Force retraction

Values in bold type show the extension forces, using the full piston area. Values in italic type are for the retraction force for various piston rod diameters. Remember that force values are theoretical, derived by calculation. Experience has shown that probably 5 per cent but... 

Due to the retractive forces in stretched mbber, the aldehyde and zwitterion fragments are separated at the molecular-relaxation rate. Therefore, the ozonides and peroxides form at sites remote from the initial cleavage, and underlying mbber chains are exposed to ozone. These unstable ozonides and polymeric peroxides cleave to a variety of oxygenated products, such as acids, esters, ketones, and aldehydes, and also expose new mbber chains to the effects of ozone. The net result is that when mbber chains are cleaved, they retract in the direction of the stress and expose underlying unsaturation. Continuation of this process results in the formation of the characteristic ozone cracks. It should be noted that in the case of butadiene mbbers a small amount of cross-linking occurs during ozonation. This is considered to be due to the reaction between the biradical of the carbonyl oxide and the double bonds of the butadiene mbber [47]. 

For the purpose of illustrating the application of the thermodynamic equation of state to experimental data, consider the plot given in Fig. 84 for the retractive force, measured at fixed length, against the absolute temperature for a hypothetical elastic substance. The slope at any temperature T gives the important quantity —(dS/dL)T,p according to Eq. (12) an increase in / with T at constant L shows immediately, therefore, that the entropy decreases with increase in length... 

Fig. 84.—The retractive force / of a hypothetical elastic body plotted against the absolute temperature at constant pressure.

On substituting in Eq. (43) and dividing by the initial cross-sectional area Vq/Lq, or F/I/o, we obtain for the retractive force r per unit initial cross-sectional area ... 

Anthony, Caston, and Guth obtained considerably better agreement between the experimental stress-strain curve for natural rubber similarly vulcanized and the theoretical equation over the range a = 1 to 4. KinelP found that the retractive force for vulcanized poly-chloroprene increased linearly with a — l/a up to a = 3.5. 

This is Mooney s equation for the stored elastic energy per unit volume. The constant Ci corresponds to the kTvel V of the statistical theory i.e., the first term in Eq. (49) is of the same form as the theoretical elastic free energy per unit volume AF =—TAiS/F where AaS is given by Eq. (41) with axayaz l. The second term in Eq. (49) contains the parameter whose significance from the point of view of the structure of the elastic body remains unknown at present. For simple extension, ax = a, ay — az—X/a, and the retractive force r per unit initial cross section, given by dW/da, is... 

Fig. 135.—The relationship between the equilibrium retractive force T(x (in lbs./in.2) at 241 °C for various multilinked poly (e-caproamides) at the extensions (a) indicated, and their equilibrium swelling ratios in m-cresol at 30°C. O, tetralinked polymers octa-linked polymers. The lines have been calculated according to Eq. (41), with appropriate revision for the octafunctional case (broken lines), an arbitrary value being assigned to the parameter Xi for each elongation. (Schaefgen and Flory.33)...

Equilibrium retractive force, referred to unit undeformed cross section, for elongated rubber (Chap. XI). Same quantity specifically for the elongation a. 

The retractive force Increases as 0) increases in this case... 

Literature data for the relative energy part of the modulus or retractive force show a broad scattering covering the range from 0.14 to 0.27 (38-44). Some of the authors cited, have found a distinct dependence on the magnitude of deformation, but surprisingly they do not indicate this findinq (43). 

Figure 5. Logarithm of the retractive force at 49% strain (lower curve) and sample temperature (upper curve) plotted against logarithm of time reduced to 263 K. Cross-links are introduced at log t/aT is 3 in the glassy state where the spike on the force curve is due to thermal contraction upon cooling below the glass transition temperature. Equilibrium force at 263 K after cross-linking is feQ. (Reproduced, with permission, from Ref. 27. Copyright 1981, Journal of Chemical Physics.)...

Figure 6. Retractive force at constant strain, A corrected for thermal expansion, plotted against temperature. Behavior is completely reversible in range of 263 to 373 K. Serious degradation takes place above 393 K.

The structure of hydrogels that do not contain ionic moieties can be analyzed by the Flory Rehner theory (Flory and Rehner 1943a). This combination of thermodynamic and elasticity theories states that a cross-linked polymer gel which is immersed in a fluid and allowed to reach equilibrium with its surroundings is subject only to two opposing forces, the thermodynamic force of mixing and the retractive force of the polymer chains. At equilibrium, these two forces are equal. Equation (1) describes the physical situation in terms of the Gibbs free energy. 

Here, AGeiastic is the contribution due to the elastic retractive forces developed inside the gel and A6mixi g is the result of the spontaneous mixing of the fluid molecules with the polymer chains. The term AGmjXjng is a measure of the compatibility of the polymer with the molecules of the surrounding fluid. This compatibility is usually expressed by the polymer-solvent interaction parameter, xi (Flory, 1953). 

The change of chemical potential due to the elastic retractive forces of the polymer chains can be determined from the theory of rubber elasticity (Flory, 1953 Treloar, 1958). Upon equaling these two contributions an expression for determining the molecular weight between two adjacent crosslinks of a neutral hydrogel prepared in the absence of... 

PET is not strictly Newtonian, or else it could not be fiber-forming. Polymers with the latter property develop increasing tension due to retraction forces as they become oriented, so that localized necks do not grow and become discontinuities. At high shear rates, molecular orientation will also reduce the resistance to shearing. 

As pointed out earlier, an elastomer cross-linked above its gel point will not dissolve in a solvent, but will absorb it and swell. The swelling will continue until the forces of swelling balance the retractive forces of the extended chains of the network. The cross-link density can then be calculated from the degree of swelling using the Flory-Rehner Equation ... 

If the freely swollen gel is subjected to a unidirectional strain, its degree of swelling will change from q to q and a retractive force will arise, similar to the dry case given by Eq. (III-ll)... 

Differentation of Eq. (IV-15) with respect to Lx gives the retractive force for unilateral extension and compression. Remembering that the unstrained material may actually not be in the state of normal coiling (used as a basis for Eq. IV-15), we obtain, analogously to the Gaussian case of Eq. (III-l 1),... 

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