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All sources NASA NTRS DOE OSTI

DOE OSTI2023

Uniqueness of relaxation times determined by dielectric spectroscopy

Dielectric spectroscopy is extremely powerful to study molecular dynamics, because of the very broad frequency range. Often multiple processes superimpose resulting in spectra that expand over several orders of magnitude, with some of the contributions partially hidden. For illustration, we selected two examples, (i) normal mode of high molar mass polymers partially hidden by conductivity and polarization and (ii) contour length fluctuations partially hidden by reptation using the well-studied polyisoprene melts as example. The intuitive approach to describe experimental spectra and to extract relaxation times is the addition of two or more model functions. Here, we use the empirical Havriliak-Negami function to illustrate the ambiguity of the extracted relaxation time, despite an excellent agreement of the fit with experimental data. We show that there are an infinite number of solutions for which a perfect description of experimental data can be achieved. However, a simple mathematical relationship indicates uniqueness of the pairs of the relaxation strength and relaxation time. Sacrificing the absolute value of the relaxation time enables to find the temperature dependence of the parameters with a high accuracy. For the specific cases studied here, the time temperature superposition (TTS) is very useful to confirm the principle. However, the derivation is not based on a specific temperature dependence, hence, independent from the TTS. We compare new and traditional approaches and find the same trend for the temperature dependence. The important advantage of the new technology is the knowledge of the accuracy of the relaxation times. Relaxation times determined from data for which the peak is clearly visible are the same within the experimental accuracy for traditional and new technology. However, for data where a dominant process hides the peak, substantial deviations can be observed. Finally, we conclude that the new approach is particularly helpful for cases in which relaxation times need to be determined without having access to the associated peak position.

36 MATERIALS SCIENCE↗

NASA NTRS1993

Stress relaxation of low pressure plasma-sprayed NiCrAlY alloys

The stress relaxation behavior of three NiCrAlY alloys that are commonly used as bond coats for thermal barrier coatings (TBCs) has been directly measured. The relaxation study was conducted at temperatures of 800-1000 C and over a wide range of stresses. It was established that all three bond coat alloys relaxed quite rapidly at temperatures of 900 C and above. Since the upper use temperatures for bond coats in gas turbine engines are between 900 and 1000 C, bond coat relaxation is expected to occur in service. Therefore, relaxation of the bond coat has the potential to affect TBC life. Furthermore, the relaxation differences observed between the three alloys offers a possible explanation for the differences in TBC life observed for these bond coats. While bond coat relaxation is expected to occur for a TBC in service, the mechanism for a relaxation effect on TBC life, if it exists, is yet to be determined.

Brindley, W. J.↗

NASA NTRS1993

Stress relaxation of low pressure plasma-sprayed NiCrAlY alloys

Brindley, W. J.↗

NASA NTRS1987

Wall relaxation in growing stems: comparison of four species and assessment of measurement techniques

This study was carried out to develop improved methods for measuring in-vivo stress relaxation of growing tissues and to compare relaxation in the stems of four different species. When water uptake by growing tissue is prevented, in-vivo stress relaxation occurs because continued wall loosening reduces wall stress and cell turgor pressure. With this procedure one may measure the yield threshold for growth (Y), the turgor pressure in excess of the yield threshold (P-Y), and the physiological wall extensibility (phi). Three relaxation techniques proved useful: "turgor-relaxation", "balance-pressure" and "pressure-block". In the turgor-relaxation method, water is withheld from growing tissue and the reduction in turgor is measured directly with the pressure probe. This technique gives absolute values for P and Y, but requires tissue excision. In the balance-pressure technique, the excised growing region is sealed in a pressure chamber, and the subsequent reduction in water potential is measured as the applied pressure needed to return xylem sap to the cut surface. This method is simple, but only measures (P-Y), not the individual values of P and Y. In the pressure-block technique, the growing tissue is sealed into a pressure chamber, growth is monitored continuously, and just sufficient pressure is applied to the chamber to block growth. The method gives high-resolution kinetics of relaxation and does not require tissue excision, but only measures (P-Y). The three methods gave similar results when applied to the growing stems of pea (Pisum sativum L.), cucumber (Cucumis sativus L.), soybean (Glycine max (L.) Merr.) and zucchini (Curcubita pepo L.) seedlings. Values for (P-Y) averaged between 1.4 and 2.7 bar, depending on species. Yield thresholds averaged between 1.3 and 3.0 bar. Compared with the other methods, relaxation by pressure-block was faster and exhibited dynamic changes in wall-yielding properties. The two pressure-chamber methods were also used to measure the internal water-potential gradient (between the xylem and the epidermis) which drives water uptake for growth. For the four species it was small, between 0.3 and 0.6 bar, and so did not limit growth substantially.

NASA Program Space Biology↗

NASA NTRS2022

Employing Relaxed Smoothness Constraints on Imaginary Part of Refractive Index in AERONET Aerosol Retrieval Algorithm

In the Aerosol Robotic Network (AERONET) retrieval algorithm, smoothness constraints on the imaginary part of the refractive index provide control of retrieved spectral dependence of aerosol absorption by preventing the inversion code from fitting the noise in optical measurements and thus avoiding unrealistic oscillations of retrievals with wavelength. The history of implementation of the smoothness constraints in the AERONET retrieval algorithm is discussed. It is shown that the latest version of the smoothness constraints on the imaginary part of refractive index, termed standard and employed by Version 3 of the retrieval algorithm, should be modified to account for strong variability of light absorption by brown-carbon-containing aerosols in UV through mid-visible parts of the solar spectrum. In Version 3 strong spectral constraints were imposed at high values of the Ångström exponent (440–870 nm) since black carbon was assumed to be the primary absorber, while the constraints became increasingly relaxed as aerosol exponent deceased to allow for wavelength dependence of absorption for dust aerosols. The new version of the smoothness constraints on the imaginary part of the refractive index assigns different weights to different pairs of wavelengths, which are the same for all values of the Ångström exponent. For example, in the case of four-wavelength input, the weights assigned to short-wavelength pairs (440–675, 675–870 nm) are small so that smoothness constraints do not suppress natural spectral variability of the imaginary part of the refractive index. At longer wavelengths (870–1020 nm), however, the weight is 10 times higher to provide additional constraints on the imaginary part of refractive index retrievals of aerosols with a high Ångström exponent due to low sensitivity to aerosol absorption for longer channels at relatively low aerosol optical depths. The effect of applying the new version of smoothness constraints, termed relaxed, on retrievals of single-scattering albedo is analyzed for case studies of different aerosol types: black- and brown-carbon-containing fine mode aerosols, mineral dust coarse mode aerosols, and urban industrial fine mode aerosol. It is shown that for brown-carbon-containing aerosols employing the relaxed smoothness constraints resulted in significant reduction in retrieved single-scattering albedo and spectral residual errors (compared to standard) at the short wavelengths. For example, biomass burning smoke cases showed a reduction in single-scattering albedo and spectral residual error at 380 nm of ∼ 0.033 and ∼ 17 %, respectively, for the Rexburg site and ∼ 0.04 and ∼ 12.7 % for the Rimrock site, both AERONET sites in Idaho, USA. For a site with very high levels of black-carbon-containing aerosols (Mongu, Zambia), the effect of modification in the smoothness constraints was minor. For mineral dust aerosols at small Ångström exponent values (Mezaira site, UAE), the spectral constraint on the imaginary part of the refractive index was already relaxed in Version 3; therefore the new relaxed constraint results in minimal change. In the case of weakly absorbing urban industrial aerosols at the GSFC site, there are significant changes in retrieved single-scattering albedo using relaxed assumption, especially reductions at longer wavelengths: ∼ 0.016 and ∼ 0.02 at 875 and 1020 nm, respectively, for 440 nm aerosol optical depth (AOD) ∼ 0.3. The modification of smoothness constraints on the imaginary part of the refractive index has a minor effect on retrievals of other aerosol parameters such as the real part of the refractive index and parameters of the aerosol size distribution. The implementation of the relaxed smoothness constraints on the imaginary part of the refractive index in the next version of the AERONET inversion algorithm will produce significant impacts at some sites in short wavelength channels (380 and 440 nm) for some biomass burning smoke cases with significant brown carbon content and possibly in mid-visible channels (500 and 675 nm) to near-infrared channels (870 to 1020 nm) for some urban industrial aerosol types. However, most differences in single-scattering albedo retrievals between those applying the new relaxed constraint and the standard constraint will be within the uncertainty of the single-scattering albedo retrievals, depending on the level of aerosol optical depth, Ångström exponent, brown carbon content and wavelength.

Aliaksandr Siniuk↗

DOE OSTI2025

Molecular Dynamics Simulation and Theoretical Analysis of Structural Relaxation, Bond Exchange Dynamics, and Glass Transition in Vitrimers

Vitrimers are a class of polymer networks featuring dynamic covalent cross-links that can undergo associative bond exchange. There has been recent interest in these materials due to their promise as recyclable thermosets or self-healing polymers because of the ability of vitrimer networks to rearrange at the molecular level and undergo macroscopic flow. However, the practical use of these materials often occurs in the supercooled regime or glassy state, where the implications of dynamic bonds are complicated by the interplay between slow activated segmental dynamics, cross-link (i.e., bond-exchange) kinetics, and ultimately material properties. Here, in this paper, we combine coarse-grained molecular dynamics simulation and microscopic statistical mechanical theory to understand how cross-linking kinetics affect material dynamics and how this couples to segmental relaxation of the polymeric network strands across a spectrum of length and time scales, especially in the supercooled regime. We characterize the Kuhn segmental alpha relaxation time and bond exchange time for vitrimer systems across various cross-link densities, temperatures, and bond exchange rates. Simulation and theory both exhibit a bending-up behavior for bond exchange time upon cooling, suggesting a coupling between bond exchange dynamics and segmental relaxation that intensifies with faster bond exchange kinetics. We also found bond exchange dynamics have an impact on Kuhn segment alpha relaxation time, which is most significant at higher cross-link densities. Both these effects are most prominent when the bond exchange time is similar to the Kuhn segment alpha relaxation time, and the resulting coupling of these two relaxation processes is tied to both the probability of a free end to find a bonded pair and the time scale of the constraints imposed by the dynamic cross-links. This relationship is reflected by a cross-link dependence of a theoretical parameter which represents the quantitative degree of coupling between bond exchange and segmental dynamics. Overall, the combination of simulation and theory clarifies the intricate interaction between bond kinetics and segmental relaxation and demonstrates the ability to provide molecular-level insights into vitrimer dynamics over a wide temperature range.

dynamic relaxation↗

DOE OSTI2022

Entropy–Preserving and Entropy–Stable Relaxation IMEX and Multirate Time–Stepping Methods

In this work, we propose entropy-preserving and entropy-stable partitioned Runge–Kutta (RK) methods. In particular, we extend the explicit relaxation Runge–Kutta methods to IMEX–RK methods and a class of explicit second-order multirate methods for stiff problems arising from scale-separable or grid-induced stiffness in a system. The proposed approaches not only mitigate system stiffness but also fully support entropy-preserving and entropy-stability properties at a discrete level. The key idea of the relaxation approach is to adjust the step completion with a relaxation parameter so that the time-adjusted solution satisfies the entropy condition at a discrete level. The relaxation parameter is computed by solving a scalar nonlinear equation at each timestep in general; however, as for a quadratic entropy function, we theoretically derive the explicit form of the relaxation parameter and numerically confirm that the relaxation parameter works the Burgers equation. Several numerical results for ordinary differential equations and the Burgers equation are presented to demonstrate the entropy-conserving/stable behavior of these methods. We also compare the relaxation approach and the incremental direction technique for the Burgers equation with and without a limiter in the presence of shocks.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

Strain Relaxation and Relative Defect Density with Thickness in MBE-Grown Ge 0.85 Sn 0.15 on Ge(001)

Germanium–tin (GeSn) alloys are emerging as promising materials for mid-infrared optoelectronics and silicon-compatible photonic devices, owing to their tunable direct bandgap. However, the growth of high-quality GeSn films with high Sn content remains challenging due to strain-induced defect formation. In this study, we investigate the role of film thickness on strain-induced relaxation, defect density, and Sn segregation. A series of five samples with varying thicknesses and ∼15% Sn-containing GeSn layers were grown, ranging from the critical thickness for strain relaxation to the onset of Sn segregation. All GeSn samples were analyzed using X-ray diffraction reciprocal space mapping (XRD-RSM) to explore the evolution of strain-induced relaxation as a function of thickness. Photoluminescence measurements reveal that increasing the GeSn thickness enhances strain relaxation while reducing defect-related emission, indicating a decrease in effective defect density prior to reaching the threshold thickness of GeSn layer. At a thickness of ∼150 nm, the GeSn layer shows the onset of Sn segregation, evident in the XRD-RSM spectrum, marking the threshold thickness for Sn segregation. This work defines an effective growth window in terms of thickness (35 to 150 nm) for fabricating relaxed, defect-suppressed GeSn layers with 15% Sn content. These findings emphasize the crucial role of thickness control in balancing strain relaxation and defect suppression, advancing the fabrication of high-quality, high Sn-content relaxed GeSn using molecular beam epitaxy.

Defects↗

DOE OSTI2021

Pressure Effects on the Relaxation of an Excited Ethane Molecule in High-Pressure Bath Gases

Here, we use molecular dynamics to calculate the rotational and vibrational energy relaxation of C 2 H 6 in Ar, Kr, and Xe bath gases over a pressure range of 10 to 400 atm and at temperatures of 300 K and 800 K. The C 2 H 6 is instantaneously excited by 80 kcal/mol randomly distributed into both vibrational and rotational modes. The computed relaxation rates show little sensitivity to the identity of the noble gas in the bath. Vibrational relaxation rates show a non-linear pressure dependence at 300 K. At 800 K the reduced range of bath gas densities covered by the range of pressures do not yet show any non-linearity in the pressure dependence. Rotational relaxation is characterized with two relaxation rates. The slower rate is comparable to the vibrational relaxation rate. The faster rate has a linear pressure dependence at 300 K but an irregular, nonlinear pressure dependence at 800 K. To understand this, a model was developed based on approximating the periodic box used in the molecular dynamics simulations by an equal-volume collection of cubes where each cube is sized to allow only single occupancy by the noble gas or the molecule. Combinatorial statistics then leads to a pressure and temperature dependent analytic distribution of the bath gas species the molecule encounters in a collision. This distribution, the dissociation energy of molecule/bath gas complexes and bath gas clusters, and the computed energy release per collision combine to show that only at 300 K is the energy release sufficient to dissociate likely complexes and clusters. This suggests that persistent and pressure-dependent clusters and complexes at 800 K may be responsible for the non-linear pressure dependence of rotational relaxation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

A Spectrochemical Series for Electron Spin Relaxation

Controlling the rate of electron spin relaxation in paramagnetic molecules is essential for contemporary applications in molecular magnetism and quantum information science. However, the physical mechanisms of spin relaxation remain incompletely understood, and new spectroscopic observables play an important role in evaluating spin dynamics mechanisms and structure–property relationships. Here, we use cryogenic magnetic circular dichroism (MCD) spectroscopy and pulse electron paramagnetic resonance (EPR) in tandem to examine the impact of ligand field (d–d) excited states on spin relaxation rates. We employ a broad scope of square-planar Cu(II) compounds with varying ligand field strength, including CuS 4 , CuN 4 , CuN 2 O 2 , and CuO 4 first coordination spheres. An unexpectedly strong correlation exists between spin relaxation rates and the average d–d excitation energy (R 2 = 0.97). The relaxation rate trends as the inverse 11th power of the excited-state energies, whereas simplified theoretical models predict only an inverse second power dependence. These experimental results directly implicate ligand field excited states as playing a critical role in the ground-state spin relaxation mechanism. Furthermore, ligand field strength is revealed to be a particularly powerful design principle for spin dynamics, enabling formation of a spectrochemical series for spin relaxation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Relaxation dynamics of deformed polymer nanocomposites as revealed by small-angle scattering and rheology

Here, the relaxation dynamics of polystyrene (PS)/silica nanocomposites after a large step deformation are studied by a combination of small-angle scattering techniques and rheology. Small-angle X-ray scattering measurements and rheology show clear signatures of nanoparticle aggregation that enhances the mechanical properties of the polymer nanocomposites (PNCs) in the linear viscoelastic regime and during the initial phase of stress relaxation along with accelerated relaxation dynamics. Small-angle neutron scattering experiments under the zero-average-contrast condition reveal, however, smaller structural anisotropy in the PNCs than that in the neat polymer matrix, as well as accelerated anisotropy relaxation. In addition, the degrees of anisotropy reduction and relaxation dynamics acceleration increase with increasing nanoparticle loading. These results are in sharp contrast to the prevailing viewpoint of enhanced molecular deformation as the main mechanism for the mechanical enhancement in PNCs. Furthermore, the observed acceleration of stress relaxation and reduction in structural anisotropy point to two types of nonlinear effects in the relaxation dynamics of PNCs at large deformation.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Viscoelastic relaxation and topological fluctuations in glass-forming liquids

In this study, a method for characterizing the topological fluctuations in liquids is proposed. This approach exploits the concept of the weighted gyration tensor of a collection of particles and permits the definition of a local configurational unit (LCU). The first principal axis of the gyration tensor serves as the director of the LCU, which can be tracked and analyzed by molecular dynamics simulations. Analysis of moderately supercooled Kob–Andersen mixtures suggests that orientational relaxation of the LCU closely follows viscoelastic relaxation and exhibits a two-stage behavior. The slow relaxing component of the LCU corresponds to the structural, Maxwellian mechanical relaxation. Additionally, it is found that the mean curvature of the LCUs is approximately zero at the Maxwell relaxation time with the Gaussian curvature being negative. This observation implies that structural relaxation occurs when the configurationally stable and destabilized regions interpenetrate each other in a bicontinuous manner. Finally, the mean and Gaussian curvatures of the LCUs can serve as reduced variables for the shear stress correlation, providing a compelling proof of the close connection between viscoelastic relaxation and topological fluctuations in glass-forming liquids.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Kinetic relaxation and nucleation of Bose stars in self-interacting wave dark matter

We revisit kinetic relaxation and soliton/boson star nucleation in fuzzy scalar dark matter featuring short-ranged self-interactions H int = − λ | ψ | 4 / 2 m 2 , alongside gravitational self-interactions. We map out the full curve of nucleation timescale for both repulsive ( λ < 0 ) and attractive ( λ > 0 ) short-ranged self-interaction strength and in doing so reveal two new points. Firstly, besides the two usual terms, ∝ G 2 and ∝ λ 2 , in the total relaxation rate Γ relax , there is an additional cross term ∝ G λ arising due to interference between gravitational and short-ranged self-interaction scattering amplitudes. This yields a critical repulsive interaction strength λ cr ≃ − 2 π G m 2 / v 0 2 , at which the relaxation rate is smallest and serves as the transition point between typical net attractive self-interaction ( λ ≳ λ cr ) and net repulsive self-interaction ( − λ ≳ − λ cr ). Secondly, while in the net attractive regime, nucleation timescale is similar to inverse relaxation timescale τ nuc ∼ Γ relax − 1 ; in the net repulsive regime, nucleation occurs at a delayed time τ nuc ∼ ( λ / λ cr ) Γ relax − 1 . We confirm our analytical understanding by performing 3D field simulations with varying average mass density ρ ¯ , box size L and grid size N . Published by the American Physical Society 2024

Astronomy & Astrophysics↗

NASA NTRS1972

Biaxial stress relaxation in glassy polymers - Polymethylmethacrylate.

Biaxial stress relaxation studies were performed on glassy polymethylmethacrylate in combined torsion-tension strain fields using a specially designed apparatus with exceptionally high stiffness and low cross talk between the torsional and tensile load measuring transducers. It was found that at low strain levels uniaxial tension relaxation is slower than pure torsion relaxation; tensile-component relaxation rates are unaffected by the level of torsional strain; torsional-component relaxation rates decrease as tensile strain is increased; uniaxial tension relaxation rates approach the pure torsion rates at higher strains (about 2%). A phenomenological treatment is presented which shows that relaxation rates can be coupled to the strain fields in which they are observed and yet be consistent with the concepts of linear viscoelasticity and the Boltzmann superposition integral.

Sternstein, S. S.↗

NASA NTRS1977

Aerodynamic sound in a relaxing medium

A theory of aerodynamic sound propagation, when inhomogeneities characterized by a relaxation process are present in both the source and propagation region, is formulated. The details of the relaxation process need not be specified at the outset, although the relaxation process is characterized by a relaxation time and by an equilibrium and a frozen sound speed in a propagation region which is otherwise in equilibrium. Propagation is described in terms of a D'Alembertian characterized by the frozen sound speed relaxing toward one characterized by the equilibrium sound speed, while the source is interpreted in terms of a frozen Lighthill stress tensor relaxing toward the equilibrium stress tensor. An appropriate Green's function for the three-dimensional relaxing wave propagation operator is used to construct an exact integral for the aerodynamic sound. The sound generated far from the source is then estimated in terms of the aerodynamic sound source.

Liu, J. T. C.↗

NASA NTRS1987

Finite element models of non-Newtonian crater relaxation

The effects of a non-Newtonian rheology on the profiles of relaxing craters (such as those seen on the surfaces of the icy Galilean and Saturnian satellites) were studied. Two-dimensional finite element simulations of non-Newtonian viscous flow were performed, and the results were compared with those associated with Newtonian rheology. Viscous relaxation of craters in a non-Newtonian medium was significantly different from that in a Newtonian medium. Crater rims are observed to relax at a more rapid rate in a non-Newtonian region as a result of the movement of the low viscosity region to underneath the crater rim after the initial relaxation of the bowl. Significant differences are also found when central depth is plotted as a function of time. For a Newtonian medium, crater relaxation is exponential in form. In contrast, non-Newtonian crater relaxation is initially rapid, in response to the large initial stresses and small viscosities; however, as stresses decrease, this relaxation becomes extremely gradual.

Thomas, Paul J.↗

NASA NTRS1988

Relaxation of impact basins on icy satellites

The problem of relaxation of very large impact craters on icy satellites is addressed and the extent to which such studies can help place constraints on the nature of such satellite interiors is investigated. Very general calculations aimed at understanding the nature of relaxation of large impact structures, including the directions, relaxation velocities, and stress levels, are presented. The dependence of relaxation on such factors as silicate core size and viscosity gradients in the ice is examined. The general results are used to address whether comparing the current morphology of impact basins to estimates of their original shape will yield an understanding of the thermal and mechanical structure of the interiors of the icy satellites. It is found that the relaxation rates derived from models of satellite interiors can provide constraints on viscous layer thicknesses. High thermal gradients can permit substantial relaxation even in thin viscous layers. Finally, the constraints on the internal structure of Tethys arising from the extremely relaxed state of the Odysseus basin and the existence of Ithaca Chasma are discussed.

Thomas, Paul J.↗

NASA NTRS1989

Crater relaxation on Ganymede - Implications for ice rheology

Controversy has existed over whether or not viscous relaxation is an important process on the icy satellites. Previous models involved large extrapolations of Newtonian flow laws for ice, whereas ice is known to exhibit non-Newtonian behavior. Recently, the flow law parameters for ice at the appropriate temperatures and stresses have been measured. Numerical modeling of the viscous relaxation of basins on Ganymede using these parameters has given implausibly short relaxation times. However, this model treated ice as a purely viscous substance, so that no elastic lithosphere could develop near the surface. Here, ice is treated as a Maxwell visco-elastic material and numerically model the relaxation of basins on Ganymede. It is found that realistic Young's moduli lead to little relaxation occurring in basins even 4.0 Ga after their formation. Further, it is shown that within braod limits the near surface temperature gradient has little effect on this result. Finally, examination of the distribution of Maxwell times in the vicinity of the crater shows that most viscous relaxation occurs early in the basin's history when stresses are high, and thus Maxwell time is short. As stresses are relieved, the Maxwell time becomes long, and relaxation essentially ceases.

Hillgren, Valerie J.↗