Linear Birefringence Measurements

A sample characterized by a retardation, S, an extinction, 6 , and coaxial orientation angle, 0 = 8 = 0 , can be analyzed by the optical arrangement shown below [34,37,38], 

For each of these optical trains, except the (P/PEM)pSG system, the intensity measured at the detector is 

In the absence of dichroism, this equation is similar in form to equation (8.27) and the extraction of the retardation and orientation angle follows the same strategy as described for the measurement of dichroism in the previous subsection. However, when dichroism cannot be neglected, the measured signal will depend on both optical anisotropies. In this case, two separate measurements will be necessary one using the optical trains of the previous section (which simply has the PSA section of the instrument replaced by (-) psA) to determine the dichroism, and a second measurement to obtain the combined 

Unlike the previous designs, this arrangement is not convenient when dichroism is not negligible. This is because the contribution of dichroism is not easily subtracted out as it is with equation (8.33). When dichroism is set to zero we have 

The following ratios can be measured by analyzing the Fourier content of the signal and with the knowledge of the calibration constants, J1 (A) and J2 (A)  

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Phase transitions are not only characterized by atomic or molecular structural changes - they can also be characterized by significant modifications in the microstmcture and domains and at a much larger size scale. One notable example has been recently reported by Glazer et al. [110] using linear birefringence measurements in LiTaOs and LiTa cNbi c03 crystals at high temperature. 

From these measurements of linear dichroism, it can be concluded, that the linkage of l-l.c. s to a polymer backbone generally reduces the nematic order. This effect has been found so far for poly(acrylates), poly(methacrylates) and poly-(siloxanes) and is established by NMR 59,60), ESR61) and birefringence measurements. 

This approach is based on the introduction of molecular effective polarizabilities, i.e. molecular properties which have been modified by the combination of the two different environment effects represented in terms of cavity and reaction fields. In terms of these properties the outcome of quantum mechanical calculations can be directly compared with the outcome of the experimental measurements of the various NLO processes. The explicit expressions reported here refer to the first-order refractometric measurements and to the third-order EFISH processes, but the PCM methodology maps all the other NLO processes such as the electro-optical Kerr effect (OKE), intensity-dependent refractive index (IDRI), and others. More recently, the approach has been extended to the case of linear birefringences such as the Cotton-Mouton [21] and the Kerr effects [22] (see also the contribution to this book specifically devoted to birefringences). 

Birefringences are mostly observed in condensed phases, especially pure liquids or solutions, since the strong enhancement of the effects allows for reduced dimensions (much shorter optical paths) of the experimental apparatus. Nowadays measurements of linear birefringences can be carried out on liquid samples with desktop-size instruments. Such measurements may yield information on the molecular properties, molecular multipoles and their polarizabilities. In some instances, for example KE, CME and BE, measurements (in particular of their temperature dependence) have been carried out simultaneously on some systems. From the combination of data, information on electric dipole polarizabilities, dipole and quadrupole moments, magnetizabilities and higher order properties were then obtained. 

Measurements of the linear birefringences of Table 2.6 imply the determination of n, e, the density p and of the constant sW(solutlon)(a>, 7) for the solution. Also, sW(SOL)( , 7) is assumed to be known. An extrapolation to infinite dilution is then made, according to Equation (2.235), often under the further assumption that all parameters of the solution depend linearly on xsol. 

Cao XL, Dukor RK, Nafie LA (2008) Reduction of linear birefringence in vibrational circular dichroism measurement use of a rotating half-wave plate. Theor Chem Acc 119 69-79... 

When chirality is involved, information on solid-state structures and supra-molecular properties must be obtained by solid-state circular dichroism (CDf spectroscopy, as certain characteristics may be lost upon dissolution. However extreme care is required to obtain artifact-free solid-state CD spectra. This is because CD spectra in the solid state (except for special homogeneous cases [9,10]) are inevitably accompanied by parasitic signals that originate from thd macroscopic anisotropies of a sample such as LD (linear dichroism) and LB (linear birefringence) [11-16]. We have been working in the field of solid-state chirality for the last 30 years and recently developed a novel universal chiroptical spectrophotometer, UCS J-800KCM, for the measurement of true CD and circular birefringence (CB) spectra in the solid state [17]. 

Ellipsometry can also be applied to transmission measurements linear birefringence and dichroism of an anisotropic sample cause differences in amplitudes and phase shifts for waves of different polarization azimuths. Such experiments seem to be of considerable interest for partially ordered systems such as liquid crystals (cf. Sec. 4.6), here the degrees of polarization P and Ppf, reveal information related to order and reorientation processes (Korte et al., 1993 Reins et al., 1993). 

If X, y and z are respectively the flow, gradient and vorticity directions, birefringence measurements in the y-z and x-z planes also lead to the second and third normal stress differences, providing the material verifies the linear... 

Before then, measurements of CD were restricted to solution, glasses, fine powder and uniaxial crystals with light propagated along the optic axis, since the signal was otherwise distorted by interference from linear birefringence and linear dichroism. 

The measurement of optical activity in single crystals has been studied most extensively by transmission techniques, although recent development of emission methods has also been reported (2,1). Transmission methods are limited to those compounds which can be obtained in suitably large and perfect single crystals. In addition, only in non-biaxial crystals can the complications of linear birefringence be avoided easily. (However, a two-angle method for cancelling these effects has... 

Figure C3.1.13. Experimental configuration for far-UV nanosecond CD measurements using a frequeney-upconverted Ti sapphire laser as a probe source. Pj and 2 are MgF2 Roehon polarizers at eross orientations. SPj is a strained transparent plate with about 1° of linear birefringence for quasi-null ellipsometric CD deteetion. Prism PMj and the iris select the far-UV fourth harmonie of the argon laser-pumped Ti-sapphire laser s near-IR fundamental output to probe the elliptieity of the sample. A seeond laser beam at 532 nm is used to pump CD...

Birefringence measurements (Figirre 17) are plotted showing a linear increase respect to their crystallization teriQ)erature. It also shows a remarteible increase of... 

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