Brillouin scattering in amorphous polymeric solids

Brillouin scattering of laser light has been used to study the temperature dependence of phonon velocity in a variety of amorphous polymeric systems, particularly internally and externally plasticized methacrylates. Discontinuities in the temperature coefficient of the hypersound velocities are observed at the glass transition temperatures (T_g). This phenomenon is related to changes in the temperature behavior of the specific volume accompanied by corresponding discontinuities in certain second-order thermodynamic quantities. This method was also used to examine the temperature dependence of the Landau-Placzek ratio. This ratio is relatively large in polymer systems and appears to be independent of temperature in the region of the glass transition, provided that there are no internal strains in the sample at the temperature of measurement. Evidence is presented which suggests that the abrupt changes in this ratio at T_g reported by earlier workers were due to kinetic effects related to the relaxation of internal strains above T_g, and the results of recent studies by other investigators, both corroborating and supplementing the present work, are reviewed.     

Analysis of Generalised Galerkin methods in the numerical solution of elliptic equations

The Petrov-Galerkin projection method is outlined for the solution of the linear elliptic equation Lu = f with homogeneous boundary conditions. By choosing appropriate finite dimensional trial and test spaces, the methods of weighted residuals, collocation, and H¹ Galerkin can be interpreted within the Petrov-Galerkin projection method framework. The important question of how best to choose the trial and test functions to suit a particular type of problem is then discussed. Objective criteria associated with the matrix which governs the Petrov-Galerkin numerical process are proposed.     

Ordering in colloidal systems

The role played by statistical mechanics in the ordering of colloidal systems is examined. This role is made explicit through a study of phase (order-disorder) transitions in 1, 2 and 3 dimensions which exist in the examples provided by clay plate, tobacco mossaic virus and latex sphere suspensions. Essentially the statement is that the extrapolation of DLVO theory which attributes stability to a balance between attractive and repulsive two-body forces is not always a panacea. The ideas of Langmuir and Onsager who dealt with statistical mechanics and repulsive forces and considered that attractive long-range forces are not always important are paramount for some systems and must be built into existing theories.     

Group IV organometal derivatives of pyridine. I—A 1H and 13C NMR investigation of trialkylmetal derivatives of pyridine

The proton and carbon-13 NMR spectra of thirteen trialkylmetal derivatives of pyridine, several of which were previously unknown, have been recorded and analysed. The proton NMR spectra show variations in proton chemical shifts but not in proton-proton coupling constants when the metal substituent is changed; the ring proton-metal coupling constants ⁿJ(M? H) in the tin and lead derivatives correspond closely with the corresponding proton-proton couplings ⁿJ(H? H) in pyridine. The carbon-13 chemical shifts of the carbons bound to the metal can apparently be correlated with the electron-donating ability of the trialkylmetal group. In the trimethylstannylpyridines the value of ¹J(Sn? C_ring) varies greatly with the position of the Me₃Sn group.     

The structure of the charge transfer complex in olefin quenching of benzophenone phosphorescence

The phosphorescence lifetimes of ω-alkenyl esters of p-benzophenone-carboxylic acid have been measured in dilute solution in degassed acetic acid solution. The lifetimes were extrapolated to infinite dilution. Intramolecular quenching was not very significant in benzophenone-4-CO₂(CH₂)_nCHCH₂ for n = 1, 2 or 4. For n = 9 the phosphorescence lifetime was found to be 2 μs compared to 70 μs for n = 1, 2. These results are interpreted to mean that the quenching complex has a specific geometric requirement with the CHCH₂ group approaching within a van der Waals distance of the ketone carbonyl group.