Strain optical coefficient

Dynamo-optical and strain-optical coefficients can be estimated from measurements of birefringence An under elongational flow or shear flow, correspondingly... 

The strain-optical coefficient O(w), defined by equation (10.22), can be corresponded to dynamic modulus calculated in Section 6.4.2. Taking all the previous speculations into account, an expression for the strain-optical coefficient can be written in general way as... 

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... 

As mentioned above, values of conformation dependent properties such as those for the root mean square chain distance ((R )), the dipole moment or the strain optical coefficient can be derived by the RIS approximation. For example, the values of (R ) for a given chain are calculated (assuming no interaction between rotational angles on adjacent bonds) from (see equation 2F.23, Appendix 2F). 

Time dependent dichroic measurements during the stress relaxation of low density polyethylene have been reported by Gotoh et alP and more recently by Fukui et alP and by Uemura and Stein. Fukui and coworkers determined both crystalline and amorphous orientation functions at a constant strain between 2-5 and 5%. At room temperature, values of —f and —f>, estimated from data on the 730 and 720 cm" bands respectively, increased with time towards steady values which were attained after about 10 s. These time dependencies were considered to largely determine the observed time dependence of the strain-optical coefficient. Values of f from the 1352 cm" band showed little time dependence, but the amorphous orientation was estimated to contribute the larger amount to the magnitude of the strain-optical coefficient. 

Here, Cs is the coefficient of strain, which is related to the strain optic coefficient Pe- The coefficient of temperature is made up of the thermal expansion coefficient of the optical fibre, ota, and the thermo-optic coefficient, 0. These parameters are slightly dependent on the FBG manufacturer, but typical values are 0.79 for Cs, and 0.55E - 6 and 8.6E - 6 for a and respectively. 

Figure 5.10. Temperature dependence of the strain-optical coefficient for a segmented polyester-urethane. Note that the STOC values are independent of percent prestrain. (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... 

These relations are valid for x 1, 5 S> 1- It is determined by five relaxation branches, while the first conformational branch, which is an analogue of the reptation branch, does not contribute practically to the strain-optical coefficient as well to the dynamic modulus. So that it is not essential that this branch is not correctly described in the linear theory. 

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...

Expression (163) allows us to describe different types of the frequency dependence of the strain-optical coefficient which were discovered by Inoue et al [123] and Okomoto et al [124]. As an example a frequency dependence of the real and imaginary parts of the strain-optical coefficient, together with the contributions from different relaxation branches, is shown in Fig. 4. One can notice that the plot on Fig. 4 resembles the empirical picture for polymers discovered by Okomoto et al [124]. So, the mesoscopic theory gives an alternative explanation to the curious behaviour of the strain-optical coefficient... 

In numeric simulations, the parameters of the FBG sensor are the same as those used in the corresponding experiments. The core radius, cladding radius and the effective refractive index are 4.25 pm, 62.5 pm and 1.46, respectively. The strain-optic coefficients Pj j and taken as 0.113 and 0.252, respectively. 

Strain-optic coefficient Index of refraction Elastic modulus Poisson s ratio... 

Takemesa, M Chiba, A. (2001). Gelatin mechanism of K and i-Carrageenan investigated by correlation between the strain-optical coefficient and the dynamic shear modulus. Macromolecules, Vol. 34, No. 21, pp. 7427-7434, ISSN 0024-9797. 

As a practical matter, these results demonstrated to the experimental stress analyst that it was easy for the polymer chemist to modify the strain optical coefficient of a resin if the analyst... 

Figure Reduced strain-optical coefficient curve for the same material as Figure 3.(from Arenz, Ferguson and Williams, Ref. 5)...

Given t = 3.048 mm and D = 5.080 mm a fit to this equation for V yields 5.36 X 10 m N , and assuming v = 0.5 then E = 4.45 MPa, which is in agreement with the nominal value given by the manufacturer of 4 GPa. From this value of , the value of the strain-optical coefficient is found to be 0.0087. The strain-optical coefficient has a nominal value given by the manufacturer of 0.009 and is the unitless strain version of the stress-optical coefficient K. 

The thermal birefringence was calculated based on a linear viscoelastic and a photoviscoelastic constitutive equation as given in [7] along with a measured stress- and strain-optical coefficient functions [8]. For a onedimensional quenching problem... 

In this study, two optical grade polycarbonates, Lexan OQ1030 and OQ3820 from General Electric Company, have been used to obtain master curves on both relaxation modulus and the strain-optical coefficient (for details see Ref. [8]). The complex viscosities as a function of frequency at various temperatures were obtained by ARES rheometer. The fitted and experimental data are shown in Fig. 1. 

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