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At least 55 records · Page 3

Effect of CMAS viscosity on the infiltration depth in thermal barrier coatings of different microstructures

Calcium magnesium aluminum silicate (CMAS) is one of the leading concerns for the gas turbine industry. The effects of CMAS viscosity and the coating microstructure on CMAS infiltration depth were explored by conducting a time dependent interaction study. Three CMAS compositions were used from literature, and their viscosities predicted through FactSage viscosity module were drastically different. The interaction was carried out on three different TBCs synthesized using the solution precursor plasma spray process (SPPS): two of the TBCs were made of yttrium aluminum garnet (YAG) having different microstructures that promote different modes of CMAS infiltration, and one TBC was made of gadolinium zirconate (GZO). All samples had stress relieving vertical cracks and different intensities of horizontally banded porosity, (inter pass boundaries IPBs). A concentration of 100 mg/cm 2 of CMAS was applied on the TBCs which were then subjected to a 5-minute interaction at 1300 °C. Samples were analyzed using scanning electron microscopy (SEM), electron dispersive X-ray spectroscopy (EDXS), and transmission electron microscopy (TEM). Low viscosity CMAS readily penetrated the TBCs while more viscous CMAS showed less penetration. The depth of CMAS infiltration depended on the coating microstructure. In the YAG with IPBs, the CMAS spread horizontally in the IPBs before infiltrating deeper, resulting in reduced infiltration depth compared to other samples in spite of having wider vertical cracks. TEM and EDXS analysis were performed to investigate the phases present in the CMAS-TBC interaction region in YAG. Two regions were chosen, the top TBC surface in direct contact with the sea of CMAS, and the region at the CMAS penetration ended within the coating. Finally, the results showed that no secondary phases like apatite were observed in YAG, thus it can be concluded that the arrest of CMAS happened solely because of CMAS viscosity and the short infiltration time.

36 MATERIALS SCIENCE↗

The Sensitivity of Joint Inversions of Seismic and Geodynamic Data to Mantle Viscosity

Seismic tomography has revealed the existence of large-scale velocity heterogeneities in the mantle. The interpretation of seismic velocity anomalies in terms of temperature and chemical composition is nonunique. We use geodynamic observations including gravity, plate motions, dynamic topography, and excess ellipticity of the core-mantle boundary combined with seismic observations to investigate the thermo-chemical structure of the mantle through joint inversions. An outstanding issue, however, is the physical connection between mantle density anomalies and the surface geodynamic observations, which requires knowledge of the mantle viscosity structure. Here we perform joint inversions assuming different viscosity profiles and examine the dependence of the results on the viscosity. We first assume that mantle heterogeneity is due to thermal variations, which places a constraint on the relation between seismic velocity and density, and we subsequently relax the constraint to allow for potential nonthermal effects. In all of our joint inversions, a nonthermal origin of density anomalies is required to explain the geodynamic data, though the amount varies with the assumed viscosity structure. A common observation is a high-density chemical signal in the center of the large low-shear-velocity provinces at the base of the mantle resulting in a near neutral or slightly dense overall buoyancy there. Using the derived density models and their corresponding viscosity profiles, we also calculate instantaneous mantle flow fields. The predicted flow fields derived from joint inversions are generally similar but are quite different from flow fields using density models derived from a posteriori scaling of pure seismic tomography models.

58 GEOSCIENCES↗

Estimating viscosity of individual substrate-deposited particles from measurements of their height-to-width ratios

Airborne particles alter the radiative forcing of climate and have further consequences on air visibility, atmospheric chemistry, and human health. Recent studies reported the existence of highly viscous semisolid and even solid amorphous organic aerosol (OA) particles. Particle viscosity has an impact on the heterogeneous chemistry, gas-particle partitioning, and ice nucleation properties. Consequently, variations in particle viscosity must be considered when predicting the atmospheric impact of OA. Here, in this work, we use scanning electron microscopy (SEM) and scanning transmission X-ray microscopy (STXM) to estimate the viscosity of individual particles deposited on substrates based on their characteristic height-to-width ratios, which are affected by changes in morphology upon deposition. The height-to-width ratios obtained from SEM and STXM exhibit a strong correlation, demonstrating that both imaging approaches can be applied separately for viscosity assessment of the substrate-deposited particles. While these metrics are largely qualitative, this method enables rapid assessment of particle viscosity ranges, distinguishing between semisolid (>10 10 Pa·s), viscous (10 4– 10 8 Pa·s), and liquid (10°–10 1 Pa·s) particles within ensembles of ambient particles collected for microscopy studies.

54 ENVIRONMENTAL SCIENCES↗

Projecting the likely importance of weak-interaction-driven bulk viscosity in neutron star mergers

ABSTRACT In this work, we estimate how much bulk viscosity driven by Urca processes is likely to affect the gravitational wave signal of a neutron star coalescence. In the late inspiral, we show that bulk viscosity affects the binding energy at fourth post-Newtonian order. Even though this effect is enhanced by the square of the gravitational compactness, the coefficient of bulk viscosity is likely too small to lead to observable effects in the waveform during the late inspiral, when only considering the orbital motion itself. In the post-merger, however, the characteristic time-scales and spatial scales are different, potentially leading to the opposite conclusion. We post-process data from a state-of-the-art equal-mass binary neutron star merger simulation to estimate the effects of bulk viscosity (which was not included in the simulation itself). In that scenario, we find that bulk viscosity can reach high values in regions of the merger. We compute several estimates of how much it might directly affect the global dynamics of the considered merger scenario, and find that it could become significant. Even larger effects could arise in different merger scenarios or in simulations that include non-linear effects. This assessment is reinforced by a quantitative comparison with relativistic heavy-ion collisions where such effects have been explored extensively.

79 ASTRONOMY AND ASTROPHYSICS↗

The Viscosity and Atomic Structure of Volatile-Bearing Melilititic Melts at High Pressure and Temperature and the Transport of Deep Carbon

Understanding the viscosity of mantle-derived magmas is needed to model their migration mechanisms and ascent rate from the source rock to the surface. High pressure–temperature experimental data are now available on the viscosity of synthetic melts, pure carbonatitic to carbonate–silicate compositions, anhydrous basalts, dacites and rhyolites. However, the viscosity of volatile-bearing melilititic melts, among the most plausible carriers of deep carbon, has not been investigated. In this study, we experimentally determined the viscosity of synthetic liquids with ~31 and ~39 wt% SiO 2 , 1.60 and 1.42 wt% CO 2 and 5.7 and 1 wt% H 2 O, respectively, at pressures from 1 to 4.7 GPa and temperatures between 1265 and 1755 °C, using the falling-sphere technique combined with in situ X-ray radiography. Our results show viscosities between 0.1044 and 2.1221 Pa·s, with a clear dependence on temperature and SiO 2 content. The atomic structure of both melt compositions was also determined at high pressure and temperature, using in situ multi-angle energy-dispersive X-ray diffraction supported by ex situ microFTIR and microRaman spectroscopic measurements. Our results yield evidence that the T–T and T–O (T = Si,Al) interatomic distances of ultrabasic melts are higher than those for basaltic melts known from similar recent studies. Based on our experimental data, melilititic melts are expected to migrate at a rate ~from 2 to 57 km·yr -1 in the present-day or the Archaean mantle, respectively.

36 MATERIALS SCIENCE↗

Viscosity-temperature relation based on the evolution of medium-range structures of silica

The viscosity of glass is the most important technological property to glass manufactures and various applications. Practically, finding an accurate equation to express the glass viscosity behavior in the entire glass transition temperature range is tremendously challenge because it spans more than ten orders of magnitude. After a brief review of existing empirical viscosity equations, this work focuses on the correlating silica viscosity behavior with the evolution of glass medium-range structure, based on the recently proposed nanoflake model. From this new model, a new equation is constructed, which correctly describes the Arrhenius-type behavior of silica viscosity η above the melting temperature Tm, and non-Arrhenius-type behavior from Tm to a critical temperature Tc. At temperature lower than Tc, the equation predicts Arrhenius-type behavior again for the viscous flow with increased activation energy. The new equation agrees with experimental data in the entire temperature spanned from extremely high to extremely low. Furthermore, the application of the new equation is shown to extend to sodium silicate glasses as well.

36 MATERIALS SCIENCE↗

Revisiting the validity of eddy viscosity models for predicting airflow over water waves

In this study, we revisit the validity of eddy viscosity models for predicting wave-induced airflow disturbances over ocean surface waves. We first derive a turbulence curvilinear model for the phase-averaged Navier–Stokes equations, extending the work of Cao, Deng & Shen (2020 J. Fluid Mech. 901, A27), by incorporating turbulence stress terms previously neglected in the linearised viscous curvilinear model. To verify our formulation, we perform a priori tests by numerically solving the model using mean wind and turbulence stress profiles from large-eddy simulations (LES) of airflow over waves across various wave ages. Results show that including turbulence stress terms improves wave-induced airflow predictions compared with the previous viscous curvilinear model. We further show that using a standard mixing-length eddy viscosity yields inaccurate predictions at certain wave ages, as it fails to capture wave-induced turbulence, which fundamentally differs from mean shear-driven turbulence. The LES data show that accurate representations of wave-induced stresses require a complex-valued eddy viscosity. The maximum magnitude of this eddy viscosity scales as ∼𝑢 𝜏 ⁢𝜁 𝑖𝑛𝑛𝑒𝑟 , where 𝑢 𝜏 is the friction velocity and 𝜁 𝑖𝑛𝑛𝑒𝑟 is the inner-layer thickness, the height at which the eddy-turnover time matches the wave advection time scale. This scaling aligns with the prediction by Belcher & Hunt (1993 J. Fluid Mech. 251, 109–148). Overall, the findings demonstrate that traditional eddy viscosity models are inadequate for capturing wave-induced turbulence. More sophisticated turbulence models are essential for the accurate prediction of airflow disturbances and form drag in wind–wave interaction models.

16 TIDAL AND WAVE POWER↗

Numerical minimization of neoclassical poloidal viscosity for supersonic equilibria in tokamak geometry

Extensive experimental evidence has shown that the presence of poloidal flow in tokamaks can dramatically improve transport properties. However, theory indicates that poloidal flows are damped by poloidal viscosity, thus necessitating external drivers, such as neutral beam injection or radio frequency heating. In this work, ideal magnetohydrodynamic equilibria are calculated via the FORTRAN code FLOW [Guazzotto et al., Phys. Plasmas 11, 604 (2004)] and a postprocessor is used to estimate the neoclassical poloidal viscosity. The equilibrium inputs, which correspond to intuitive physical quantities, are then numerically optimized to reduce a viscosity figure of merit. We present supersonic equilibria in tokamak geometry with minimized neoclassical poloidal viscosities for various velocity free function inputs, plasma aspect ratios, and collisionality regimes. Benchmarks are made against an analytic theory as well as a classical expression of poloidal viscosity. Numerical confirmation of the analytic theory is obtained in the high aspect ratio and high collisionality limit. Good agreement is also seen near the plasma core and edge, with discrepancies arising in the intermediate region. Outside of these limits, rotation input function profiles are found that provide ∼order of magnitude improvements over the analytic theory, with additional progress being made toward predictions for tokamak-relevant equilibria.

Physics↗

Taking control of compressible modes: bulk viscosity and the turbulent dynamo

Many polyatomic astrophysical plasmas are compressible and out of chemical and thermal equilibrium, introducing a bulk viscosity into the plasma via the internal degrees of freedom of the molecular composition, directly impacting the decay of compressible modes, $\mathrm{{\boldsymbol {\mathit {v}}}}_{\parallel }(\boldsymbol {k})$. This is especially important for small-scale, turbulent dynamo processes in the interstellar medium (ISM), which are known to be sensitive to the effects of compression. To control the viscous properties of $\mathrm{{\boldsymbol {\mathit {v}}}}_{\parallel }(\boldsymbol {k})$, we perform trans-sonic, visco-resistive dynamo simulations with additional bulk viscosity $\nu _{\text{bulk}}$, deriving a new $\nu _{\text{bulk}}$ Reynolds number $\text{Re}_{\text{bulk}}$, and viscous Prandtl number $\text{P}\nu \equiv \text{Re}_{\text{bulk}}/ \text{Re}_{\text{shear}}$, where $\text{Re}_{\text{shear}}$ is the shear viscosity Reynolds number. We derive a framework for decomposing $E_{\rm mag}$ growth rates into incompressible and compressible terms via orthogonal tensor decompositions of $\boldsymbol {\nabla }\otimes \mathrm{{\boldsymbol {\mathit {v}}}}$, where $\mathrm{{\boldsymbol {\mathit {v}}}}$ is the fluid velocity. We find that $\mathrm{{\boldsymbol {\mathit {v}}}}_{\parallel }(\boldsymbol {k})$ play a dual role, growing and decaying $E_{\rm mag}$, and that field-line stretching is the main driver of growth, even in compressible dynamos. In the absence of $\nu _{\text{bulk}}$ ($\text{P}\nu \rightarrow \infty$), $\mathrm{{\boldsymbol {\mathit {v}}}}_{\parallel }(\boldsymbol {k})$ pile up on small-scales, creating a spectral bottleneck, which disappears for $\text{P}\nu \approx 1$. As $\text{P}\nu$ decreases, $\mathrm{{\boldsymbol {\mathit {v}}}}_{\parallel }(\boldsymbol {k})$ are dissipated at increasingly larger scales, in turn suppressing incompressible modes through a coupling between high-k modes. We emphasize the importance of further understanding the role of $\nu _{\text{bulk}}$ in compressible astrophysical plasmas, which we estimate could be as strong as the shear viscosity in the cold ISM, and highlight that compressible direct numerical simulations without bulk viscosity have unresolved compressible mode dissipation scales.

MHD↗

Shear viscosity from perturbative quantum chromodynamics to the hadron resonance gas at finite baryon, strangeness, and electric charge densities

Through model-to-data comparisons from heavy-ion collisions, it has been shown that the quark gluon plasma has an extremely small shear viscosity at vanishing densities. At large baryon densities, significantly less is known about the nature of the shear viscosity from quantum chromodynamics (QCD). Within heavy-ion collisions, there are three conserved charges: baryon number (B), strangeness (S), and electric charge (Q). Here we calculate the shear viscosity in two limits using perturbative QCD (pQCD) and an excluded-volume hadron resonance gas at finite BSQ densities. We then develop a framework that interpolates between these two limits such that shear viscosity is possible to calculate across a wide range of finite BSQ densities. We find that the pQCD and hadron resonance gas calculations have different BSQ density dependencies such that a rather nontrivial shear viscosity appears at finite densities.

Phenomenology↗

Bulk viscosity from Urca processes: npeμ matter in the neutrino-trapped regime

In this work, we extend our previous study of the bulk viscosity of hot and dense npe matter induced by the Urca process in the neutrino trapped regime to npeμ matter by adding the muonic Urca processes as well as the purely leptonic electroweak processes involving electron-muon transition. Here, the nuclear matter is modeled in a relativistic density functional approach with two different parametrizations which predict neutrino dominated matter (DDME2 model) and anti-neutrino dominated matter (NL3 model) at temperatures for which neutrinos/anti-neutrinos are trapped. In the case of neutrino-dominated matter, the main equilibration mechanism is lepton capture, whereas in the case of antineutrino-dominated matter this is due to neutron decay. We find that the equilibration rates of Urca processes are higher than that of the pure leptonic processes, which implies that the Urca bulk viscosity can be computed with the leptonic reactions assumed to be frozen. We find that the bulk viscosity decreases with temperature as ζ~T –2 at moderate temperatures. At high temperatures this scaling breaks down by sharp drops of the bulk viscosity close to the temperature where the proton fraction is density-independent and the matter becomes scale-invariant. This occurs also when the matter undergoes a transition from the antineutrino-dominated regime to the neutrino-dominated regime where the bulk viscosity attains a local maximum. We also estimate the bulk viscous dissipation timescales and find that these are in the range ≳ 1 s for temperatures above the neutrino trapping temperature. These timescales would be relevant only for long-lived objects formed in binary neutron star mergers and hot proto-neutron stars formed in core-collapse supernovas.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Verification study of xRAGE’s multi-ion viscosity model

This report on the adequacy of the plasma viscosity model implemented in LANL’s ASC program code, xRAGE is organized as follows. Section I provides a brief introduction on the kinetic theory which underpins plasma viscosity, and Section II describes how plasma kinetic theory can be used to calculate plasma viscosity coefficients accurate within the hydrodynamic limit. Section III describes the existing model for calculating the plasma viscosity coefficient in xRAGE. Next, Section IV shows tests of the xRAGE viscosity model against established hydrodynamic theory in the case of binary and trinary plasma mixtures.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Optimization of artificial viscosity in production codes based on Gaussian Regression surrogate models

To accurately model flows with shock waves using staggered-grid Lagrangian hydrodynamics, artificial viscosity has to be introduced to convert kinetic energy into internal energy, thereby increasing the entropy across shocks. Determining the appropriate strength of the artificial viscosity is an art and strongly depends on the particular problem and experience of the researcher. The objective of this study is to pose the problem of finding the appropriate strength of artificial viscosity as an optimization problem and solve this problem using machine learning (ML) tools, specifically using surrogate models based on Gaussian Process regression and Bayesian analysis. We describe the optimization method and discuss various practical details of its implementation. The shock-containing problems for which we apply this method all have been implemented in the LANL code FLAG. First, we apply ML to find optimal values to isolated shock problems of different strengths. Second, we apply ML to optimize viscosity for a 1D propagating detonation problem based on Zel’dovich-von Neumann-Doring (ZND) detonation theory using a reactive burn model. We compare results for default (currently used values in FLAG) and optimized values of artificial viscosity for these problems demonstrating the potential for significant improvement in the accuracy of computations.

42 ENGINEERING↗

Locally adaptive artificial viscosity strategies for Lagrangian hydrodynamics

To accurately model inviscid flow with shock waves using staggered-grid Lagrangian hydrodynamics, artificial viscosity is introduced to convert kinetic energy into internal energy, thereby providing a mechanism to generate the required entropy increase across shocks. In this paper, we propose a new method for constructing an adaptive, artificial viscosity in the context of one-dimensional, staggered-grid Lagrangian hydrodynamics. Our adaptive, artificial viscosity is defined in terms of two parameters that depend on density locally in a neighborhood around a shock, and hence, vary cell-by-cell. Our methodology is based on building a reference set of pre-computed optimal, globally constant artificial viscosity coefficients for a family of isolated shock test problems. For arbitrary flows, the evaluation of the unknown coefficients is automated by first estimating shock intensity locally, and second computing the corresponding adaptive parameter value via interpolation over the data from the pre-computed reference set of optimal, globally constant coefficient values. To illustrate the performance of our new approach, we compare our results against two existing methods. The first method is a limiter-based approach, which relies on estimating velocity gradients of the flow, and the second method is utilized in several commercial codes. Finally, we demonstrate that our new adaptive methodology produces more accurate results for a variety of tests with propagating shock waves, as well as for the aforementioned family of isolated shock problems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Lattice-scale variations in viscosity are correlated with solution structure at mineral-water interfaces

At solid-liquid interfaces, the viscosity increases markedly from the bulk due to the collective interactions of ions and water molecules, influencing phenomena relevant to nanofluidics, colloidal dynamics, and electrochemistry. Here, in this study, we investigated dissipative forces at the boehmite-water interface using 3D atomic force microscopy. We observed an increase in interfacial solution viscosity, η, by 10-100-fold as the nanoprobe approached the surface in normal direction, with up to four oscillatory features showing average peaks of η/η bulk = 44-71. Moreover, the viscosity showed sub-nanometer variations within 0.5 nm from the interface, templated by the underlying crystal lattice and correlated with the interfacial solution structure. Beyond a near-wall region of approximately 1.2 nm, the dissipative response was comparable to that in bulk solution. Molecular dynamics simulations, along with statistical mechanical analyses, provided details on hydrodynamic structures near the interface. Specifically, the lattice-dependent dissipative responses are correlated with extensive hydrogen bonding by interfacial water molecules, which increased friction, particularly along the [001] direction. These results demonstrate how solution viscosity at mineral-water interfaces is anisotropic and correlated with the local solution structure, providing insights into the dynamics of nanocrystal attachment.

Viscosity↗

Viscosity anomaly of a metallic glass-forming liquid under high pressure

Viscosity, as a critical property closely associated with the glass-forming ability of a liquid, has been extensively studied with varying temperatures. However, its pressure dependence has not been well explored yet due to experimental difficulties. Here, we measured the viscosity of a metallic glass-forming liquid, Zr 46 Cu 37.6 Ag 8.4 Al 8 , at pressures up to 6.1 GPa above the melting points by falling-sphere viscometry with ultrafast synchrotron x-ray imaging. Overall, the viscosity increases with pressure, while surprisingly, there is an abrupt drop between 3.2 GPa and 3.7 GPa, indicating the possible existence of a pressure-induced liquid-to-liquid transition. Pressure could change the short- and medium-range orders in the multicomponent glass-forming liquid, as suggested by the different crystalline outcomes after cooling to room temperature at high- and low-pressure ranges. In conclusion, our work extended the viscosity investigation of metallic glass-forming liquids to the high-pressure regime, which will expand our understanding of liquid-liquid transitions and metallic glass formation.

36 MATERIALS SCIENCE↗

Volatility Basis Set Distributions and Viscosity of Organic Aerosol Mixtures: Insights from Chemical Characterization Using Temperature-Programmed Desorption–Direct Analysis in Real-Time High-Resolution Mass Spectrometry

Quantitative assessment of gas-particle partitioning of individual components within complex atmospheric organic aerosols (OA) mixtures is critical for predicting and comprehending the formation and evolution of OA particles in the atmosphere. This investigation leverages previously documented data obtained through a temperature programmed desorption - direct analysis in real time – high resolution mass spectrometry (TPD-DART-HRMS) platform. This methodology facilitates the bottom-up construction of volatility basis set (VBS) distributions for constituents found in three biogenic secondary organic aerosol (SOA) mixtures produced through the ozonolysis of a-pinene, limonene, and ocimene. The apparent enthalpies (ΔH*, kJ mol -1 ) and saturated vapor mass concentrations (C T *, µg∙m -3 ) of individual SOA components, determined as a function of temperature (T, K), facilitated an assessment of changes in VBS distributions and gas-particle partitioning with respect to T and atmospheric total organic mass loadings (tOM, µg∙m -3 ). Further, the VBS distributions reveal distinct differences in volatilities among monomers, dimers, and trimers, enabling their categorization into separate volatility bins. At the ambient temperature of T = 298 K, only monomers efficiently partition between gas and particle phases across a broad range of atmospherically relevant total organic mass loadings (tOM) values of 1–100 µg∙m -3 . Partitioning of dimers and trimers becomes notable only at T > 360 K and T > 420 K, respectively. The viscosity of SOA mixtures is assessed using a bottom-up calculation approach, incorporating the input of elemental formulas, ΔH*, C T *, and particle-phase mass fractions of the SOA components. Through this approach, we are able to accurately estimate the variations in SOA viscosity that result from the evaporation of its components. These variations are, in turn, influenced by atmospherically relevant changes in tOM and T. Comparison of the calculated SOA viscosity and diffusivity values with literature reported experimental results shows close agreement, thereby validating the employed calculation approach. These findings underscore the significant potential for TPD-DART-HRMS measurements in enabling the untargeted analysis of organic molecules within OA mixtures. This approach facilitates quantitative assessment of their gas-particle partitioning and allows for the estimation of their viscosity and condensed-phase diffusion, thereby contributing valuable insights to atmospheric models.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Effects of Methylating Imidazolium-Based Ionic Liquids on Viscosity: New Insights from the Compensated Arrhenius Formalism

Methylation of the C(2) carbon on imidazolium-based room temperature ionic liquids (RTILs) causes an unexpected increase in viscosity when paired with the anion bis(trifluoromethylsulfonamide) [Tf 2 N] – , but the viscosity decreases when the methylated imidazolium is paired with a tetracyanoborate [B(CN) 4 ] – anion. Herein, this paper investigates these different observations in viscosity using the compensated Arrheniusformalism (CAF) for fluidity (inverse viscosity), which assumes fluidity to be a thermally activated process. CAF activation energies are determined for imidazolium [Tf 2 N] – and methylated imidazolium [Tf 2 N] – and compared to imidazolium [B(CN) 4 ] – and methylated imidazolium [B(CN) 4 ] – . The results show that the activation energy increases with methylation for [Tf 2 N] – , but it decreases with methylation for [B(CN) 4 ] – . The CAF results also yield information concerning the entropy of activation, which are compared for the two systems

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗