Perfect double covers with paths of length four

It is shown that for any 4-regular graph G there is a collection F of paths of length 4 such that each edge of G belongs to exactly two of the paths and each vertex of G occurs exactly twice as an endvertex of a path of F. This proves a special case of a conjecture of Bondy. © 1996 John Wiley & Sons, Inc.     

(Diazoalkyl)Phosphoranes from [4 + 1]-cycloadditions of tetrahalo-orthobenzoquinones to (diazoalkyl)phosphanes [1]

The (diazoalkyl)phosphanes 4a–e undergo [4 + 1]-cycloaddition reactions with the tetrahalo-orthobenzoquinones 5a,b to furnish the previously unknown (diazoalkyl)phosphoranes 6a–h . The structure of product 6h has been investigated by X-ray crystallography.     

Swelling and fractal heterogeneities in networks

In this paper we revisit old swelling data on polymer networks that have not been interpreted theoretically on a closed molecular basis. If the osmotic pressure of the swollen network is compared to the osmotic pressure of the corresponding uncrosslinked solution unsolved problems appear, when the relative osmotic pressure is plotted against the degree of swelling, i.e. the deformation due to swelling. A significant maximum appears which cannot be explained by any of the recently derived elastic models, such as junction constraint or other entanglement models. It is suggested in this paper that the maximum is a consequence of structural heterogeneities of fractal nature. If such fractal heterogeneities are assumed a strong maximum in the relative osmotic pressure can be reproduced. The physical reason is the different thermodynamic behavior of uncrosslinked linear chains and crosslinked self-similar (non-linear) polymers. The conclusion is supported by numerical (Monte Carlo) simulations.     

Effect of filler networking on the dynamic mechanical properties of crosslinked polymer solids

The strain amplitude dependence of the viscoelastic properties of eight different carbon blacks dispersed in two different rubbery networks is investigated and evaluated within the Cole-Cole approach for the complex elastic modulus at fixed temperature and frequency. This approach is based on the Kraus model of strain-dependent filler agglomeration-deagglomeration rates. We find a non-integer universal shape exponent of the Cole-Cole process that obviously depends only on the surrounding polymer matrix but is independent of the filler grade. The exponent can be related to the fractal dimension of the carbon black surface.     

Dynamic mechanical investigations of different substituted cellulose o-silyl ethers

In contrast to many cellulose derivatives, the cellulose O-silyl ethers with bulky side groups exhibit scarcely a change in glass transition temperature by a variation of the degree of substitution (DS) or degree of polymerization (DP) or by introducing phenyl carbamate groups for the remaining hydroxyls along the main chain. However, a substitution of these hydroxyls by flexible acetate groups lowers the glass transition temperature considerably. The secondary dispersion (relaxation) behavior is strongly influenced by the various substituents and can be correlated to specific motions of the molecules. The dynamic mechanical properties are also dependent on the kind of preconditioning of the samples.