Surface relaxivity parameters

R. L. Kleinberg 1996, (Utility of NMR T2 distributions, connections with capillary pressure, day effect, and determination of the surface relaxivity parameter n >). Magn. Reson. Imaging 14 (7/8), 761—767. 

However, there are a number of important limitations to this method, which will be discussed in the next subsections. First, the mathematical analysis to obtain the distribution of relaxation times is itself a problem. Secondly, the surface relaxivity parameter is required in order to obtain a pore size distribution. Thirdly, the model assumes that diffusion within the pore is rapid and that interpore coupling can be neglected. Finally, differences in magnetic susceptibility between the solid and fluid phase complicate the interpretation of... 

A major drawback in using NMR relaxation times to obtain pore size distributions is a lack of knowledge of the surface relaxativity parameters p and p2 in Eqs (8) and (9). It is usually assumed that the surface relaxivity is constant for a particular sample, though some workers have allowed it to vary within a sample. In the case when surface relaxivity is a constant, differentiation of Equation (10) shows that the initial slope of the spin-echo magnetization data will obey ... 

This permits measurement of pi provided that an independent measurement of S/V ratios is available. A similar method can be applied to estimate p using inversion-recovery data. However, different values of the surface relaxivity parameters are obtained depending on the technique used to determine S/V ratios. For instance, pore size distributions for sandstones using BET surface... 

Calculations of the spin-echo intensity are complicated by the fact that surface relaxation may play a significant role. A general formalism for calculating PFG spin-echo attenuation for restricted diffusion in isolated pores has recently been proposed that allows for wall relaxation effects. Expressions have been obtained for the cases of diffusion within a sphere, and for planar and cylindrical geometries.These show that diffraction effects are still apparent even when surface relaxation is rapid. Also, the locations of the minima in the spin-echo intensities are not particularly affected by varying the surface relaxation parameter, Analysis of PFG spin-... 

Thus measurements of Z)app at short A times may be used to measure the surface area to volume ratio of the pores. " This is a particularly useful measurement, as it may be compared with the results of relaxation time measurements (discussed in Section 3), and thus provide an independent measurement of the surface relaxivity parameters p and... 

Figure 7.24 CPMG Tj results for a vyhite cement paste mixed at w/c = 0.40 and cured sealed throughout the hydration at 20°C measured with a 7.5 MHz spectrometer. Data are presented from 28 minutes after mixing up to 62 days of sealed hydration. Distinct water populations are rapidly observed being, from short to long relaxation times, C-S-H interlayer water, C-S-H gel water, interhydrate water and water in large capillary pores. Tj times can be translated into pore size using the fast-exchange model described in Section 7.2.4. For this, the surface relaxivity parameter is required. (Adapted from Muller 2014.)...

If several nuclei could be observed in high-resolution NMR techniques to monitor similarities or differences in both chemical shifts or integrals, other parameters can be monitored by using LF 1H NMR. In this case, relaxation parameters are usually measured as intrinsic discriminating values. As pointed out in several studies, T2 relaxation decay has a multiexponential decay in both muscles and fish tissues. This suggests the presence of different "pools" in tissues and water distribution was assumed to be present in three distinct compartments, namely (a) "bound water," (b) "entrapped water," and (c) "free water." In those three pools, water acts with different relaxation times because it can be bound to proteins, involved in the conversion of muscle to meat and entrapped by weak surface forces, showing relaxation values in the range of 1-10,10-100, and 100-400 ms, respectively. 

Figure 3.18 shows different surface relaxation modes and the corresponding viscoelastic parameters [59],... 

We emphasize two natural limitations of the finite cluster model. It does not allow to make a statement about the dependence of essential parameters such as adsorption and transition energies on the level of surface coverage, and it does not account adequately for charge delocalization or surface relaxation phenomena. Further, it excludes by definition any information about the modification of the surface band structure as a consequence of the organic molecule adsorption. The following case study of 1-propanol on Si(001) - (2 x 1) is intended to clarify how these elements can be consistently incorporated into the description of the Si surface interaction with organic species. 

Mix, Phase jj parameter corresponding to the ratio of the coordination number in the surface to that in the bulk considering the surface relaxation. " In particular, for the solid solutions, here we use the value 0.75 as by assuming that the coordi-... 

The relation between W and Ws, the domain wall widths in the bulk and at the surface, can be seen in Figure 8. The effect of the surface relaxation is clearly visible as the order parameter at the surface Qs never reaches the bulk value Qo- The distribution of the square of the order parameter at the surface shows the structure that some of the related experimental works have been reported (Tsunekawa et al. 1995, Tung Hsu and Cowley 1994), namely a groove centred at the twin domain wall with two ridges, one on each side. 

In addition, the square of the surface order parameter is proportional to the chemical reactivity profile of the twin domain wall interface at the surface (Locherer et al. 1996, Houchmanzadeh et al.(1992). Intuitively, one would expect the chemical reactivity of the surface to be largest at the centre of the twin domain wall, falling off as the distance from the centre of the wall increases. Contrary to the expected behaviour, a more complex behaviour is found. The reactivity, a monotonic function of Q, is expected to fall off as the distance from the centre of the wall increases, but only after if has reached a maximum of a distance of - 3 IF from the centre of the domain wall. If such a structure is expected to show particle adsorption (e.g. in the MBE growth of thin films on twinned substrates) we expect the sticking coefficient to vary spatially. In one scenario, adsorption may be enhanced on either side of the wall while being reduced at the centre. The real space topography of the surface is determined by both sources of relaxation-twin domain wall and the surface. These are distinct and, when considered separately, the wall... 

Unresolved problems include overall theory and related experiments on the contribution of chemical reactions at interfaces to the relaxation spectrum for a better theoretical description of surface rheological parameters. As discussed above each chemical reaction is characterised by at least one relaxation time. On the other hand surface rheological properties, for example dilational elasticity, are connected to relaxations taking place at interfaces. 

The major problem with tight-binding calculations is the change of parameters from bulk values when the surface relaxes, causing first and second nearest neighbour bond distances to change. This is resolved, however, by the availability of self-consistent calculations for relaxed surfaces. The method as developed by Pandey and Phillips assumes that the wave functions of a thin slab can be written as... 

Signal enhancements were obtained in H — O cross-polarization experiments without spinning, and reliable second-order quadrupolar powder patterns were observed [1291. Relaxation parameters involved in cross-polarization transfer were shown to be characteristic of the various sites, so that they can be used for signal assignment. In addition, in some cases the differences in crosspolarization rates were used to edit spectra by a selective enhancement of protonated oxygen resonances, such as those from surface hydroxyl groups in amorphous silica. The latter method can be applied to complicated systems, provided dipolar H — O interactions for the various sites are different. We illustrate this procedure by using a static H — O CP spectrum [126] of talc. 

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