Modification of chemical additives to elastomeric compositions

Abstract

Ashtekar and Samuel have shown that Bianchi cosmological models with compact spatial sections must be of Bianchi class A. Motivated by general results on the symmetry reduction of variational principles, we show how to extend the Ashtekar-Samuel results to the setting of weakly locally homogeneous spaces as defined, e.g., by Singer and Thurston. In particular, it is shown that any m-dimensional homogeneous space G/K admitting a G-invariant volume form will allow a compact discrete quotient only if the Lie algebra cohomology of G relative to K is non-vanishing at degree m.Spatially homogeneous spacetimes have been studied extensively as both classical and quantum cosmological models (see, e.g., [1,2]). In 3+1 dimensions all spatially homogeneous models but one (the Kantowski-Sachs model) admit a freely acting three-dimensional Lie group of isometries. These models are known as 'Bianchi models' since they can be classified-up to topology-according to Bianchi's classification of three-dimensional Lie algebras. It was noted by Ashtekar and Samuel [3] that the orbit manifolds (the preferred spatial slices) for the Bianchi models can be compact only if the Lie algebra of the homogeneity group is Bianchi class A. They also consider a class of locally homogeneous geometries and show that the restriction to Bianchi class A Lie algebras is still necessary for compact spatial sections in this more general setting. It is straightforward to generalize the Ashtekar-Samuel results to orbit manifolds of any dimension. The result is the same provided one generalizes 'Bianchi class A' to 'unimodular' 1 . However, to our knowledge it is unknown how to extend these results to the large class of 'weakly locally homogeneous spaces' 2 of Singer, Thurston,

Eutectic alloys in sulfur‐based rubber vulcanizing systems and related problems

“…Taking all this into consideration, the aim of this work was to study conditions for the creation of eutectic alloys of these ingredients, an important investigation because the formation in binary and complex systems of simple eutectic alloys of chemical additives makes it possible both to obtain more uniform rubber compounds and to reduce their concentrations in sulfur-based vulcanizing systems without a decrease or even with an increase in effectiveness. [1][2][3][4][5] However, to ensure that the optimal properties are used in sulfur-based curing system, chemical additives should be dispersed well in elastomers. Zinc stearate, as it is a saturated aliphatic zinc soap, is insoluble in rubber, and the estimation of its dispersion is very important.…”

Eutectic alloys in sulfur-based rubber vulcanizing systems and related problems

“…On the other hand, the melting temperature of solids depends on their initial properties and whether they are individual components or, under some conditions, eutectic alloys. Taking all this into consideration, the aim of this work was to study conditions for the creation of eutectic alloys of these ingredients, an important investigation because the formation in binary and complex systems of simple eutectic alloys of chemical additives makes it possible both to obtain more uniform rubber compounds and to reduce their concentrations in sulfur‐based vulcanizing systems without a decrease or even with an increase in effectiveness 1–5. However, to ensure that the optimal properties are used in sulfur‐based curing system, chemical additives should be dispersed well in elastomers.…”

The Change in the Crystal Structure of Zinc Oxide in a Binary ε-Caprolactam–Stearic Acid Melt

“…It is well known [1] that the activating capacity of a crystalline substance depends on the degree of defectiveness of its structure, and that structural defects affect the improvement in dispersion of crystalline substances because they lead to an increase in entropy and free energy. It is likely that substances with more defective crystals, breaking down into nanosized particles, exhibit higher diffusion and chemical activity.…”