Pulsed-gradient spin-echo method self-diffusion coefficient

The dynamic characteristics of adsorbed molecules can be determined in terms of temperature dependences of relaxation times [14-16] and by measurements of self-diffusion coefficients applying the pulsed-gradient spin-echo method [ 17-20]. Both methods enable one to estimate the mobility of molecules in adsorbent pores and the rotational mobility of separate molecular groups. The methods are based on the fact that the nuclear spin relaxation time of a molecule depends on the feasibility for adsorbed molecules to move in adsorbent pores. The lower the molecule s mobility, the more effective is the interaction between nuclear magnetic dipoles of adsorbed molecules and the shorter is the nuclear spin relaxation time. The results of measuring relaxation times at various temperatures may form the basis for calculations of activation characteristics of molecular motions of adsorbed molecules in an adsorption layer. These characteristics are of utmost importance for application of adsorbents as catalyst carriers. They determine the diffusion of reagent molecules towards the active sites of a catalyst and the rate of removal of reaction products. Sometimes the data on the temperature dependence of a diffusion coefficient allow one to ascertain subtle mechanisms of filling of micropores in activated carbons [17]. 

The self-diffusion coefficient measurements were made using the pulsed-gradient spin-echo (PGSE) method which has recently been reviewed (JLL). For a nucleus in an isotropic solution, the PGSE-NMR normalized signal intensity, 1/1q is given by ... 

Diffusions NMR spectroscopy (e.g. PGSE = Pulsed Gradient Spin Echo STE = Stimulated Echo DOSY = Diffusion Ordered Spectroscopy) is a straightforward and accurate method for determination of the self-diffusion coefficient of a molecule. Its principal use in dendrimer chemistry is for size determination of dissolved dendrimers since the self-diffusion coefficient is directly correlated with the hydrodynamic radius of the molecule via the Stokes-Einstein equation [24]. Although one-dimensional and multidimensional diffusion NMR experiments can thus make an important contribution to structural characterisation of dendrimers, they have been used comparatively rarely until recently [25, 26]. 

Diffusion of Water in poly[PFSA] Membranes To describe diffusion of water through the membrane in the presence of a water activity gradient, an appropriate interdiffusion coefficient must be determined. Experimental methods used to study diffusion of water in these polymers, such as radiotracer and pulsed gradient spin-echo NMR techniques, probe intrad-iffusion coefficients, often referred to as tracer or self-diffusion coefficients, determined in the absence of a chemical potential gradient. Intra- and interdiffusion coefficients are related for the case of diffusion of a small molecule in a polymeric matrix as follows [28] ... 

Self-diffusion coefficients could be determined separately for cations and anions of some RTILs by the pulsed-gradient spin-echo NMR signals of H and according to Noda et al. [364], The authors applied this method to RTILs with the Camim and C4Py cations and the BF4 and NTF2 anions, the self-diffusion coefficients obeying a VFT-type expression ) = 7lDexp[BD/(r — To,)]. The Stokes-Einstein relationship ... 

There are a number of NMR methods available for evaluation of self-diffusion coefficients, all of which use the same basic measurement principle [60]. Namely, they are all based on the application of the spin-echo technique under conditions of either a static or a pulsed magnetic field gradient. Essentially, a spin-echo pulse sequence is applied to a nucleus in the ion of interest while at the same time a constant or pulsed field gradient is applied to the nucleus. The spin echo of this nucleus is then measured and its attenuation due to the diffusion of the nucleus in the field gradient is used to determine its self-diffusion coefficient. The self-diffusion coefficient data for a variety of ionic liquids are given in Table 3.6-6. 

Nowadays, self-diffusion coefficients are almost exclusively measured by NMR methods, through the use of methods such as the 90-8-180-8-echo technique (Stejs-kal and Tanner sequence) [10-12]. The pulse-echo sequence, illustrated in Figure 4.4-2, can be divided into two periods of time r. After a 90° radio-frequency (RF) pulse the macroscopic magnetization is rotated from the z-axis into the x-y-plane. A gradient pulse of duration 8 and magnitude g is appHed, so that the spins dephase. 

Pulsed field gradient methods may be used in combination with a spin-echo pulse sequence to measure average molecular displacements in a time In liquids, PFG methods can therefore be used to measure self-diffusion coefficients (i.e. the rate of diffusion due to Brownian motion in the absence of a concentration gradient). In porous media, there is the possibility of obtaining information about the pore geometry because the pore boundaries will influence molecular transport. PFG techniques can measure restricted diffusion and thus provide valuable information on pore sizes in the range 5-100 (im. 

Abstract The self-diffusion coefficients of water and lysozyme in aqueous solution have been measured over a wide range of the protein concentration and over a wide range of temperature by means of the pulsed-high-field-gradient spin-echo H NMR method, and also the 0 NMR spectra of water in the protein solutions have been measured by means of a solution 0 NMR method, in order to elucidate the structure and dynamics of water and the protein, and intermo-lecular interactions between water and the protein. From these experimental results, it is found that there exist two types of water molecules with different diffusion components... 

A similar series of samples as in the SANS experiments was studied in cooperation with the group of Prof. Wokaun by NMR self-diffusion experiments. Tbe pulsed field gradient spin echo (PGSE) method [67, 68] allows the determination of the self-diffusion coefficient of each of the individual constituent components in particular water, surfactant, and hydrocarbon. Here, in order to obtain simpler NMR spectra the hydrocarbon was cyclohexane. The molar ratio of C14DMAO cyclohexane was chosen to be 1 1.2, with three samples in the Lj phase and three samples in the cubic phase. 

---