INDEX stress coefficients

V. Galiatsatos, R.O. Neaffer, S. Sen and B.J. Sherman, Refractive index, stress optical coefficient, and optical configuration parameter of polymers. In J.E. Mark (Ed.), Physical Properties of Polymers Handbook, Springer-Verlag, New York, 1996, p. 535. 

Galiatsatos V, "Refractive Index, Stress-Optical Coefficient and Optical Configuration Parameters of Polymers", in Mark JE (Ed), "Physical Properties of Polymers Handbook", Springer-Verlag, 2nd Ed 2007. Chap. 50. 

Refractive Index, Stress-Optical Coefficient, and Optical Configuration Parameter of... 

Galiatsatos, V. Neaffer, R. O. Sen, S. Sherman, B. J., Refractive Index, Stress Optical Coefficient, and Optical Configuration Parameter of Polymers. In Physiccd Properties of Polymers Handbook, Mark, J. E., Ed. Springer-Verlag New York, 1996 pp 535-543. 

The rheological properties of a particular suspension may be approximated reasonably well by either a power-law or a Bingham-plastic model over the shear rate range of 10 to 50 s. If the consistency coefficient k is 10 N s, /m-2 and the flow behaviour index n is 0.2 in the power law model, what will be the approximate values of the yield stress and of the plastic viscosity in the Bingham-plastic model ... 

Data compiled by Hanks (1983) show that, contrary to earlier notions, the m coefficient in Equation 1 may be affected by the genotype. A relatively greater net gain of carbon for the same rate of transpiration under stress may be reflected in the m coefficient (Equation 1), in the ratio between assimilation and transpiration (assimilation ratio) or in the agronomic index, WUE (Equation 2). 

A film of paint, 3 mm thick, is applied to a flat surface that is inclined to the horizontal by an angle 9. If the paint is a Bingham plastic, with a yield stress of 150 dyn/cm2, a limiting viscosity of 65 cP, and an SG of 1.3, how large would the angle 9 have to be before the paint would start to run At this angle, what would the shear rate be if the paint follows the power law model instead, with a flow index of 0.6 and a consistency coefficient of 215 (in cgs units) ... 

The latter form is required to reflect the fact that the direction of the shear stress must reverse when the shear rate is reversed, and to overcome objections such as y , and therefore r, having imaginary values when y is negative. The power n is known as the power law index or flow behaviour index, and K as the consistency coefficient. 

An LDPE resin was used for this study. The resin had a melt index of 2.0 dg/min (2.16 kg, 190 °C) and a solid density of 0.922 g/cmT The shear viscosity was reported previously [37] thermal properties are provided in Chapter 4 bulk density as a function of temperature and pressure is provided in Fig. 4.4 and the coefficients of dynamic friction are provided in Appendix A5. The lateral stress ratio was measured at 0.7 [38] using the device shown in Fig. 4.8. 

Birefringence induced by applied stress is caused by the two components of the refracted light traveling at different velocities. This generates interference which is characteristic of the material. The change in refractive index, An, produced by a stress S is often related by a factor C called the stress-optical coefficient as follows ... 

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. 

Fig. 18. Dependence of the stress-optica] coefficient C on the refractive index of swollen polyacrylamide gel n (O) nonionized network, ( ) ionized network. Taken from [31]...

A jumpwise volume change in the transition correlates with a jumpwise change in the shear equilibrium modulus, the refractive index, the stress-optical coefficient and in the components of complex permittivity e and complex modulus G. ... 

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... 

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