Strain Stress optical coefficient

The photoelastic behavior of nonionized PAAm network and ionized P(AAm/MNa) network prepared by the copolymerization of AAm with MNa ( MNa = 0.05) was investigated in water-acetone mixtures [31]. For a pure PAAm network, the dependences of all photoelastic functions (see Eqs. (15) and (16)), i.e. modulus G, strain-optical function A and stress-optical coefficient C, on the acetone concentration in the mixtures are continuous (Fig. 17). At ac = 54 vol %, the ionized network undergoes a transition which gives rise to jumpwise change in G, A and C also the refractive index of the gel n8 changes discontinuously. While in the collapsed state the optical functions A and C are negative, in the expanded state they are positive. 

The stress optical coefficient C merits special attention, because it leads directly to the parameter F2 that characterizes the optical anisotropy of the network chain under strain. F2 is defined by (13)... 

Strain and Stress Optical Coefficients. The relationship between A and is usually defined in terms of results obtained in the customary stress relaxation experiment in which a specimen is deformed to a constant strain, and a (or in this case A) is measured as a function of time. The strain optical coefficient, K(t), is defined as... 

FIGURE 6.17 (Bottom) Birefringence for uncrosslinkedPIB after imposition of a shear strain = 2.5. Linear fitting yields 3.07 GPa - for the stress optical coefficient. (Top) Ratio of refractive index components (1 is the flow direction and 2 the direction of the gradient), which equals the value of the shear strain, in accord with the Lodge-Meissner relation (Eq. (6.66)) (Balasubramanian et al., 2005). 

Because these materials stress-soften on extension, their stress-optical behavior depends upon strain level and degree of prestrain (Estes et a/., 1969,1970 Koutsky et a/., 1970). The classical equation for the stress-optical coefficient (SOC) derived from the theory of photoelasticity (Treloar, 1958) is not obeyed ... 

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.)...

The expression for the strain-optical coefficient 0 u ) for a system of weakly-coupled macromolecules is quite similar to the expression for the dynamic modulus, if the stress-optical coefficient C does not depend neither on frequency nor on the relaxation branch. In this case components of the strain-optical coefficient can be calculated according to formula (131) and have the same form as the components of the dynamic modulus, which are shown in Fig. 3. However, to explain experimental data [123, 124], we must admit that the stress-optical coefficient C depends either on frequency or on the relaxation branch. So as the different relaxation branches are assumably connected with different types of motion, one ought to ascribe different values of the stress-optical coefficient to contributions from different relaxation branches, and the expression for the strain-optical coefficient aquires the following form... 

Fig. 4. Strain-optical coefficient of polystyrene. The theoretical dependencies were calculated for polystyrene studied by Onogi et al [97] (see Fig. 3). The separate contributions from relaxation branches are shown by dashed curves 1 - conformational branch 2 -orientation or viscoelastic branch 3, 4, 5 - glassy branches. The values of parameters are B = 3000, E = 20, 000, x = 0.08, r = 5 x 10 s, nT = 1.7 x 10 Pa. The stress-optical coefficient is taken different for different relaxation branches Cl = C2 = — 1, C3 = C4 = C5 = 0.1. The characteristic features of the dependence of the strain-optical coefficient on frequency reminds us the empirical ones discovered by Inoue et al [123] for polystyrene with longer macromolecules...

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