Dichroic difference

Normal incidence transmission IRLD measurements are used to study thin films (typically 100 pm thickness and less, depending on the molar extinction coefficient of the bands) with in-plane uniaxial orientation. Two spectra are recorded sequentially with the radiation polarized parallel (p) and perpendicular (s) to the principal (machine) direction of the sample. The order parameter of the transition moment of the studied vibration is calculated from either the dichroic ratio (R — Ap/As) or the dichroic difference (AA = Ap—As) as ... 

A more complex but faster and more sensitive approach is polarization modulation (PM) IRLD. For such experiments, a photoelastic modulator is used to modulate the polarization state of the incident radiation at about 100 kHz. The detected signal is the sum of the low-frequency intensity modulation with a high-frequency modulation that depends on the orientation of the sample. After appropriate signal filtering, demodulation, and calibration [41], a dichroic difference spectrum can be directly obtained in a single scan. This improves the time resolution to 400 ms, prevents artifacts due to relaxation between measurements, and improves sensitivity for weakly oriented samples. However, structural information can be lost since individual polarized spectra are not recorded. Pezolet and coworkers have used this approach to study the deformation and relaxation in various homopolymers, copolymers, and polymer blends [15,42,43]. For instance, Figure 7 shows the relaxation curves determined in situ for miscible blends of PS and PVME [42]. The (P2) values were determined... 

Figure 7 Relaxation of orientation measured simultaneously for both components in miscible PS/PVME blends following a rapid deformation (1 m/s) to a draw ratio of 2 at Tg +15°C. The time-resolved dichroic difference spectra were acquired using PM-IRLD. Reproduced with permission from Pellerin et al. [42]. Copyright 2000 American Chemical Society.

The IR apparatus and dichroism methods used in this work have been previously described (11,12). In the differential dichroism experiment, the samples were stretched from both ends simultaneously at a true strain rate of approximately 30% per min. A motorized stretching jig was used which fits inside the instrument in the path of the common beam at a 45° angle. Wire grid polarizers were set at 45° in the reference and sample beams, and the instantaneous dichroic difference A A — AM — Aj was recorded with the instrument operating in constant, wave-number mode. 

The orientation functions and dichroic difference data for a commercial polyester-urethane from B. F. Goodrich showed that, in static stretching, the soft domains reached orientation saturation before the hard domains. On the timescale of the static experiment, plasticisation diminished the ability of both domains to reorient, while the plasticiser itself did not orient (55). 

The recorded output was the dichroic difference, from which the orientation function (F ) could be calculated [140, 363], which is unity for perfect orientation in the stretch directions, -1 /2 for perfect orientation transverse to the stretch direction, and zero for random orientation. 

The optical anisotropy, as characterized by the difference between the absorption of IR light polarized in the directions parallel and perpendicular to the reference axis (i.e., the direction of applied strain), is known as the IR linear dichroism of the system. For a uniaxially oriented polymer system [10, 28-30], the dichroic difference, A/4(v) = y4 (v) - Ax v), is proportional to the average orientation, i.e., the second moment of the orientation distribution function, of transition dipoles (or electric-dipole transition moments) associated with the molecular vibration occurring at frequency v. If the average orientation of the transition dipoles absorbing light at frequency is in the direction parallel to the applied strain, the dichroic difference AA takes a positive value on the other hand, the IR dichroism becomes negative if the transition dipoles are perpendicularly oriented. 

Polarized FTIR spectroscopy has been used extensively to study polymer orientation (i.e., the dichroic ratio and dichroic difference are normally obtained from spectra recorded sequentially with the infrared radiation polarized parallel and perpendicular to a reference direction). To improve the sensitivity of this technique, and to follow accurately the dynamics of orientation, FTIR spectroscopy has been coupled with a polarization modulation (PM) technique whereby the dichroic difference spectrum is recorded directly, thus minimizing instrumental and sample fluctuations (this is discussed later in the chapter). 

Figure 20.29 (a) Synchronous 2D-FTIR correlation map of poly DRl M-co-BEM. with a DRl M mole fraction of 0.23 during the photo-induced orientation process. In this figure, the negative peaks are indicated by a minus sign and the one-dimensional (ID) spectra are the dichroic difference spectra recorded after 5 min (dashed line) and 60 min (solid line) of irradiation (b) Asynchronous 2D-FTIR... 

In the dynamic transmission mode, information about two-dimensional dynamic dichroic differences can be attained [46]. It is useful to study uniaxially oriented polymers such as strongly elongated fibres. However, the orientation of most polymer films should be considered biaxial, even with uniaxially drawn films, which still show slight biaxial orientation at the surface [52]. This fact suggests that the two-dimensional dynamic dichroic data obtained from transmission mode is not necessarily adequate for evaluating most (biaxially oriented) polymer films. 

Absorbance spectra measured with p- and 5-polarization are denoted as Ap(v) and A5(v), respectively. Ap(y) — A5(v) is known as the dichroic difference, and Ap v)/As v) is the dichroic ratio. Quantitative treatments of molecular orientation often require knowledge of the dichroic ratio. However, in regions where the sample absorption is very weak, calculation of the dichroic ratio involves taking the ratio of noise on the baseline of Ap(v) and A5(v) when both parameters are approximately zero. Thus, if qualitative or semiquantitative information is all that is required, the dichroic difference spectrum is more useful than the dichroic ratio. 

Figure 12.4. Spectrum of an undeformed 300-pm PET film in the high-wavenumber region and the dichroic difference spectra recorded with a PEM at the end of the deformation and after 30 and 300 s of relaxation. (Reproduced from [3], by permission of the Society for Applied Spectroscopy copyright 2002.)...

The complete theory of how the output signals from the five lock-in amplifiers are treated in order to obtain static and dynamic spectra was originally given by Noda et al. [3] and Noda [4,5]. The inclusion of the full theory is beyond the scope of this book. Suffice it to say that the end result is calculation of the average static absorbance spectmm, the in-phase and quadrature components of the parallel and perpendicular absorbances, and the static and dynamic dichroic difference spectra. Of these, the in-phase and quadrature DIRLD spectra give the most important information about the rheological behavior of the polymer on a submolecular level. 

Time-resolved dichroic difference spectra of atactic polystyrene generated from the spectra shown in Figure 21.3 over a little more than one cycle of the stretcher are shown in Figure 21.4, along with the variation of the applied strain over the same period. From this curve, the variation in intensity and phase of each of the bands in the spectrum can be visualized. Under the same scan conditions, it would... 

The dynamic dichroic difference signal takes the form... 

The IR linear dichroism (i.e., the anisotropic absorption) is characterized by the integrated absorbances A and Ax measured at the band under inspection with light polarized parallel and perpendicular to the fixed reference direction, respectively. Commonly, the optical anisotropy of uniaxially oriented samples is characterized by the dichroic ratio Rdkhro = A /Ax, the dichroic difference AA = A — Ax, or by the... 

Figure 7.5 X-ray magnetic circular dichroism shown in a one-electron model. By use of circularly polarized X-rays, the spin moment (a) and orbital moment (b) can be determined from the dichroic difference intensities A and B, as explained in the text [26].

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