Tobolsky-Eyring

The concept of slipping of secondary bonds was applied by Tobolsky and Eyring in 1943 to the breaking of polymeric threads under — uniaxial — load [44]. The 

For large values of stress the flow of bonds takes place almost exclusively as breakage and not as reformation. In that case one may use Eq. (3.17) instead of (3.19). If one substitutes there NkT by one obtains a solution in terms of 

The lower limit of integration isyQ = NokT = w/kT. Equation (3.21) 

Within the range of validity of this approximation the logarithm of lifetime, log tb, is almost linearly related to w, i.e., to the applied stress. Exactly this behavior is exhibited by a large number of stressed metals, ceramics, or polymers. Together with Eyring s original interpretation this has laid the foundations of the kinetic theory of fracture, to which — as indicated above — subsequently a large number of researchers have contributed. 

---

The second is developped from a chemiqal approach of the rupture according to the Tobolsky-Eyring theory [14, I5J. This model considers that the activation energy for the interfacial bond breaking reaction depends on the chemical and mechanical state of the interface. When this dependency is strong enough, two solutions... 

A comparison of different reaction rate models was made by Henderson et al. [76] who found that the bond rupture theories (Tobolsky-Eyring, Zhurkov-Bueche) gave better agreement with fracture data on filled polybutadiene and filled and unfilled PVC than the bond slippage hypothesis. Primary uncertainties exist, however, with respect to a repair reaction and to the temperature dependence of jS and 7. The question of the true meaning of the activation volumes P and 7, of the stress ratio 0/ 0 > of the role of chain stretching and chain scission in macroscopic fracture will be resumed in Chapters 7 to 9. 

In a recent version of the Tobolsky and Eyring formulation, the rate of mechanochemical degradation was considered as a Thermally Activated Barrier to Scission (TABS) process. The elastic energy function f(v /) was explicitly considered in terms of the frictional hydrodynamic drag force acting over the entire macromolecule [100]. A more detailed account of this model will be presented in Sect. 5.1. 

There has been a prevailing theory that oxidative degradation is accelerated by mechanical stress [100]. This theory is based on fracture kinetic work by Tobolsky and Eyring [101], Bueche [102, 103, 104], and Zhurkov and coworkers [105, 106, 107]. Their work resulted in an Arrhenius-type expression [108] sometimes referred to as the Zhurkov equation. This expression caused Zhurkov to claim that the first stage in the microprocess of polymer fracture is the deformation of interatomic bonds reducing the energy needed for atomic bond scission to U=U0-yo, where U0 is the activation energy for scission of an interatomic bond, y is a structure sensitive parameter and o is the stress. 

A reaction rate model was first used by Tobolsky and Eyring to describe the viscoelastic mechanical properties of rubber-like materials. Zhurkov and Korsukov showed that the same model could be used to account for the degradation of a number of polymers under an applied stress. " They derived Eq. (10) for the time to failure, tf, in which A and are the Arrhenius constants for the fracture process, a is a constant (sometimes called the activation volume), and a is the applied stress. 

From a chemical viewpoint, bond scission under stress is a particular case of a un-imolecular dissociation reaction whose rate is enhanced by mechanical stress. As such, it could be treated with Eyring s transition-state theory [Eq. (37)], which permits one to bring the treatment of rate processes within the scope of thermodynamic arguments. By combining de Boer s thermodynamic formulation and the transition-state theory, Tobolsky and Eyring in 1943 developed the rate theory for thermally activated fracture of polymeric threads. When put into an Arrhenius-... 

An extensive discussion of the stress relaxation function in vulcanized mbber completes this chapter. The work was performed by another emerging leader in polymer science Arthur V. Tobolsky (1919-1972). He received his Ph.D. from Princeton University in 1944 and worked with Henry Eyring and Hugh S. Taylor. Taylor was proud to present the Bingham Medal of the Society of Rheology to Tobolsky in 1956. Tobolsky also collaborated with Herman Mark on the Second Edition of his monograph [3], published in 1950. He was so successful at Princeton that he was appointed there immediately. He found himself at Brooklyn Poly as Professor of Chemistry in 1950, but returned to Princeton where he spent the rest of his life. One of the first students to graduate under the direction of Arthur Tobolsky was Richard S. Stein (1925-) in 1948. 

One of the early applications of the theory given by Glasstone, Laidler, and Eyring [43] was the prediction of the flow and diffusion behavior of liquids. From the original concept of flow, the thermally activated jump of molecules across an energy barrier, various fracture theories of solids have emerged. Tobolsky and... 

The system of Eqs. (3.26), (3.28), and (3.29) has been evaluated for a completely oriented and an unoriented network under constant uniaxial stress Gq, The case of a completely oriented network is that treated by Tobolsky and Eyring. All elements are thought to be subjected to the same stress which increases inversely proportional to the decreasing number of unbroken elements. Breakdown of the sub volume occurs with breakage of the last element within the sub volume, i.e., after f has reached zero. The time to breakdown of the subvolume, is taken from Eqs. (3.20), (3.21), and (3.26) as... 

---