Elasticity molecular origins

The various elastic and viscoelastic phenomena we discuss in this chapter will be developed in stages. We begin with the simplest the case of a sample that displays a purely elastic response when deformed by simple elongation. On the basis of Hooke s law, we expect that the force of deformation—the stress—and the distortion that results-the strain-will be directly proportional, at least for small deformations. In addition, the energy spent to produce the deformation is recoverable The material snaps back when the force is released. We are interested in the molecular origin of this property for polymeric materials but, before we can get to that, we need to define the variables more quantitatively. 

The phenomenological approach does not preclude a consideration of the molecular origins of the characteristic timescales within the material. It is these timescales that determine whether the observation you make is one which sees the material as elastic, viscous or viscoelastic. There are great differences between timescales and length scales for atomic, molecular and macromolecular materials. When an instantaneous deformation is applied to a body the particles forming the body are displaced from their normal positions. They diffuse from these positions with time and gradually dissipate the stress. The diffusion coefficient relates the distance diffused to the timescale characteristic of this motion. The form of the diffusion coefficient depends on the extent of ordering within the material. 

The Molecular Origins of Elasticity. Recall from Section 1.0.4 that atoms are held together by interatomic bonds and that there are eqnations such as Eq. (1.13) that relate the interatomic force, F, to the potential energy function between the atoms, U, and the separation distance, r ... 

We subject a sample of solid polymer material to a sudden deformation process y0, with an elastical stress o0 = Gy0 (G shear modules). The original strain gives rise to an increase of the molecular valency angles and the intermolecular distances. From these molecular deformations an elastic molecular potential A0 arises which in turn causes molecular displacements. These prevail in the direction of the original strain, decreasing the elastic potential A in that neighborhood. We can calculate... 

Priss LS (1981) Molecular origin of constants in the theory of rubber-like elasticity considering network chains steric interactions. J Pure Appl Chem 53 1581-1596 Priss LS, Gamlitski YuA (1983) Mechanism of conformation transitions in polymer chains. Polym Sci USSR 25 117-123... 

Thus, the restoring force is proportional to the extension and the onedimensional chain behaves as a Hookean spring. This important result simplifies the analysis of the normal modes of motion of a polymer. Polymer chain models can be treated mathematically by the much simpler linear differential equations because second order effects are absent. (It should be noted diat, while the elastic equation for a polymer chain is identical in form with Hooke s law, the molecular origin of the restoring force is very different). 

The mechanical spectra and temperature dependencies derived from DMA provide, as such, no immediate insight to their molecular origin. Qualitatively the various viscoelastic phenomena are linked to the energy-elastic deformation of bonds and the viscous effects due to large-amplitude movement of the molecular segments. The latter are based on internal rotation causing conformational motion to achieve the equilibrium entropy-elastic response. 

Considerable success has also been achieved in fitting the observed elastic behavior of rubbers by strain energy functions that are formulated directly in terms of the extension ratios Xi, X2, X2, instead of in terms of the strain invariants /i, I2 [22]. Although experimental results can be described economically and accurately in this way, the functions employed are empirical and the numerical parameters used as fitting constants do not appear to have any direct physical significance in terms of the molecular structure of the material. On the other hand, the molecular elasticity theory, supplemented by a simple non-Gaussian term whose molecular origin is in principle within reach, seems able to account for the observed behavior at small and moderate strains with comparable success. 

The molecular origin of the recovery from large deformations, which is the essence of rubber elasticity, was not recognized until the early 1930s. Evidence for this was the fact... 

Fig. 1.4. Sketches explaining the observations described in Fig. 1.3 in terms of the molecular origin of the elastic force or pressure [3].

It is somewhat difficult conceptually to explain the recoverable high elasticity of these materials in terms of flexible polymer chains cross-linked into an open network structure as commonly envisaged for conventionally vulcanised rubbers. It is probably better to consider the deformation behaviour on a macro, rather than molecular, scale. One such model would envisage a three-dimensional mesh of polypropylene with elastomeric domains embedded within. On application of a stress both the open network of the hard phase and the elastomeric domains will be capable of deformation. On release of the stress, the cross-linked rubbery domains will try to recover their original shape and hence result in recovery from deformation of the blended object. 

Plastics are high-molecular-weight organic compounds of natural or mostly artificial origin. In fabrication, plastics are added with fillers, plasticizers, dyestuffs and other additives, wliich are necessary to lower the price of the material, and give it the desired properties of strength, elasticity, color, point of softening, thermal conductivity, etc. 

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