Coefficient of optical stress

Basically, birefringence is the contribution to the total birefringence of two-phase materials, due to deformation of the electric field associated with a propagating ray of light at anisotropically shaped phase boundaries. The effect may also occur with isotropic particles in an isotropic medium if they dispersed with a preferred orientation. The magnitude of the effect depends on the refractive index difference between the two phases and the shape of the dispersed particles. In thermoplastic systems the two phases may be crystalline and amorphous regions, plastic matrix and microvoids, or plastic and filler. See amorphous plastic coefficient of optical stress compact disc crystalline plastic directional property, anisotropic ... 

COS coefficient of optical stress CRM certified reference material... 

Optical detectors can routinely measure only intensities (proportional to the square of the electric field), whether of optical pulses, CW beams or quasi-CW beams the latter signifying conditions where the pulse train has an interval between pulses which is much shorter than the response time of the detector. It is clear that experiments must be designed in such a way that pump-induced changes in the sample cause changes in the intensify of the probe pulse or beam. It may happen, for example, that the absorjDtion coefficient of the sample is affected by the pump pulse. In other words, due to the pump pulse the transparency of the sample becomes larger or smaller compared with the unperturbed sample. Let us stress that even when the optical density (OD) of the sample is large, let us say OD 1, and the pump-induced change is relatively weak, say 10 , it is the latter that carries positive infonnation. 

More recently, test products were created of a blend of PMMA with a phenyl-substituted methacrylate these products have a glass-transition temperature of around 125°C, a significantly reduced water absorption compared to pure PMMA of about 0.32%, but also a higher birefringence (a stress-optic coefficient of 5.2 X 10 , compared with 0.3 X 10 for PMMA and 6.8 x 10 for BPA-PC). 

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. 

Figures 6 and 7 give the data of Fukuda et al. (3) and that of Saunders (52). The variation of stress optical coefficient of the high cis and high trans, 1,4-polybutadiene is plotted against Me in Figure 6, where it is compared with...

Eqs. (4.140) and (4.150)-(4.152) are used to evaluate the response of the model composites in cyclic loading and the displacements 6 and 8, can be expressed as a function of the alternating stress, Aff, and the number of cycles, N. In experiments, degradation of the interface properties, e.g., the coefficient of friction, p or A(= 2pjfc/a), can also be expressed in terms of the cyclic loading parameters, Aoptical methods (with a microscope) or by means of more complicated instruments (see for example Naaman et al. (1992)) in fiber pull-out. Alternatively, they can be directly determined from the load and load-point displacement records in the case of fiber push-out. 

Expressions for the optical anisotropy AT of Kuhn s random link (an equivalent to the stress-optical coefficient) of stereo-irregular and multirepeat polymers are derived on the basis of the additivity principle of bond polarizabilities and the RIS approximation for rotations about skeletal bonds. Expressions for the unperturbed mean-square end-to-end distance , which are required in the calculation of Ar, are also obtained. 

The stress-optical coefficient of PE networks is calculated, and results are compared with experimental data. Observed temperature coefficients of AT and the optical anisotropy for unswollen samples are much larger than those calculated using acceptable values of E(g), the energy of the gauche conformation, relative to that of Vans. It is concluded that observed temperature coefficients should Include some contributions other than those implied in the theory, i.e., those arising from the conformational change with temperature. 

The stress-optical behaviour of an unswollan elastomeric network of PMTHF is measured for different elongation ratios at several temperatures. Values of 4a range from 2.4 to 2.8 in units of 10 A cm3, in the temperature range studied. Theoretical calculations carried out with the RIS model give values of 4a noticeably smaller than the experimental results however, a small increase in the backbone valence angles improves the theoretical results. Theoretical and experimental values of the temperature coefficient of 4a are in clear disagreement a qualitative explanation for this discrepancy is discussed. 

Quantitative data, as to the magnitude of the stress-optical coefficient for various polymer systems, will be given in Chapter 2, where other properties of this coefficient will be discussed. 

A special advantage of this method is that the high shear rate range becomes available. It appears that one can measure nu — n33 up to the critical shear stress, at which extrusion defect (melt-fracture) occurs. On the other hand, entrance effects can also be studied, when the windows are located sufficiently close to the entrance. With the aid of the stress-optical coefficient, the corresponding normal stress difference can be... 

For a complete derivation of the stress-optical coefficient, as given by eq. (2.24), one can proceed along the lines traced out by Kuhn and Grun (64). For the purpose, the well-known expression for the molar refraction, i.e. ... 

Table 2.1. Stress-optical coefficient of (atactic) polystyrene...

Table 2.2, which shows results for some polyolefines, indicates for these polymers a similar insensitivity of the stress-optical coefficinet to molecular weight and concentration as Table 2.1 for polystyrene. A typical solvent effect is noticed for all the three types of polyolefins, viz. that the stress-optical coefficient in decalin is considerably smaller than that in aromatic solvents. This effect was discovered by Garmonova (71). 

From the foregoing it becomes evident that only a measure of the magnitude of the form birefringence, but not of its influence on the extinction angle, can be given. For this purpose the reader may be reminded that the stress-optical coefficient of an infinitely dilute solution can be expressed by one half of the ratio of Maxwell constant to intrinsic viscosity [eq. (2.33)]. In the absence of the form birefringence the limiting... 

Dynamic viscoelastic and stress-optical measurements are reported for blends of crosslinked random copolymers of butadiene and styrene prepared by anionic polymerization. Binary blends in which the components differ in composition by at least 20 percentage units give 2 resolvable loss maxima, indicative of a two-phase domain structure. Multiple transitions are also observed in multicomponent blends. AU blends display an elevation of the stress-optical coefficient relative to simple copolymers of equivalent over-all composition. This elevation is shown to be consistent with a multiphase structure in which the domains have different elastic moduli. The different moduli arise from increased reactivity of the peroxide crosslinking agent used toward components of higher butadiene content. 

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... 

The last column in Table III shows a weighted mean, using empirical weight factors of 0.73 and 0.27 for parallel and series coupling, respectively. These values fit the observed stress-optical coefficients within experimental error. The elevation of the stress-optical coefficient, together... 

Expressions for the stress-optical coefficient based on the above models are written easily. One assumes that the birefringences contributed by the various elements of the model are additive by volume and are given by the product of the stress in the element and the stress-optical coefficient of the appropriate component. The resulting equations are ... 

As discussed in section 7.1.6.4, semidilute solutions of rodlike polymers can be expected to follow the stress-optical rule as long as the concentration is sufficiently below the onset of the isotropic to nematic transition. Certainly, once such a system becomes nematic and anisotropic, the stress-optical rule cannot be expected to apply. This problem was studied in detail using an instrument capable of combined stress and birefringence measurements by Mead and Larson [109] on solutions of poly(y benzyl L-glutamate) in m-cresol. A pretransitional increase in the stress-optical coefficient was observed as the concentration approached the transition to a nematic state, in agreement of calculations based on the Doi model of polymer liquid crystals [63]. In addition to a dependence on concentration, the stress-optical coefficient was also seen to be dependent on shear rate, and on time for transient shear flows. 

The stress-optical coefficient C is defined by equation (10.27) and the relaxation times t,1 and t][ are defined by relations (2.30). One can see that the dynamo-optical coefficient of dilute polymer solutions depends on the non-dimensional frequency t w, the measure of internal viscosity ip and indices zv and 6... 

The orientation of the swelling agent (solvent or free chains) has to be taken into account in the analysis of the stress-optical behaviour of swollen networks. Specifically, the segment polarisability (relative to the network chains or to the diluent chains), as currently derived from stress-optical coefficients [33], may not be representative of intrinsic properties of isolated chains. Short-range orientational interactions between the probe molecules and network chains (and between the chains of the matrix itself) must be considered in the interpretation of opticoelastic properties of swollen (and dry) rubbers [67]. 

We shall now discuss in more detail the different phase types of polymers as far as data of birefringence, stress-optical coefficient and anisotropies in polarisability are available. 

Table 10.6 shows the data of the stress-optical coefficients as calculated by means of Eq. (10.25). The values are low for aliphatic polymers (about 5 x 10-12 Pa- ) aromatic rings directly linked as side groups on the backbone chain increase the value of C ... 

TABLE 10.6 Stress-optical coefficients of glassy polymers in Brewster s (= 10 12 Pa )... 

Table 10.8 gives the available values of the stress-optical coefficients for several polymer types, again calculated by means of Eq. (10.25). These values are higher by some orders of magnitude than those of the glassy polymers. The simplest polymer structure, polymethylene, has a Ca of about 2000 x 10 12 Pa 1. Side groups and side chains do decrease the Cff-value. 

---