Article ID Journal Published Year Pages File Type
5191878 Polymer 2005 7 Pages PDF
Abstract

The random networks that are formed in typical elastomer cure or cross-linking reactions obey the statistics of local chemical reactions, but it is the long-range, and not the local, properties of the structures that determine their desirable material properties. Properties such as the gel point and cycle rank are determined by the global structure of a network. Forging a connection between local statistics and global structure has been a challenging problem. Tracking the evolution of random structures during the course of cross-linking reactions has been the object of a considerable body of theoretical research. However, much of this research has ignored the space-filling requirements of the resulting statistically branched structures. As especially emphasized by Gordon and co-workers, the chemical structures that are formed in typical cross-linking reactions can be understood within the context of graph theory. However, a pure mathematical graph has no metrical information, which means that any information on the embedding of the graph in three-space will be impossible to infer from the graph alone. Here it is shown that one can introduce physically meaningful metrical information on the graph structure by imposing a spatial distribution of cross-links and chains from the beginning. This ensures that the resulting statistical networks are capable of being embedded in the space of that generates the distribution.

Related Topics
Physical Sciences and Engineering Chemistry Organic Chemistry
Authors
,