The rotational dynamics of chemically similar systems based on freely jointed and freely rotating chains are studied. The second Legendre polynomial of vectors along chain backbones is used to investigate the rotational dynamics at different length scales. In a previous study, it was demonstrated that the additional bond-angle constraint in the freely rotating case noticeably perturbs the character of the translational relaxation away from that of the freely jointed system. Here, it is shown that differences are also apparent in the two systems' rotational dynamics. The relaxation of the end-to-end vector is found to display a long time, single-exponential tail and a stretched exponential region at intermediate times. The stretching exponents beta are found to be 0.75+/-0.02 for the freely jointed case and 0.68+/-0.02 for the freely rotating case. For both system types, time-packing-fraction superposition is seen to hold on the end-to-end length scale. In addition, for both systems, the rotational relaxation times are shown to be proportional to the translational relaxation times, demonstrating that the Debye-Stokes-Einstein law holds. The second Legendre polynomial of the bond vector is used to probe relaxation behavior at short length scales. For the freely rotating case, the end-to-end relaxation times scale differently than the bond relaxation times, implying that the behavior is non-Stokes-Einstein, and that time-packing-fraction superposition does not hold across length scales for this system. For the freely jointed case, end-to-end relaxation times do scale with bond relaxation times, and both Stokes-Einstein and time-packing-fraction-across-length-scales superposition are obeyed.
Simulation results for the diffusive behavior of polymer chain/penetrant systems are analyzed. The attractive range and flexibility of simple chain molecules were varied in order to gauge the effect on dynamics. In all cases, the dimensionless diffusion coefficient, D*, is found to be a smooth, single-valued function of the packing fraction, eta. The functions D*(eta) are found to be power laws with exponents that are sensitive to both chain stiffness and particle type. For a specific system type, the D*'s for both penetrant and chain-center-of-mass extrapolate to zero at the same packing fraction, eta0. This limiting packing fraction is interpreted to be the location of the glass transition, and (eta0-eta), the distance to the glass transition.
Understanding the properties and behavior of biomembranes is fundamental to many biological processes and technologies. Microdomains in biomembranes or 'lipid rafts' are now known to be an integral part of cell signaling, vesicle formation, fusion processes, protein trafficking, and viral and toxin infection processes. Understanding how microdomains form, how they depend on membrane constituents, and how they act not only has biological implications, but also will impact Sandia's effort in development of membranes that structurally adapt to their environment in a controlled manner. To provide such understanding, we created physically-based models of biomembranes. Molecular dynamics (MD) simulations and classical density functional theory (DFT) calculations using these models were applied to phenomena such as microdomain formation, membrane fusion, pattern formation, and protein insertion. Because lipid dynamics and self-organization in membranes occur on length and time scales beyond atomistic MD, we used coarse-grained models of double tail lipid molecules that spontaneously self-assemble into bilayers. DFT provided equilibrium information on membrane structure. Experimental work was performed to further help elucidate the fundamental membrane organization principles.3 4
Process Compensated Resonance Testing (PCRT) is a nondestructive evaluation method that measures and analyzes the resonance frequencies of a component for material state characterization, defect detection and process monitoring. PCRT inspections of gas turbine engine components have demonstrated the sensitivity of resonance frequencies to manufacturing defects and in-service thermal and mechanical damage. Prior work on PCRT modeling has developed forward modeling and model inversion techniques that simulate the effects of geometry variation, material property variation, and damage on Mar-M-247 nickel-based superalloy samples. Finite element method (FEM) forward model simulations predicted the effects of variation in geometry, material properties and damage on resonance frequencies. Model inversion used measured resonance frequencies to characterize the material state of components. Parallel work developed a process for uncertainty quantification (UQ) in PCRT models and measurements. The UQ process evaluated the propagation of uncertainty from various sources, identified the most significant uncertainty sources, and enabled uncertainty mitigation to improve model and measurement accuracy. Current efforts have expanded on those developments in several areas. One-factor-at-a-time (OFAT) forward model simulations were conducted on cylindrical dog bone coupons made from Mar-M-247. The simulations predicted the resonance frequency response to variation in geometry, elastic properties, crystallographic orientation, creep strain and cracking. The OFAT studies were followed by forward model Monte Carlo simulations that predicted the effects of multiple, concurrent sources of variation and damage on resonance frequencies, allowing characterization of virtual populations and quantification of uncertainty propagation. The Monte Carlo simulation design points were used to demonstrate the generation of a virtual database of components for training PCRT inspection applications, or "sorting modules." Virtual database training sets can potentially overcome the limitations imposed by the availability of components and material states for training sets based on physical examples. Forward modeling tools and techniques were applied to titanium to simulate the effects of material variation, damage, and crystallographic texture. Forward modeling was also applied to more complex geometries, including a notional turbine blade, to demonstrate the application of modeling tools to shapes representative of gas turbine engine components. Model inversion tools and techniques have also advanced under the current effort. Prior inversion methods relied on iterative fitting to polynomial expressions for simple geometries and bulk material properties. Current efforts have demonstrated FEM-based model inversion which allows characterization of complex shapes and material states. FEM-based design spaces were generated, model inversion was carried out for surrogate modeled resonance spectra, and inversion performance was evaluated. Analysis of PCRT m...
Dynamical properties of short freely jointed and freely rotating chains are studied using molecular dynamics simulations. These results are combined with those of previous studies, and the degree of rheological complexity of the two models is assessed. New results are based on an improved analysis procedure of the rotational relaxation of the second Legendre polynomials of the end-to-end vector in terms of the Kohlrausch-Williams-Watts (KWW) function. Increased accuracy permits the variation of the KWW stretching exponent beta to be tracked over a wide range of state points. The smoothness of beta as a function of packing fraction eta is a testimony both to the accuracy of the analytical methods and the appropriateness of (eta(0)-eta) as a measure of the distance to the ideal glass transition at eta(0). Relatively direct comparison is made with experiment by viewing beta as a function of the KWW relaxation time tau(KWW). The simulation results are found to be typical of small molecular glass formers. Several manifestations of rheological complexity are considered. First, the proportionality of alpha-relaxation times is explored by the comparison of translational to rotational motion (i.e., the Debye-Stokes-Einstein relation), of motion on different length scales (i.e., the Stokes-Einstein relation), and of rotational motion at intermediate times to that at long time. Second, the range of time-temperature superposition master curve behavior is assessed. Third, the variation of beta across state points is tracked. Although no particulate model of a liquid is rigorously rheologically simple, we find freely jointed chains closely approximated this idealization, while freely rotating chains display distinctly complex dynamical features.
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