Rubber birefringence

Equation (32a) has been very successful in modelling the development of birefringence with extension ratio (or equivalently draw ratio) in a rubber, and this is of a different shape from the predictions of the pseudo-affine deformation scheme (Eq. (30a)). There are also very significant differences between the predictions of the two schemes for P400- In particular, the development of P400 with extension ratio is much slower for the network model than for the pseudo-affine scheme. 

Birefringence. The birefringence of a crosslinked Gaussian rubber subjected to an affine deformation is described by the theories of Kuhn and Grun (1 ) and Treloar (2). These predict a stress-optical coefficient given by... 

Deterioration of rubbers, fibres or plastics resulting from attack by living organisms. Birefringence... 

Fig. 32. Stress-strain and birefringence-strain data of a chemically crosslinked polyurethane rubber in Mooney-Rivlin type representations (Eq. IV-26a and Eq. IV-29). Data reported by Blokland (14)...

Priss LS (1980) The theory of high elasticity and birefringence of rubber. Int J Polym Mater... 

Thurston GB, Peterlin A (1967) Influence of finite number of chain segments, hydrodynamic interaction, and internal viscosity on intrinsic birefringence and viscosity of polymer solutions in an oscillating laminar flow field. J Chem Phys 46(12) 4881 4884 Treloar LRG (1958) The physics of rubber elasticity. Oxford University Press, London Tsenoglou C (2001) Non-Newtonian rheology of entangled polymer solutions and melts. Macromolecules 34 2148-2155... 

The results discussed in this chapter demonstrate that 2H NMR is a powerful technique for investigating microscopic properties in rubber networks. Most of the experiments described here are easy to handle on standard NMR equipment. Due to the absence of interactions between 2H nuclei, spectra and line shapes are easy to interpret and give quite direct information, at least in the first step of analysis, which is that generally required to correlate microscopic to macroscopic properties in these systems. Additionally, in contrast to optical techniques (as birefringence, infrared dichroism, fluorescence polarisation) the information which is obtained is very specific, because spatial and temporal averaging processes are clearly distinguishable in NMR. 

For rubber-elastic materials (i.e. cross-linked polymers above their Tg) theory predicts that the degree of orientation is directly proportional to the retractive stress, and the birefringence directly proportional to the orientation. Thus, for uniaxial tension, the birefringence and the retractive stress are related by the simple equation ... 

From data on flow birefringence of polymer solutions, values of the segmental anisotropy, Aa = ai — a2, can be calculated by means of Kuhn s equation on flexible rubber chains ... 

To illustrate the usefulness of birefringence measurements in orientation studies, we now briefly discuss two simple models of orientation leading to different expressions of the second moment of the orientation function the affine deformation model for rubbers and the pseudo-affine model more frequently used for semi-crystalline polymers. 

PARA with rubber-modified PS transparent, having near-zero birefringence Angeli Maresca, 1990... 

Microscopy. The polarized optical micrographs of thin films of HX-205 and F-185 neat resins were obtained using a Zeiss ultraphot microscope equipped with a polarizer and an analyzer. Thin films, approximately 100 microns thick, were prepared by thln-sectlonlng the resin sheet with a razor blade at room temperature. The domains were observable because of light scattering as a result of refractive Index mismatch between the rubber domain and the epoxy matrix, as well as to stress-induced birefringence produced by the thermal stress Imposed on the domains. 

For the polymer considered in the previous section the birefringence measurements and the stretching or shrinkage took place at different times the birefringence was measured in the frozen-in state of orientation. It is, however, possible to measure the birefringence of a real rubber when it is still under stress at a temperature above its glass-transition temperature. This provides a simultaneous test of the predictions of the rubber deformation theory for both orientation and stress. 

This equation shows that the ratio of the birefringence to the true stress should be independent of stress. The expression on the RHS of equation (11.13) is known as the stress-optical coefficient. A test of equation (11.13) can be made by plotting An against cr, when a straight line should be obtained. Such plots for a vulcanised natural rubber at various temperatures are shown in fig. 11.5. The hysteresis shown in the curves for the lower temperatures is interpreted as being due to stress crystallisation, with the crystallites produced being oriented in the stretching direction and... 

Fig. 11.5 The relation between birefringence and stress for natural rubber at various temperatures , strain increasing and O, strain decreasing. Data for the various temperatures are offset along the birefringence axis. (Reproduced by permission of the Royal Society of Chemistry.)...

The variation of birefringence with draw ratio for a set of uniaxially drawn samples of a certain polymer is found to be consistent with the simplest version of the affine rubber model when the draw ratio is less than 3.5. If the birefringence is 7.65 x 10 for draw ratio 3.0, calculate its value for a sample of draw ratio 1.5. If the birefringence for a very highly oriented sample is 0.045, what is the effective number of random links per chain ... 

Deduce whether the affine rubber or the pseudo-affine aggregate model better describes these data. Given that the birefringence observed for a very highly uniaxially oriented sample of the polymer is 0.078, deduce what numerical information you can about a sample with draw ratio 3.0. 

An independent method of determining stress, especially useful for materials under flow, is from the optical birefringence. Of course, it is limited to transparent materials, which precludes application to filled polymers. Because of the need for transparency, stress birefringence has been used more often for plastics than rubber. Residual anisotropy due to unrelaxed orientation can also be assessed using birefringence this is commonly known as the photoelastic effect. Generally the birefringence is directly proportional to the tme stress... 

FIGURE 6.16 Optical birefringence for 1,4-polybutadiene and natural rubber networks under tension and compression the stress optical coefficient is given by the slopes = 3.6 and 2.0 GPa, respectively (Mott and Roland, 1996). 

The wavelength dispersion of orientation birefringence must be controlled precisely for color display. Based on the Kuhn and Griin model proposed for the stress-optical behavior of cross-linked rubbers, the orientation birefringence Anin(l] of an oriented polymer is expressed as follows [20, 23-27] ... 

Such ideas formed the basis of the Kuhn and Grun model for the stress-optical behaviour of rubbers. The birefringence of a uniaxially stretched rubber is given by... 

This expression has been shown to provide a quantitative understanding of the behaviour of rubbers. Because of the many configurational possibilities for the chains between the network junction points, the segmental orientation for strains 1(K)-2(X)% is much less than the orientation of the lines joining the junction points. The development of birefringence which reflects this segmental orientation is therefore slow, particularly at low extensions where the chains are still close to the... 

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