Reversible Networks made of Star Polymers: Mean Field Treatment with Consideration of Finite Loops

Abstract We develop a theoretical approximation for the micro-structure and the properties of reversible networks made of star polymers based upon a set of suitable balance equations. Our model is tested by Monte-Carlo simulations of model systems with a controlled formation of cyclic structures. If only pending loops are considered, both irreversible and reversible networks develop a unique critical concentration $c_{\text{crit}}$ for gelation in the limit of high functionality $f\rightarrow\infty$ of the star polymers. Intra-molecular reactions are preferred in reversible networks as compared to irreversible systems at the same concentration and fraction of bound reactive groups. Odd-even effects develop at small f once pending loops are possible and these regard the critical concentration, network properties like weight fraction of gel, weight fraction of the elastically active material, and modulus. A precise consideration of loops involving $g\ge2$ junctions requires consideration of correlations between connected pairs of stars.