Detection of finite mechanisms in symmetric structures

Using group representation theory, it is possible to block-diagonalise the equilibrium matrix of a symmetric structure. This analysis can identify the symmetry properties of any states of self-stress or mechanisms present in the structure. This paper will show that in some cases, this linear analysis, combined with symmetry arguments, can show that particular mechanisms of a symmetric structure must be finite.     

A study of the blending of ethylene–styrene copolymers differing in the copolymer styrene content: Miscibility considerations

Blends of two or more ethylene–styrene (ES) copolymers that differed primarily in the comonomer composition of the copolymers were studied. Available thermodynamic models for copolymer–copolymer blends were utilized to determine the criteria for miscibility between two ES copolymers differing in styrene content and also between ES copolymers and the respective homopolymers, polystyrene and linear polyethylene. Model estimations were compared with experimental observations based primarily on melt‐blended ES/ES systems, particularly via the analysis of the glass‐transition (T_g ) behavior from differential scanning calorimetry (DSC) and solid‐state dynamic mechanical spectroscopy. The critical comonomer difference in the styrene content at which phase separation occurred was estimated to be about 10 wt % for ES copolymers with a molecular weight of about 10⁵ and was in general agreement with the experimental observations. The range of ES copolymers that could be produced by the variation of the comonomer content allowed the study of blends with amorphous and semicrystalline components. Crystallinity differences for the blends, as determined by DSC, appeared to be related to the overlapping of the T_g of the amorphous component with the melting range of the semicrystalline component and/or the reduction in the mobility of the amorphous phase due to the presence of the higher T_g of the amorphous blend component. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 2976–2987, 2000     

When is a symmetric body-bar structure isostatic?

Body-bar frameworks provide a special class of frameworks which are well understood generically, with a full combinatorial theory for rigidity. Given a symmetric body-bar framework, this paper exploits group representation theory to provide necessary conditions for rigidity in the form of very simply stated restrictions on the numbers of those structural components that are unshifted by the symmetry operations of the framework. We give some initial results, and conjectures, for when these conditions are also sufficient for rigidity.     

Heats of immersion of titanium dioxide pigments in alcohol—water mixtures

The heats of immersion of partially dried anatase and rutile pigments in mixtures of water with methanol, ethanol, and n-propanol were measured by a differential calorimetric method. The anatase heats of immersion could best be explained by assuming preferential adsorption of the alcohols, the effect being greatest for n-propanol The rutile pigment, however, appeared to adsorb water preferentially in methanol—water and ethanol—water mixtures over the whole concentration range. In propanol—water mixtures the rutile pigment preferentially adsorbed water below an alcohol mol fraction of 0.25, and preferentially adsorbed propanol at mol fractions of alcohol greater than 0.25. The differences in behaviour between the two pigments may be explained qualitatively from the point of view of their surface morphology.