Order in polymeric liquids under oscillatory shear flow

Abstract

We examine the second order orientation tensor for the simplest molecular model relevant to a polymeric liquid in large-amplitude oscillatory shear (LAOS) flow, the rigid dumbbell suspension. For this, we use an approximate solution to the diffusion equation for rigid dumbbells, an expansion for the orientation distribution function truncated after the fourth power of the shear rate amplitude. We then calculate the second order orientation tensor, and then use this to calculate the order parameter tensor. We next examine the invariants of both the second order orientation tensor and the order parameter tensor. 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. Our work gives a first glimpse into macromolecular order in LAOS. Our work also provides analytical benchmarks for numerical solutions to the diffusion equation for both oscillatory and steady shear flows.

Van Gurp–Palmen relations for long-chain branching from general rigid bead-rod theory

“…By low frequency, we mean low Deborah number, that is λω < 1. In this paper, from general rigid bead-rod theory [6,5,11,12,13,14], we arrive at an interesting explanation for these descents. We explore the effects of branching along a straight chain in small-amplitude oscillatory shear flow, and thus, on the complex viscosity, and thus, on the van Gurp-Palmen plots.…”

“…INTRODUCTION Since its conception in [1,2,3], the complex viscosity has become by far the most commonly measured viscoelastic property for exploring the physics of polymeric liquids. Interpreting the measured frequency dependences of both the real and (minus) the imaginary parts of the complex viscosity in terms of polymer structure remains an important challenge [4,5,6]. Much progress along these lines has been achieved experimentally.…”

Complex viscosity of star-branched macromolecules from analytical general rigid bead-rod theory

“…(54) into Eqs. ( 14) through (16), we get the principal moments of inertia for a center-beaded planar star:…”

“…) Substituting Eq. ( 31) of [1] and [16], for general rigid bead-rod theory, for the polymer contribution to the real part of the complex viscosity we get:…”

Unveiling Temporal Nonlinear Structure–Rheology Relationships under Dynamic Shearing

“…Specific choices ought to be driven by the needs of a particular application, material, or process. For instance, numerous structure parameters have been used in the study of oscillatory shearing, including, but not limited to: microscopic yielding rate [17]; alignment factor [20,28,38]; order parameter [11,26,39,40]; degree of order [12]; degree of banding [41]; fractional extension [21]; and nematic order parameter [42]. Within our proposed framework, the structural measure could be any one of these parameters, or another measure not listed here.…”