Abstract
The formation of networks of various types has been simulated by using a physically realistic model that allows for intramolecular reactions to take place, thus forming loops of any size. The shortcomings of the kinetic approach, where systems are composed of functional groups that are selected at random without spatial constraint, and of the percolation method where an ordered arrangement is assured, are avoided. The reported simulations of the end-linking process illustrate the influence of intramolecular reactions on gel-sol distributions. Rings form in both phases, gel and sol. Neglect of the presence of cyclics in the sol underestimates the extent of the crosslinking reaction by several percent. On the other hand, in the gel fraction, loop defects are formed as the result of short-ranged intramolecular reactions. These defects do not vanish at complete conversion, and as a result they reduce the cycle rank in proportion to the number of primary chains reacting to form loops. The higher the molecular weight of the prepolymer chains, the closer to the perfect network the formed structure will be. Diffusion effects play an increasingly important role as the degree of polymerization goes up, so that reactions involving the end-linking of very long chains may never come into completion. The simulation results show that sol structures are highly dependent upon the functionality of the crosslinking agent used in the end-linking process. The intramolecular reactions which occur in substantial proportion at higher degrees of crosslinking necessarily favor formation of cyclics. In the case of tetrafunctional networks, this results in a bimodal molecular weight distribution of the sol constituents. It is important to realize that, according to the results of our simulation, networks obtained near complete conversions are very close to perfect. In the case of the random networks cured by high-energy radiation, we show that their properties are quite different when compared to those resulting from other crosslinking techniques. The defect structures account for a large portion of the mass of the networks and their mechanical moduli, as represented by the cycle rank per chain, are substantially smaller than the model networks. Results on both poly(dimethylsiloxane) and polyethylene show that chain scission is rather important. It should be kept in mind that primary chain branching and the molecular weight distribution affect the behavior of a polymeric system when it is exposed to radiation. The fact that the algorithm gives reliable results for more than one polymeric system shows the flexibility of the simulation program; it also proves that the assumptions used to build the model form a realistic basis for future work. A number of upgrades are being incorporated in the model at the present time. Instead of relying on the Gaussian distribution of chain ends, a more realistic model incorporating Flory's rotational isomeric state theory is being used to generate the prepolymer chains. The simulations are being applied to a number of different systems, including polyoxypropylene- and polyoxyethylene-based urethane networks. In addition, filled networks and sulfur vulcanization systems are slated to be explored in order to try to understand their rather complicated behavior. Computer simulations prove to be a powerful tool to study network structure problems. Questions about the detailed structure of the elastomer, sol-gel transitions, and the mechanical properties can be given reliable answers. Wherever there is sufficient knowledge of the reaction system and enough experimental data for comparison, computer simulations can provide information of unprecedented depth and accuracy.
LIFO-search: A min–max theorem and a searching game for cycle-rank and tree-depth
