EXPERIMENTAL MEASUREMENT OF RELAXATION TIMES

Ti reports on fast dynamics on a timescale of ps-ns, whereas T2 relaxation depends on both fast and slower dynamics (ps-ns and xs-ms). The experimentally measured T2 relaxation times include an exchange contribution that can be measured by a Carr-Purcell-Meiboom-Gill (CPMG) pulse train (25, 26) or an effective spin-lock field (27-29). The combination of T2 and Tip measurements allows determination of the contribution of chemical exchange to the relaxation time. Eurthermore, relaxation dispersion experiments have been developed to measure slow time-scale xs-ms dynamic processes (30-35). 

Studies of molecular dynamics have focused on the effect of temperature due largely to experimental convenience. Isobaric measurements of relaxation times and viscosities are carried out routinely as a function of temperature. From these experiments it is well established that the shape of the a-dispersion (i.e., the KWW stretch exponent fiKWW), when compared at Tg or some other reference value of xa, varies among different glass-formers [45,46]. Many experimental studies have shown also that for a given material, very often the distribution of relaxation times systematically broadens with decreasing temperature [47-50]. 

Ideally, measurements should be made at as many magnetic field strengths as possible, so that a unique fit of the experimental data to a particular model, may be obtained. As already mentioned, in addition to measuring the p values, measurement of relaxation times will help to substantiate the model chosen. 

Figure 78 shows the dependence of experimentally measured rotational relaxation times (tJ of AP, PRODAN, and anthracene on rjIT in four morpholinium ILs. The calculated (upper solid line) and (lower dashed line) values from the SED theory are also shown. 

Thus, by measuring the zero-shear viscosity of the entangled polymer, we can estimate its longest Rouse relaxation time. A similar method has been developed by Pattamaprom and Larson [18], but using an experimentally measured longest relaxation time as the input, and scaling this using the ratio of MJM to the power -1.4 to get the Rouse time (see Eq. 11.41 in Chapter 11) and note that Tj = 2 %. 

Another, purely experimental possibility to obtain a better estimate of the friction coefficient for rotational motion in chemical reactions consists of measuring rotational relaxation times of reactants and calculating it according to equation (A3,6,35) as y. =... 

Condensed phase vibrational or vibronic lineshapes (vibronic transitions create vibrational excitations of electronic excited states) rarely provide infonnation about VER (see example C3.5.6.4). Experimental measurements of VER need much more than just the vibrational spectmm. The earliest VER measurements in condensed phases were ultrasonic attenuation studies of liquids [15], which provided an overall relaxation time for slowly (>10 ns) relaxing small molecule liquids. 

The several experimental methods allow a wide range of relaxation times to be studied. T-Jump is capable of measurements over the time range 1 to 10 s P-jump, 10 to 5 X 10" s electric field jump, 10 to 10 s and ultrasonic absorption, 10 to 10 " s. The detection method in the jump techniques depends upon the systems being studied, with spectrophotometry, fluorimetry, and conductimetry being widely used. 

The Fourier transform of a pure Lorentzian line shape, such as the function equation (4-60b), is a simple exponential function of time, the rate constant being l/Tj. This is the basis of relaxation time measurements by pulse NMR. There is one more critical piece of information, which is that in the NMR spectrometer only magnetization in the xy plane is detected. Experimental design for both Ti and T2 measurements must accommodate to this requirement. 

The measurement of correlation times in molten salts and ionic liquids has recently been reviewed [11] (for more recent references refer to Carper et al. [12]). We have measured the spin-lattice relaxation rates l/Tj and nuclear Overhauser factors p in temperature ranges in and outside the extreme narrowing region for the neat ionic liquid [BMIM][PFg], in order to observe the temperature dependence of the spectral density. Subsequently, the models for the description of the reorientation-al dynamics introduced in the theoretical section (Section 4.5.3) were fitted to the experimental relaxation data. The nuclei of the aliphatic chains can be assumed to relax only through the dipolar mechanism. This is in contrast to the aromatic nuclei, which can also relax to some extent through the chemical-shift anisotropy mechanism. The latter mechanism has to be taken into account to fit the models to the experimental relaxation data (cf [1] or [3] for more details). Preliminary results are shown in Figures 4.5-1 and 4.5-2, together with the curves for the fitted functions. 

Experimental verification of the universal wing shape (4.90) is not only an important way of checking the dominant role of spectral exchange but also an additional spectroscopic way to measure energy relaxation time even before collapse (in rare gases). Unfortunately it has not been done yet due to lack of accuracy far beyond the spectral edge. 

Here m is electron mass, N is the number density of gas molecules, B is the rotational constant, and q = (8/15)jta02Q2, ag and Q being respectively the Bohr radius and the quadrupole moment of the molecule. The experimental energy loss rate for nitrogen agreed well with Eq. (8.1) over the ambient temperature range 300-735 K. Typical values are -0.5 ts at 300 K and 6 torr, and -1 p.s at 735 K and 4 torr. The variation of relaxation time with gas temperature and pressure are also well predicted. For oxygen, Mentzoni and Rao (1965) measure relaxation times -160-350 ns for T = 300-900 K and at 3 torr. 

Experimental measurement of Hall mobility produces values of the same order of magnitude as the drift mobility their ratio r = jij/l may be called the Hall ratio. If we restrict ourselves to high-mobility electrons in conducting states in which they are occasionally scattered and if we adopt a relaxation time formulation, then it can be shown that (Smith, 1978 Dekker, 1957)... 

Distributions of relaxation or retardation times are useful and important both theoretically and practicably, because // can be calculated from /.. (and vice versa) and because from such distributions other types of viscoelastic properties can be calculated. For example, dynamic modulus data can be calculated from experimentally measured stress relaxation data via the resulting // spectrum, or H can be inverted to L, from which creep can be calculated. Alternatively, rather than going from one measured property function to the spectrum to a desired property function [e.g., Eft) — // In Schwarzl has presented a series of easy-to-use approximate equations, including estimated error limits, for converting from one property function to another (11). 

An interesting new experimental approach has been taken in order to separate overlapping EPR spectra as they appear e.g. in the multi Fe/S centre containing complex I. Inversion- and saturation-recovery measurements which allow to measure Ti relaxation times are used in a inversion-recovery filter which is subsequently applied to separate EPR signals on account of their Trdifferences. In addition, this filter can be used in conjunction with high-resolution hyperfine measurements e.g. by ESEEM and thus the separated centres can be characterized in depth.211... 

In this respect, another insufficiency of Lodge s treatment is more serious, viz. the lack of specification of the relaxation times, which occur in his equations. In this connection, it is hoped that the present paper can contribute to a proper valuation of the ideas of Bueche (13), Ferry (14), and Peticolas (13). These authors adapted the dilute solution theory of Rouse (16) by introducing effective parameters, viz. an effective friction factor or an effective friction coefficient. The advantage of such a treatment is evident The set of relaxation times, explicitly given for the normal modes of motion of separate molecules in dilute solution, is also used for concentrated systems after the application of some modification. Experimental evidence for the validity of this procedure can, in principle, be obtained by comparing dynamic measurements, as obtained on dilute and concentrated systems. In the present report, flow birefringence measurements are used for the same purpose. 

---