Propagator molecular displacement

Figure 3.1.1, bottom left, illustrates a situation where PFG NMR may provide immediate evidence about the existence and intensity of additional transport resistances on the surface of the individual crystallites, the so-called surface barriers [60, 61]. This option is based on the sensitivity of PFG NMR towards molecular displacements. Molecules traveling over distances exceeding the typical crystallite sizes have to leave the individual crystallites (and are captured by some other crystallite(s) on their further trajectory). This fraction of molecules contributes to the broad part of the propagator. Plotting the relative intensity of the broad part of the propagator as a function of t we thus obtain the relative number y (t) of molecules, which have left their (starting) crystallites at time t. The function y(t) is... 

Owing to its ability to monitor the probability distribution of molecular displacements over microscopic scales from hundreds of nanometers up to several millimeters, PFG NMR is a most versatile technique for probing the internal structure of complex materials. As this probing is based on an analysis of the effect of the structural properties on molecular propagation, the properties of the material studied are those which are mainly of relevance for the transport processes inherent to their technical application. 

It is also possible to perform a two-dimensional PFG spin-echo experiment employing two orthogonal magnetic field gradients. This yields a two-dimensional propagator Ps X, Y, A) that corresponds to the joint probability for molecular displacements X and Y in time A. Results have been obtained on a packed bed of glass spheres and on a sandstone, and have been compared with those predicted by numerical simulation of the flow assuming pore network models. ... 

If the mean molecular displacements in the interval between the two field-gradient pulses are much larger than the crystalhte diameters, the diffusivity resulting from PFG NMR measurements reflects the rate of molecular propagation through the bed of crystalhtes. This coefficient of long-range diffusion may be shown to be determined by [84]... 

Y is either a solvated electron (displaced electron formed during the radiolytic reaction) or the product of the electron having reacted with some compound in the reaction system [Allen et al., 1974 Hayashi et al., 1967 Kubota et al., 1978 Williams et al., 1967]. If Y is an electron, the propagating carbocation centers are converted to radical centers that subsequently undergo reaction with some species in the reaction system to form molecular species. The termination rate is given by... 

One of the most important parameters in the S-E theory is the rate coefficient for radical entry. When a water-soluble initiator such as potassium persulfate (KPS) is used in emulsion polymerization, the initiating free radicals are generated entirely in the aqueous phase. Since the polymerization proceeds exclusively inside the polymer particles, the free radical activity must be transferred from the aqueous phase into the interiors of the polymer particles, which are the major loci of polymerization. Radical entry is defined as the transfer of free radical activity from the aqueous phase into the interiors of the polymer particles, whatever the mechanism is. It is beheved that the radical entry event consists of several chemical and physical steps. In order for an initiator-derived radical to enter a particle, it must first become hydrophobic by the addition of several monomer units in the aqueous phase. The hydrophobic ohgomer radical produced in this way arrives at the surface of a polymer particle by molecular diffusion. It can then diffuse (enter) into the polymer particle, or its radical activity can be transferred into the polymer particle via a propagation reaction at its penetrated active site with monomer in the particle surface layer, while it stays adsorbed on the particle surface. A number of entry models have been proposed (1) the surfactant displacement model (2) the colhsional model (3) the diffusion-controlled model (4) the colloidal entry model, and (5) the propagation-controlled model. The dependence of each entry model on particle diameter is shown in Table 1 [12]. 

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