Intrinsic relaxation times

Having introduced the concept of exchange in a pictorial way, we treat now the more general case of exchange between two sites of different population and different intrinsic relaxation times. Under such conditions relaxation is not a single exponential but rather a double exponential process, where the individual... 

This remarkable scaling property, which is shared by some liquid crystalline polymers (see Section 11.3.4), by nematic surfactant solutions (Section 12.4.2), and by some particulate suspensions, is a consequence of the lack of an intrinsic relaxation time. In the case... 

In other words, unless the concentration of bound sites is the s u e within the volume of space s u pled by any one water molecule in its own intrinsic relaxation time, then, on average, non-exponential decay must be observed. 

However, his suggestion that the measured intrafibre relaxation time (rather than the intrinsic relaxation time of free water) determines the space S unpled by any water molecule appears to be unnecessary. 

As mentioned in the previous section, the time constant which describes the decay of the magnetization in the x-y plane is T. We define an intrinsic relaxation time which is characteristic of the magnetization decay in one of the spin... 

The Influence of 3q spin exchange on T is non-existent when all carbons have the same Intrinsic relaxation time. 

In order to monitor the diffusion of the probe molecules the sample is illuminated for a short time interval gating the laser with a Kerr cell (Fig. 20.4). The length of the excitation pulse must be careMly matched to the intrinsic relaxation time of the photochromic probe. After terminatio of excitation the grating is washed out by diffusion of both, excited and unexcited dye molecules. Hence, the diffraction efficiency of the grating is diminished and the intensity I t) of the diffracted probe laser beam decreases according to the equation... 

The decay constant t is influenced by both, the intrinsic relaxation time Tdye of the probe (i.e. the time constant of relaxation of the photoisomer produced) and the diffusion constant D, according to the equation... 

However, the of the PVOH component was lowered by increasing the amount of starch in the blend. Whilst this depression of the of PVOH is an indication of mixing, the fact that no averaging takes place between the of PVOH and starch is a sign that their miscibility is limited, most likely to local regions such as interfaces. It should also be noted that the intrinsic relaxation time of the starch component in the blends is shorter in comparison with values in unblended PIS, indicating that the molecular mobilities of the starch are also... 

Modem NMR tools can acquire data at various measurement conditions, such as multiple wait times (TW) and interecho times (TE) in a single logging pass (Hursan et al., 2005). As a result, data acquisition delivers a view into fluid properties, using not only one, but two or three parameter domain dimensions (2D and 3D NMR). They all based on differences of T, T2, and D between the different fluids (water/brine, oil, gas). Frequently used are 2D maps (plots) of T versus T2 (Fig. 3.12a), D versus T2 (Fig. 3.12b), and ratio R = T /T2,app versus 72,app (Fig. 3.12c). The axes in such plots are logarithmically scaled. Ti and T2 are the intrinsic relaxation time. 72 pp is the transverse relaxation time defined by ... 

The first term is the intrinsic relaxation time, T2, which depends oti the bulk fluid and the formation properties. The sectmd term represents the decay caused by the molecular diffusion in a gradient magnetic field, where y is the proton gyromagnetic ratio, G is the magnetic field gradient that varies with frequency. The large diffusion contrast controls the ratio Ti/T2 pp and makes this technique suitable for separating gas from liquids (Hursan et al., 2005). 

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