A Generalized Mechano-statistical Transient Network Model for Unravelling the Network Topology and Elasticity of Hydrophobically Associating Multiblock Copolymers in Aqueous Solutions

In this contribution, we unravel the transient network topology and elasticity of micellar networks formed by hydrophobically associating multiblock copolymers in aqueous solutions. Unlike studies on conventional triblock copolymers bearing hydrophobic blocks as end groups, our research focuses on alternating poly(ethylene oxide) (PEO) and poly(propylene oxide) (PPO) multiblock copolymers having multiple hydrophobic PPO blocks along the chain. We adopt a combinatorics approach to extend and generalize the mechano-statistical transient network model developed by Annable et al. for telechelic triblock copolymers [ Journal of Rheology, 1993, 37, 695] to multiblock copolymers. The model allows one to predict the concentration dependent elasticity of networks formed by multiblock copolymers with known molecular characteristics by using knowledge of the micellar network microstructure. The spatial distribution of the hydrophobic nodes is inferred from Small-Angle X-ray Scattering (SAXS) by converting the structure factor to the radial distribution function. The number of closely neighboring micellar cores between which an elastic bridge can be formed (nm) is calculated by spherical integration of the radial distribution function up to a distance of the radius of gyration of an intermediate soluble PEO block. Using the evolution of nm with concentration as an input for the model, the predictions show good agreement with experimental elasticity data, as inferred from the plateau modulus in linear shear rheology. The network evolves from loop-dominated, poorly elastic with cross-linking nodes with low functionality at low concentrations to bridge-dominated, highly elastic with higher node functionalities at more elevated concentrations. It is anticipated that our generalized mechano-statistical transient network model can also be used for equally spaced, multisticker associating polymers forming networks by multifunctional interactions other than micellar aggregation.