(381e) Quantifying Topology, Gelation and Elasticity of Polymer Networks
Despite the ubiquity of applications, much of our fundamental knowledge about polymer networks is based on an assumption of ideal end-linked structure. However, polymer networks invariably possess topological defects: loops of different orders which have profound effects on network properties. Here, we develop a kinetic graph theory which demonstrates that all different orders of cyclic topologies are a universal function of a single dimensionless parameter characterizing the conditions for network formation. The theory is in excellent agreement with both experimental measurements of hydrogel loop fractions and Monte Carlo simulations without any fitting parameters. The one-to-one correspondence between the network topology and primary loop fraction demonstrates that the entire network topology is characterized by measurement of just primary loops; different cyclic defects cannot vary independently, in contrast to the intuition that the densities of all topological species are freely adjustable. Using kinetic Monte Carlo simulation, we are able to predict the gel point for real polymer networks which is in good agreement with experimental results with no fitting parameters. The critical exponents increases with the loop defects, in contrast to the prediction from both the classical Flory-Stockmayer theory and percolation theory. Furthermore, to bridge the network topology and gel elasticity, we develop a real elastic network theory (RENT) that systematically accounts for the impacts of cyclic defects. We demonstrate that small loops have vital effect on the modulus; whereas this negative impact decreases rapidly as the loop order increases, especially for networks with higher junction functionalities. RENT provides predictions that are highly consistent with experimental observations of polymer network elasticity, providing a quantitative theory of elasticity that is based on molecular details of polymer networks.