A central goal of the polymer rheological community for a number of years has been the connection of polymer melt dynamics at different length scales. The interplay of entropic elasticity and entanglement constraints at the molecular level [Doi and Edwards (1986); McLeish (2002)] led to the subtle and emergent non-Newtonian fluid properties at length scales that average over many molecular interactions. Furthermore, these local fluid properties determine, in principle, the stress and velocity fields in a polymer melt constrained by the complex geometries of processlike flows. Until now, however, there have been few attempts to link molecularly based model calculations across these length scales in the context of experimental data.

Classically, polymer melts have been rheologically characterized, then modeled by parameter fitting one of a family of phenomenological differential or integral constitutive equations [Rajagopalan et al. (1993); Baaijens et al. (1997)]. This approach suffers from the drawback that models created without reference to molecular physics may fail to represent even qualitative features of the material behavior. This is especially true of long chain branched melts [McLeish and Larson (1999)]. In this case, the recognition that branch points enormously increase the stretch relaxation times of polymer chains within their "tubes" produced a new constitutive equation. This approach has been very successful in accounting for the rheology of both model H-shaped monodisperse materials [McLeish and Larson (1999)] and polydisperse melts of low density polyethylene [Verbeeten et al. (2001)]. It successfully predicted a qualitatively new feature in the outflow of highly branched melts when coupled to a flow solver [Lee et al. (2001)].

Other "micro-macro" approaches have attempted to couple stochastic simulations of the coarse-grained molecular dynamics within the finite elements of a flow simulation [Laso and Öttinger (1993); Peters et al. (2000)]. This is, of course, the ideal multilevel approach, but with current levels of computing power, it is not possible to achieve sufficient noise reduction by local ensemble averaging while also addressing the demands of a complex flow field calculation.

Both the molecular constitutive equation and molecular simulation approaches to the problem of multiscale modeling of polymer melts have been constrained by a further problem. The most natural subjects of the model in either case are monodisperse chains that do not require the addressing of complications that arise from the mutual interactions of high and low molecular weight fractions in the distribution. However, although it is possible to synthesize such materials by anionic methods in sufficient quantities for rheological measurements in viscometric flows, the large amounts usually required for complex flow studies have not before been accessible. This is true even for monodisperse linear melts, let alone the more exacting architectures of star, H, and comb molecules [McLeish (2002)].

In this article, we begin to address this missing link by scaling up the anionic synthesis of linear melts of polystyrene (PS) and polybutadiene (PB), and simultaneously scaling down a representative complex flow. The former will supply quantities of polymer of the order of tens of grams, rather than grams. The latter, based on the "Multipass Rheometer" of the Cambridge group [Mackley et al. (1995)] permits an effectively 4/1 or 11/1 constriction flow. The complex flow, including two sets of re-entrant corners, reversing extensional profile, and transient flow structure, may be analyzed by stress birefringence and pressure difference, but requires only material quantities of this order.

At the same time, we will seek to model the nonlinear rheology and flow properties of this melt by calling on the most recent advances in molecular modeling of entangled polymers. The first versions of the "tube model" dealt restrictively with the two processes of reptation, which diffuses molecules within their entanglement field of tubelike constraints, and retraction, which maintains a constant topological path length for the chains [Doi and Edwards (1986)]. Since then, additional molecular processes have been identified that are essential to a quantitative account of the dynamics of linear entangled chains as probed by both rheology [Likhtman and McLeish (2002a)] and neutron scattering [Wischnewski et al. (2002)]. Contour length fluctuation (CLF) permits the extremities of chains to relax faster than the reptation time, while constraint release (CR) links the relaxation of the tube constraint itself to the reptation and CLF of neighboring chains [Likhtman and McLeish (2002)]. In nonlinear deformations, convective CR (CCR) adds to the rate of reconfiguration of the tubes, while stretch suppresses tube reconfiguration and enhances values of stress above the plateau modulus [Mead et al. (1998); Ianniruberto and Marrucci (2001)]. This removes the unphysical maximum in shear stress with shear rate that followed from the original approximations of the tube model. Additionally, it permits the prediction of scattering patterns in quantitative agreement with data on strongly sheared entangled melt [Milner et al. (2001); Bent et al. (2003); Graham et al. (2003)]. The level of sophistication, at which all of these molecular processes are presently dealt with in the most detailed accounts of viscometric flows, leads to a level of formalism that would be prohibitive in computations of complex flows. Fortunately, approximations to the full constitutive behavior of models that account for reptation, CLF, CCR, and chain stretch, can be cast in simple, if unfamiliar, forms [Likhtman and Graham (2003)]. This will be the basis of our numerical calculations.

In the next section, we detail the experimental procedures in synthesis and characterization of our materials, the laboratory rheological testing, and the complex flow rheology. In Sec. III, we briefly review the theoretical derivation of the molecular constitutive equations employed to analyze both laboratory viscometric and complex flows. In Sec. IV, we present the experimental phenomena exhibited by monodisperse melts in a constriction flow for the first time, and compare with the model calculations.