A Comparison of Electron Transfer Kinetics of Three Common Carbon Electrode Surfaces in Acetonitrile and in Room Temperature Ionic Liquid 1‐Butyl‐3‐Methylimidiazonium Hexafluorophosphate: Correlation to Surface Structure and the Limit of the Diffusion Domain Approximation

We report the comparison of electron transfer kinetic parameters of the ferrocene redox couple in both acetonitrile and in room temperature ionic liquid (RTIL) 1‐butyl‐3‐methylimidiazonium hexafluorophosphate ([C₄mim] [PF₆]), using edge plane pyrolytic graphite (EPPG), basal plane pyrolytic graphite (BPPG) and glassy carbon (GC) electrodes. Each electrode surface was characterized using SEM and AFM and the surface morphology was analyzed in terms of surface heterogeneity including the distribution of edge plane defects. The experimental data were modeled using both one and two dimensional simulations to correlate the electron transfer parameters obtained with the different surface structure of each electrode. Furthermore, we show that the diffusion domain approximation (commonly used to accurately simulate electron transfer kinetics at graphitic surfaces) breaks down when a BPPG electrode is used in RTIL and demonstrate the near impossibility of assigning rate constant to the basal plane surface.     

On the computational complexity of membership problems for the completely positive cone and its dual

Copositive programming has become a useful tool in dealing with all sorts of optimisation problems. It has however been shown by Murty and Kabadi (Math. Program. 39(2):117–129, 1987) that the strong membership problem for the copositive cone, that is deciding whether or not a given matrix is in the copositive cone, is a co-NP-complete problem. From this it has long been assumed that this implies that the question of whether or not the strong membership problem for the dual of the copositive cone, the completely positive cone, is also an NP-hard problem. However, the technical details for this have not previously been looked at to confirm that this is true. In this paper it is proven that the strong membership problem for the completely positive cone is indeed NP-hard. Furthermore, it is shown that even the weak membership problems for both of these cones are NP-hard. We also present an alternative proof of the NP-hardness of the strong membership problem for the copositive cone.     

Effect of surface character of filler particles on rheology of heat-set whey protein emulsion gels

Small-deformation and large-deformation rheological properties of heat-set whey protein emulsion gels containing active and inactive filler particles have been investigated using a controlled stress rheometer. The results suggest that the contributions to the gel network are quite different for pure protein gels and emulsion gels having similar storage moduli. An emulsion gel containing inactive filler has a larger phase angle due to the energy dissipation at the ‘slippery’ droplet surface under the influence of the applied shear stress. The large-deformation rheology of the heat-set protein gel has behaviour intermediate between that for an entropic biopolymer gel and that for a particle gel. Emulsion gels containing active or inactive fillers behave more like typical particle gel systems.     

Biomimetic anchors for antifouling and antibacterial polymer brushes on stainless steel

Barnacle cement (BC) was beneficially applied on stainless steel (SS) to serve as the initiator anchor for surface-initiated polymerization. The amine and hydroxyl moieties of barnacle cement reacted with 2-bromoisobutyryl bromide to provide the alkyl halide initiator for the surface-initiated atom transfer radical polymerization (ATRP) of 2-hydroxyethyl methacrylate (HEMA). The hydroxyl groups of HEMA polymer (PHEMA) were then converted to carboxyl groups for coupling of chitosan (CS) to impart the SS surface with both antifouling and antibacterial properties. The surface-functionalized SS reduced bovine serum albumin adsorption, bacterial adhesion, and exhibited antibacterial efficacy against Escherichia coli (E. coli). The effectiveness of barnacle cement as an initiator anchor was compared to that of dopamine, a marine mussel inspired biomimetic anchor previously used in surface-initiated polymerization. The results indicate that the barnacle cement is a stable and effective anchor for functional surface coatings and polymer brushes.     

Electron-beam-induced fracture of polymers

When a notched polymeric material is stressed, the notch opens into a wide crack tip, exposing a region of high stress concentration. The consequences of electron bombardment of the tip of such a stressed material under vacuum are explored here for the first time. Evidence is presented for electron-induced crack growth at stress far below that needed for crack growth due to stress alone. The electron current densities used in these experiments are sufficiently small that thermal heating of the zone near the crack tip is minimal. To provide information on the phenomena involved, we present simultaneous measurements of electron current, gas pressure, and sample load in response to periodic bombardment of the sample. Experiments involving the bombardment of un-notched polymers under stress are also described. Fractography of the unique structures obtained by fracture due to the combination of electron bombardment and stress are presented and interpreted in terms of a crosslinking mechanism.     

Some Statistical Results in the Combination of Forecasts

Forecasts may be combined using a minimum variance criterion to yield a composite forecast of smaller error variance than any of the components. This paper considers the sampling distributions of the weights to be attached to the components and of the error variance of the combined forecast. Confidence limits are derived for the estimates of the weights and of the variance of a composite forecast with two components. The theoretical analysis reveals that, in practice, it is doubtful whether combined forecasts offer much improvement because of the unreliability of the weight estimates.