Molecular elongation

Molecules, of course, are generally no closer to ellipsoids than to spheres. Nonetheless, the results of Perrin clearly show the order of magnitude of the effects of molecular elongation and flattening—and by implication the effects of other geometric distortions as well. 

Consequently, elements of the matrix corresponding to nonexisting path-distance pairs contain zero frequency value, ivhereas all nonzero values indicate the molecular elongation, size, and variegation of the surface. 

By using simple scaling laws for the polarizability and first hyperpolarizability as a function of the molecular size, Hurst and Munn [93] addressed, within the point dipole approximation, the relationship between nd molecular elongation and found that very large can be obtained for compact molecules, provided that the ratio between the polarizability and the molecular volume is large. 

It may be worth while to return here to the definition of molecular elongation. For one particular coil, the dimensionless elongation A(d can be constructed from the radius of gyration R in the distorted state... 

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. 

A great many liquids have entropies of vaporization at the normal boiling point in the vicinity of this value (see benzene above), a generalization known as Trouton s rule. Our interest is clearly not in evaporation, but in the elongation of elastomers. In the next section we shall apply Eq. (3.21) to the stretching process for a statistical—and therefore molecular—picture of elasticity. 

An important application of Eq. (3.39) is the evaluation of M, . Flory et al.t measured the tensile force required for 100% elongation of synthetic rubber with variable crosslinking at 25°C. The molecular weight of the un-cross-linked polymer was 225,000, its density was 0.92 g cm , and the average molecular weight of a repeat unit was 68. Use Eq. (3.39) to estimate M. for each of the following samples and compare the calculated value with that obtained from the known fraction of repeat units cross-linked ... 

Fig. 8. Elongational viscosity at 180°C of polypropylene of different molecular weight and distribution (30) see Table 4 for key.

C. Characteristically, these nematic melts show the persistence of orientational order under the influence of elongational flow fields which result in low melt viscosities under typical fiber formation conditions even at high molecular weights. 

Fluoroplastics. Conventional plasticizers are used as processing aids for duoroplastics up to a level of 25% plasticizer. However, certain grades of Kel-E (chlorotriduorethylene) contain up to 25 wt % plasticizer to improve elongation and increase softness the plasticizers used are usually low molecular weight oily chloroethylene polymers (5). 

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