Crosslinking index, molecular weight distribution and rubber equilibrium shear modulus during polyfunctional crosslinking of existing polymer. Part 5. Primary polymer with a discrete distribution of the molecular weights

In previous papers, theoretical and experimental results were presented about a statistical theory concerning network formation by means of polyfunctional crosslinking of already existing polymers, having a uniform, a Flory, a Schulz-Flory, a cumulative Flory or a cumulative Schulz-Flory distribution of the molecular weights. In the present paper, network parameters for a crosslinking process of primary polymers with a discrete distribution of the molecular weights will be calculated. Furthermore results of a hypothetical crosslinking process of primary polymers with bimodal distributions consisting of monodisperse polymers with molecular weights of 20 and 400 kg/mol are presented. Relationships are derived for the equilibrium sheer modulus, the sol fraction, the network fraction, the fraction of dangling ends, the weight and number average crosslinking indices and the molar masses in between the crosslinks. Apparent anomalies in network parameters in the bimodal systems can be explained. These anomalies might be responsible for the anomalous behaviour observed in the mechanical properties of vulcanised rubbers prepared from polymers with a bimodal distribution of the molecular weights. (C) 2000 Elsevier Science B.V. All rights reserved.