Viscoelasticity and extensional rheology of model Cayley-tree polymers of different generations

We investigated the rheology of a series of anionically synthesized, model symmetric Cayley tree poly(methylmethacrylates) having from 1 to 4 generations of identical molar mass. The hierarchical relaxation of the different generations was assessed from the linear data by accounting for both the plateau modulus and the characteristic relaxation times. Using a tube-model time-marching analysis based on the concept of hierarchy of motion, we described quantitatively the frequency spectra without adjustable parameters. We also performed uniaxial extensional measurements using the Sentmanat extensional rheometer fixture. The samples tested exhibited significant strain hardening compared to their linear analogs at lower and intermediate Hencky strain rates. This hardening was more pronounced with increasing number of generations, hence branch points. The extracted effective steady extensional viscosity was found to scale with the extensional rate with a power exponent of about -0.5, in agreement with earlier findings with linear polystyrenes. We also extended the time-marching-algorithm to predict the extensional behavior of these polymers using the conceptual framework developed recently for pom-pom and Cayley-tree polymers. Comparison between theoretical and experimental results was satisfactory when the maximum stretch which can be supported by the molecule was estimated by accounting for the recently proposed inter-chain pressure effects. (C) 2010 The Society of Rheology. [DOI: 10.1122/1.3368724]