A large number of industrial processes involve chemical reactions between reactive groups which are attached to high molecular weight flexible polymers. Examples includes: (1) the production of linear chains by radical and condensation polymerization; (2) the manufacture of rubber elastomers and gels by cross-linking long polymer chains either chemically or through the action of high energy radiation; and (3) reactive processing methods producing high strength composites. While small molecule reactions also occur in these situations, the main difficulty concerns the macromolecular reactions since the ability of reactive species to meet is determined by the dynamical and static properties of the polymers to which they are attached. The objective of this research is to determine a fundamental mechanism for these processes by calculating reaction rates for the case when two long unbranched polymers each carrying one active group located somewhere along their respective backbones, such that if ever the two groups are brought to within a certain distance of one another ( the "capture radius") they will react with certain probability per unit time. The two polymer coils must diffuse through space and then penetrate one another significantly before reaction may proceed (typical polymer coil and capture radius dimensions are 300 Angstroms and 10 Angstroms respectively). The PI is planning to develop a molecular theory of reaction rates between high molecular weight polymers in solution and to predict reactions rates as a function of polymer molecular weight and concentration for polymers in dilute, semi-dilute (where polymers overlap strongly giving rise to some concentration effects) and dense solutions (melt). The reaction rates are dependent on concentration because if the polymers are dilute in a monomeric background, the coils diffuse relatively quickly through space but strongly repel one another on close encounter, while if the chains are dense (in a melt) and long, such repulsions are screened but diffusion is drastically slowed down by entanglements. An additional outcome expected of this research is that it will increase knowledge about the nature of an equilibrium system to which irreversible reactions are added (polymer reactions are an example of a non-equilibrium thermal system).
