As in many dynamic and static spectroscopic measurements, a dynamic reference is needed in the polymer stretching experiment. In this experiment, a chopper* is used as an ideal elastic reference to set the reference phases for each demodulation such that the in-phase responses of both the phase and sample modulations are maximized. This sample modulation phase setting maximizes the elastic response of the sample in the dynamic in-phase channel since the IR intensity varies simultaneously with the chopper.
These procedures yield six interferograms simultaneously from a single SDM experiment. When the phase angles for ΦM and SM modulation, θΦM, and θSM, are optimized through the use of the elastic reference as described above, only three channels, one static channel Is(I) and two dynamic channels ΔId(I,I) and ΔQd(I,Q), contain significant signals. The Is spectrum gives the static single-beam spectrum of the polymeric sample. The ΔId and ΔQd are the dynamic single-beam spectra of the polymeric sample in response to the sample modulation. ΔId and ΔQd spectra are then ratioed to Is to yield the dynamic transmission spectra, ΔId/Is, ΔQd/Is, and differential absorbance spectra ΔAI and ΔAQ for in-phase and quadrature channels are then obtained by using Equations (3-12) and (3-13):
The signal gain factor difference between the dynamic (ΔId, ΔQd) and the static (Is) channels should be calibrated before applying the above two Equations.
Digital Signal Processing (DSP) in SDM. Initially, the dynamic FT-IR polymer stretching experiment were equipped with two lock-in amplifiers. The first lock-in amplifier was used to demodulate the raw signal of the phase modulation with maximized in-phase output, and the second was used to demodulate the signal of the sample modulation. The DSP-based research-grade Nicolet FT-IR spectrometers have considerably simplified this experiment by using multiple digital processors (DSPs). The DSPs may be perceived as built-in digital lock-in amplifiers with large dynamic ranges. At each mirror position, the raw detector signal of the synchronized double modulation (ΦM and SM), SDM, can be mathematically described by Equation (3-14):
where ωΦM=2πfΦM, and ωSM=2πfSM are angular frequencies of phase and sample modulations, respectively. The first term in Equation (3-14) is demodulated at the ΦM frequency to produce the static reference. The second term contains the dynamic information at the sample modulation frequency. By performing fast Fourier transform (FFT) on the detector raw signal into the frequency-domain (Hz), the demodulated dynamic signal (interferometric data points) can be determined from the amplitude at either fΦM+fSM or fΦM-fSM as implied by Equation (3-15) and is illustrated in Figure 3.15.
The dynamic in-phase and quadrature interferometric data points are then obtained with real and imaginary FFT's respectively. The phase angles determined from the chopper (the elastic reference) are used in signal processing to maximize both the "static" (phase modulation) and dynamic (sample modulation) in-phase channels. The DSP demodulation board also allows FFT calculations and interferometric data display in real time during the data collection process. Further processing after data collection generates single beams, and then the dynamic absorbance spectra can be obtained using Equations (3-12) and (3-13).
Spectroscopic data analysis approaches and applications of SMM. Spectroscopic data analysis approaches used in dynamic polymer stretching experiments include: direct comparison between in-phase and quadrature dynamic spectra, conventional 2D-IR correlation, (also see Chapter 7), phase and power (magnitude) spectral analysis. In addition, the dynamic polymer stretching experiment can be easily extended to study dynamic dichroic properties of polymeric materials by coupling a polymer stretcher to a photoelastic modulation (PEM). The open architecture design of the DSPs on the research-grade Nicolet FT-IR systems allow easy accommodation of any other sample modulation experiment with different perturbations, such as ekectrochemical reactions and liquid crystal dynamics, where an AC current is used as perturbation. For these sample modulation experiments modulated by eletric current, an instantly responding reference such as the chopper described in the polymer stretching experiment, is also needed to set both ΦM and SM demodulation phase angles. Other sample modulation studies or SMM applications include pressure modulation of polymer films and dynamic Raman spectroscopy of fiber, where an ATR or Raman probe is coupled to a step-scan FT interferometer.
3.4.3 Application Example Isotactic and Syndiotactic Polypropylene (iPP and sPP). Isotactic polypropylene (iPP) was one of the first samples studied by the SMM technique. Because of its well-known properties, it is commonly used to test the performance of the spectrometer and the experimental setup for running other samples. The molecular structures of isotactic and syndiotactic crystalline polypropylene are shown in Figure 3.16. The static (top) and dynamic in-phase and quadrature (bottom) spectra of iPP collected at ΦM of 400Hz and SM of 20Hz at room temperature are shown in Figure 3.17. The dynamic single-beam to yield the dynamic transmission spectra. The fact that the dynamic bands are much stronger in the in-phase spectrum than those in the quadrature spectrum indicates that the sample is very elastic under these experimental conditions, and the response to the stretching is almost instantaneous. The major band assignments are illustrated in Table 3.3. The lager dynamic bands are all related to the backbone (C-C chain) stretching. The weaker dynamic band at 995cm-1 is related to non-backbone rocking (CH3).
Shown in Figure 3.18 are the static and dynamic in-phase and quadrature spectra of syndiotactic polypropylenes. Similarly, a weak dynamic signal is observed at 995cm-1 band which is associated with non-backbone chain vibrations. However, the detailed spectral feature of sPP are different from that of iPP, even through they have the same chemical composition. These spectral distinctions arise from the molecular conformation differences between iPP and sPP. From the dynamic spectra, it is not difficult to see: 1) As the polymer is stretched, a reorientation of the backbone chain occurs, leading to peak shifts and intensity changes across the spectrum; 2) Comparison of the dynamic spectra for isotactic and syndiotactic polypropylene samples reveals that the application of sinusoidal mechanical deformation induces changes to both the crystalline and amorphous components of the two samples; and 3) The following IR absorbance bands have contributions from either crystalline, and/or amorphous phases; Iso: 999cm-1 (cryst); 975cm-1 (am + cryst); Syndio: 999cm-1 (cryst); 976cm-1 (am + cryst); and 963cm-1 (cryst).
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