Topologically Frustrated Dynamical State of Polymers Trapped in Ideal Uniform Tetra-PEG Gels

When very long polymers are trapped into multiple entropic traps created by the meshes of host hydrogels, our recent discovery shows that the guest polymer chains are entropically frozen into a nondiffusive topologically frustrated dynamical state (TFDS) at intermediate confinements. Outside the confinement boundaries of the TFDS, the guest molecules diffuse, whereas in the TFDS regime, the center of mass diffusion coefficient is essentially zero due to the macromolecule being localized into long-lived metastable states with extreme free-energy barriers for the escape of the macromolecule. However, the segmental dynamics of the macromolecule is active with hierarchical dynamics. A key assumption to explain this hierarchical segmental dynamics of the macromolecule in the TFDS regime has been that the number of monomers in the various entropic traps is polydisperse. The validity of this assumption is tested in the present paper by experimentally investigating the segmental dynamics using the ideal tetra-PEG hydrogel as the host matrix and sodium poly-(styrene sulfonate) as the guest macromolecule. We find that all features of TFDS previously observed using poly-(acrylamide-co-acrylate) hydrogels with the polydisperse distribution of mesh size are recovered in the present system of uniform mesh size as well. Thus, the present study, with the chemical details different from those of our previous systems, adds credence to the universality of the phenomenon of TFDS. Furthermore, the present finding suggests that the polydispersity in the number of monomers in the various entropic traps must arise from conformational fluctuations emanating from the local exchange dynamics of segments among neighboring meshes.