STRUCTURE OF SEVERAL RUBBER VULCANIZATION ACCELERATORS. (PART II)

Vulcanization and the Properties of Rubber

Rubber is composed of long stringlike polymer molecules, which are pinned together at random points by crosslinks. As the density of crosslinks is increased, the molecules get localized and the system undergoes a phase transition from a liquid to an amorphous solid state. The elastic properties of the resulting solid are very different from those of metals, and are primarily due to changes in t...

From Vulcanization to Isotropic and Nematic Rubber Elasticity

– A Landau theory is constructed for the vulcanization transition in cross-linked polymer systems with spontaneous nematic ordering. The neo-classical theory of the elasticity of nematic elastomers is derived via the minimization of this Landau free energy; this neoclassical theory contains the classical theory of rubber elasticity as its isotropic limit. Our work not only reveals the statistic...

Part II Linguistic Structure

Several Integrability Formulas of Special Functions. Part II

In this article, we give several differentiation and integrability formulas of special and composite functions including the trigonometric function, the hyperbolic function and the polynomial function [3]. For simplicity, we adopt the following rules: r, x, a, b denote real numbers, n, m denote elements of N, A denotes a closed-interval subset of R, and Z denotes an open subset of R. One can pr...

Several Differentiable Formulas of Special Functions. Part II

The papers [11], [13], [14], [1], [8], [10], [2], [4], [7], [5], [6], [9], [15], [3], and [12] provide the notation and terminology for this paper. For simplicity, we use the following convention: x, a denote real numbers, n denotes a natural number, Z denotes an open subset of R, and f , f1, f2 denote partial functions from R to R. One can prove the following propositions: (1) If a > 0, then e...