Dynamic Relaxation Time Research Articles

A Weak Field EPR Study of TANOL in Water and Water-Oil Using Dynamic Nuclear Polarization

Abstract Solutions of 4-hydroxy-TEMPO(TANOL) in water and water-soyabean oil were investigated in the concentration range 0.1 mM-10mM. Dynamic nuclear polarization (DNP) and electronic relaxation time T1e measurements were performed at each well resolved hyperfine line. In the TANOL/water-soyabean oil solutions, the effect of the presence of soyabean oil was an increase in the measured relaxation rates and a decrease in the observed enhancements. In addition, the observed enhancements diminished in time. For all of the samples, the relaxation rates decreased as the frequency of the transition increased.

Calculation of relaxation time in polyurethanes using additive group contributions

The method of additive properties was used to calculate the dynamic mechanical relaxation time for a series of polyurethanes. Calculations were also made of density and glass transition temperature. Group contributions for nine component groups were determined. With these group values, the densities of the 12 polymers used to determine the groups were calculated and found to agree with measured values within an average of 0.2%. Calculated glass transition temperatures also agreed with measured values within 0.2%. The relaxation time, defined as a parameter in the Havriliak-Negami equation, was shown to be correlated with the glass transition temperature, allowing relaxation time to also be expressed as an additive property. Calculated logarithms of relaxation times agree with measured values to within 7% over a range of relaxation times covering many decades. © 1996 John Wiley & Sons, Inc.

Calculation of relaxation time in polyurethanes using additive group contributions

The method of additive properties was used to calculate the dynamic mechanical relaxation time for a series of polyurethanes. Calculations were also made of density and glass transition temperature. Group contributions for nine component groups were determined. With these group values, the densities of the 12 polymers used to determine the groups were calculated and found to agree with measured values within an average of 0.2%. Calculated glass transition temperatures also agreed with measured values within 0.2%. The relaxation time, defined as a parameter in the Havriliak-Negami equation, was shown to be correlated with the glass transition temperature, allowing relaxation time to also be expressed as an additive property. Calculated logarithms of relaxation times agree with measured values to within 7% over a range of relaxation times covering many decades. © 1996 John Wiley & Sons, Inc.

Relationship between enthalpy relaxation and dynamic mechanical relaxation of engineering plastics

The enthalpy relaxation and dynamic modulus relaxation processes of amorphous poly(ether imide) (PEI) and two types of crystalline poly(aryl-ether-ether-ketone) (PEEK), low and high crystallinity, were analyzed by the Kohlrausch-Williams-Watts equation. Both crystalline PEEKs and amorphous PEI showed almost the same relationship between enthalpy relaxation time and T g − T a in the temperature difference range 10 K < T g − T a < 25 K. The enthalpy relaxation time was increased slightly with the increase in degree of crystallinity at a given T g − T a. A good correlation was observed between the enthalpy relaxation time and the dynamic modulus relaxation time for both PEI and PEEK, in particular, a linear relationship with slope equal to unity was obtained for PEI.

The effect of curing of unsaturated polyester resin on the dynamic relaxation time

AbstractThe effect of hot curing of unsaturated polyester resin on the dynamic relaxation time was studied using dielectric measurements along with two dynamic mechanical measurement methods. It was found that the dynamic response during cure was a material frequency dependent property and did not depend on the measurement method. All relaxation times, measured during cure, by all three measurement methods used, converged to a single equation: τ(t)av=atb where t= curing time, a, b=constants. The increase of the relaxation time during cure followed the same trend as a friction factor, which was found to increase with conversion. The crosslinking density was found to increase slowly with conversion, while the relaxation time increased exponentially. These two different modes of behavior during cure explain the high resolution of dynamic measurements as a cure monitoring tool, which can easily detect small curing changes. This behavior of the relaxation time was explained by the sharp rise of activation energy due to a parallel decrease of free volume at high conversion.

Continuous models of the motion of inertial particles in laminar and turbulent flows based on the Fokker-Planck equations

A methodology of continuous description of the motion of inertial particles in hydrodynamic flows has been developed. This methodology involves the following main elements: the equations of motion for a single particle in a given velocity field of the carrier medium in the presence of a random disturbing force such as white noise; the Fokker-Planck equation with a diffusion term in velocity space, which is treated as an instantaneous equation relative to the large-scale motion; the moment (for the Fokker-Planck equation) relations which are treated as instantaneous continuous equations in physical space; the closing of the continuous equations on the basis of phenomenological relations or by means of an approximate asymptotic solution of the Fokker-Planck equation for a short particle dynamic relaxation time. The direct interaction of the particles and their reciprocal action on the motion of the carrier medium are not taken into account. In the case of laminar motion, the random disturbing force results from Brownian fluctuations (the interaction between the particles and the molecules of the carrier medium) and the Fokker-Planck equation for this situation can be written in a natural way. For turbulent motion of the carrier medium it is assumed that the fluctuating field can be broken down into small- and large-scale motions (in relation to the particle dynamic relaxation time); in the random force, besides Brownian perturbations the small-scale turbulent fluctuations are included, while the velocity field is averaged over the small scales. In this case the Fokker-Planck equation (and its moment analogs) becomes an instantaneous equation with respect to the large-scale turbulent fluctuations. The continuous equations are analyzed and in the case of the turbulent motion elementary closing methods are proposed. Estimates of the small-scale turbulent particle diffusion coefficient are given.

Rates of collapse and evaporation of globular clusters

Of the known galactic globular clusters, ~ 140 in number, about one-fifth have undergone core collapse, and an unknown number have evaporated altogether. From observational estimates of the dynamical relaxation times of globular clusters, measured at their cores and at their half-light radii, we estimate here the present rates at which core collapse and evaporation are occurring. We find a core collapse rate of 2 ± 1 per Gyr, which for a galactic age of ~ 12 Gyr agrees well with the fact that 27 clusters have surface brightness profiles with the morphology expected for the post-collapse phase. We find a destruction and evaporation rate of 5±3 per Gyr, suggesting that a significant fraction of the Galaxy's original complement of globular clusters have perished, through the combined effects of mechanisms such as relaxation-driven evaporation and shocking due to interaction with the galactic disk and bulge.

Intraband relaxation time in highly excited semiconductors.

This work consists of two parts. In the first part we determine the static-conductivity relaxation time \ensuremath{\tau} as a function of temperature for highly excited silicon. The anisotropy and many-valley character of the conduction band are fully taken into account. The anisotropy leads to additional contributions to 1/\ensuremath{\tau} from electron-electron scattering. The second part is devoted to the dynamical relaxation time of a model semiconductor. Here the dependence on frequency, temperature, and plasma density is explored, and from these results the optical properties of the plasma are determined.

Unstable breakup of a linearly accelerated, dense plasma

A dense plasma, accelerated by magnetic pressure, is used in an electromagnetic launcher to propel small masses. Such plasmas have been observed to disperse or fragment, and this has been related to a loss of projectile acceleration. We are concerned here with the potential mechanisms of plasma breakup, and with the associated limitations on projectile velocity. An unsteady, one-dimensional model of the plasma is described, which incorporates a simple correction for the effect of wall ablation. Two limiting cases are examined, one where ablation is small, and another where it is large. For the first of these cases, we show that a reduction in magnetic pressure will induce a decelerating body force at the tail of the plasma. It is shown that, if this force is generated on a time scale comparable with the dynamic relaxation time of the plasma, it is accompanied by a substantial reduction in plasma density. To the extent that this results in a loss of plasma conductivity, such a force reversal could lead to the formation of multiple current paths. For the second case, we show that a high level of ablation results in the formation of a parasitic current sheet at the tail of the plasma. Again, this is accompanied by a local deceleration of the tail. It is a matter of debate as to whether or not this leads to fragmentation of the plasma. However, irrespective of whether breakup occurs, the formation of such a current sheet imposes an upper limit on the achievable projectile velocity.

Pulsed ESR studies of graphite intercalation compounds

Time resolved ESR studies of some acceptor type GIC, HOPG/AsF 5 and HOPG/BF 3/F 2, are reported. Free induction decay (FID) spectroscopy yields the dynamical relaxation time T 2 ∗ associated with mobile spins. T 2 ∗ was found to be almost isotropic and only slightly temperature dependent. T 2 ∗ times are consistent with CW-ESR linewidths measured on the same samples. In additionn, we found a weak Hahn echo at g ≈ 2 for several HOPG/AsF 5 GIC below T = 20K. The Hahn echo signal is attributed to localized spins on the graphite layers.

Photochemical Damping of Inertio–Gravity Waves

A simple model is developed for the coupling effect of radiative heating and ozone photochemistry on inertio-gravity waves in the region 16-70 km. It is found that the photochemical damping rate is the weighted sum of the rates caused by two individual processes. One, suggested by Craig and Ohring, involves the temperature dependence of ozone reaction rate coefficients; the other, suggested by Leovy, involves the vertical gradient of the ozone mixing ratio. The relative importance of these two processes depends on the ratio of dynamical and chemical relaxation times. Calculations show that the most important region for coupling is near 48 km where the total relaxation time is 8 days for equinox and 6 days for summer midlatitude.

Relaxational interactions and viscoelasticity of polymer melts. Part I: model development

Rheological equations of state for the concentrated solutions and melts of high polymers are derived by applying a structural approach. The dynamics of a macromolecule are considered on the basis of the fundamental model of the polymer chain, e.g., the bead-spring model. The drag forces describing correlations of motion macromolecules are determined by means of the relaxation equations. The oscillatory shearing flow of the melts is studied on the basis of the equations derived. Expressions for the dynamic modulus and relaxation times are determined. As can be judged from the form of the dependence of the dynamic modulus on frequency, the relaxation time distribution is the same as in real materials. The relaxation spectrum of high polymers has a terminal zone with abnormally long relaxation times.

Fluctuation theory of the mass flux from the stars

The mass flux from a star is adopted to result from a fluctuation of the photosphere, which is not in complete thermal equilibrium. Because of the large difference between the dynamical and thermal relaxation times, its state can be approximated by a partial equilibrium. Using a theory of thermodynamic fluctuations, the mass flux is expressed in a correlation function of gravitational perturbations of the photosphere. A hypothesis is proposed that the susceptibility to these perturbations, if normalized to the available thermal energy, is the same for all stars. Its value is obtained by considering the upper limit to the mass flux. This results in a mean mass loss ofL3/2 (R/M)9/4/G7/4, where the symbols have their common meaning. The result is compared to empirical data on the mass flux from some 50 stars of various luminosities and luminosity classes. With a possible exception for late-type (super) giants the agreement is good, in many cases within a factor 2.

Aerosol size spectrum analysis using relaxation time measurement

An experimental method has been developed to measure the dynamic relaxation times of aerosol particles. The particle relaxation time (τp) is determined from the ratio of the velocity amplitude of an aerosol particle (vp) to the velocity amplitude of the medium (ug) while the aerosol is subjected to acoustic excitation of a known frequency. A differential laser Doppler velocimeter is used to measure vp, while a microphone is used to measure ug. From the value of τp, the aerodynamic diameter of the particle can be determined if the particle density is known. The method can be applied to real−time in situ measurement of size distribution of an aerosol containing both solid particles and liquid droplets in the range of 0.1−10.0−μm diameters.

The Cluster of Compact Galaxies ZW CL 0152+33

Redshifts have been determined for 14 seventeenth-magnitude, mostly red, compact galaxies which form an elongated system at the center of the cluster Zw Cl 0152+33. This cluster was discovered by Zwicky to contain a vast preponderance of compact galaxies and, in this respect, is very unusuaL The mean redshift is 26,304 km s ' and the apparent distance modulus of the cluster is (`n - M) = 38.2. The brightest galaxy in the cluster, which is a compact galaxy according to Zwicky, has Mp = -21.2. All the observed galaxies except one have late-type absorption spectra; the remaining galaxy is blue and has an emission-line spectrum. It is argued that the galaxies in the elongated system do not form a linear chain, but are in a flattened system seen nearly edge-on. An application of the virial theorem is complicated by the fact that the galaxies on the outer parts of the region considered have a higher velocity dispersion &lt;r than those in the center. As a result we find that the center of the cluster is probably a bound system while the outer members are escaping from the cluster on a timescale of about 10 years. This is smaller by a factor of 100 than the estimated dynamical relaxation time in the cluster; as a result the overall dynamics of the cluster are not understood.

Random Gravitational Encounters and the Evolution of Spherical Systems. IV Isolated Systems of Identical Stars

view Abstract Citations (140) References (19) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Random Gravitational Encounters and the Evolution of Spherical Systems. IV Isolated Systems of Identical Stars Spitzer, Lyman, Jr. ; Thuan, Trinh X. Abstract Models of isolated stellar systems with stars all of the same mass have been recomputed, allowing for the exact dependence of the velocity diffusion coefficients on stellar velocity, and extending to later evolutionary phases than before. The results show that the inner 10 percent of the mass collapses to a singularity in a time about equal to 18 t , where is the dynamical relaxation time at the mean density inside the median radius rh during the early life of the system. This behavior is in general agreement with earlier results by Larson. Early in the evolution the energy released by the contracting core goes primarily into stars which accumulate in the outer halo, with some drain also into stars which escape from the system. Toward the end of the development the energy goes into a readjustment of the intermediate regions of the system; this later stage appears unrelated to buildup of the outer halo or to stellar escape but is similar to the "gravo-thermal instability" discussed by Lynden-Bell and Wood. These models permit a comparison of escape rates with a "local" theory, where the velocity distribution function at any point is arbitrarily assumed to be the same as that obtained from the Fokker-Planck equation for a homogeneous system, with a rectangular profile for the potential (r), and where , the overall probability of escape per star per interval of time, is computed by averaging over the entire system the local escape probability at each point. The "observed" for the isolated systems rises to about 0.3 percent per time interval t , as compared with about 0 8 to 1 percent predicted by the local theory. If escaping stars are taken to include those which accumulate in the outer halo, which outnumber the true escapers by about two to one at intermediate evolutionary phases, the results from the computer models are in reasonable agreement with the simple theory at these intermediate times. Publication: The Astrophysical Journal Pub Date: July 1972 DOI: 10.1086/151537 Bibcode: 1972ApJ...175...31S full text sources ADS | Related Materials (7) Part 1: 1971ApJ...164..399S Part 2: 1971ApJ...166..483S Part 3: 1972ApJ...173..529S Part 5: 1973ApJ...183..565S Part 6: 1975ApJ...200..339S Part 7: 1975ApJ...201..773S Part 8: 1980ApJ...241..618S

Liquid Viscoelasticity under Rare-Gas Infusion

Experimental measurements have been made of the complex frequency-dependent shear modulus for hexachlorobiphenyl (Aroclor 1260) both with and without, in turn, helium- and argon-gas infusion to capacity, over the temperature range 5°–25°C and the pressure range ambient atmospheric to 4000 psi. Static viscosity results derived from the data are presented and analyzed with the aid of the Macedo–Litovitz hybrid equation to find changes in relative free volume brought about by rare-gas impregnation. Limiting high-frequency shear-compliance data are also presented, to which a phenomenological formulation for shear compliance in molecular-bonded liquids is applied as a means for assessing the additional equilibrium number of intermolecular bonds that are bent or broken under rare-gas infusion. Changes are noted in dynamic shear rigidity, loss modulus, and viscoelastic relaxation times brought about by the presence of each rare-gas impregnant in the recipient liquid, all as influenced by temperature and applied static pressure. Some effects on the dynamic shear spectra that are directly related to evaluated changes in free volume and intermolecular bond density are cited. We find that, except at low pressure, an increase in relative free volume is manifest upon Aroclor infusion with helium or argon gas over our temperature and pressure range. This added free-volume characteristic applies for all pressures at low temperatures where the free volume is small. The effect is found to be larger the higher the pressure (greater infusion) at all temperatures. Additional equilibrium numbers of broken bonds occurring upon infusion are enhanced with increasing temperature and, in general, with decreasing pressure. Viscoelastic relaxation times are decreased in Aroclor upon rare-gas impregnation, the reduction being more pronounced the lower the temperature or the higher the applied pressure. Infusion with the larger argon molecule has over all a more prominent impact on changes in free volume, bond density, and shear-rigidity spectra than has impregnation with helium molecules. However, no appreciable differences are detected between the two gas-infusion cases insofar as their impact on the relaxation time is concerned.

Measurements of Attenuation and Dispersion of Sound by an Aerosol

Attenuation and dispersion of sound by an aerosol, composed of oleic acid and a nitrogen carrier gas, are measured with an acoustic interferometer. Mean particle size and concentration are measured in situ by spectrophotometric tests. The measurements of attenuation and dispersion show good agreement with the theory in the range of ω(τd)32 covered, where ω is circular frequency and (τd)32, is dynamic relaxation time of the particles. In particular, the maximum attenuation per wavelength and the maximum dispersion, which are predicted by the theory, are confirmed experimentally.

Attenuation and Dispersion of Sound by Particulate-Relaxation Processes

The temperature and velocity of a particle suspended in an acoustic field are subject to fluctuations that may lag behind those of the surrounding fluid. A theory for acoustic attenuation and dispersion in an aerosol based on these particulate-relaxation processes is given. The close relationship between particulate relaxation and relaxation mechanisms due to lagging molecular or atomic internal degrees of freedom is displayed. The particulate-relaxation theory predicts attenuation and dispersion by small, heavy particles, in close agreement with existing, more-detailed theories, for values of ωτd, (ω is the circular acoustic frequency, τd is the dynamic relaxation time of the particle) smaller than and including order unity. Comparison with existing experimental data of attenuation and dispersion [J. W. Zink and L. P. Delsasso, J. Acoust. Soc. Am. 30, 765–771 (1958)] shows good agreement. However, the existence of a maximum attenuation per wavelength, when ωτd ≈ 1, that is predicted by the theory is not tested by the above experiments, which were conducted with ωτd &amp;gt; 1. Similarly, the maximum dispersion that occurs at the low-frequency limit was not tested in the previous experiments.

Propagation of Sound in an Aerosol

Sound attenuation and dispersion by small, dense particles suspended in a gas are studied analytically and experimentally. A theory for attenuation and dispersion based on particulate relaxation processes is given. The close relationship between particulate relaxation and relaxation mechanisms due to lagging molecular or atomic internal degrees of freedom is displayed. The particulate relaxation theory predicts attenuation and dispersion, in close agreement with existing, more-detailed theories in the vicinity of ωτd=1, where the attenuation per unit wavelength is a maximum (ω is the circular frequency, τd is the dynamic relaxation time of the particles). The experimental study consists of measurements of attenuation and dispersion in an acoustic interferometer. The interference tube is filled with an aerosol composed of oleic acid particles in nitrogen. Particle size and concentration are measured in situ by spectrophotometric tests. Dispersion measurements, taken at low values of ωτd where no previous measurements have been made, indicate good agreement with the theory. Attenuation measurements taken in the range of ωτd from 0.1 to 4.0 show good agreement with the theory. In particular, they confirm the existence of the predicted maximum. [Work supported by the Power Branch of the U. S. Office of Naval Research.]