# Two dimensional correlation spectroscopy applications in vibratioal and optical spectroscopy - Isao N.

ISBN 0-471-62391-1

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?(t) = ? sin Mt (8.2)

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Dynamic 2D Correlation Spectroscopy Based on Periodic Perturbations

Figure 8.1 Schematic diagram of a dynamic IR linear dichroism (DIRLD) spectrometer. Dynamic reorientation of molecular constituents induced by a small-amplitude repetitive strain is monitored with a pair of polarized IR beam. (Reproduced with permission from I. Noda Appl. Spectrosc., 44, 550 (1990). Copyright (1988) Society for Applied Spectroscopy.)

The resulting change in the orientation distribution of submolecular constituents of the system induced by the macroscopic strain perturbation will manifest itself as dynamic variations of IR dichroism intensities.

AA(v,t) = AA(v) sin[«t + fi(v)] (8.3)

The dynamic dichroism signal AA(v, t) is usually not in phase with the applied strain signal e (t), and there is a finite phase angle difference ji(v) reflecting the rate-dependent nature of the reorientation processes experienced for sub-molecular constituents induced by a macroscopic perturbation (Figure 8.2). In general, not only the amplitude A A (v) of the response signal but also the phase angle ji(v) is dependent on the IR wavenumber v, indicating the local independence of the reorientational processes of submolecular constituents. As it is possible to trace the time-dependent variations of dichroism intensities at any different wavenumber v, the measured dynamic IR dichroism may be regarded as a form of time-resolved bilinear spectrum (Figure 8.3). The dynamic IR dichroism (Equation 8.3) may be expressed in terms of the sum of two spectral components orthogonally varying with time

AA(v, t) = AA(v) cos f}(v) sin rnt + AA(v) sin f}(v) cos rnt (8.4a) = AA'(v) sin rnt + AA"(v) cos rnt (8.4b)

where AA'(v) and AA''(v) are commonly known as the in-phase spectrum and quadrature spectrum of the dynamic dichroism. The overall reorientability of

Dynamic 2D IR Spectroscopy

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Figure 8.2 Comparison between dynamic strain e (t) and dynamic IR dichroism AA (v,t). The dynamic dichroism response is not fully synchronized with the applied strain, such that there is a finite phase angle (v) between the two signals. (Reproduced with permission from Ref. No. 4. Copyright (1999) Wiley-VCH.)

dipole transition moments, which relates to the mobility of submolecular groups contributing to the molecular vibrations at the wavenumber v, is characterized by the so-called power spectrum P(v) of the dynamic dichroism

P(v) = i[A A,2(v) + A A//2(v)] = ±A A2(v) (8.5)

which is proportional to the square of the amplitude of dichroism fluctuation.

8.1.4 2D CORRELATION ANALYSIS OF DYNAMIC IR DICHROISM

A proper manipulation of time-dependent optical anisotropy data such as DIRLD spectra yields an estimate of change in the ensemble average of submolecular

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Dynamic 2D Correlation Spectroscopy Based on Periodic Perturbations

Figure 8.3 Strain-induced time-resolved dynamic IR linear dichroism (DIRLD) spectrum as a function of time and wavenumber. (Reproduced with permission from I. Noda et al, Appl. Spectrosc., 42, 203 (1988). Copyright (1988) Society for Applied Spectroscopy.)

structure orientations. The reorientability (i.e., local rotational mobility) of chemical functional groups is strongly influenced by the presence of various inter- and intramolecular interactions. The reorientational rate of electric dipole transition moments thus provides valuable information on the local chemical environment, as well as the structure of functional groups contributing to the molecular vibrations detected by IR.

Specific reorientation rates of individual dipole transition moments, which are determined by the type and local environment of functional groups contributing to the molecular vibrations, can be used as convenient spectroscopic labels to differentiate highly overlapped IR bands. Wavenumber-dependent variations of dynamic dichroism intensities reflecting the non-uniformity of reorientation rates among various dipole transition moments are analyzed quite effectively by a 2D correlation method. Fortunately, 2D correlation spectra of dynamic spectral signals having a well-defined sinusoidal waveform are readily calculated from the closed form analytical expressions derived previously (Equations 2.19-2.22). For a pair of dynamic IR dichroism signals measured at two different wavenum-bers, A A (v1, t) and A A (v2, t), the synchronous (coincidental) and asynchronous (quadrature) correlation intensities, 0(v1, v2) and ^(v1, v2), of the dynamic IR dichroism signals are given by2

<h(vi,v2) = ^A?(vi) • AA(v2)cos[j0(vi) -j0(v2)] (8.6a)

= ±[AA'Oh) • AA'(v2) + AA"(Vl) • AA"(v2)] (8.6b)

Dynamic 2D IR Dichroism Spectra of Polymers

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and

^(vi, v2) = |AA(vi) • AA(v2) sin[j0(vi) - j0(v2)] (8.7a)

= ±[AA"{Vl) • AA'(v2) - AA'(vO • AA>2)] (8.7b)

Close observation of Equations (8.6a) and (8.7a) reveals the basic nature

of synchronous and asynchronous 2D correlation intensities in terms of the

phase angle relationship, at least for simple sinusoidally varying signals. The synchronous correlation intensity 0(v1; v2) represents the degree of coherence between two separate signals measured simultaneously, and the intensity becomes a maximum if the variations of two dynamic dichroism signals studied by the correlation analysis are totally in phase with each other (i.e., ji(v1) and ji(v2) are the same) and a minimum if they are antiphase (i.e., n out of phase) with each other. Signals nearly orthogonal to each other (i.e., ±n/2 out of phase) should give out little synchronous correlation intensity. The asynchronous correlation intensity ^(v1;v2), on the other hand, characterizes the degree of coherence between signals measured at two different instances separated by a phase shift of ±n/2. Thus, the asynchronous correlation intensity becomes either maximum or minimum when the dynamic signals are n/2 out of phase with each other and vanishes for a pair of signals exactly in phase or antiphase with each other. 2D IR spectra are obtained as usual by plotting these correlation intensities as function of two independent wavenumbers, v1 and v2.

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