Strain birefringence

Eq. (IV-26a) can be confronted with birefringence-strain data, which can also be written in a Mooney-Rivlin type equation. Remembering that the measured birefringence refers to the strained cross-section, the classical result for the Gaussian part is (171)... 

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)...

The mechanical and rheo-optical properties of Kraton 101 have been studied by Stein136) using films cast from methylethyl ketone and from toluene solutions. The stress-strain curves, birefringence-strain curve, stress relaxation, birefringence relaxation, and dynamic mechanical spectra are dependent upon the morphology of the copolymer which in turn is dependent upon the conditions of preparations of the samples. 

The temperature dependence of birefringence and stress vi/ere measured under the conditions of constant force or constant deformation of the sample. Both experimental techniques lead to the same results of the quotient An/X -X" The stress - strain and birefringence - strain measurements do not differ from these generally received for common rubbers, vi/here cr and An linearly depend on the deformation factor (X -X M. With respect of the formation of the anisotropic phase at lovi/ temperatures especially the temperature dependence of An and cr are of interest. Therefore in order to obtain results vi/hich are comparable i/ith results of amorphous rubbers having no mesogenic side chains wie plotted the product CT versus temperature. 

Figure 4. Entanglement network cross-linked in a state of simple extension. Birefringence-strain curves calculated for cross-link network, trapped entanglement network, and their sum also expermentally measured (0, exp , calc.), for Polymer B at 20.0°C. v = 0.97x10 ", v., = 1.85x10 " mol...

Optical Microscopy. Traditionally, light microscopy has played an important role in the visualization of ordered polymers, and a range of different approaches can be adopted to enhance the contrast, phase contrast, polarized light microscopy, orientation birefringence, strain birefringence, modnlated contrast, interference microscopy, etc (132,141-144). Light microscopy rarely provides resolution better than several micrometers bnt can give a quick and easy assessment of the extent of order in the polymer material. 

Cail, J.J., Stepto, R.F.T. and Ward, I.M. (2007) Experimental studies and molecular modelling of the stress-optical and stress-strain behaviour of poly(ethylene terephthalate). Part 111 Measurement and quantitative modelling of birefringence-strain, stress-strain and stress-optical properties. Polymer, 48, 1379. 

Figure C3.1.13. Experimentai configuration for far-UV nanosecond CD measurements using a frequency-upconverted Ti sapphire iaser as a probe source. Pj and P2 are Mgp2 Rochon poiarizers at cross orientations. SP is a strained transparent piate with about i ° of iinear birefringence for quasi-nuii eiiipsometric CD detection. Prism PMj and the iris Ij seiect the far-UV fourth hannonic of the argon iaser-pumped Ti-sapphire iaser s near-IR fundamentai output to probe the eiiipticity of the sampie. A second iaser beam at 532 nm is used to pump CD...

Venus probe. References should be consulted for the details of the optical transparency of the different type diamonds (9,14,16—19). The direct band gap for diamond is 5.47 eV. Natural diamond exhibits many colors, and color modification by irradiation and annealing is common (36). Though cubic, most natural diamonds show strain birefringence under crossed polaroids. 

The above description refers to a Lagrangian frame of reference in which the movement of the particle is followed along its trajectory. Instead of having a steady flow, it is possible to modulate the flow, for example sinusoidally as a function of time. At sufficiently high frequency, the molecular coil deformation will be dephased from the strain rate and the flow becomes transient even with a stagnant flow geometry. Oscillatory flow birefringence has been measured in simple shear and corresponds to some kind of frequency analysis of the flow... 

Alicyclic dianhydrides are interesting for electronic applications. The polyimides obtained from them are colorless with high transparency in the visible range, exhibit low birefringence,125 and have a low dielectric constant.126 The reactivity of the polycyclic aliphatic dianhydride has been investigated. For example, bicyclo-[2,2,2]-oct-7-ene tetracarboxylic dianhydride reacts quickly with an aromatic amine because the bicyclo-imide is less strained than the corresponding dianhydride.127... 

An example of a relevant optical property is the birefringence of a deformed polymer network [246]. This strain-induced birefringence can be used to characterize segmental orientation, both Gaussian and non-Gaussian elasticity, and to obtain new insights into the network chain orientation (see Chapter 8) necessary for strain-induced crystallization [4,16,85,247,248]. 

Figure 18 shows the percent crystallinity obtained by birefringence measurements for NR at various elongations as a function of temperature. The relative shapes of the curves in this Figure show the pronounced temperature and strain dependence on the strain induced crystallization of NR. Of particular importance is the relatively high amounts of crystallinity that develop at room temperature. 

Such curves, illustrated in Figure 7, show no deviations from linearity which could be attributed to strain-induced crystallization. Similarly, birefringence-temperature measurements also carried out at a > au show no deviations from linearity that could be attributed to crystallization, or to other inter-molecular orderings of the network chains. Typical results of this type are shown in Figure 8 (16),... 

If the filament or ribbon is made of a material showing intense stress birefringence, the birefringence pattern caused by the load W would be compared with that calculated from the strain energy. A reasonable agreement would indicate that W is suspended by the whole volume of the solid, not by its surface layer alone. On the other hand, if the specimen shows no birefringence when stressed by the load W, then Eq. (30) would gain in respectability. 

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