Diffusion experiments, with

Figure 2. Spin-echo -NMR spectra from a diffusion experiment with a cubic phase of dDAVP (10%), MO (60%) and 2H20 (40%). Temperature 40 C, t=20 ms, A=24 ms, g=l 19 gauss/cm and 8=1.0,2.0..., 9.0 ms. The inset shows the aromatic region originating from dDAV P at a higher amplification. Also shown is the pulse sequence used in the NMR-diffusion method (see text for details).

In this chapter we will focus on molecular ordering and confinement effects in pores. Diffusion experiments with the pulse-field gradient method ([162-165] and references therein) and characterization of the surface properties using NMR of noble gases such as 129Xe ([166-171] and references therein), or 83Kr [172], will be omitted due to excellent reviews that have appeared quite recently in these areas. 

Hydrodemetallation reactions require the diffusion of multiringed aromatic molecules into the pore structure of the catalyst prior to initiation of the sequential conversion mechanism. The observed diffusion rate may be influenced by adsorption interactions with the surface and a contribution from surface diffusion. Experiments with nickel and vanadyl porphyrins at typical hydroprocessing conditions have shown that the reaction rates are independent of particle diameter only for catalysts on the order of 100 /im and smaller (R < 50/im). Thus the kinetic-controlled regime, that is, where the diffusion rate DeU/R2 is larger than the intrinsic reaction rate k, is limited to small particles. This necessitates an understanding of the molecular diffusion process in porous material to interpret the diffusion-disguised kinetics observed with full-size (i -in.) commercial catalysts. 

With Cu-Zr, in an interval of 1000°C it amounts to 1 %. If initial dimensions, LCu and LZr, are 1 cm each, then the relative displacement of the phases is 100 pm which value is close on the order of magnitude to layer thicknesses encountered in reaction-diffusion experiments. With brittle compound layers formed and insufficiently ductile initial phases, this appears to be more than sufficient to cause any couple to rupture. 

Fig. 12.9. Results of two complementary transient diffusion experiments with a tubular /ycor glass membrane. The figure shows development of the pressure difference between the two sides ofthe membrane after exchanging...

Short Tube.—By way of contrast diffusion experiments with a short tube were finally made. The dimensions were / = 35 cm. d 2f = 1.7 cm. As the fringe displacements are small they were read off directly... 

Initial hydrogen diffusion experiments with metal membranes began as early as the middle of the nineteenth century with palladium [3-5], Since these experiments, Pd has been the most widely investigated membrane material with the most acknowledged studies being conducted in the mid-twentieth century [6-11], Additionally, several comprehensive reviews have been published that summarize the developments of palladium membrane technologies over the past 150 years [12, 13],... 

A more sensitive and reliable test for the presence of convection is to record two or more diffusion experiments with differing values of the diffiision period A under otherwise identical conditions. In the absence of convection (or where its influence has been suppressed), the value of D obtained should not differ between data sets. In contrast, the apparent diffusion coefficients measured in the presence of convection will vary with A, as indicated by Eq. (9.11), and produce progressively larger values of />app with longer diffusion periods. This influence is readily apparent for quinine 9.1 in CDCI3 recorded at the slightly elevated temperature of 313 K but may also be observed at a much reduced level at 298 K where probe temperature regulation is employed (Fig. 9.12). 

Figure 18 Illustration of the double-oil self-diffusion experiment with a cyclohexane-hexadecane mixture. K = D /D2, where D and Dj are the cyclohexane and hexadecane diffusion coefficients, respectively. In the pure oil mixture the ratio of the two diffusion coefficients is K = Kq— 1.69. For a water-in-oil droplet structure the two oil molecules have the same diffusion coefficient, that of the micelle, and the ratio A equals unity. In a bicontinuous structure, on the other hand, a molecular diffusion mechanism is dominating and the ratio K equals that of the pure oil mixture, Kq. By monitoring the diffusion coefficient ratio, the droplet-to-bicontinuous transition could be studied.

Figure 19 Double-oil diffusion experiment with nonionic surfactant, (a) Self-diffusion coefficients and (b) diffusion coefficient ratio A" as a function of temperature in a water-rich microemulsion with nonionic surfactant. A transition from oil-in-water droplets to a bicontinuous microstructure occurs with increasing temperature (decreasing spontaneous curvature of the C12E5 surfactant film). The maximum in K indicates that an attractive interaction between the micelles is operating prior to the formation of a bicontinuous structure. Kq = 1.69 is the diffusion coefficient ratio in the pure oil mixture and is indicated as a broken line in (b). Note that the initial decrease of the self-diffusion coefficients shows that the droplets grow in size before the bicontinuous transition. The phase boundary at 25.7 C is indicated as a vertical broken line. (Data from Ref 43.)...

Fig.7. Flow-trough-cell for diffusion experiments with ion selective membranes conditioned on one side with 3 mol/1 KSCN solutions, or with 2 mol/l KCl solutions, and with distilled H2O on the other side.

For the uncoated catalyst, we have the highest reaction rate and thus the strongest influence of pore diffusion. To investigate the influence of pore diffusion, experiments with different particle diameters (<25 pm up to 2 mm) were conducted both with the uncoated Ni catalyst and with the SCILL catalyst for a pore filling degree of 15%. Figure 14.8 clearly shows that for the uncoated catalyst and a particle size of less than about 80 pm, an effectiveness factor of 1 is reached. For the SCILL catalyst, pore diffusion has less impact on the effective rate of COD conversion. The intrinsic rate constant is smaller and the effectiveness factor is still almost 1 up to a particle diameter of around 200 pm. 

Boltzmann and Matano showed [22, 23] how the concentration dependent chemical diffusion coefficient D (c) can be determined from the data obtained in a diffusion experiment with two semi-infinite regions and the initial conditions of Fig. 5-5 for the case where the molar volume Km binary system is independent of concentration. 

Defects can be discovered and determined by different experimental methods. By measurement of the electrical conductivity (see to Mixed Conductors, Determination of Electronic and Ionic Conductivity (Transport Numbers)) in dependence on partial pressure and temperature [5, 6] and the heat capacity in dependence on temperature [7], the defect formation could be detected. Hund investigated the defect structure in doped zirconia by measurement of specific density by means of XRD and pycnometric determination [8]. Transference measurements [9] and diffusion experiments with tracers [10-12] or colored ions [4] are suited for verifying defects. 

Figure 2.3 Typical experimental data from a PFG-NMR diffusion experiment with the fitted Stejskal-Tanner equation fEq. 2.5 shown as the linel.

With nonionic surfactants, it is possible to generate an oil-in-water droplet to bicontinuous structural transition at constant composition by increasing the temperature. This transition can be studied in more detail by using self-diffusion experiments with mixed solvents. In a system where the oil was an equal weight mixture of cyclohexane (1) and hexadecane (2) the transition from normal oil-swollen micelles to a bicontinuous microstructure was studied by monitoring the variation of the self-diffusion coefficient ratio, K = as a... 

Riley, J.J. and Patterson, G.S., Jr. (1974). Diffusion Experiments with Numerically Integrated Isotropic Turbulence. Phys. Huid, Vol. 17, pp. 292-297. 

A.M. Torres, G. Zheng, W.S. Price, J-compensated PGSE an improved NMR diffusion experiment with fewer phase distortions, Magn. Reson. Chem. 48 (2010) 129-133. 

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