Application of binary interaction theory to linear and nonlinear rheology of star-branched polymers

The binary interaction (BI) theory recently developed by David W. Mead, Ronald G. Larson, and Masao Doi (1998) is based on two fundamental postulates strongly supported by experimental data: (1) stress-optic rule, (2) binary interaction principle. The BI theory is general and in principle applies to all entangled flexible polymers regardless of molecular architecture. Three parameters are required in the BI theory to establish the length and time scales for the system: the plateau modulus, the entanglement molecular weight, and the Rouse relaxation time scale.; This thesis focuses on the first application of the BI theory to polymers with long-chain branches (LCB): star polymers. A mathematically simplified star model is derived analytically by performing a boundary layer analysis on the full BI model, resulting in an entanglement flux balance between star tip fluctuational penetration inward and convective constraint release (CCR)/convection outward from the star core. The simplified BI star theory for small deformations is compared with the well-established Ball-McLeish model. Juxtaposition of both simulations shows essentially quantitative equivalence.; The empirical Cox-Merz viscosity rule for star-branched polymers is analytically derived from the simplified BI star model. The underlying physical basis of the validity of the Cox-Merz relationship for fast, nonlinear flows is a direct consequence of the combined effect of CCR and convection.; Simulations from the simplified BI star model agree well with experimental dynamic moduli and flow curves of melts/concentrated solutions of various polymer species from literature data with no adjustable parameters. Flow curve crossover phenomena and subsequent merger reported for matched star and linear polymers are quantitatively predicted by the BI theory. The flow curve crossover of a matched set of star and linear polymers represents a transition of material response from Brownian-motion-governed linear viscoelasticity to CCR/convection-dominated nonlinear rheology. The merger of star and linear flow curves at high shear rates further supports the hypothesis that the high-deformation-rate portion of the shear flow curve is independent of molecular weight, molecular weight distribution, and molecular architecture.