Network topology and the theory of rubber elasticity

The earliest investigations on rubber elasticity, commencing in the 19th century, were necessarily limited to phenomenological interpretations. The realisation that polymers consist of very long molecular chains. commencing c. 1930, gave impetus to the molecular theory of rubber elasticity (1932-). according to which the high deformability of an elastomer, and the elastic force generated by deformation, stem from the configurations accessible to long molecular chains. Theories of rubber elasticity put forward from 1934-1946 relied on the assumption that the junctions of the rubber network undergo displacements that are affine in macroscopic strain. The theory of James and Guth (1947) dispensed with this premise, and demonstrated instead that the mean positions of the junctions of a ‘phantom’ network consisting of Gaussian chains devoid of material properties are affine in the strain. The vital significance of the distinction between the actual distribution of chain vectors in a network and their distribution if the junctions would be fixed at their mean positions went unnoticed for nearly 30 years. Experimental investigations, commencing with the incisive work of Gee in 1946. revealed large departures from the relationship of stress to strain predicted by the theories cited. This discrepancy prompted extensive studies, theoretical and experimental, during succeeding years. Inquiry into the fundamentals of polymer networks, formed for example by interlinking very long polymer molecules, exposed the need to take account of network imperfections, typically consisting of chains attached at only one end to a network junction. Various means were advocated to make corrections for these imperfections. The cycle rank ζ of the network has been shown (1976) to be the fundamental measure of its connectivity, regardless of the junction functionality and pattern of imperfections. Often overlooked is the copious interpenetration of the chains comprising typical elastomeric networks. Theories that attempt to represent such networks on a lattice are incompatible with this universal feature. Moreover, the dense interpenetration of chains may limit the ability of junctions in real networks to accommodate the fluctuations envisaged in the theory of phantom networks. It was suggested in 1975 that departures from the form predicted for the elastic equation of state are due to constraints on the fluctuations of junctions whose effect diminishes with deformation and with dilation. Formulation of a self-consistent theory based on this suggestion required recognition of the non-affine connection between the chain vector distribution function and the macroscopic strain in a real network, which may partake of characteristics of a phantom network in some degree. Implementation of the idea was achieved through postulation of domains of constraint affecting the equilibrium distribution of fluctuations of network junctions from their mean positions. This led in due course to a theory that accounts for the relationship of stress to strain virtually throughout the ranges of strain accessible to measurement. The theory establishes connections between structure and elastic properties. This is achieved with utmost frugality in arbitrary parameters.     

Practice, working memory, and the ACT* theory of skill acquisition: A comment on Carlson, Sullivan, and Schneider (1989).

The major results reported by R. A. Carlson et al (see record 1989-24864-001) confirm predictions of J. R. Anderson's (1983) ACT* theory. In particular, ACT* predicts the detrimental effects of the transition to randomized practice because of the need to learn new productions, the complexity effect of gate and judgment type because of more complex production conditions, the effects of practice and its interaction with complexity because of the strengthening mechanisms, and the effects of memory load because of the need to hold information active in working memory so that it can be matched by production conditions. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Cooperation between memory systems: Acetylcholine release in the amygdala correlates positively with performance on a hippocampus-dependent task.

The present experiment examined the relationship between release of acetylcholine (ACh) in the amygdala and performance on a hippocampus-dependent spatial working memory task. Using in vivo microdialysis, the authors measured ACh release in rats during testing on a spontaneous alternation task. Amygdala ACh release was positively correlated with performance on the hippocampus-dependent task. These findings suggest that activation of the amygdala promotes processing in other neural systems important for learning and memory. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

An adaptive descent method for non-linear viscoplasticity

A forming model based on a viscoplastic flow formulation is derived which includes the effects of small elastic strains. A significant feature of the formulation is its reliance on the dominant inelastic material characteristics in the formation of the stiffness matrix for large strain problems. The resultant non-linear system of equations is solved by an adaptive descent method which combines the rapid convergence of Newton's method near the solution with the robustness of a method of successive approximations. The use of the adaptive descent method effectively extends the viscoplastic flow formulations into the nearly rate-insensitive range of behaviours exhibited, for example, by metals at low temperature, where slow convergence of the non-linear solution algorithm has traditionally hampered their use.     

The hot blow forming of AZ31 Mg sheet: Formability assessment and application development

The hot blow forming of magnesium sheet offers significant opportunity for forming complex, lightweight parts for automotive applications. This paper characterizes the elevated-temperature formability of AZ31 magnesium sheet materials and the effect of processing conditions on the performance of these materials. In addition, magnesium sheet application development at General Motors Corporation is reviewed.     

Immobilization and activation of vanadium(III) and titanium(III) single‐site catalysts for ethylene polymerization using MgCl2‐based supports

Significant increases in the activity of vanadium(III) amidinate catalysts for ethylene polymerization have been obtained by immobilization on a MgCl₂‐based support prepared by reaction of AlEt₃ with a MgCl₂/ethanol adduct. Catalyst immobilization and activation on this type of support prevents the rapid decay in activity observed under homogeneous polymerization conditions with unsupported catalysts. Stable polymerization activity is also observed with analogous titanium(III) complexes. Polyethylene with narrow molecular weight distribution and spherical particle morphology is obtained without reactor fouling. Copyright © 2005 Society of Chemical Industry     

N.m.r. line shape-relaxation correlation analysis of bitumen and oil sands

The first results of the analysis of bitumen and oil sands using the recently developed n.m.r. spingrouping technique are presented. The n.m.r. relaxation experiments were carried out on bitumen, and on natural and dried oil sands samples. The results indicate that the spin-grouping can resolve and quantify several components of the samples studied. The bitumen and bitumen fraction of the oil sands are resolved according to their spin-spin relaxation times into three major groups: solid-like (rigid), solid-like (mobile) and semi-liquid. The water in the oil sands exists in two different environments. Tentatively one environment is assigned to be the bridges between the sand grains, while the other is assigned to be the clay surface. One can conclude that with spin grouping of complex mixtures the decomposition (in which components are resolved according to their dynamic state) is possible. The accuracy of such resolution is of the order of a few per cent.