Frequency domain measurements spectroscopy

The methods described in this chapter and this book apply to electrochemical impedance spectroscopy. Impedance spectroscopy should be viewed as being a specialized case of a transfer-function analysis. The principles apply to a wide variety of frequency-domain measurements, including non-electrochemical measurements. The application to generalized transfer-function methods is described briefly with an introduction to other sections of the text where these methods are described in greater detail. Local impedance spectroscopy, a relatively new and powerful electrochemical approach, is described in detail. 

This part provides a conceptual understanding of stochastic, bias, and fitting errors m frequency-domain measurements. A major advantage of frequency-domain measurements is that real and imaginary parts of the response must be internally consistent. The expression of this consistency takes different forms that are known collectively as the Kramers-Kronig relations. The Kramers-Kronig relations and their application to spectroscopy measurements are described. Measurement models, used to assess the error structure, are described and compared with process models used to extract physical properties. 

Impedance spectroscopy is, of course, not a religion, but an application of a frequency-domain measurement to a complex system that cannot be easily visu-... 

Applications The potential use of 2D correlation spectroscopy is very wide [1007], Most multidimensional techniques arise from the correlation of frequency domains in the presence of external perturbations, as in NMR. For applications of multidimensional NMR spectroscopy and NMR diffusion measurements, see Sections 5.4.1 and 5.4.1.1. 

In order to better quantify the absolute value of chromophore concentrations, time of flight (TOF) must be measured in addition to light attenuation. This may be achieved using time-resolved or frequency domain methods. Time-resolved spectroscopy (TRS) was first pioneered by Delpy et. al. [19], Patterson et. al. [85] and Chance et al. [12, 13]. 

An obvious extension to 3D spectroscopy from 2D spectroscopy is the homonu-clear NOESY-NOESY [34]. There are two t variable times and one tj, which after Fourier transform provide three frequency domains. The 3D NOESY-NOESY spectrum of met-myoglobin cyanide, which contains low spin iron(III) in a heme moiety (see Fig. 5.7), has been successfully measured [35]. In Fig. 8.22 a slice of the 3D spectrum is shown at the I2-CH3 height. On the diagonal it shows all the dipolar connectivities between I2-CH3 and other protons off-diagonal... 

Three techniques are actually available for measuring the fluorescence lifetime Strobe, Time Correlated Single Photon Counting (TCSPC), and multifrequency and crosscorrelation spectroscopy. Strobe and TCSPC are based on measurement in the time domain, while multifrequency and cross-correlation spectroscopy measure fluorescence lifetimes in the frequency domain. The time domain allows direct observation of fluorescence decay, while the frequency domain is a more indirect approach in which the information regarding the fluorescence decay is implicit. 

The experimental techniques adopted to measure linear and nonlinear optical properties are quite different and must be discussed separately. In broad terms, linear properties can be measured using low intensity probes and high spectral resolution. They are usually understood in the frequency domain. Nonlinear responses on the contrary need very large intensities, typically achieved in short pulses, and are discussed in the time domain. In addition to these physical considerations, we have to remember that time-resolved spectroscopy and optical characterization usually require good optical quality samples, so our understanding of the physics of these materials is closely linked to their quality. 

A remedy obviously should be available using polarization tricks. In conventional Raman spectroscopy, the isotropic and anisotropic components are deduced from linear combinations of the polarized and depolarized spectra, while a nonresonant part is not clearly recognized (41). In frequency-domain CARS it is known how to suppress the nonresonant contribution and solely measure resonant scattering (isotropic plus anisotropic part) (42). In time-domain CARS, polarization interference can do an even better job with three magic cases (derived in Refs. 35,39). These authors derived explicit expressions for the coupling factors F in Equations (2)-(4) ... 

We shall conclude this chapter with a few speculative remarks on possible future developments of nonlinear IR spectroscopy on peptides and proteins. Up to now, we have demonstrated a detailed relationship between the known structure of a few model peptides and the excitonic system of coupled amide I vibrations and have proven the correctness of the excitonic coupling model (at least in principle). We have demonstrated two realizations of 2D-IR spectroscopy a frequency domain (incoherent) technique (Section IV.C) and a form of semi-impulsive method (Section IV.E), which from the experimental viewpoint is extremely simple. Other 2D methods, proposed recently by Mukamel and coworkers (47), would not pose any additional experimental difficulty. In the case of NMR, time domain Fourier transform (FT) methods have proven to be more sensitive by far as a result of the multiplex advantage, which compensates for the small population differences of spin transitions at room temperature. It was recently demonstrated that FT methods are just as advantageous in the infrared regime, although one has to measure electric fields rather than intensities, which cannot be done directly by an electric field detector but requires heterodyned echoes or spectral interferometry (146). Future work will have to explore which experimental technique is most powerful and reliable. 

Measurement of the linear viscoelastic properties is the basic rheological characterization of polymer melts. These properties may he evaluated in the time domain (mainly creep and relaxation experiments) or in the frequency domain in this case we will talk about mechanical spectroscopy, where the sample experiences a harmonic stimulus (either stress or strain). 

We will discuss in this section the variations of the viscoelastic parameters derived from linear viscoelastic measurements all these parameters may be derived from any t3rpe of measurement (relaxation or creep experiment, mechanical spectroscopy) performed in the relevant time or frequency domain. The discussion will be focused however on the complex shear modulus which is the basic function derived from isothermal frequency sweep measurements performed with modem rotary rheometers. 

The unification of the frequency domain up to 10 Hz has been primarily the result of advances in e qjerimental technique, notably the development of laser sources and of interferometric spectroscopy in the far-i.r. As a result it has become necessary, for the theoretical interpretation of the measurements, to take account in detail of the ways in which the random motions of molecules diiSer from simple difiiision of position or of orientation. ... 

The statistical properties described above for frequency-domain stochastic errors are based on the equations for the instruments actually used for the measurement of complex quantities. While the statistical properties are developed here for electrochemical impedance spectroscopy, they are also valid for measurement of other complex quantities so long as the complex quantities are measured through similar physical principles. 

This part introduces methods used to measure impedance and other transfer functions. The chapters in this section are intended to provide an understanding of frequency-domain techniques and the approaches used by impedance instrumentation. This understanding provides a basis for evaluating and improving experimental design. The material covered in this section is integrated with the discussion of experimental errors and noise. The extension of impedance spectroscopy to other transfer-function techniques is developed in Part III. 

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