As discussed earlier, the phase spectra can be used directly for both qualitative and quantitative analysis. Figure 3.12 shows both the magnitude and phase spectra of the Kapton sample collected at a ΦM frequency of 400Hz. The phase angles at all bands on the magnitude spectrum can be read directly from the phase spectrum. It can be seen the Teflon band at 1225cm-1 has the smallest phase lag whereas all polyimide bands between 1800-1350cm-1 have much larger phase lags. Among these polyimide bands, the strongest one at 1700cm-1 has the smallest phase lag, thus it is a more “surface” representative for the polyimide layer. By using a simplified version of Equation (3-6), the thickness of the top layer can be calculated as follows:

楼主辛苦了，佩服佩服。

In this calculation, the thermal diffusivity of the Teflon layer, α=0.82*10-3 cm2/sec, was used in Equation(3-2) to determine μ400Hz. This result is in close agreement with the real thickness of 12μm for the Teflon layer.

PMMA on PS on PP. An important advantage of using PA signal phase in depth profiling is the enhancement of spatial resolution (as high as on the sub-micron level, beating the IR diffraction limit) within a given probing depth defined by the modulation frequency and material properties. Figure 3.13 illustrates the PA magnitude (top) and phase spectrum (bottom) of a three-layer sample: 0.5μm ploy(methyl methacrylate) (PMMA), on 0.5μm polystyrene (PS), on 2mm polypropylene (PP), collected at a ΦM frequency of 200Hz and amplitude of 3.5λHe-Ne. The phase spectrum, as shown in Figure 3.13, clearly distinguishes characteristic bands from different layers by phase angle. The relative phase lags of 0.1°, 3° and 18° correspond to distinctive bands of PMMA (1727cm-1, C=O stretch), PS(748cm-1, aromatic C-H deformation), respectively. In addition, the top two layers agree with the phase difference model for thermal thin or optically transparent layers, as shown by Equation (3-6). Thus the thickness of the PMMA layer, dPMMA, can then be also determined by the phase difference model:

Again, this result is very close to the actual thickness of about 0.5μm. The ability of PAS to discriminate between sub-micron layers using the phase information is clearly beyond the diffraction limit encountered in IR microscopy.

谢谢楼主,辛苦了,

3.4 Sample Modulation FT-IR - Polymer Rheo-Optical Characterizations
3.4.1 Introduction
As discussed in Chapter 1, step-scan FT-IR decouples the time-dependent Fourier effect, and it has been demonstrated to be the technical choice to obtain dynamic spectral information from samples under a repeatable, sinusoidal modulation of a physical parameter. These parameters can be of any physical quantity, such as mechanical strain, electric potential or temperature, etc.

One of these typical sample modulation experiments is polymers stretching. This experiment has been studied extensively in the field of materials rheology using dynamic mechanical analysis (DMA). However, DMA only allows macroscopic information of a sample (stress relaxation or strain creeping) to be obtained. The chemistry behind rheological properties remains unknown from DMA. coupling a polymer stretcher with a step-scan FT-IR allows both microscopic and macroscopic information on a polymeric material under study to be collected simultaneously. The dynamic IR spectra reveal molecular level responses of polymeric films undergoing flow, deformation, and relaxation under mechanical strain. In particular, the dynamic IR spectra refer to the degree of association in polymer blends, coherence of functional group motions within molecules, resolution of closely spaced bands, and quantitative correlation between macroscopic phase delays. A typical sample modulation experiment involves multiple (two or three) modulations concurrently applied to the system. Therefore, it is also referred to as a synchronous multiple modulation (SMM) experiment. Usually, the frequency of sample modulation is relatively low, thus a fast carrier frequency, such as phase modulation, is simultaneously employed to increase the responsivity of mercury cadmium telluride (MCT) detector and reduce or eliminate 1/f noise.

3.4.2 Experiment Setup and Data Process
Experiment Setup. For a typical synchronous double modulation (SDM, i.e. phase modulation and sample modulation) polymer stretching experiment, the stretcher is mounted directly on a base plate in the sample compartment of a research-grade Nicolet Ft-IR spectrometer. Because the Vectra-Piezo interferometer is virtually immune to laboratory environmental vibrations, the stretcher can be mounted between the two jaws of the stretcher. One jaw is driven by a piezoelectric transducer to produce a sinusoidal strain at a frequency and amplitude set by the stretcher controller. A polarizer (P) with polarization direction parallel to the stretching direction and an optical filter (F) for under sampling are placed in the IR beam path before the sample. The optical filter is needed since in most cases the dynamic signature bands are located in the fingerprint region, thus under sampling will reduce data collection time substantially. The sinusoidal function of the stretcher is generated by the spectrometer, allowing the best synchronization of the experiment for both phase and sample modulations.

In an example of typical mid-IR polymer stretching experiments, the IR beam is modulated by dithering the fixed mirror, i.e. phase modulation, ΦM, at 400Hz with modulation amplitude of 3.5 λHe-Ne. The sample is modulated at 20Hz by the polymer stretcher that is referenced to a synchronous sinusoidal signal generated by the bench DSP processor. The superposition of two sinusoidal waves (400 and 20Hz), measured at the detector, produces two beat frequencies (the sum, ΦM+SM, at 420Hz and the difference, ΦM-SM, at 380Hz), in addition to the remaining ΦM component as illustrated in Figure 3.15.