Stress optical coefficient temperature

More recently, test products were created of a blend of PMMA with a phenyl-substituted methacrylate these products have a glass-transition temperature of around 125°C, a significantly reduced water absorption compared to pure PMMA of about 0.32%, but also a higher birefringence (a stress-optic coefficient of 5.2 X 10 , compared with 0.3 X 10 for PMMA and 6.8 x 10 for BPA-PC). 

Figure 7. Stress optical coefficient X temperature as a function of temperature (3). PBD is poly butadiene. Key O, p-xylene A. toluene , benzene CClt all of swollen trans-/,4 PBD.

The stress-optical coefficient of PE networks is calculated, and results are compared with experimental data. Observed temperature coefficients of AT and the optical anisotropy for unswollen samples are much larger than those calculated using acceptable values of E(g), the energy of the gauche conformation, relative to that of Vans. It is concluded that observed temperature coefficients should Include some contributions other than those implied in the theory, i.e., those arising from the conformational change with temperature. 

Fig. 42. Temperature dependence of the product of stress optical coefficient and temperature CT for natural rubber (NR), poly(ethylene) (PE) and the l.c. elastomer No. 2a from Table 10...

Here n is the average refractive index, k is Boltzman s constant, and T is absolute temperature (13). If a polyblend were to form a homogeneous network, the stress would be distributed equally between network chains of different composition. Assuming that the size of the statistical segments of the component polymers remains unaffected by the mixing process, the stress-optical coefficient would simply be additive by composition. Since the stress-optical coefficient of butadiene-styrene copolymers, at constant vinyl content, is a linear function of composition (Figure 9), a homogeneous blend of such polymers would be expected to exhibit the same stress-optical coefficient as a copolymer of the same styrene content. Actually, all blends examined show an elevation of Ka which increases with the breadth of the composition distribution (Table III). Such an elevation can be justified if the blends have a two- or multiphase domain structure in which the phases differ in modulus. If we consider the domains to be coupled either in series or in parallel (the true situation will be intermediate), then it is easily shown that... 

Ca is called the stress optical coefficient. The value of C depends on the chemical structure of the polymer and is somewhat temperature-dependent. The theory of rubber elasticity leads to the following expression ... 

TABLE 10.8 Stress-optical coefficients of polymer melts and elastomers (above their melting temperatures)... 

Table 8.1. Stress-optic coefficients Ca of glassy and rubbery amorphous polymers, and of melts of semicrystalline polymers, in Brewsters (=1(H2 Pa). T denotes the measurement temperature. 

Table 14.4, which lists some requirements for CDs, allows the elimination of some contending plastics. Polystyrene has too low a resistance to crazing and stress cracking, and the disc birefringence would be too high because the relatively elastic melt has a high stress-optical coefficient (defined in Eq. 9.9). Values for melts differ from values for glassy polymers given in Table 11.5. PVC has too low a heat distortion temperature, and its lack of thermal stability makes the injection moulding of high definition surfaces difficult. Silicate glass cannot be moulded with sufficient surface detail, and is brittle.

Similar results for this stress-optical coefficient were obtained for a different family of LCEs [2]. In addition it was shown that the birefringence, An, is linear in the applied stress for the range of temperatures investigated, a result one would expect on the basis of linear stress optics these results are summarized in Fig. 7. 

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... 

An estimate of the number of monomer units per equivalent random link can be obtained by dividing the value of Aa calculated from the stress-optical coefficient by the anisotropy of the polarisability of the monomer unit calculated from bond polarisabilities. This number can more interestingly be expressed in terms of the number of single bonds in the equivalent random link and is found to be about 5 for natural rubber, about 10 for gutta percha and about 18 for polyethylene. (For the last two the values are extrapolated from measurements at elevated temperature.) The number for polyethylene is considerably higher than the value of 3 suggested by the assumption of totally free rotation around the backbone bonds (see section 3.3.3 and problem 3.7). 

This equation predicts that the birefringence is directly proportional to the applied stress, inversely proportional to temperature and independent of the degree of crosslinking and elongation. Experiments [11-15] have confirmed these predictions. Brewster in 1816 first observed the proportionality that is the basis for the photoelastic analysis of structures. The stress-optical coefficient is expressed in units of Brewsters (10 cm2/dynes). The above theory is formulated in terms of the anisotropy (b - - property of the statistical segment that is a... 

Figure 5.9. Effect of strain history on the stress-optical coefficient (measured at 10% strain) for a segmented polyester-urethane at various temperatures. (Estes et al, 1969.)...

An is the difference in the refractive indices n in the plane of the dra i/ing direction and n perpendicular to iti n = (n, + 2n )/3 is the mean refractive index of the sample and Aa the difference of the polarizabilities of the statistical segment (Aa = optical anisotropy) parallel and perpendicular to the axis of the segment. The quotient of orientational birefringence and stress is defined as the stress optical coefficient C. From the simple model of the network chains the product CT (equation 3) should be independent of T if a slight temperature dependence of n is neglected. CT is proportional to the optical anisotropy of the statistical segment. 

Balancing the injection moulding conditions so as to reduce the birefringence would be less critical. If the stress optical coefficient C r of PC would be smaller. Cor of a polymer can be related to Boltzmann s constant k, to the temperature T, to the average refractive Index n, and is directly proportional to the difference in polarizability parallel and perpendicular to the polymer backbone (a - 0L2) ... 

In some samples, further crystallization occurs on stretch ing. In Figure 3 are shown the stress optical coefficient [ratio (a/temperature interval. The stress optical coefficient would be invariant with temperature, if no crystallization occurred such was found to be the case for Sample D, up to -30 C. However, Sample A, starts crystallizing at about 50 C and the crystallization is complete by 0 C. Sample starts crystallizing at about 30 C and the process is not complete until about -30 C. Sample C. does not crystallize above 0 C and shows only a slight tendency to crystallize even below this temperature. 

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