Inverse gas chromatography for natural fibre characterisation: dispersive and acid-base distribution profiles of the surface energy

Inverse Gas Chromatography (IGC) is a gas sorption technique to determine the surface energy of natural fibres. The surface energy is directly related to the thermodynamic work of adhesion and it reflects the fibre adsorption capacity and its wettability. However, natural fibres have a complex surface chemistry of numerous organic species and present physical asperities that render the surface energetically heterogeneous. Since IGC is typically performed at infinite dilution where only the higher energetic sites interact with the solvent, a single measure of surface energy is likely to be misleading as the surface energy changes with changing chemical composition. Here we present the dispersive and acid-base surface energy profiles of flax and kenaf fibres as well as continuous filament fibres produced by a dry jet, wet spinning process (cellulose B). We injected a series of n-alkanes at finite dilution to obtain the dispersive energy distribution profile at \(30\,^{\circ }\hbox {C}\) and 0% RH. The acid-base contributions were determined by injection of mono polar probes (dichloromethane, ethylacetate) at the same surface coverages and applying the Van Oss method. The cellulose B fibres were the most energetically homogeneous, while the bast fibres were shown to have a higher polar component and much broader surface energy distributions than the cellulose fibres.     

Uncountable cofinalities of automorphism groups of linear and partial orders

We demonstrate the uncountable cofinality of the automorphism groups of various linear and partial orders. We also relate this to the ‘Bergman’ property, and discuss cases where this may fail even though the cofinality is uncountable.     

Rheological Behaviors of Poly(Vinylidene Fluoride)/“Bud-Branched” Nanotubes Nanocomposites

Bud-branched nanotubes, fabricated by growing metal particles on the surfaces of multiwall carbon nanotubes (MWCNTs), were used to prepare poly(vinylidene fluoride) (PVDF)-based nanocomposites. The melt viscoelastic behaviors of PVDF and its nanocomposites were characterized. The results showed that the introduction of both the MWCNTs and bud-branched nanotubes (MWCNTs-B) increased the storage modulus, loss modulus, and complex viscosity of the nanocomposites. However, the bud-branched nanotubes were more efficient to increase the elasticity than the MWCNTs that have relatively smooth surfaces. In particular, it was observed that the bud-branched nanotubes caused an increase of normal force and crossover modulus, while for MWCNTs, no variation in the normal force and a decrease of the crossover modulus were observed.     

The categoricity of the group of all computable automorphisms of the rational numbers

We prove that there is a first-order sentence ϕ such that the group of all computable automorphisms of the ordering of the rational numbers is its only model among the groups that are embeddable in the group of all computable permutations. Supported by a Scheme 2 grant from the London Mathematical Society. __________ Translated from Algebra i Logika, Vol. 46, No. 5, pp. 649–662, September–October, 2007.     

Stochastic fatigue limits and fatigue life variability for unplasticised PVC pipes

This paper uses the random fatigue limit (RFL) model of Pascual and Meeker to address fatigue limits for PVC pressure pipes. This model differs from previous ways of describing fatigue data for PVC by recognising that the fatigue limit is a stochastic quantity rather than a single valued stress amplitude below which fatigue failures will not occur. By analysing published fatigue data, it is demonstrated that the RFL model is capable of quantifying fatigue limit variability and its influence on fatigue life variability. Moreover, the RFL model was used to illustrate the risks associated with defining fatigue limits based on small quantities of high-cycle fatigue data. In particular, it is shown that fatigue failure can occur below the mean fatigue limit and that the RFL model is capable of quantifying the probability of failure at a given level of stress amplitude.     

The dependence of yield behavior on temperature,pressure, and strain rate for linear polyethylenes of different molecular weight and morphology

The temperature, strain-rate, and pressure dependences of the yield stress have been determined for two polyethylene homopolymers of differing molecular weights and for a polyethylene copolymer. Samples were prepared by slowly cooling from the melt, and also by quenching in order to assess the effects of morphology on the yield behavior. The data have been analyzed on the basis of two Eyring processes acting in parallel. Comparison of all data sets reveals the existence in general of three distinct activated processes each with its own temperature, strain-rate, and pressure dependences. The relative contribution of each process is dependent on the molecular weight, morphology, etc. Also discussed is the relation of these three yield processes to the well-known loss processes of linear viscoelasticity.     

Undecidability of automorphism groups

We give a simple (and easy to apply) technique that gives the undecidability of the theory of many automorphism groups: Let G be a group of automorphisms of a structure. Suppose that is not the identity and has no non-singleton finite orbits. If the centraliser of g is transitive on the support of g and satisfies a further technical condition, then the subgroup generated by g is equal to the double centraliser of g. Thus if G contains such an element g that is conjugate to all its positive powers, then one can interpret addition and multiplication of natural numbers in the theory of G using the parameter g; consequently, G has undecidable theory. Received: 9 October 2000 / in final form: 2 October 2001 / Published online: 29 April 2002     

Small Sets which meet all the n-Term Arithmetic Progressions in the Interval [1, n2]

For any positive integers n and k, let f(n, k) denote the smallestsize of a subset of the integer interval I =[l, n] which meetsall the k-term arithmetic progressions contained in I. We showthat n+(1/2)n^1/2–2 < f(n²,n) , where p is the largest prime n, and for any real number x,[x] is the least integer x.