Birefringence magnitude

The analyzed signal in the last equation is a quadratic function on a whose minimum abscissa is the pump-induced dichroism A0"(o)., t) and whose minimum ordinate is the pump-induced birefringence magnitude A0 (< ><, t). Measurements of T for several different angles a provide A< " and A0 as solutions of Eq. 16 without knowing the incident probe intensity E the detector sensitivity, and the sample transmission expt-2< "(o>., t)] in either the ground or the excited state. 

Such measurement provides the magnitude of birefringence, but not its sign. In addition, identical transmission values will be observed for multiple birefringence orders, that is, whenever the optical path difference, dAn, becomes a multiple of X. The main interest of this method arises from its excellent time resolution, below 1 ms, that is readily achieved using a low-power (e.g., 5 mW) continuous-wave laser and a photodiode. If the sample is initially isotropic, it is possible to follow the birefringence order to obtain quantitative results. For improved accuracy, a second (reference) photodiode or a beam chopper and a lock-in amplifier can be used. 

Certainly for real samples where the distribution function is intermediate between the isotropic and Ising limits the susceptibilities also lie between. Two interesting points can be made. 1) Disregarding variation of F, the macroscopic nonlinearity can be enhanced by up to a factor of five over the maximum achievable in isotropic media by use of liquid crystal host and 2) The nonlinearity which might be used for noncritical phase-matched SHG via the birefringence (which must depend on the magnitude of... 

Birefringence is a useful property to monitor orientation [1,12,38], Birefringence occurs as the molecular chains are aligned in the process of orientation the magnitude and sign of the effect are determined by the chemical nature of the polymer. 

This equation gives an estimation of the direction of the transition moment. Again, it should be noted that the CD of an anisotropic system can be falsified by interference with the effects of linear birefringence and linear dichroism. One should have in mind that the linear birefringent or linear dichroism contributions are three orders of magnitude larger than that of the intrinsic CD. 

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... 

The anisotropy of polarizability can be positive (eg, polycarbonate) as well as negative (eg, polystyrene). This offers the possibility of minimizing birefringence by copolymerization or blending of suitable polymers with the right mixture ratio, eg, blends of poly(phenylene ether) (PPE) and polystyrene (PS). The magnitude of birefringence of axial-symmetrically oriented polymers vs their molecule orientation has been described (182). 

Analysis of Stress—Optical Data. The slight, if indeed real, improvement of the isotropic model over the Takayanagi model would be of little consequence were it not for a more pronounced difference between the two models in their ability to describe the stress-optical data. When the parameters obtained from the dynamic data (Table IV) are substituted into Equations 8 and 9, Equation 8 produces results which are uniformly too low. Equation 9 also underestimates the magnitude of Ka but only by an average 7% (Figure 14). For most blends the discrepancy is less than 5%, and all calculated values show the characteristic elevation of the birefringence attributed to the multiphase structure. 

Equations (8.5) bring out an additional problem that is inherent in any birefringence experiment, and that is that the measured intensity is a sinusoidal function of the retardance. This means that there can be ambiguity regarding the absolute magnitude of the retardance, since it will not have a unique value for a given measurement of the intensity. The intensity will oscillate and pass through a maximum whenever S = wtc, where n = 1, 3,. .. and will be zero when n = 0, 2, This problem represents a serious lim-... 

The flow-strength criteria stated in equation (10.2) has been examined experimentally by Fuller and Leal [72] and Dunlap and Leal [149] using four- and two-roll mills, respectively. These devices allow one to systematically vary the flow type (the relative amount of pure extension to pure rotation). The birefringence was measured for dilute and semidilute polymer solutions as a function of both the magnitude and type of the flow. Simple molecular models of flexible polymer chains suggest that such data, when plotted as a... 

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