Elasticity and Density

2 Mecisurement of Activeness and Deformability 4.2.1 Elasticity and Density Measurement method 

The elastic modulus was estimated by the following procedure. Simple experiment was conducted without testing machine. When beam-shaped gel was placed horizontally in the air, deformation of the gel caused by its own weight was observed. It was hypothesized that sinface cmve of the gel represented elasticity of the gel. 

The parameters h, L, were selected to satisfy that h is small enough to compare with L, h K Vmax in order to consider as an elastic body. With strip satisfying above condition (6.23[mm]x5[mm]xl.31[mm], the first row of Table 4.1), deformation curve is measured every 1 [mm]. 

Measurement results and estimated Young s modulus are shown in Table.4.1. Density was determined beforehand, pd = 2.2[mg/mm ]. The average of five measurement, calculated Young s modulus of the gel was 3.5 x 10 [Pa], which is very small. Both Young s modulus and density depend on a swelling rate, which is affected by a polymerizations condition but their order is accurate. Yormg s modulus was a dimension of 10 [Pa]. 

Poisson s ratio is 0.5, which means the material doesn t change volume when the loads are applied. This is t3rpical of soft material like gel whose molecular attraction is small. 

---

The Appendix referred to contains Southern s letter to Watt on the steam experiments that he and William Creighton conducted in 1803. From measurements of the elasticity and density of steam, Southern stated that These results appear to support the conclusion that the density of steam is nearly if not accurately, proportional to its elasticity. And subsequently he states The opinion which I entertain from these experiments as to the latent heat of steam is,... 

Jalkanen V, Andersson BM, Bergh A et al. (2008) Explanatory models for a tactile resonance sensor system-elastic and density-related variations of prostate tissue in vitro. Physiol Meas 29 729-745... 

The development of detailed models of the layered elastic and density stmcture of the Earth in the 1970s and 1980s made possible the accurate forward calculation of the seismic wavefield caused by forces acting in the Earth. In particular, in the formalism of the Earth s long-period elastic normal modes, the excitation of seismic waves by body forces and moment-tensor sources is straightforward (Gilbert 1971). Linear elastic wave theory thus provides the framework in which earthquake source characteristics can be deduced from observed seismic waves. At long periods, the seismic wavefield is simple and can be explained by a small number of fundamental earthquake parameters. 

Content of Ot-Olefin. An increase in the a-olefin content of a copolymer results in a decrease of both crystallinity and density, accompanied by a significant reduction of the polymer mechanical modulus (stiffness). Eor example, the modulus values of ethylene—1-butene copolymers with a nonuniform compositional distribution decrease as shown in Table 2 (6). A similar dependence exists for ethylene—1-octene copolymers with uniform branching distribution (7), even though all such materials are, in general, much more elastic (see Table 2). An increase in the a-olefin content in the copolymers also results in a decrease of their tensile strength but a small increase in the elongation at break (8). These two dependencies, however, are not as pronounced as that for the resin modulus. 

In contrast, various sensors are expected to respond in a predictable and controlled manner to such diverse parameters as temperature, pressure, velocity or acceleration of an object, intensity or wavelength of light or sound, rate of flow, density, viscosity, elasticity, and, perhaps most problematic, the concentration of any of millions of different chemical species. Furthermore, a sensor that responds selectively to only a single one of these parameters is often the goal, but the first attempt typically produces a device that responds to several of the other parameters as well. Interferences are the bane of sensors, which are often expected to function under, and be immune to, extremely difficult environmental conditions. 

The ultrasonic relaxation loss may involve a thermally activated stmctural relaxation associated with a shifting of bridging oxygen atoms between two equihbrium positions (169). The velocity, O, of ultrasonic waves in an infinite medium is given by the following equation, where M is the appropriate elastic modulus, and density, d, is 2.20 g/cm. ... 

Table 3 Room-temperature elastic constants, density, and the Debye temperature p of a number of Pd-Ni-P and Pd-Cu-P bulk amorphous alloys. The elastic moduli are in units of GPa and the density p is in units of g/cm. ...

Important physical properties include the density, melt flow index, crystallinity, and average molecular weight. Mechanical properties of a polymer, such as modulus (the ratio of stress to strain), elasticity, and breaking strength, essentially follow from the physical properties. 

Seismic observations furnish our only probe of the inner lithosphere. The shock waves initiated by an earthquake travel through the interior of the earth in paths that are bent in accordance with the elastic properties and density of the medium they penetrate. From these paths, seismologists have been able to determine the existence of zones within the lithosphere. The... 

The help of many collegues is gratefully acknowledged The polyglycidyl compound was synthesized by Dr. Ch. Monnier. Ms. Ch. Irrgang and Dr. J. Vogt studied visco-elasticity and Dr. W. Sieber provided results on the density of the polymers. Mr. D. Martin and Mr. P. Rohrbasser assisted the experimental work. 

The most useful of such properties would appear to be an ensemble-averaged momentum and density (their ratio being velocity) or elastic modulus, weighting the likelihood... 

This behavior is similar to the cut growth and fatigue behavior of rubber compounds. The rate of the growth of a cut is a function of the tearing energy [38,39] which itself is proportional to the stored elastic energy density in the test piece. The exact value depends on the shape of the test piece. 

The third equation is the kinetic equation, which describes the evolution of the one-particle density matrix p(r, r, E) of the electron in the process of multiple elastic and inelastic scattering in a solid... 

When we compared the viscosities of solutions of natural rubber and of guttapercha and of other elastomers and later of polyethylene vs.(poly)cis-butadiene, with such bulk properties as moduli, densities, X-ray structures, and adhesiveness, we were greatly helped in understanding these behavioral differences by the studies of Wood (6) on the temperature and stress dependent, melting and freezing,hysteresis of natural rubber, and by the work of Treloar (7) and of Flory (8) on the elasticity and crystallinity of elastomers on stretching. Molecular symmetry and stiffness among closely similar chemical structures, as they affect the enthalpy, the entropy, and phase transitions (perhaps best expressed by AHm and by Clapeyron s... 

---