step was also observed for almost all the samples but was not analyzed since the rate was too small. For PMMA/SiO₂ dispersions, the crystal size (0.17–0.3 mm) and v ₁ (43–166 μm/s) did not show any relation to the particle concentration but showed a linear relationship with the molecular weight of PMMA. These results suggest the important role of the excluded-volume effects of the polymer layers around the silica surface. The contribution of the repulsion due to the electrical double layers is still effective in the colloidal crystallization in acetonitrile. Received: 6 June 2001 Accepted: 20 September 2001