Dynamic relaxation experiments

Another way to describe deviations from the simple BPP spectral density is the so-called model-free approach of Lipari and Szabo [10]. This takes account of the reduction of the spectral density usually observed in NMR relaxation experiments. Although the model-free approach was first applied mainly to the interpretation of relaxation data of macromolecules, it is now also used for fast internal dynamics of small and middle-sized molecules. For very fast internal motions the spectral density is given by ... 

The effect of oxidative irradiation on mechanical properties on the foams of E-plastomers has been investigated. In this study, stress relaxation and dynamic rheological experiments are used to probe the effects of oxidative irradiation on the stmcture and final properties of these polymeric foams. Experiments conducted on irradiated E-plastomer (octene comonomer) foams of two different densities reveal significantly different behavior. Gamma irradiation of the lighter foam causes stmctural degradation due to chain scission reactions. This is manifested in faster stress-relaxation rates and lower values of elastic modulus and gel fraction in the irradiated samples. The incorporation of O2 into the polymer backbone, verified by IR analysis, conftrms the hypothesis of... 

Exponential decay often occurs in measurements of diffusion and spin-relaxation and both properties are sensitive probes of the electronic and molecular structure and of the dynamics. Such experiments and analysis of the decay as a spectrum of 7i or D, etc., are an analog of the one-dimensional Fourier spectroscopy in that the signal is measured as a function of one variable. The recent development of an efficient algorithm for two-dimensional Laplace inversion enables the two-dimensional spectroscopy using decaying functions to be made. These experiments are analogous to two-dimensional Fourier spectroscopy. 

On macroscopic length scales, as probed for example by dynamic mechanical relaxation experiments, the crossover from 0- to good solvent conditions in dilute solutions is accompanied by a gradual variation from Zimm to Rouse behavior [1,126]. As has been pointed out earlier, this effect is completely due to the coil expansion, resulting from the presence of excluded volume interactions. 

The dynamic mechanical experiment has another advantage which was recognized a long time ago [10] each of the moduli G and G" independently contains all the information about the relaxation time distribution. However, the information is weighted differently in the two moduli. This helps in detecting systematic errors in dynamic mechanical data (by means of the Kramers-Kronig relation [54]) and allows an easy conversion from the frequency to the time domain [8,116]. 

The effort of comparing such models with appropriate non-thermo-dynamic experiments, such as diffraction experiments and NMR relaxation experiments, is still at an early stage. 

C relaxation experiments are useful in studying the molecular motions of crown ethers and cryptands. Uncomplexed dibenzo[18]crown-6 shows a segmental mobility which disappears on complexation. Similarly, alkyldiammonium salts have shorter relaxation times when complexed by large cylindrical cryptands (Figure 15). The dynamic coupling of the molecular motions of substrate and receptor increases with their structural complementarity in the complex (81CC833). 

In this field, the resolution of DMR is promising. However, experiments on deuterated molecules have just begun, and the nuclear relaxation was not yet analyzed. We can just present here some preliminary ideas that were obtained from proton relaxation experiments (19). Because of the nature of dipolar interaction, we are dealing with a multispin system this entails some complex problems of nuclear spin dynamics which are beyond the scope of this discussion. The quantitative analysis of proton relaxation data is thus far from straight-forward (20). We shall limit ourselves to a qualitative interpretation of the frequency dependence of the relaxation rate that is summarized schematically in Figure 4. Important relaxation effects appear in both high and low frequency regions. 

In the glassy state, these Ar-Al-PA exhibit local chain dynamics which are largely controlled by the chemical structure. Recently, the local motions that may occur in the glassy state and might take part in secondary transitions, have been investigated on a series of Ar-Al-PA of various chemical structures by using dielectric relaxation, 13C and 2H solid-state NMR and dynamic mechanical experiments [57-60]. 

The combined investigations of a series of aryl-aliphatic copolyamides (xTyl -y and MT) by dielectric relaxation, solid-state 13C and 2H NMR, and dynamic mechanical experiments demonstrate the existence of three secondary transitions y, ft and co, in order of increasing temperature. 

At 60 °C, 25% of the ester groups undergo one (or an odd number of) n-flip at a frequency higher than 10 kHz, with no more than 25° deviation in the flip angle. The flips are accompanied by rotational readjustments with an amplitude of ca. 20° around the local chain axis. The flips occur between energetically inequivalent sites (thus they are active in dynamic mechanical and dielectric relaxation experiments). 

The importance of intermolecular relaxation processes (Hertz, 1967) in the interpretation of proton-relaxation data necessitates a rather deep understanding of the mechanics of liquids. Thus the H nucleus, although most extensively used in work concerned with chemical shifts and spin coupling constants, was not really taken as a probe for the molecular dynamics of complex organic molecules. It is only very recently that there has been a significant increase in literature on 7", for protons in organic molecules (Hall and Preston, 1974) stimulated most likely by 13C relaxation work. The nC nucleus, however, developed to be the abundant nucleus of relaxation experiments for three main reasons ... 

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