Relaxation Time Of Material Research Articles

Wave Propagation in a Viscous Incompressible Fluid Contained in Flexible Viscoelastic Tubes

The dispersion attenuation of waves in viscoelastic tubes filled with a viscous incompressible fluid are analyzed, with special attention to two cases: where the constitutive relation of the wall is that (1) of a Voigt material, and (2) of a standard linear solid. Explicit expressions show the dependence of the phase-velocity and damping factor on the various parameters characterizing the fluid and the viscoelastic tube. In comparison with elastic tubes, viscoelastic tubes have a higher phase velocity and attenuation coefficient. Also, as the ratio of the relaxation time of the viscoelastic material to the period of the oscillation increases, there is a marked difference between the behavior of the waves for the two types of materials considered. The frequency equation for a stretched elastic tube is also derived. The analysis is restricted to waves whose amplitude is infinitesimal with the wavelength large and the wall thickness small as compared with the radius of the tube.

Space-Charge Effects in Insulators Resulting from Electron Irradiation

A detailed model of space-charge effects resulting from trapping of thermalized irradiation electrons in insulating materials is presented. Analytical solutions for a particular insulating material (polyethylene terephthalate) have been obtained. When the trapping sites are uniformly distributed in energy below the energy level where charge transport occurs, the rate of charge buildup and release depends primarily on a ratio of the material relaxation time constant ρε to a release rate of electrons from traps. Agreement between theory and experiment is reasonably good in the case of polyethylene terephthalate when this ratio of time constants is approximately unity.

Rolling and Sliding Friction of Polymeric Materials

The coefficient of rolling friction for a hard sphere and a cylinder over a polymeric material are derived as a function of mechanical loss. A few assumptions were made to clarify the quantitative relation between rolling friction and dynamic modulus of polymeric material. Viscoelastic properties of polymeric material are represented by the generalized Voigt model. Contact deformation of base material owing to the rolling object is assumed to be a periodic phenomenon. From this assumption, the strain and stress for surface deformation is expressed by Fourier series and the stress is also obtained as a function of the dynamic modulus. Spectrum of the relaxation time of polymeric materials is assumed to be moderate and this leads to the correspondence between the rolling velocity and the angular frequency of the dynamic modulus.The coefficient of rolling friction for a rigid sphere is obtained as follows, λs=βs(W/E1)1/4r-3/4, where W, r, and E1 are the load, the radius of the sphere, and the real component of complex the dynamic modulus, respectively. βs is a function of mechanical loss. For a small range of mechanical loss, βs is linearly proportional to mechanical loss. λs is entirely proportional to mechanical loss. Temperature dependence of λs is explained by that of mechanical loss and modulus E1. The rolling velocity corresponds to the angular frequency of dynamic modulus and correspondence between them is obtained as follows v=0.7(Wr/E1)1/4ω. From these relations, the coefficient of rolling friction for any temperature or any rolling velocity can be calculated from the dynamic data, or the dynamic data can be presumed from the rolling friction measurement. Consistency of the rolling frictional measurement for several polymers and theoretical results is quantitatively very good.The coefficient of sliding friction for a hard sphere over a polymeric materials were measured. Temperature dependence of sliding friction of NBR resembles that of mechanical loss. Above glass temperature, however, it deviates from the tendency of mechanical loss curve. This may be due to the ploughing effect.

A Note on the Analysis of the Line Shape of Nuclear Magnetic Resonance Dispersion; Relation between Spin-Lattice Relaxation Time and Modulation Frequency

The line shape change of nuclear magnetic resonance dispersion at high r. f. field, γ H 1 ≫ω m , was discussed as a function of modulation frequency ω m and spin-lattice relaxation time. The expression of first derivative line shape of nuclear magnetic resonance dispersion was derivated after Redfield's theory. New convenient method to estimate spin-lattice relaxation time of material was proposed from the analysis of the dispersion line shape at a proper modulation frequency and slow scanning. And it was also shown that the dispersion line shape was not so sensitive to the circumstances of resonant nuclei as in the case of absorption, such as Lorentzian or Gaussian. Experiments was done for a simplest case of T 1 = T 2 , and the agreement with the theory was satisfactory.

Exchange Collisions, Wall Interactions, and Resettability of the Hydrogen Maser

Experiments were performed in order to verify the resettability of the hydrogen maser. The method consisted of measuring the output frequency of one maser against the hydrogen pressure. It was found that at a given tuning of the cavity no shift larger than 2.1 parts in 1013 was observed for a change of 4 to 1 in pressure. This experiment also showed that the pressure shift due to exchange collisions, predicted by Bender, could not be observed for the field-independent transition in the hydrogen maser. Two masers, having the same storage bulb design and the same wall coating, were tuned by this technique and were found to have a frequency difference of 7.6 parts in 1013. Experiments on the wall coating of the hydrogen maser storage bulb were made. Relaxation and decorrelation times of various materials were measured. The hyperfine splitting of the ground state of hydrogen measured against cesium is also given.

Flow Rates Using Nuclear or Electron Paramagnetic Resonance Techniques with Applications to Biological and Chemical Processes

The equations for measuring flow rates are derived using NMR and EPR relaxation time determinations. Several experimental procedures are discussed. One method of measurement depends upon the difference between static relaxation times and the apparent relaxation time of materials flowing through the observation region. Another procedure utilizes saturated or inverted spins as a ``tracer'' to measure flow rates. These schemes may readily be applied to blood flow velocity measurements in humans or animals, or to mineral and chemical flow rate determinations. The advantage of this spin resonance flowmeter is that the flow channel is not disturbed. Thus blood flow velocities are readily measured without the necessity of breaking the skin.