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Strong changes in bulk properties, such as modulus and viscosity, are observed near the glass transition temperature, Tg, of amorphous materials. For more than a century, intense efforts have been made to define a microscopic origin for these macroscopic changes in properties. Using transition state theory (TST), we delve into the atomic/molecular level picture of how microscopic localized unit relaxations, or “cage rattles,” evolve to macroscopic structural relaxations above Tg. Unit motion is broken down into two populations: (1) simultaneous rearrangement occurs among a critical number of units, nα, which ranges from 1 to 4, allowing a systematic classification of glass formers, GFs, that is compared to fragility; and (2) near Tg, adjacent units provide additional free volume for rearrangement, not simultaneously, but within the “primitive” lifetime, τ1, of one unit rattling in its cage. Relaxation maps illustrate how Johari–Goldstein β-relaxations stem from the rattle of nα units. We analyzed a wide variety of glassy materials and materials with a glassy response using literature data. Our four-parameter equation fits “strong” and “weak” GFs over the entire range of temperatures and also extends to other glassy systems, such as ion-transporting polymers and ferroelectric relaxors. The role of activation entropy in boosting preexponential factors to high “unphysical” apparent frequencies is discussed. Enthalpy–entropy compensation is clearly illustrated using the TST approach. 

The linear viscoelastic response, LVR, of a hydrated polyelectrolyte complex coacervate, PEC, was evaluated over a range of frequencies, temperatures, and salt concentrations. The PEC was a nearly-stoichiometric blend of a quaternary ammonium poly([3-(methacrylamido)propyl]trimethylammonium chloride), PMAPTAC, and poly(2-acrylamido-2-methyl-1-propanesulfonic acid sodium salt), PAMPS, an aliphatic sulfonate, selected because they remain fully charged over the conditions of use. Narrow molecular weight distribution polyelectrolytes were prepared using fractionation techniques. A partially deuterated version of PMAPTAC was incorporated to determine the coil radius of gyration, Rg, within PECs using small angle neutron scattering. Chain dimensions were determined to be Gaussian with a Kuhn length of 2.37 nm, which remained constant from 25 to 65 0C. The LVR for a series of matched molecular weight PECs, mostly above the entanglement threshold, exhibited crossovers of modulus versus frequency classically attributed to the reptation time, relaxation between entanglements, and the relaxation of a Kuhn length of units (the “monomer” time). The scaling for zero shear viscosity, η0, versus chain length N, was η0 ~ N3.1, in agreement with “sticky reptation” theory. The lifetime and activation energy, Ep, of a pair between polyanion and polycation repeat units, Pol+Pol-, were determined from diffusion coefficients of salt ions within the PEC. The activation energy for LVR of salt-free PECs was 2Ep, showing that the key mechanism limiting the dynamics of undoped PECs is pair exchange. An FTIR technique was used to distinguish whether SCN- acts as a counterion or a co-ion within PECs. Doping of PECs with NaSCN breaks Pol+Pol- pairing efficiently, which decreases effective crosslinking and decreases viscosity. An equation was derived that quantitatively predicts this effect. 

Pinhole-free ultrathin films of polyelectrolyte complex assembled using layer-by-layer deposition were used to evaluate electron transfer from a redox species in solution to an electrode over the distance range 1 to 9 nm. Over this thickness, the polyelectrolytes employed wet the surface and the polymer molecules flatten to less than their equilibrium size in 3-dimensions. A decay constant β for current as a function of distance of about 0.3 nm-1 placed this system in the regime expected for multistep hopping versus a one-step tunneling event. Discreet hopping sites within the films were identified as ferrocyanide ions with an equilibrium concentration of 0.032 M and an average separation of 3.7 nm. The Butler-Volmer (BV) expression for electron transfer as a function of overpotential was modified by distributing the applied voltage evenly amongst the hopping sites. This modified BV expression fit both the distance dependence and the applied potential dependence well, wherein the only freely adjustable parameter was the electron transfer coefficient. The finding that β is simply the inverse of the hopping range is consistent with previous conclusions that electrons within conjugated molecule sites are delocalized, or, for non-conjugated systems, spread over more than one repeat unit by lattice distortions