Bulk viscoelasticity illustrations

The surface forces, of van der Waals type for rubber-like materials, are able to grandly modify the stress tensor provided by the contact of a blunt asperity applied against the flat and smooth surface of a rubber sample. It will be shown how the coupling of surface adhesion properties and bulk viscoelastic behavior of rubber-like material allows us to solve adherence problems. This will be illustrated through three examples the spontaneous peeling due to the intervention of internal stresses the no-rebound of balls on the smooth surfoce of a soft elastomer and the adhesive contact and rolling of a rigid cylinder under a smooth-surfaced sheet of rubber. 

It seems desirable at this point to familiarize the reader with some concrete examples of the viscoelastic phenomena defined in the preceding chapter, and to provide an idea of their character as exhibited by various types of polymeric systems. Linear viscoelastic behavior in shear will be illustrated in considerable detail, with a few additional examples of bulk viscoelastic behavior and nonlinear phenomena. The examples are accompanied by some qualitative remarks about molecular interpretation, anticipating Chapters 9 and 10 where molecular theories will be discussed more quantitatively. 

Molecular motions very similar to some of these may also occur in vitrifying liquids of low molecular weight near and below Tg. Indeed, the bulk viscoelastic properties, as evidenced by the course of volume contraction near Tg illustrated in Fig. 11 -7 and discussed further in Chapter 18, seem to be very similar for both polymers and small molecules (Section B1 of Chapter 18). In shear viscoelastic properties, however, there are some characteristic differences, and it is instructive to examine the behavior of small molecules first. 

CR 3nd tp are the contributions from chain recoiling and interfacial dynamics (i.e. drag forces and disentanglement), respectively, and / ve is the viscoelastic loss function which has interfacial and bulk parts. / is a characteristic length of the viscoelastic medium, t is the contact time and n is the chain architecture factor. Fig. 21 illustrates the proposed rate dependency of adhesion energy. 

Several excellent treatments of molecular viscoelasticity are available. (See the references of Chapter 1.) The book by Professor Ferry, in particular, is an exhaustive and complete exposition. The question may then be asked, why the necessity for still another text and one restricted to bulk amorphous polymers, at that Such a question must send each of the authors scurrying in quest of an "apologia pro vita sua." The answer to the question lies in the use of the word "introduction" in the title. What we have attempted to do is to provide a detailed grounding in the fundamental concepts. This means, for example, that all derivations have been presented in great detail, that concepts and models have been presented with particular attention to assumptions, simplifications, and limitations, and that problems have been provided at the end of each chapter to illustrate points in the text. The level of mathematical difficulty is such that the average baccalaureate chemist should be able to readily grasp it. Where more advanced mathematical techniques are required, such as transform techniques, the necessary methods are developed in the text. 

Samples of bulk polymers respond to applied stresses in several ways some materials behave as elastic solids, some as viscous liquids, and stiU others exhibit viscous as well as elastic properties. The latter are called viscoelastic solids. If a constant force is applied to a viscoelastic sample, the extension of this solid may be divided into three parts (1) an instantaneous elastic deformation, (2) a delayed elasticity or creep, and (3) a viscous flow. This may be seen best by referring to Fig. 15-17 which illustrates an example of a tensile force Fo applied at zero time, maintained until... 

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