Phenol methylation over nanoparticulate Co2FeO4 inverse spinel catalysts:the effect of morphology on catalytic performance

A series of CoFe2O4 nanoparticles have been prepared via co-precipitation and controlled thermal sintering, with tunable diameters spanning 7–50 nm. XRD confirms that the inverse spinel structure is adopted by all samples, while XPS shows their surface compositions depend on calcination temperature and associated particle size. Small (<20 nm) particles expose Fe3+ enriched surfaces, whereas larger (∼50 nm) particles formed at higher temperatures possess Co:Fe surface compositions close to the expected 1:2 bulk ratio. A model is proposed in which smaller crystallites expose predominately (1 1 1) facets, preferentially terminated in tetrahedral Fe3+ surface sites, while sintering favours (1 1 0) and (1 0 0) facets and Co:Fe surface compositions closer to the bulk inverse spinel phase. All materials were active towards the gas-phase methylation of phenol to o-cresol at temperatures as low as 300 °C. Under these conditions, materials calcined at 450 and 750 °C exhibit o-cresol selectivities of ∼90% and 80%, respectively. Increasing either particle size or reaction temperature promotes methanol decomposition and the evolution of gaseous reductants (principally CO and H2), which may play a role in CoFe2O4 reduction and the concomitant respective dehydroxylation of phenol to benzene. The degree of methanol decomposition, and consequent H2 or CO evolution, appears to correlate with surface Co2+ content: larger CoFe2O4 nanoparticles have more Co rich surfaces and are more active towards methanol decomposition than their smaller counterparts. Reduction of the inverse spinel surface thus switches catalysis from the regio- and chemo-selective methylation of phenol to o-cresol, towards methanol decomposition and phenol dehydroxylation to benzene. At 300 °C sub-20 nm CoFe2O4 nanoparticles are less active for methanol decomposition and become less susceptible to reduction than their 50 nm counterparts, favouring a high selectivity towards methylation.

Inverse space-dependent force problems for the wave equation

The determination of the displacement and the space-dependent force acting on a vibrating structure from measured final or time-average displacement observation is thoroughly investigated. Several aspects related to the existence and uniqueness of a solution of the linear but ill-posed inverse force problems are highlighted. After that, in order to capture the solution a variational formulation is proposed and the gradient of the least-squares functional that is minimized is rigorously and explicitly derived. Numerical results obtained using the Landweber method and the conjugate gradient method are presented and discussed illustrating the convergence of the iterative procedures for exact input data. Furthermore, for noisy data the semi-convergence phenomenon appears, as expected, and stability is restored by stopping the iterations according to the discrepancy principle criterion once the residual becomes close to the amount of noise. The present investigation will be significant to researchers concerned with wave propagation and control of vibrating structures.