Elasticity experimental determination

Experimentally-determined values of T0 for PDMS networks are plotted in Figure 3 against values of Mc calculated from the elastic coefficient C by means of equation 2. TQ was found to be accurately proportional to M, in accordance with equation 1, with the coefficient of proportionality K being about 0.30, 0.25, and 0.23 J/m2/(molecular weight unit) for the A4, A3, and randomly-linked materials, respectively. These differences are small, barely significant, but in the expected direction. Values of T0 are also shown in Figure 3 for the other materials examined. 

The experimental determination of RBA, however, is difficult but some attempts have been made and these include direct observation, measurements of electrical conductivity, shrinkage energy, gas adsorption and light scattering. The linear elastic response of paper has been explained in terms of various micromechanical models which take into account both fibre and network properties, including RBA. An example of one which predicts the sheet modulus, Es is given below ... 

For our purposes, work is done when a displacement occurs under the influence of a force the amount of work is taken as the product of a force by the displacement. Because force and displacement can be given suitable operational significance, the term work also will share this characteristic. The measurement of the displacement involves experimental determinations of a distance, which can be carried out, in principle, with a measuring rod. The concept of force is somewhat more complicated. It undoubtedly originated from the muscular sensation of resistance to external objects. A quantitative measurement is obtained readily with an elastic body, such as a spring, whose deformation can be used as a measure of the force. However, this definition of force is limited to static systems. For systems that are being accelerated, additional refinements must be considered. Because these considerations would take us far... 

The elasticity coefficient, e, of an enzyme is an experimentally determined measure of how responsive the enzyme is to changes in the concentration of a metabolite or regulator molecule. 

Stratton,R.A., Butcher,A.F. Experimental determination of the relationships among various measures of fluid elasticity. J. Polymer ScL Pt. A-2 9,1703-1717 (1971). 

Experimental determination of the components of the elastic force thus requires measurements of the changes in force with temperature at constant volnme and length. The constant volume requires the application of hydrostatic pressure during measurement of the force-temperature coefficient. This experiment is extremely difficult to perform 22-i3). 

The statistical theory of rubber elasticity predicts that isothermal simple elongation and compression at constant pressure must be accompanied by interchain effects resulting from the volume change on deformation. The correct experimental determination of these effects is difficult because of very small absolute values of the volume changes. These studies are, however, important for understanding the molecular mechanisms of rubber elasticity and checking the validity of the postulates of statistical theory. 

The coefficients Cn are called elasticity constants and the coefficients Su elastic compliance constants (Azaroff, 1960). Generally, they are described jointly as elasticity constants and constitute a set of strictly defined, in the physical sense, quantities relating to crystal structure. Their experimental determination is impossible in principle, since Cu = (doildefei, where / i, and hence it would be necessary to keep all e constant, except et. It is easier to satisfy the necessary conditions for determining Young s modulus E, when all but one normal stresses are constant, since... 

Experimental Determination of Elastic and Viscous Mechanical Properties 185... 

Elastic and viscous stress-strain curves can be experimentally determined from incremental stress-strain curves measured on samples of different tendons. Typical elastic and viscous stress-strain curves for rat tail and turkey tendons are shown in Figures 7.4 and 7.5. For both types of tendons the curves at high strains are approximately linear. As we discuss in Chapter 8, the elastic modulus can be calculated for collagen, because most of the tendon is composed of collagen and water, by dividing the elastic slope by the collagen content of tendon. When this is done the value of the elastic modulus of collagen in tendon is somewhere between 7 and 9 GPA. 

Note that the residual stress aM — 0 on the elastic properties becomes homogeneous (Ef = Em = EL). While connections between the residual stresses and constituent properties are rigorous, experimental determination is still necessary, because ft is not readily predictable. In general, ft includes terms associated with the thermal expansion difference, ay— am, as well as volume changes that occur either upon crystallization or during phase transformations. For CVI systems, intrinsic stresses may also be present. 

A qualitative evidence of the above are the data reported in [52]. It has been established that there is a correlation between the calculated rate of internal diffusion foam collapse and the experimentally determined rate. To obtain a stable foam from poor surfactants (alcohols, acids, etc.) under these conditions is hardly possible because of either insufficient dynamic elasticity of foam films or the lack of equilibrium elasticity (for films from insoluble surfactants). Furthermore, the n barrier for films from acid or alcohol solutions is low and the typical capillary pressures for a real foam are sufficient to induce disturbance of the film equilibrium and, respectively, foam collapse. 

The average length (or molecular weight) of network chains in a crosslinked polymer can be experimentally determined from the equilibrium rubbery modulus. This relationship is a direct result of the statistical theory of rubber-like elasticity . In the last decade or so, modem theories of rubber-like elasticity 2127) further refined this relationship but have not altered its basic foundation. In essence, it is... 

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