Crystal structure of 2,2-diphenylethyl 2,4,6-trimethylphenyl ketone: Kohler's ketone. Mechanism of stereospecific enolization reaction with grignard reagents

The title compound crystallizes in the monoclinic space group P2₁/n with a = 10.875(2), b = 6.039(5), c- 29.015(8)A, and β = 91.29(2). The observed density for Z = 4 la 1.14(1) Mgm^-3 (D_c - 1.155 Mgm^-3). The reliability factors for 1127 unique reflections are R - 0.066 and R_w = 0.064. The dihedral angle between the mesityl ring and the carbonyl to α- carbon plane is 114.4° in contrast to an angle of 89.9° reported earlier for a substituted t-butyl mesityl ketone. A mechanism is proposed for the formation of an E-magnesium enolate from the reaction of Kohler's ketone with Grignard reagents.     

Localization in the metallic regime of granular Cu—SiO2 films

The temperature dependences of the electrical resistivity of sputterd Cu—SiO₂ films measured in the range 4–300 K show minima which depend on the composition. A linear temperature dependence of ? is observed above the minimum, and an appropriate log T dependence is found below. The latter is attributed to electron localization. The magnetoresistance is found to be negative and the Hall constant shows no appreciable temperature dependence.     

In-situ fluorescence imaging of sol-gel thin film deposition

Pyranine was used as a fluorescence probe to monitor the chemical evolution in-situ during thin film deposition by the dip coating process. The sensitivity of the pyranine luminescence to protonation/deprotonation effects was used to quantify changes in the water/alcohol ratio in real time within the depositing film as the substrate was withdrawn from the coating reservoir. The spatially resolved spectral results clearly showed that preferential evaporation of alcohol occurred with increasing distance from the reservoir and that the maximum water content reached rather high values near the drying line. Correlation of the luminescence results with the interference pattern of the drawn films allows the solvent composition in the film to be mapped as a function of film thickness. These experiments demonstrate for the first time that luminescent organic molecules may be applied to the processing science of sol-gel thin film deposition.     

Finite element error bounds for a curve shrinking with prescribed normal contact to a fixed boundary

We approximate the evolution of a curve subject to motion bycurvature by linear finite elements. The curve evolves insidea given domain and meets orthogonally. We derive optimal boundsfor the error with respect to the L²- and H¹-norms and presentsome computed examples.     

The 1/N-expansion as a perturbation about the mean field theory: A one-dimensional fermi model

We examine a family of probability measures onR ^L with real parameter >0 and integer parametersN,L>0. Each such measure is equivalent to the lattice version of a one-dimensional discrete chiral-invariant fermionic quantum field theory with quartic interaction, withN the number of flavours. After applying the Matthews-Salam formula, the model becomes a statistical mechanical model of a chain of continuous Gaussian spins, coupled with a certain non-standard weight function. Finally, the model can also be considered as a probability measure on the set of tridiagonal matrices with fixed off-diagonal and random diagonal entries.Our analysis shows how to develop an asymptotic expansion in 1/N, valid for allL and , for the fundamental expectation values. From this it follows that the two point fermion correlation function decays with a mass which agrees to the leading order in 1/N with the mean field value calculated by the argument of Gross-Neveu. The analytical technique we develop in essence combines a transfer matrix method with the Laplace method (steepest descent) for asymptotics of integrals.Partially supported by FAPESP and CNPq.Partially supported by CNPq.Supported by the Natural Sciences and Engineering Research Council of Canada.