Thermoelastic measurements

Table XXXIII.—Thermoelastic Measurements of Joule on Vulcanized Rubber...

The dipole moment ratio and the temperature coefficient of both the dipole moment and the unperturbed dimensions of the polyesters PDA and PDS are measured. The experimental value of dlln 0) / d Tshows an anomalous dependence on the elongation ratio of the networks at which the thermoelastic measurements are performed. Although the rotational states scheme gives a fairly good account of the polarity of the chains, it fails in reproducing the experimental values of d (In 0) / d T, the causes of this disagreement are discussed. 

The measurements of the temperature dependence of the restoring force are usually carried out in the temperature range 350 100 K. Determination of f requires a rather far extrapolation of experimental results and it restricts the accuracy of this method. This type of thermoelastic measurements requires equilibrium conditions. Most widely, this method is used for simple elongation and seldom for compression 67) and torsion 68,69). 

This type of thermoelastic measurements is based on the relation... 

The E-modulus in the isotropic phase can be determined from both stress-strain and thermoelastic measurements and Me can be calculated according to Me = 3 when the density p of the elastomer is known. The degree of... 

Thermoelastic measurements on such samples reveal a spontaneous elongation along n at the transition to the smectic phase, indicating a prolate polymer backbone conformation in the smectic elastomer [137]. On another hand, SANS results for end-on side-chain polymers in the smectic phase indicate an oblate chain conformation, with the backbone preferentially confined in the plane of the layers (Sect. 2.2). Thus, the chain distribution and macroscopic shape of the smectic elastomer change their sign if crosslinking is made under uniaxial mechanical stress in the isotropic and/or nematic phase. This result is remarkable and indicates that the oblate chain conformation of a smectic end-on polymer can be easily turned into prolate by a low uniaxial extension during solvent evaporation. 

Force-temperature ( thermoelastic ) measurements may therefore be used to obtain experimental values of the fraction f /f of the force which is energetic in origin. Such experiments carried out at constant volume are the most direct, and can be interpreted through use of the purely thermodynamic relationship... 

As an alternative to dilute solution techniques, thermoelastic measurements on strained, amorphous polymer networks can also yield k. Mark [211,212] has reviewed this technique, which is based on the equation... 

Fig. 3.3 Temperature variation of the chain anisotropy r deduced from the thermoelastic measurements. L is the length of the films in the direction of the nematic director, normalized with respect to the length Lq measured at high temperature in the weakly anisotropic state. The data for the NE obtained by photo cross-linking a NP oriented by an H-field were taken by F. Brommel (unpublished result)...

UQstrained rubber. Equations 2 and 6 are equivalent. However, the latter is not as sensitive to the experimental errors normally encountered in thermoelastic measurements. Equation 2 depends on X to the inverse third power, which magnifies any error in the extension ratios. 

Most of the thermoelastic measurements were carried out by keeping the stretched length of the sample constant, and following the changes in the elastic force as the temperature was varied. 

Equations (83) and (84) provide a molecular interpretation of the thermoelastic data through equation (89). This equation establishes the relationship between the purely thermodynamic quantity f /f and its molecular counterpart of dlno/dT, which can be interpreted in terms of the rotational isomeric state theory of chain configurations. It permits comparison of the change of the unperturbed dimensions o obtained by thermoelastic measurements on polymer chains in the bulk (in network structures) with that obtained by viscosity measurements on chains of the same polymer, essentially isolated in dilute solution. 

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