The Elastic Strain Theory

The correlation between the effective strain of a polymer chain and its absorption energy, established from direct absorption measurements on stretched polymer fibres allows an independent determination of the length of the repeat unit as a function of X via optical absorption measurements Data obtained by this method display a systematic deviation from the theoretical plot (Fig. 7) as do data derived from resonant Raman measurements . This indicates that the agreement between experimental data and predictions of the elastic strain (ES)-theory is fulfilled only 

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Finally, there is experimental evidence that the thermal polymerization of some monomers with mismatches comparable to PTS cannot be described by the elastic strain theory... 

One of the shortcomings of the elastic strain theory which leaves room for further improvements is the fact that assumptions must be made about the individual initiation, propagation and termination steps which cannot be observed independently but are calculated from the overall reaction rate. 

In contrast, some theories consider the elastic strain energy field to be important. Dissolution in-hibitors appear to slow down dissolution by adsorbing at special surface sites namely, kinks in crystallographic steps. 

Arrays of Fault Planes. When we consider arrays of CS planes we can use the Fourier Transform method of evaluating the elastic-strain energy of the array, as well as the classical theory. This allows us to evaluate not only the elastic strain in the matrix between CS planes, but also to obtain some measure of the relaxation energy of the ions in the CS planes themselves. In this Section we will initially discuss the matrix strain, and then consider calculations which include relaxation. 

If a crystal is subjected to small strain elastic deformation it is convenient to imagine the energetics of the strained solid in terms of the linear theory of elasticity. As we noted in chap. 2, the stored strain energy may be captured via the elastic strain energy density which in this context is a strictly local quantity of the form... 

To see how the fracture energy may be used in the initiation of chemical reactions, the concepts of fracture mechanics are introduced, including the strain rate and temperature dependence of the ductile-brittle behavior. The starting point is the Griffith theory which in its simplest form applies to perfectly brittle materials and states that for a crack to form, the elastic strain energy available must be at least sufficient to provide the energy of the new surfaces formed [74]. 

In the foregoing treatment, the influence of the elastic strain energy has deliberately been neglected. With the help of the theory of elastically deformed bodies, it is found that, in the case where there is a change in lattice constant with composition, the free energy has an additional term which is positive and reads ... 

The simplest model of this kind is the elastic bar theory studied by Ericksen [11]. He considers the static theory of bars governed by a one-dimensional, nonlinearly elastic stress-strain relation shown in Fig. 6. 

In the classical theory of elasticity, the stress tensor Cy is linearly dependent on the elastic strain tensor, i.e.. 

The elastic theory of SmC has beep considered by the Orsay groupand by Rapini. Both approaches use the Oseen description of smectic A, neglecting all changes in internal parameters such as density, interlayer distance, and tilt angle. The Orsay group used the Lagrai an description for the elastic strains with a vector IKF) describing the local rotation of the director. In order to be consistent with the elastic theory for NLC s, we shall use the Eulerian description developed by Rapini based on the director. 

The maximum strain theory can be determined by assuming that the material is linearly elastic up to the ultimate failure. The ultimate strains in Eqs. 2-29, 2-30, and 2-31 as well as 2-32 and 2-33 can be related directly to the strengths as follows ... 

Theoretical analyses of titis phenomenon, for flow in roimd capU-laries, are available [41-45] in which the most basic [44] of them is built upon the free recovery calculations set down by Lodge [13] using the theory of Berstein, Kearsley and Zapas [46]. The developed expression for die swell S in which the elastic strain recovery Sr is balanced by the shear stresses arising in the die, is given by,... 

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