Nanostructure-Dependent Marcus-Type Correlation of the Shape Recovery Rate and the Young’s Modulus in Shape Memory Polymer Aerogels

Thermodynamic–kinetic relationships are not uncommon, but rigorous correlations are rare. On the basis of the parabolic free-energy profiles of elastic deformation, a generalized Marcus-type thermodynamic–kinetic relationship was identified between the shape recovery rate, Rt(N), and the elastic modulus, E, in poly(isocyanurate-urethane) shape memory aerogels. The latter were prepared with mixtures of diethylene, triethylene, and tetraethylene glycol and an aliphatic triisocyanate. Synthetic conditions were selected using a statistical design of experiments method. Microstructures obtained in each formulation could be put into two groups, one consisting of micron-size particles connected with large necks and a second one classified as bicontinuous. The two types of microstructures could be explained consistently by spinodal decomposition involving early versus late phase separation relative to the gel point. Irrespective of microstructure, all samples showed a shape memory effect with shape fixity and shape recovery ratios close to 100%. Larger variations (0.35–0.71) in the overall figure of merit, the fill factor, were traced to a variability in the shape recovery rates, Rt(N), which in turn were related to the microstructure. Materials with bicontinuous microstructures were stiffer and showed slower recovery rates. Thereby, using the elastic modulus, E, as a proxy for microstructure, the correlation of Rt(N) with E was traced to a relationship between the activation barrier for shape recovery, ΔA#, and the specific energy of deformation, (reorganization energy, λ), which in turn is proportional to the elastic modulus. Data were fitted well (R2 = 0.92) by the derived equations. The inverse correlation between Rt(N) and the elastic modulus, E, provides a means for qualitative predictability of the shape recovery rates, the fill factors, and the overall quality of the shape memory effect.