A MONTE-CARLO STUDY OF RING FORMATION AND MOLECULAR CONFIGURATIONS DURING STEP-GROWTH ON A LATTICE IN 3 DIMENSIONS

The formation of ring and chain molecules during an irreversible step growth polymerization has been modeled on a three-dimensional 26-choice cubic lattice, and examined by the Monte-Carlo method. The limiting value of the extent of reaction was found to be p = 0.98333 (+/-0.00002) in this static simulation, when all neighboring pairs of monomers and end groups had reacted mutually to form bonds. Then the mean number of lattice sites within a molecule was 60, which may correspond to a molecular weight of 30 000 for a real polymer. In the simulation the number fraction of molecules found as rings was 0.291 (+/-0.007), but the weight fraction was much smaller-0.0395 (+/-0.0016). Ring number distribution functions were found to be closely fitted by a power law, the exponents decreasing as the reaction proceeded, and larger rings then were able to accumulate at a greater rate. The limiting value of the ring distribution exponent was -2.68 (+/-0.02), a number slightly greater than the appropriate equilibrium distribution value. The chain number distribution functions were perturbed from the conventional Flory expression, particularly toward the end of the process, mainly because the small chains were depleted by the ring formation process. The weight distribution function for all products displays a broad feature for chains and a sharp feature for rings at lower molecular weights. Polydispersities of the distribution functions for rings, for chains, and for both species together were all found to be greater than 2.00. The configurational characteristics of the chains and rings produced by this novel process have been examined and found to lie between self-avoiding walk and the random flight models. They tend toward patterns close to Flory Theta conditions as the reaction proceeds.