Transition stress, molecular theory

Stress-strain measurements in uniaxial extension have revealed that real networks have a behavior closest to the affine limit at small deformations and approach the phantom limit at large deformations. The recent molecular theory developed by Flory and Erman accounts for this transition. In this model, the restrictions on junction... 

Several attempts to relate the rate for bond scission (kc) with the molecular stress ( jr) have been reported over the years, most of them could be formally traced back to de Boer s model of a stressed bond [92] and Eyring s formulation of the transition state theory [94]. Yew and Davidson [99], in their shearing experiment with DNA, considered the hydrodynamic drag contribution to the tensile force exerted on the bond when the reactant molecule enters the activated state. If this force is exerted along the reaction coordinate over a distance 81, the activation energy for bond dissociation would be reduced by the amount ... 

Three theories were proposed to explain wall-slip (a) adhesive failure at the wall, (b) cohesive failure within the material as a result of disentanglement of chains in the bulk and chains absorbed on the wall, and (c) the creation of a lubricating surface layer at the wall either by a stress-induced transition, or by a lubricating additive. If the polymer contains low molecular weight components or slip-additives, their diffusion to the wall will create a thin lubricating layer at the wall, generating apparent slip. 

Above about 45°C, however, considerable yielding can be observed. Note that the transition between brittle and ductile behavior occurs at a temperature that is significantly below the T. Various theories have been advanced to explain yielding phenomena in polymers, some involving free volume arguments while others involve various types of molecular motion. As far as we can make out, none of these are entirely satisfactory and we won t discuss them here. Instead, we will finish off our discussion of stress/strain behavior by considering rubber elasticity. 

Dispersive interaction has a dramatic effect on the molecular layers closest to the surface, and can be explained in terms of the rate theory for viscous flow.f Within the rate theory, a flow event comprises the transition of a flow unit from its normal or quiescent state, through a flow-activated state, to a region of lower free energy in an external stress field. For small molecules, the flow unit is the whole molecule, while for longer chains, the flow unit is a segment of the entire molecule. By analogy with chemical reaction rate theory, there is a flow-activation enthalpy, and entropy, for transition into the flow-activated state. 

The goal of the work reported here was to devise a theory that predicts the polar/nonpolar phase separation as a favorable thermodynamic process. In addition, the effects of each of the physicochemical forms on the thermodynamic and structural characteristics of the biphasic material were sought. The current molecular model was not developed to predict mechanical or thermal behavior of ionomers. Hence, properties like glass transition and melt temperatures, storage, and shear moduli cannot be determined from the current model. We must also stress that this modeling work is still in its infancy. As such, it has used several tenuous assumptions that must be tested. The formalism is a start, but not the end, to devising a comprehensive treatment of ionomeric structure. 

During the three productive years of a postdoctoral stay in Mark s Laboratory, Robert extended Einstein s equation (originally derived for linear stress gradient) to parabolic Poiseuille flow. There were excursions with Eirich into kinetic theory and viscosity of gaseous paraffins, as well as viscosity, surface tension, and heat of vaporization correlations of chain molecular fluids. The latter made use of the recently formulated transition-state theory of Eyring, Polanyi, and Wigner. 

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