A Extension ratio

Figure 4. Tensile curves reduced to unit strain rate for silicone specimens at different temperatures (2) A, extension ratio (empirical correction (2)) S, load and R, strain rate.

Fig. 7.1. Load-extension curve registered for a sample of natural rubber (A extension ratio azz- tensile stress). Comparison with the function Eq. (7.31) derived for an ideal rubber (broken line). Results from Treloar [71]...

Fig. 8.1. Load (azz nominal tensile stress)-extension (A extension ratio) curve of a sample of PE (M = 3.6 10 , drawing velocity dX/dt = 2.4 lO s ). The changes in the shape of the sample are schematically indicated...

Figure C2.1.16. Tensile stress as a Hmction of the extension ratio registered for a sample of natural mbber (circles). The broken curve is calculated from equation (C2.1.20). (Data from [79].)...

Working-Capital Ratios Financial analysts make extensive use of ratios in assessing the economic health of a company. For evaluating the ability of a company to successfully maintain and develop its immediate business activities, analysts apply a current ratio and a quick (or acid-test) ratio, as given by... 

The average force f(r) in the chain when the ends are held a distance r apart could then be obtained from Eq. (10) providing the appropriate configuration distribution function p(r) is known. In the limit of a small extension ratio, p(r) is approximately proportional to peq(r) ... 

Equation (13) is valid for r/Nlp < 0.25 (Fig. 3). At much higher extension ratios, the force must increase indefinitely since the molecule is almost straightened out. The thermodynamic approach to the problem of coil stretching for a freely-jointed chain was considered by Treloar [32], who obtained the following expression for the stress-strain relationship when the two chain ends are kept a distance r apart ... 

From the standpoint of thermodynamics, the essential quantity which governs the course of a chemical reaction is the chemical potential of the system or, in the case of interest, the free energy storage within the molecular coil. This quantity, unfortunately, is difficult to evaluate in non-steady flow. At modest extension ratios (X < 4), the free energy storage of a freely-jointed bead-spring chain is... 

It is also comparatively straightforward to-calculate P200, P220, P420 and P o for a biaxially oriented aggregate of transversely isotropic units in terms of the principal extension ratios Xx, X2 and (with X,X2 3 = 1). 

Equation (32a) has been very successful in modelling the development of birefringence with extension ratio (or equivalently draw ratio) in a rubber, and this is of a different shape from the predictions of the pseudo-affine deformation scheme (Eq. (30a)). There are also very significant differences between the predictions of the two schemes for P400- In particular, the development of P400 with extension ratio is much slower for the network model than for the pseudo-affine scheme. 

A rubber network which is deformed to three independent extension ratios Xt, X2 and X3 takes the form of a biaxially oriented aggregate defined by coefficients P,mo. For example, we have... 

A widely used glass is phosphosilicate (PSG), which is used extensively in semiconductor devices as a passivation and planarization coating for silicon wafers. It is deposited by CVD by the reaction of tetraethyl orthosilicate (TEOS) (C2H50)4Si, and trimethylphosphate PO(OCH3)3, in a molecular ratio corresponding to a concentration of 5 to 7% P. Deposition temperature is usually 700°C and pressure is 1 atm. 

Me the molecular mass between cross-links M the primary molecular mass (28,492 Da) a the extension ratio... 

The potential of NSR catalysts in the removal of NO from mobile sources has motivated in the last few years extensive investigations from both the academic and the industrial world, and several studies have been published in the open literature dealing with fundamental and practical aspects of LNT catalysts [4-53], However, the mechanisms that operate the NO adsorption and the respective subsequent reduction have not been completely clarified so far. It has been shown that under oxidizing conditions, NO are stored on the surface of a Ba-containing catalyst in various forms (surface nitrites/nitrates), whose precise nature is, however, still a matter of debate [9-29], Even less clear are the mechanisms, which are responsible for the reduction of stored NO when the A/F ratio is set to rich and the stored NO species are reduced over Pt to N2, ammonia, N20 or back to NO [11],... 

The state of macroscopic deformation may be characterized by considering the deformation of a rectangular prism, with extension ratios Xx, Xz, along the x, y,... 

X-ray diffraction pictures taken with a flat-film camera show that crosslinked SE-BR samples crystallize on stretching. Sharp reflections are observed at an extension ratio of 4 1 (Figure 4). With samples having different degrees of stereoregularity the order for increasing strain-induced crystallization is the same as the order for the rate of low temperature crystallization. 

Figure 19 shows the temperature dependence of the percent crystallinity for high trans SBR, prepared with a Ba-Li catalyst and containing 757. trans-1,4 content with 14 wt.7. styrene, at 3 extension ratios. The percent crystallinity that develops is temperature dependent, there being an increase in the amount of crystallinity with a decrease in temperature. However, the amount of crystallinity that develops is essentially independent of strain. The amount of crystallinity that develops at room temperature, regardless of the level of strain, is extremely small ( 9) ... 

Figure 20 shows the percent crystallinity as a function of temperature and extension ratio for high trans SBR (227. styrene, 877. trans) prepared with a Ba-Mg-Al catalyst. A... 

The results of stress-strain measurements can be summarized as follows (1) the reduced stress S (A- A ) (Ais the extension ratio) is practically independent of strain so that the Mooney-Rivlin constant C2 is practically zero for dry as well as swollen samples (C2/C1=0 0.05) (2) the values of G are practically the same whether obtained on dry or swollen samples (3) assuming that Gee=0, the data are compatible with the chemical contribution and A 1 (4) the difference between the phantom network dependence with the value of A given by Eq.(4) and the experimental moduli fits well the theoretical dependence of G e in Eq.(2) or (3). The proportionality constant in G for series of networks with s equal to 0, 0.2, 0.33, and 0. Ewas practically the same -(8.2, 6.3, 8.8, and 8.5)x10-4 mol/cm with the average value 7.95x10 mol/cm. Results (1) and (2) suggest that phantom network behavior has been reached, but the result(3) is contrary to that. Either the constraints do survive also in the swollen and stressed states, or we have to consider an extra contribution due to the incrossability of "phantom" chains. The latter explanation is somewhat supported by the constancy of in Eq.(2) for a series of samples of different composition. 

Figure 3. Modulus contributions from chemical cross-links (Cx, filled triangles) and from chain entangling (Gx, unfilled symbols) plotted against the extension ratio during cross-linking, A0, for 1,2-polybutadiene. Key O, GN, equibiaxial extension , G.v, pure shear A, Gx, simple extension Gx°, pseudo-equilibrium rubber plateau modulus for a polybutadiene with a similar microstructure. See Ref. 10.

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