Applications of Relaxation Measurements

For H relaxation in poly(2,6-dimethyl-l,4-phenylene oxide), four motions satisfactorily fitted data on CH3 relaxation as a function of molecular weight (a) overall molecular tumbling, (b) segmental motion according to the sharp cut-off model, (c) rotation of the aromatic rings about the colinear C—O bonds, 

Schriever and co-workers - have published a series of papers on H and D relaxation in poIy(methacrylic acid) solutions. In the first two papers, methylene D Tj, and data and methyl H and carboxylic D Ti and data were investigated as a function of frequency, and the results interpreted empirically in terms of a biexponential autocorrelation function. As a function of d ee of neutralization (x ), the time constants of both exponential terms decrease sharply from a = 0 to 0.5, but thereafter remain constant. Similar conclusions were drawn from methyl linewidths and D solvent relaxation in D2O solutions.  

Price et a/. have reported C Ti and NOE measurements on narrow fractions of poly(y-benzyl-L-glutamate) in the helix-supporting solvent dimethyl formamide. The strong molecular weight dependence of Tx and was satisfactorily interpreted on the basis of anisotropic rotational diffusion of a rigid helix. 

Several papers are concerned with motions of polymers containing backbone sulphur atoms. - In poly(phenyl thiirane), it is found that backbone correlation times are an order of magnitude shorter than in polystyrene. An unusual feature of relaxation in poly(alkene sulphones) is that C Ti s are independent of molecular weight whereas dielectric relaxation times are not. This has been rationalized in terms of specific conformational transitions which re-orient C—H bonds but not the sulphone dipole. 

has been used to probe various aggregation phenomena. Heatley and Begum observed that mieellization of styrene-butadiene-styrene tri-block copolymers in non-solvents for butadiene is accompanied by marked hindrance to butadiene mobility. Bovey et a/. have shown that C Ti s for poly(vinylidene fluoride) and PMMA are the same in a mixed solution as in single solutions. The unusual compatibility of these two polyn rs therefore does not arise from complex formation. Self-association of stereo-r ular PMMA s in dilute solution has been studied. In toluene, isotactic PMMA is 10—17% associated at 27 C whereas a highly syndiotactic sample is 76% associated. 

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The application of relaxation measurements to non-ionic solutes, also incidentally showing up solvent effects, is illustrated by some results on... 

Small molecules in low viscosity solutions have, typically, rotational correlation times of a few tens of picoseconds, which means that the extreme narrowing conditions usually prevail. As a consequence, the interpretation of certain relaxation parameters, such as carbon-13 and NOE for proton-bearing carbons, is very simple. Basically, tlie DCC for a directly bonded CH pair can be assumed to be known and the experiments yield a value of the correlation time, t. One interesting application of the measurement of is to follow its variation with the site in the molecule (motional anisotropy), with temperature (the correlation... 

This report has been written in order to demonstrate the nature of spin-state transitions and to review the studies of dynamical properties of spin transition compounds, both in solution and in the solid state. Spin-state transitions are usually rapid and thus relaxation methods for the microsecond and nanosecond range have been applied. The first application of relaxation techniques to the spin equilibrium of an iron(II) complex involved Raman laser temperature-jump measurements in 1973 [28]. The more accurate ultrasonic relaxation method was first applied in 1978 [29]. These studies dealt exclusively with the spin-state dynamics in solution and were recently reviewed by Beattie [30]. A recent addition to the study of spin-state transitions both in solution and the... 

Recent applications of relaxation dispersion measurements to concrete or cement-based materials are promising for characterizing reactive nanopor-ous materials, the structure of which may evolve over time (75-78). The MRD profiles have provided, for the first time, a direct means for characterizing the specific surface area, Sp, of a hydrated cement-based material (79), without exposing the sample to extremes of temperature or pressure (80-83). The interest in such a surface area is to provide information on the microsctruc-ture and its impact on macroscopic or structural properties. The method is based on a clear separation of surface and bulk contributions of the overall... 

A unique feature of NMR is its sensitivity for dynamic processes. Using different techniques, from the well-known lineshape analysis to the application of relaxation time measurements, the correlation times of dynamic processes which can be studied span a... 

A further application of relaxation rate measurements is that similar 1/71 ratios in a series of lanthanide complexes may be taken to indicate an isostructural series. However, this approach has the limitation that if only part of the complex is studied, perhaps an organic ligand, its 71 ratios would be independent of changes, for example changes in the extent of hydration in the remainder of the complex, provided that the conformation of the ligand relative to the lanthanide ion were preserved. An excellent example of the use of 71 data in a quite different way is its use to determine hydration numbers of lanthanide dipicolinate complexes.562... 

Despite the enormous problems encountered in interpreting relaxation times of molecules of low molecular weight as described in this article, the measurement of relaxation times of even more complex systems commonly studied in biochemistry is currently a very widely accepted method. In general, biochemical application of relaxation time measurements can be divided into three main areas ... 

Relaxation times of quadrupolar halogen nuclei may also be used to obtain sample information. One application of relaxation time measurements in the solution states is the ability to probe the level of ordering present in a solution, and it is of particular interest when compared directly to the solid state, an advantage of NMR spectroscopy highlighted earlier. 

Industrial applications of moisture measurement by nucrowave absorption are numerous they are relative rather than absolute measurements, strongly dependent upon calibration they must compete with othe-techniques, such as neutron absorption. A popular frequency band is 3—10 GHz at lower frequencies the electrolytic conductivity can mask the absorption due to dipolar relaxation, so that the technique becomes inconveniently electrolyte-sensitive at higher frequendes the penetration is usually insufficient the technique is normally carried out in transmission, but measurement by reflection is also possible. Kilohertz frequencies are also popular in studies of systems containing bound water. 

An interesting application of ultrasonic measurements was to aqueous solutions of certain metal salts. The sound-absorption characteristics of several 2 2 electrolytes of the type MX have been measured, and found to have two maxima (cf Fig. 12) from which two relaxation times can be determined ". It was not obvious with which relaxation processes these times should be associated, especially since the (diffusion-controlled) rate coefficients for ion-pair formation (which is known to occur at the concentrations used, 10 -10 M) give relaxation times too short to be observed. It seemed, then, that when the two ions and had... 

The application of relaxation time measurements to study segmental motion (in polymers) as well as diffusional chain motion is very well documented but is still a subject of study, particularly using the frequency dependence of relaxation times to test the detailed predictions of models (McBriety and Packer 1993). The anisotropy of reorientation can also be studied conveniently, and recent interest in motion of molecules on surfaces (e.g. water on porous silica) has been investigated with great sueeess (Gladden 1993). Since the dipolar interaction is usually both intermolecular and intramolecular, the relaxation of spin- /2 nuclei (e.g. H) in the same molecule as a quadrupolar nucleus (e.g. H) can permit a complete study of reorientation and translation at a microscopic level (Schmidt-Rohr and Spiess 1994). 

Kinetic applications of relaxation phenomena result from their time dependent nature. From measurements of line widths, line shapes, and direct determinations of relaxation times, many fast chemical reactions (/j < ca. 1 s) can be studied (sect. 4.22). Slower processes (t > ca. 60 s)... 

Another application of the knowledge of is to employ it for the interpretation of another relaxation measurement in the same system, an approach referred to as the dual spin probe teclmique. A rather old, but... 

One example of this occurs with stress relaxation. If a polymer is deformed to a fixed strain at constant temperature the force required to maintain that strain will decay with time owing to viscous slippage of the molecules. One measure of this rate of decay or stress relaxation is the relaxation time 0, i.e. the time taken for the material to relax to 1/e of its stress on initial application of strain. 

Many designs incorporate the phenomenon of stress-relaxation. For example, in many products, when plastics are assembled they are placed into a permanently deflected condition, as for instance press fits, bolted assemblies, and some plastic springs. In time, with the strain kept constant the stress level will decrease, from the same internal molecular movement that produces creep. This gradual decay in stress at a constant strain (stress-relaxation) becomes important in applications such as preloaded bolts and springs where there is concern for retaining the load. The amount of relaxation can be measured by applying a fixed strain to a sample and then measuring the load with time. 

The most popular, and also a very accurate, experimental method for measuring nonselective spin-lattice relaxation-rates is the inversion recovery (180°-r-90°-AT-PD)NT pulse sequence. Here, t is the variable parameter, the little t between pulses, AT is the acquisition time, PD is the pulse delay, set such that AT-I- PD s 5 x T, and NT is the total number of transients required for an acceptable signal-to-noise ratio. Sequential application of a series of two-pulse sequences, each using a different pulsespacing, t, gives a series of partially relaxed spectra. Values of Rj can... 

The most significant results obtained for complexes of iron(II) are collected in Table 3. The data derive from laser Raman temperature-jump measurements, ultrasonic relaxation, and the application of the photoperturbation technique. Where the results of two or three methods are available, a gratifying agreement is found. The rate constants span the narrow range between 4 x 10 and 2 X 10 s which shows that the spin-state interconversion process for iron(II) complexes is less rapid than for complexes of iron(III) and cobalt(II). 

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