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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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DOE OSTI2024

Determining Exact RANS Operators with the Macroscopic Forcing Method (Final Report)

This report contains a compilation of key results and findings from the ACT project “Determining Exact RANS Operators with the Macroscopic Forcing Method.” The Macroscopic Forcing Method (MFM), a numerical tool for determining closure operators, is used to measure eddy diffusivity moments in Rayleigh-Taylor (RT) instability. It is first applied to low-Atwood 2D RT instability; that work is then extended to 3D RT at different finite Atwood numbers. It is found that nonlocality is important for modeling the mean scalar transport closure operator in RT mixing. Additionally, work is done to improve the statistical convergence of MFM for chaotic problems like RT mixing.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

On the design of stable, consistent, and conservative high-order methods for multi-material hydrodynamics

Obtaining stable and high-order numerical solutions for multi-material hydrodynamics is an open challenge. Although slope limiters are widely used to maintain monotonicity near discontinuities, typical limiting procedures violate closure laws at the discrete level when applied to multi-material hydrodynamics equations. Due to this, the high-order expansions of quantities related by the closure laws are no longer consistent. The commonly observed symptom of this consistency-violation is that the numerical method fails to maintain constant pressure and velocity across material interfaces. This leads to sub-optimal convergence rates for smooth multi-material problems as well. Specialized limiting procedures that satisfy consistency while maintaining conservation need to be developed for such equations. A novel procedure that re-instates consistency into slope-limited high-order discretizations applied to the multi-material hydrodynamics equations is presented here. Using simple examples, it is demonstrated that the presented method satisfies closure laws at the discrete level, while maintaining conservative properties of the high-order method. Furthermore, this procedure involves a projection step which relies on the compact basis of the underlying spatial discretization, i.e. for discontinuous schemes (viz. DG and FV) the projection is local, and does not involve global matrix solves. Comparisons with conventional approaches emphasizes the necessity of the consistent closure-law preserving limiting approach, in order to maintain design order of accuracy for smooth multi-material problems.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Scalar flux transport models for self-similar turbulent mixing

A common approach to closing turbulent species flux in multicomponent Reynolds-averaged Navier-Stokes models is to use the standard gradient diffusion approximation. While such an approach has been shown to work well when applied to many canonical turbulent mixing configurations, a gradient diffusion approach is fundamentally limited in its ability to capture complex phenomena such as countergradient transport. For this reason, complicated mixing applications may benefit by treating the turbulent diffusivity with a model transport equation in a manner analogous to second-moment momentum closure in Reynolds-stress transport models. Here, the present work explores the development and application of two different scalar flux transport (SFT) models. Self-similarity constraints are derived for these models, and they are evaluated against gradient-diffusion-based models in several one- and two-dimensional problems of turbulent mixing. It is found that the new SFT models out-perform gradient diffusion models in problems involving rapid acceleration reversal and in problems involving anisotropic transport of materials. In addition, it is found that even a hybrid-SFT approach, in which an SFT equation is utilized along with a gradient diffusion closure, provides some measure of improvement over models that transport the mass flux rather than the scalar flux.

Reynolds-averaged Navier Stokes↗
DOE OSTI2016

A FLEXIBLE NONLINEAR DIFFUSION ACCELERATION METHOD FOR THE FIRST ORDER EIGENVALUE SN EQUATIONS DISCRETIZED WITH DISCONTINUOUS FEM

This work describes a Nonlinear Diffusion Acceleration (NDA) method for the first order SN equations that discretizes both the transport equation and the associated diffusion system using discontinuous finite elements; the diffusion system is solved on a potentially coarser mesh and with a coarser energy group structure than the SN equations. The developed method differs from current methods by allowing the SN and diffusion system to be discretized with arbitrary FEM bases and by using an additive update of the SN system. The benefit of this capability is extension of the stability region to optically thicker mesh cells and stability without the necessity to underrelax the iterative algorithm. The presented method introduces the notion of consistency of the SN and diffusion solutions and derives suitable definitions of the cross sections, drift vectors, and element face closures. The NDA equations are solved using a Picard iteration scheme. Numerical results are presented for the C5G7 benchmark problem highlighting the effectiveness of the methods when deployed with the diffusion system discretized on the same mesh as the SN system. Additional results are presented for cases where the diffusion system features a coarser mesh, coarser energy group structure, or both, demonstrating its stability and effectiveness in these cases. It is observed that the effectiveness of the NDA method reduces when reducing the resolution of the associated diffusion system.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Multi-scale calculation based on dual domain material point method combined with molecular dynamics

This dissertation combines the dual domain material point method (DDMP) with molecular dynamics (MD) in an attempt to create a multi-scale numerical method to simulate materials undergoing large deformations with high strain rates. In these types of problems, the material is often in a thermodynamically non-equilibrium state, and conventional constitutive relations are often not available. In this method, the closure quantities, such as stress, at each material point are calculated from a MD simulation of a group of atoms surrounding the material point. Rather than restricting the multi-scale simulation in a small spatial region, such as phase interfaces, or crack tips, this multi-scale method can be used to consider non-equilibrium thermodynamic e ects in a macroscopic domain. This method takes advantage that the material points only communicate with mesh nodes, not among themselves; therefore MD simulations for material points can be performed independently in parallel. First, using a one-dimensional shock problem as an example, the numerical properties of the original material point method (MPM), the generalized interpolation material point (GIMP) method, the convected particle domain interpolation (CPDI) method, and the DDMP method are investigated. Among these methods, only the DDMP method converges as the number of particles increases, but the large number of particles needed for convergence makes the method very expensive especially in our multi-scale method where we calculate stress in each material point using MD simulation. To improve DDMP, the sub-point method is introduced in this dissertation, which provides high quality numerical solutions with a very small number of particles. The multi-scale method based on DDMP with sub-points is successfully implemented for a one dimensional problem of shock wave propagation in a cerium crystal. The MD simulation to calculate stress in each material point is performed in GPU using CUDA to accelerate the computation. The numerical properties of the multiscale method are investigated as well as the results from this multi-scale calculation are compared of particles needed for convergence makes the method very expensive especially in our multi-scale method where we calculate stress in each material point using MD simulation. To improve DDMP, the sub-point method is introduced in this dissertation, which provides high quality numerical solutions with a very small number of particles. The multi-scale method based on DDMP with sub-points is successfully implemented for a one dimensional problem of shock wave propagation in a cerium crystal. The MD simulation to calculate stress in each material point is performed in GPU using CUDA to accelerate the computation. The numerical properties of the multiscale method are investigated as well as the results from this multi-scale calculation are compared with direct MD simulation results to demonstrate the feasibility of the method. Also, the multi-scale method is applied for a two dimensional problem of jet formation around copper notch under a strong impact.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2018

Discontinuous Finite Element Quasidiffusion Methods

Here in this paper, two-level methods for solving transport problems in one-dimensional slab geometry based on the quasi-diffusion (QD) method are developed. A linear discontinuous finite element method (LDFEM) is derived for the spatial discretization of the low-order QD (LOQD) equations. It involves special interface conditions at the cell edges based on the idea of QD boundary conditions (BCs). We consider different kinds of QD BCs to formulate the necessary cell-interface conditions. We develop two-level methods with independent discretization of the high-order transport equation and LOQD equations, where the transport equation is discretized using the method of characteristics and the LDFEM is applied to the LOQD equations. We also formulate closures that lead to the discretization consistent with a LDFEM discretization of the transport equation. The proposed methods are studied by means of test problems formulated with the method of manufactured solutions. Numerical experiments are presented demonstrating the performance of the proposed methods. Lastly, we also show that the method with independent discretization has the asymptotic diffusion limit.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Robust 3D multi-material hydrodynamics using discontinuous Galerkin methods

A high-order discontinuous Galerkin (DG) method is presented for nonequilibrium multi-material (m ≥ 2) flow with sharp interfaces. Material interfaces are reconstructed using the algebraic THINC approach, resulting in a sharp interface resolution. The system assumes stiff velocity relaxation and pressure nonequilibrium. The presented DG method uses Dubiner's orthogonal basis functions on tetrahedral elements. This results in a unique combination of sharp multimaterial interfaces and high-order accurate solutions in smooth single-material regions. A novel shock indicator based on the interface conservation condition is introduced to mark regions with discontinuities. Slope limiting techniques are applied only in these regions so that nonphysical oscillations are eliminated while maintaining high-order accuracy in smooth regions. A local projection is applied on the limited solution to ensure discrete closure law preservation. The effectiveness of this novel limiting strategy is demonstrated for complex three-dimensional multi-material problems, where robustness of the method is critical. The presented numerical problems demonstrate that more accurate and efficient multi-material solutions can be obtained by the DG method, as compared to second-order finite volume methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

REYNO: A Reactive Hydrodynamics Modeling Suite

REYNO is a Python library that is primarily designed as a platform for the agile development and testing of novel reactive flow models. Equations of state and multi-step rate laws can be implemented using the provided class hierarchy with different thermodynamic closure conditions. The library includes a one-dimensional Lagrangian hydrodynamic solver to simulate multi-material reactive or inert problems in planar, cylindrical, or spherical coordinates. Custom time-dependent boundary conditions are also available for problems such as ramp compression. This document describes the different numerical methods and algorithms that are included in REYNO.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Shock waves simulated using the dual domain material point method combined with molecular dynamics

Here in this work we combine the dual domain material point method with molecular dynamics in an attempt to create a multiscale numerical method to simulate materials undergoing large deformations with high strain rates. In these types of problems, the material is often in a thermodynamically nonequilibrium state, and conventional constitutive relations or equations of state are often not available. In this method, the closure quantities, such as stress, at each material point are calculated from a molecular dynamics simulation of a group of atoms surrounding the material point. Rather than restricting the multiscale simulation in a small spatial region, such as phase interfaces, or crack tips, this multiscale method can be used to consider nonequilibrium thermodynamic effects in a macroscopic domain. This method takes the advantage that the material points only communicate with mesh nodes, not among themselves; therefore molecular dynamics simulations for material points can be performed independently in parallel. The dual domain material point method is chosen for this multiscale method because it can be used in history dependent problems with large deformation without generating numerical noise as material points move across cells, and also because of its convergence and conservation properties. In conclusion, to demonstrate the feasibility and accuracy of this method, we compare the results of a shock wave propagation in a cerium crystal calculated using the direct molecular dynamics simulation with the results from this combined multiscale calculation.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Verification and Validation of High Explosive Reactive Burn Models Implemented in LANL's EAP and LAP Code Base (FY2020 L2 Milestone MRT 7129) [Slides]

Advanced reactive burn models enable phenomena to be modeled that aren’t possible with programmed burn. Programmed burn propagates a burn front at a prescribed speed from a prescribed initiation point. Reactive burn uses the hydro variables (pressure, temperature, etc.) to determine when, how rapidly, and to what extent a zone detonates. This enables a completely new set of problems to be simulated. Our goal in this milestone has been to improve the usability of reactive burn modes. Thus, the closure criteria are: 1. Perform code and solution verification of the reactive burn models using appropriate solutions and simplified HE setups. 2. Perform validation assessments using small-scale experiments. 3. Evaluate sensitivities and quantify uncertainties due to model form variations and mesh dependencies.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗
DOE OSTI2018

NIMROD Development AND Applications for Advanced Simulations of Tokamak Plasmas

Operation in a regime of zero off-normal events is an important goal for ITER, and after that DEMO. Edge Localized Modes (ELMs) are off-normal events of particular concern due to their ubiquity in the highest performing discharges and their localized energy deposition on vessel walls. To avoid damage from these events, ITER has invested in costly coils in addition to exploring other mitigation techniques. A more attractive approach is to find an operational regime that has the requisite high performance while avoiding ELMs entirely. DIII-D experimentalists have found such a regime, wherein the ELMs are prevented from occurring by the existence of a saturated instability. Although this regime is attractive, how this saturated instability occurs and how to extrapolate to ITER is not well understood. NIMROD is well suited for studying this mode, and significant progress has already been made in modeling the equilibria that give rise to this instability. Another off-normal event of concern to ITER is the sawtooth mode in the presence of energetic particles. These modes are ubiquitous in near-steady-state tokamaks, and their behavior in the presence of the energetic particles that will be found in burning plasma experiments is poorly understood. The internal kink is notorious for requiring all extended MHD effects (two-fluid, closures, vacuum regime, energetic particles) in a production level simulation. NIMROD has matured to the point where it can now address this problem, though significant expertise in the MHD physics, numerical algorithms, and large-scale computation will be required. The expertise of Tech-X in attacking the most difficult NIMROD problems has already resulted in significant improvements to the NIMROD code that benefit the larger fusion community, and we expect further improvements as we attack these challenging problems. To maximize the community benefits, Tech-X provided community outreach and code management efforts.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2019

A regularized deconvolution method for turbulent closure modeling in implicitly filtered large-eddy simulation

Turbulence closure models that are based on a regularized deconvolution method (RDM) are proposed for application to implicitly filtered Large-Eddy Simulation (LES). This method reconstructs sub-grid scale contributions by approximately recovering filtered quantities through an optimization approach. Physical principles on the boundedness and conservation of reconstructed quantities are preserved by constraining the optimization problem. Further, to account for effects of scales that are not resolved in implicitly filtered LES, a reconstruction method is proposed that combines sub-grid projection and energy-similarity to enrich unresolved scales. With this method, closure models are developed for turbulent scalar fluxes and turbulence–chemistry interaction that are intrinsically consistent with the LES formulation. These closure models are evaluated in application to a piloted turbulent jet flame with inhomogeneous inlet composition, in which combustion is represented by a two-scalar manifold model. The RDM-formulation is benchmarked against simulations obtained using a presumed PDF method and eddy diffusivity closure model. In partially-premixed flame regions, it is observed that RDM improves the prediction of turbulent mixing, and faster grid convergence is observed for results with RDM compared to simulations employing a presumed PDF method.

42 ENGINEERING↗
DOE OSTI2023

Point-particle drag, lift, and torque closure models using machine learning: Hierarchical approach and interpretability

Developing deterministic neighborhood-informed point-particle closure models using machine learning has garnered interest recently from the dispersed multiphase flow community. The robustness of neural models for this complex multibody problem is hindered by the availability of particle-resolved data. Here, the present work addresses this unavoidable limitation of data paucity by implementing two strategies: (1) by using a rotation and reflection equivariant neural network and (2) by pursuing a physics-based hierarchical machine learning approach. The resulting machine-learned models are observed to achieve a maximum accuracy of 85% and 96% in the prediction of neighbor-induced force and torque fluctuations, respectively, for a wide range of Reynolds number and volume fraction conditions considered. Furthermore, we pursue force and torque network architectures that provide universal prediction spanning a wide range of Reynolds number (0.25 ≤ Re ≤250) and particle volume fraction (0 ≤ φ ≤0.4). The hierarchical nature of the approach enables improved prediction of quantities such as streamwise torque, by going beyond binary interactions to include trinary interactions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Reduced order models for thermal radiative transfer problems based on moment equations and data-driven approximations of the Eddington tensor

Here a new group of structure and asymptotic preserving reduced-order models (ROMs) for multidimensional nonlinear thermal radiative transfer (TRT) problems is presented. They are formulated by means of the nonlinear projective approach and data compression techniques. The nonlinear projection is applied to the Boltzmann transport equation (BTE) to derive a hierarchy of low-order moment equations. Approximation of the Eddington tensor that provides exact closure for the system of moment equations is found with projection-based data-driven methodologies. These include the (i) proper orthogonal decomposition (POD), (ii) dynamic mode decomposition (DMD) and (iii) a variant of the DMD. A parameterization is derived for this ROM for the temperature of radiation incoming to the problem domain (the radiation drive temperature). This parameterization is informed from results of a dimensionless study of the TRT problem. Analysis of the ROMs is performed on the classical Fleck-Cummings TRT multigroup test problem in 2D geometry with a radiation-driven Marshak wave. Numerical results are presented to demonstrate the performance of these ROMs for the simulation of evolving radiation and heat waves. Results show these models to be sufficiently accurate for practical computations with rather low-rank representations of the Eddington tensor. As the rank of the approximation is increased, the errors of solutions generated by the ROMs gradually decreases.

42 ENGINEERING↗
DOE OSTI2017

Proposed Semi-Analytic Benchmark for Coupled Neutronics/Thermal-Hydraulics Feedback in Multiphysics Simulations

The past decade has seen considerable advancements in multiscale and multiphysics simulations that account for nonlinear effects of feedback between different physical processes within a single calculation. One area of particular interest has been multiphysics simulations that include both neutronics and thermal-hydraulics effects to accurately model the thermal feedback effects present in nuclear reactors. During this time, many groups have successfully modeled thermal feedback effects by coupling a variety of different types of neutron transport and thermal-hydraulic solvers together. However, formal verification and validation of these coupled code systems has proven challenging due to a lack of benchmark problems with well-characterized reference solutions. One approach is to confirm gross energy balance using bulk coolant properties (outlet temperature/enthalpy) for code verification purposes. Alternatively, code-to-code comparisons of results for a predefined reference/challenge problem have been used to establish reasonability of local results (neutron flux, heating, enthalpy rise) for various implementations, for example the VERA Core Physics Progression Problems. While community solutions are valuable for assessing the relative performance and fidelity of different implementations, they are not guaranteed to provide a measure of the absolute accuracy of a given implementation. In fact, these code-to-code comparisons can give a false sense of confidence by masking the effects of errors or approximations that are common to all of the solution methods tested. This is a particular concern when many methods derive from a common approach, such as Picard iteration. To this end, an analytical benchmark would be very valuable for verifying individual coupled physics implementations, as well as for providing a formal assessment of algorithm accuracy and sensitivity to model approximations such as mesh size and number of convergence iterations. However, creation of an analytical benchmark is difficult due to the complex nature of the eigenvalue form of the neutron transport equation (which does not permit a simple analytical solution for non-trivial cases) as well as the variety of different empirical closure relationships used in thermal-hydraulic modeling. In this paper we propose a benchmark for coupled neutronics/thermal-hydraulics simulations. The proposed benchmark overcomes the challenges associated with a multiphysics benchmark problem by using a fixed-source (rather than eigenvalue) formulation of the neutron transport equation and limiting fluid properties to the single-phase regime where the density and temperature of the coolant are related to enthalpy by a known relationship, while still preserving significant nuclear/thermal feedback effects within the simplified problem. The new benchmark is easy to simulate using existing coupled physics implementations, and allows for a direct comparison with a reference solution, as provided in this summary.

42 ENGINEERING↗
DOE OSTI2016

Final Technical Report

We have constructed and analyzed a series of idealized models of tropical convection interacting with large-scale circulations, with 25-50km resolution and with 1-2km cloud resolving resolution to set the stage for rigorous tests of convection closure schemes in high resolution global climate models. Much of the focus has been on the climatology of tropical cyclogenesis in rotating systems and the related problem of the spontaneous aggregation of convection in non-rotating systems. The PI (Held) will be delivering the honorary Bjerknes lecture at the Fall 2016 AGU meeting in December on this work. We have also provided new analyses of long-standing issues related to the interaction between convection and the large-scale circulation: Kelvin waves in the upper troposphere and lower stratosphere, water vapor transport into the stratosphere, and upper tropospheric temperature trends. The results of these analyses help to improve our understanding of processes, and provide tests for future high resolution global modeling. Our final goal of testing new convections schemes in next-generation global atmospheric models at GFDL has been left for future work due to the complexity of the idealized model results meant as tests for these models uncovered in this work and to computational resource limitations. 11 papers have been published with support from this grant, 2 are in review, and another major summary paper is in preparation.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2017

Internal Nozzle Flow Simulations of Gasoline-Like Fuels under Diesel Operating Conditions

Spray formation in internal combustion engines with direct injection is strictly correlated with internal nozzle flow characteristics, which are in turn influenced by fuel physical properties and injector needle motion. This paper pre-sents a series of 3D simulations that model the in-nozzle flow in a 5-hole mini-sac diesel injector. Two gasoline-like naphtha fuels, namely full-range and light naphtha, were tested under operating conditions typical of diesel applica-tions and were compared with n-dodecane, selected from a palette used as diesel surrogates. Validated methodolo-gies from our previous work were employed to account for realistic needle motion. The multi-phase nature of the problem was described by the mixture model assumption with the Volume of Fluid method. Cavitation effects were included by means of the Homogeneous Relaxation Model and turbulence closure was achieved with the Standard k-ε model in an Unsteady Reynolds-Averaged Navier-Stokes formulation. The results revealed that injector perfor-mance and propensity to cavitation are influenced by the fuel properties. Analyses of several physical quantities were carried out to highlight the fuel-to-fuel differences in terms of mass flow rate, discharge coefficients, and fuel vapor volume fraction inside the orifices. A series of parametric investigations was also performed to assess the fuel response to varied fuel injection temperature, injection pressure, and cross-sectional orifice area. For all cases, the strict correlation between cavitation magnitude and saturation pressure was confirmed. Owing to their higher volatil-ity, the two gasoline-like fuels were characterized by higher cavitation across all the simulated conditions. Occur-rence of cavitation was mostly found at the needle seat and at the orifice inlets during the injection event’s transient, when very small gaps exist between the needle and its seat. This behavior tended to disappear at maximum needle lift, where cavitation was absent for all fuels. Differences in mass flow rate between the naphtha fuels and n-dodecane were measured and ascribed to the different densities of the three fuels. Nevertheless, they were found to be smaller than expected, owing to the lower viscosity of the gasoline-like fuels. This beneficial influence of the lower viscosity was shown to be less effective at higher temperature, where the relative viscosity differences de-creased.

Torelli, R.↗
DOE OSTI2024

Polymer Macrocycles: A novel topology to control dynamics of rubbery materials (Final Report)

One of the current challenges in polymer physics and engineering is to understand the behavior of circular macromolecules. Though such molecules have been made by dilute solution ring closure methods in the past, such procedures have been limited to relatively small, unentangled rings as well as to small sample quantities. Initial studies were also hampered by issues surrounding purity of the rings, though this problem has been somewhat overcome by the use of liquid chromatography at critical conditions (LCCC) methods that separate rings and linear chains. Furthermore, in spite of the continued progress a full understanding of ring dynamics remains elusive. The present work has addressed multiple aspects of the behavior of ring molecules by using a novel synthetic route: reversible radical recombination redox polymerization (R3P) to produce poly(3,6-dioxa-1,8-octanedithiol) (PolyDODT) molecules. The synthesis conditions were chosen to produce linear (LDODT), cyclic (RDODT) and linear-cyclic mixtures (LRDODT) in order to investigate dilute solution and rheological responses of the materials. Importantly, the R3P synthesis makes larger quantities and higher molecular weights than do the dilute solution ring closure methods and also has the potential to be scaled to industrial quantities, thus becoming commercializable. We emphasize two important outcomes of the work. The first is that the rheological investigation shows that very large molecular weight the PolyDODT rings permitted the investigation of ring dynamics from glassy towards terminal flow for molecular sizes corresponding to approximately 300 entanglements of the linear counterpart. At the same time, these very large sized rings could be diluted in a solvent in order to reduce the molecular entanglement density to less than unity. The results demonstrate that ring viscosity follows a Rouse-like linear dependence on molecular weight or entanglement number to approximately 15 entanglements. This range of "Rouse-like" response is greater than what was achieved in all prior works where synthesis conditions have limited the molecular sizes achievable. After the entanglement number $Z_w$ increases beyond approximately 15, we find that the viscosity-molecular weight scaling undergoes a rapid change from the Rouse-like $η\sim{Z}^1_w$ to a very strong power-law scaling that is approximately $η\sim{Z}^{5.8}_w$. This aspect of the work strongly suggests that prior investigations on highly pure rings have invariably been performed on unentangled systems simply because ring molecules have very high entanglement thresholds. The results are further supported by plateau modulus measurements that show that in the "Rouse-like" viscosity regime, for the RDODT samples there is a corresponding lack of a rubbery entanglement plateau and once entanglement coupling is seen, the rubbery plateau also appears in the dynamic modulus data. Furthermore, upon appropriate scaling, we show that the unentangled polyDODT rings (i.e., the diluted high molecular weight rings) show virtually identical dynamics (upon appropriate scaling to account for the chain dilutions) to the dynamics of similarly unentangled LCCC fractionated polystyrene rings.

36 MATERIALS SCIENCE↗