Rubber entropy

Figure 3.3 Comparison of experiment (points) and theory [Eq. (3.39)] for the entropy elasticity of a sample of cross-linked natural rubber. [From L. R. G. Treloar, Trans. Faraday Soc. 40 59 (1944).]...

This thermodynamic behaviour is consistent with stress-induced crystallisation of the rubber molecules on extension. Such crystallisation would account for the decrease in entropy, as the disorder of the randomly coiled molecules gave way to well-ordered crystalline regions within the specimen. X-Ray diffraction has confirmed that crystallisation does indeed take place, and that the crystallites formed have one axis in the direction of elongation of the rubber. Stressed natural rubbers do not crystallise completely, but instead consist of these crystallites embedded in a matrix of essentially amorphous rubber. Typical dimensions of crystallites in stressed rubber are of the order of 10 to 100 nm, and since the molecules of such materials are typically some 2000 nm in length, they must pass through several alternate crystalline and amorphous regions. 

Fig. 113.—Comparison of observed entropies of dilution (points and solid lines with results calculated for ASi according to Eq. (28) (broken line). Data for polydimethyl-siloxane, M =3850, in benzene, A (Newing ), obtained from measured activities and calorimetric heats of dilution. Entropies for polystyrene (Bawn et in methyl ethyl ketone,, and in toluene, O, were calculated from the temperature coefficient of the activity. The smoothed results for benzene solutions of rubber, represented by the solid curve without points, were obtained similarly.

The elastic contribution to Eq. (5) is a restraining force which opposes tendencies to swell. This constraint is entropic in nature the number of configurations which can accommodate a given extension are reduced as the extension is increased the minimum entropy state would be a fully extended chain, which has only a single configuration. While this picture of rubber elasticity is well established, the best model for use with swollen gels is not. Perhaps the most familiar model is still Flory s model for a network of freely jointed, random-walk chains, cross-linked in the bulk state by connecting four chains at a point [47] ... 

Finally, we turn from solutions to the bulk state of amorphous polymers, specifically the thermoelastic properties of the rubbery state. The contrasting behavior of rubber, as compared with other solids, such as the temperature decrease upon adiabatic extension, the contraction upon heating under load, and the positive temperature coefficient of stress under constant elongation, had been observed in the nineteenth century by Gough and Joule. The latter was able to interpret these experiments in terms of the second law of thermodynamics, which revealed the connection between the different phenomena observed. One could conclude the primary effect to be a reduction of entropy... 

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... 

Rotational entropy, 36 Rotation frequency, 8 Rubber natural, 323 perishing of, 328 synthetic, 189, 322 vulcanisation, 323... 

The search for the form of W of vulcanized rubbers was initiated by polymer physicists. In 1934, Guth and Mark2 and Kuhn3) considered an idealized single chain which consists of a number of links jointed linearly and freely, and derived the probability P that the end-to-end distance of the chain assumes a given value. The resulting probability function of Gaussian type was then substituted into the Boltzmann equation for entropy s, which reads,... 

Kawabata44 has panted out on the basis of a simple network model that of the two derivatives, bW/blt and bW/bI2, the former should be related primarily to intramolecular forces such as the entropy force which plays a major role in the kinetic theory of rubber elasticity, while the latter should be a manifestation of intramolecular interactions. He predicted the possibility that bW/bI2 assumes negative values in the region of small defamation. In fact, the prediction was confirmed experimentally by Becker and also by the present authos. 

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