Diffusion relaxation

These models are designed to reproduce the random movement of flexible polymer chains in a solvent or melt in a more or less realistic way. Simulational results which reproduce in simple cases the so-called Rouse [49] or Zimm [50] dynamics, depending on whether hydrodynamic interactions in the system are neglected or not, appear appropriate for studying diffusion, relaxation, and transport properties in general. In all dynamic models the monomers perform small displacements per unit time while the connectivity of the chains is preserved during the simulation. 

Diffusion-relaxation correlation has been utilized to study biological tissues, e.g., compartmentalization in tissues [32-35]. In many reports, a sequence that combines a stimulated echo-type sequence with a pulsed field gradient and a CPMG as a detection has been described [35]. Other pulses sequences have also been used to study the diffusion-relaxation correlation, e.g., Ref. [36]. 

Figure 2.7.2 illustrates two implementations of the diffusion-relaxation experiment using the pulsed field gradient. In the first implementation, a spin-echo... 

Fig. 2.7.2 Diffusion-relaxation correlation se- The detection (2nd) segment for both is a quences using pulsed field gradients, (a) The CPMG pulse train that is similar to that in first segment is a spin-echo with the echo Figure 2.7.1. The amplitude or the duration of appearing at a time 2tcpi after the first pulse, the gradient pairs in both sequences is (b) The first segment is a stimulated echo incremented to vary the diffusion effects, appearing at a time tcpi after the third pulse.

For the spin-echo diffusion-relaxation experiment, they showed... 

The stimulated echo diffusion-relaxation experiment exhibits a kernel that is similar to that of the one with the pulsed field gradients ... 

Hence, a series of measurements with several Tcp values will provide a data set with variable decays due to both diffusion and relaxation. Numerical inversion can be applied to such data set to obtain the diffusion-relaxation correlation spectrum [44— 46]. However, this type of experiment is different from the 2D experiments, such as T,-T2. For example, the diffusion and relaxation effects are mixed and not separated as in the PFG-CPMG experiment Eq. (2.7.6). Furthermore, as the diffusion decay of CPMG is not a single exponential in a constant field gradient [41, 42], the above kernel is only an approximation. It is possible that the diffusion resolution may be compromised. 

G. J. Hirasaki 2003, (Diffusion-relaxation distribution functions of sedimentary rocks in different saturation states), Magn. Reson. Imaging 21, 305-310. 

P.T. Callaghan, S. Godefroy, and B.N. Ryland, Diffusion-relaxation correlation in simple pore structures, J. Magn. Reson., 162, 320-327 (2003). 

We might compare this with the rotational diffusion relaxation time of Debye (18) ... 

Using the Laplace inversion program, CONTIN, in the correlator, we were able to calculate G(T) from G(2>(t, q) on the basis of Eqs. 3 and 4. For a pure diffusive relaxation, r is related to the translational diffusion coefficient D as [47]... 

In Fig. 1 we have highlighted with a dark background the different types of NMR methods that are used in drug-discovery projects. These include basic ID and 2D methods that are used to confirm the identity of peptides, determine their conformation, or derive restraint information used in 3D structure calculations (left side of Fig. 1). Methods to study binding interactions (middle section of Fig. 1) can be broadly categorized as being based on NOEs, diffusion, relaxation, or chemical shift changes. NOE-based methods include the transferred NOE... 

Theory (Odijk et al., 1977/79, Mandel et al., 1983/86) predicts that in the dilute state (c < c ) most of the parameters of the solution (intrinsic viscosity, diffusivity, relaxation times) will be functions of the molar mass, but not of the polymer concentration. In the so-called semi-diluted solution state the influence of the polymer concentration (and that of the dissolved salts) becomes very important, whereas that of the molar mass is nearly absent. Experiments have confirmed this prediction. 

Predict the changes that would occur if the PS spheres were studied in a more viscous solvent like propanol. In particular, how would the time scale needed for data acquisition change Estimate the diffusive relaxation time t for your PS spheres in propanol at 25°C (for which rj = 1.945 cP and n = 1.385). 

The presence of a near and far field in and around a non-equilibrium double layer leads to the distinction between (at least) two relaxation times. Relaxation to the static situation, after switching off the external field, can take place by conduction or by diffusion. Conduction means that ions relax to their equilibrium position by an electric field. Diffusion relaxation implies that a concentration gradient is the driving force. In double layers these two mechanisms cannot be separated because excess ion concentrations that give rise to diffusion, simultaneously produce an electric field, giving rise to conduction. For the same reason, if polarization has taken place under the Influence of an external field and this field is switched off, ions return to their equilibrium positions by a mixture of conduction and diffusion. 

Diffusion relaxation is determined by the time needed to cover a certain displacement. Following (1.6.3.2) the corresponding relaxation time is... 

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