Polymeric Liquid Behavior in Oscillatory Shear Flow
One of the great challenges in chemical engineering is to predict physical properties from molecular structure. Predicting transport properties presents special challenges, especially for macromolecular structures. This thesis focuses on the properties governing momentum transport in polymeric liquids, and specifically those properties conferring elasticity to such liquids. In the first part of this thesis, we examine the second order orientation tensor for the simplest molecular model relevant to a polymeric liquid in large amplitude oscillatory shear flow (LAOS), the rigid dumbbell suspension. From the second invariant of the order parameter tensor, we calculate the scalar, the nematic order, and examine its evolution for a polymeric liquid in LAOS. We find this nematic order, our main result, to be even. We use Lissajous figures to illustrate the roles of the Weissenberg and Deborah numbers on the evolving order in LAOS. We use the low frequency limit of our main result to arrive at an expression for the nematic order in steady shear flow. This work gives a first glimpse into macromolecular order in LAOS. In the second part of this thesis, we explore general rigid bead-rod theory, which explains polymer viscoelasticity from macromolecular orientation. By means of general rigid bead-rod theory, we relate the complex viscosity of polymeric liquids to the architecture of axisymmetric macromolecules. In this work, we explore the zero-shear and complex viscosities of 24 different axisymmetric polymer configurations. When non-dimensionalized with the zero-shear viscosity, the complex viscosity depends on the dimensionless frequency and the sole dimensionless architectural parameter, the macromolecular lopsidedness. In this work, in this way, we compare and contrast the elastic and viscous components of the complex viscosities of macromolecular chains that are straight, branched, ringed, or star-branched. We explore the effects of branch position along a straight chain, branched-chain backbone length, branched-chain branch-functionality, branch spacing along a straight chain (including pom-poms), the number of branches along a straight chain, ringed polymer perimeter, branch-functionality in planar stars, and branch dimensionality. In addition, we study diblock copolymers by exploring the effects of linear density, macromolecular length, and bead number ratio on relaxation time.