Birefringence model

Equation (32a) has been very successful in modelling the development of birefringence with extension ratio (or equivalently draw ratio) in a rubber, and this is of a different shape from the predictions of the pseudo-affine deformation scheme (Eq. (30a)). There are also very significant differences between the predictions of the two schemes for P400- In particular, the development of P400 with extension ratio is much slower for the network model than for the pseudo-affine scheme. 

Although this model is quite successful as a curve-fitting exercise for birefringence data and has subsequently been shown to be consistent with stress-optical data 26), it must be regarded as an empirical procedure. 

Linearly polarized, near-diffraction-hmited, mode-locked 1319 and 1064 nm pulse trains are generated in separate dual-head, diode-pumped resonators. Each 2-rod resonator incorporates fiber-coupled diode lasers to end-pump the rods, and features intracavity birefringence compensation. The pulses are stabilized to a 1 GHz bandwidth. Timing jitter is actively controlled to < 150 ps. Models indicate that for the mode-locked pulses, relative timing jitter of 200 ps between the lasers causes <5% reduction in SFG conversion efficiency. 

Figure 10. Calculated variation with cladding thickness of the birefringence in a SOI ridge waveguide, for different Si02 cladding film stress values. The model waveguide is formed in a 2.2 [j,m thick Si layer and has a typical trapezoidal wet etched ridge profile, with a base width of 3.8 pm, a top width of 1.1 pm, and an etch depth or 1.47 pm.

The addition of water to solutions of PBT dissolved in a strong acid (MSA) causes phase separation in qualitative accord with that predicted by the lattice model of Flory (17). In particular, with the addition of a sufficient amount of water the phase separation produces a state that appears to be a mixture of a concentrated ordered phase and a dilute disordered phase. If the amount of water has not led to deprotonation (marked by a color change) then the birefringent ordered phase may be reversibly transformed to an isotropic disordered phase by increased temperature. This behavior is in accord with phase separation in the wide biphasic gap predicted theoretically (e.g., see Figure 8). The phase separation appears to occur spinodally, with the formation of an ordered, concentrated phase that would exist with a fibrillar morphology. This tendency may be related to the appearance of fibrillar morphology in fibers and films of such polymers prepared by solution processing. 

The theory of strain birefringence is elaborated in terms of the RIS model as applied to vinyl polymer chains. Additivity of the polarizability tensors for constituent groups is assumed. Stress-birefringence coefficients are calculated for PP and for PS. Statistical weight parameters which affect the Incidences of various rotational states are varied over ranges consistent with other evidence. The effects of these variations are explored in detail for isotactic and syndlotact/c chains. 

The quantity of interest in connection with flow birefringence is the reduced steady-state compliance. It is easily shown that for the free-draining model eq. (3.40) can be approximated by ... 

C0Pi6 (137) was the first to give an expression for the contribution of the form birefringence to the Maxwell constant. His theory is based on the elastic dumb-bell model, which has been used in early theories on flow birefringence and viscosity and which is identical with the model used in Sections 2.6.1 and 2.6.2. The ratio of Maxwell constant to intrinsic viscosity is probably unaffected by this simplification, when also the viscosity is calculated with the same model, as Copi6 did. For the absence of the form effect, this has strictly been shown in the mentioned Sections. In fact, in the case of small shear rates the situation is rather simple To a first approximation with respect to shear rate, the chain molecules are only oriented, their intramolecular distances which are needed for the calculation of form birefringence, being unaffected. 

As has been pointed out (63), this is a rather artificial model and, moreover, its application is quite unnecessary. In fact, (a> can be calculated from the refractive index increment (dnjdc), as has extensively been done in the field of light scattering. This procedure is applicable also to the form birefringence effect of coil molecules, as the mean excess polarizability of a coil molecule as a whole is not influenced by the form effect. It is still built up additively of the mean excess polarizabilities of the random links. This reasoning is justified by the low density of links within a coil. In fact, if the coil is replaced by an equivalent ellipsoid consisting of an isotropic material of a refractive index not very much different from that of the solvent, its mean excess polarizability is equal to that of a sphere of equal volume [cf. also Bullough (145)]. 

Three attempts have been made to introduce internal friction into the subchain model, in order to explain flow birefringence data. The first approach has been made by Cerf (179). who added to eq. (3.16) a third term. He obtained ... 

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