Diffusion molecular propagation

In zeolites Na X and ZSM-5, the self-diffusion coefficients were found to decrease with increasing concentration while for zeolite NaCa A they are essentially constant The highest diffusivities were observed in zeolite Na X. This is in agreement with the fact that due to the internal pore structure the steric restrictions of molecular propagation in zeolite Na X are smaller Aan those in Na Ca A and ZSM-5 (94). Mass transfer and chemical reaction in zeolite channels in which the individual molecules cannot pass each other (single-file... 

Here and (p denote the orientation of the principal axes of the diffusion tensor with respect to the applied field gradients. For quantitative analysis of Eq. (38) it is essential that in the case of ZSM-5 the three principal elements of the diffusion tensor are not independent of each other. Under the assumption that molecular propagation from one channel intersection to an adjacent one is independent of the diffusing molecule s history (in other words, independent of the original... 

A large variety of zeolites (e.g., ZSM-12, -22, -23, -48, AIPO4-5, -8, -11, and VPI-5) contain systems of parallel channels with diameters on the order of the molecular dimensions. Molecular propagation in this type of adsorbent represents a special case of diffusion anisotropy, since the main elements of the diffusion tensor referring to the plane perpendicular to the direction of the channel system are equal to zero. In the first PFG NMR diffusion measurements of methane in ZSM-12 and AIPO4-5, only a lower limit on the order of I0 m"s could be determined for diffusivity in the channel direction (160). This value is two orders of magnitude below the diffusivity of methane in the straight channels of zeolite ZSM-5 (see Fig. 14). Since the channel diameters of ZSM-12... 

Figure 19 compares the effect of co-adsorbed water molecules on the mobility of n-butane in zeolites NaX and NaCs(55%)X [110]. The diameter of the cesium ions (0.338 nm) is considerably larger than that of sodium (0.190 nm). What happens is that the cesium ions cause an effective obstruction of molecular propagation, leading to a decrease of the diffusivity by one order of magnitude compared to the pure sodium form. Therefore there is no dramatic influence on the butane diffusivity from the presence of a small amount of water molecules. By contrast, starting from that level of water concentration for which the butane diffusivity in NaX has dropped to the value in NaCsX, a further increase in the... 

Figure 2 summarizes the three main parameters of molecular transport accessible by PEG NMR and illustrates the conditions under which they may be obtained. Sections 3 and 4 provide examples of the message provided by the study of long-range diffusion (Dh ) and intercrystalHne exchange rates (Tjjjtra )- Since the scientific interest in molecular propagation is primarily focussed on intracrystalline diffusion, the main part of this contribution (Sect. 5) will be devoted to the measurement of Dintra. 

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]... 

Deviations from normal diffusion, i.e. from molecular propagation within a quasi-homogeneous, essentially infinitely extended medium, may be taken into account by introducing an effective diffusivity Dgff. It is defined in the same way as the self-diffusivity, i.e. via Eqs. 6 and 7, however, without the requirement of the validity of Pick s laws 1 and 2. Therefore, Dgff may become a function of the (observation) time. In the considered case of zeolitic diffusion and for intracrystalline diffusion paths being sufficiently small in comparison with the crystallite radii, the effective diffusivity may be shown to be represented by a power series [106-108], leading to... 

Like with MFI-type zeolites, structure-related diffusion anisotropy might as well be anticipated for chabazites [132]. The chabazite pore system consists of an arrangement of large cavities of the shape of prolate ellipsoids. Each cavity is connected to six adjacent ones, with the centers of three of them above and with the other three below the center of this cavity. As a consequence, molecular propagation from cavity to cavity implies correlated shifts into the direction of the longitudinal extension of the cavities (z coordinate) and within the plane perpendicular to it (xy plane). Incorporating the relevant crystal geometry yields the correlation rule [133,134]... 

It should be noted that in the literature the term single-file diffusion has sometimes been used to indicate only the mutual steric hindrance of the molecules in zeolite channels and not the additional constraint of an absolute exclusion of their mutual passage. Such terminology is clearly misleading since in this case molecular propagation would also be subjected to Pick s laws. 

Fig. 2 Various time regimes of molecular propagation in single-file systems as resulting from MD simulations. The inset indicates the channel diameters considered in the different simulations. In all cases, the diameter of the diffusants was assumed to be equal to 0.383 nm. From [35] with permission...

The mechanism of flame propagation into a stagnant fuel-air mixture is determined largely by conduction and molecular diffusion of heat and species. Figure 3.1 shows the change in temperature across a laminar flame, whose thickness is on the order of one millimeter. 

Heat is produced by chemical reaction in a reaction zone. The heat is transported, mainly by conduction and molecular diffusion, ahead of the reaction zone into a preheating zone in which the mixture is heated, that is, preconditioned for reaction. Since molecular diffusion is a relatively slow process, laminar flame propagation is slow. Table 3.1 gives an overview of laminar burning velocities of some of the most common hydrocarbons and hydrogen. 

Even though the rate of radical-radical reaction is determined by diffusion, this docs not mean there is no selectivity in the termination step. As with small radicals (Section 2.5), self-reaction may occur by combination or disproportionation. In some cases, there are multiple pathways for combination and disproportionation. Combination involves the coupling of two radicals (Scheme 5.1). The resulting polymer chain has a molecular weight equal to the sum of the molecular weights of the reactant species. If all chains are formed from initiator-derived radicals, then the combination product will have two initiator-derived ends. Disproportionation involves the transfer of a P-hydrogen from one propagating radical to the other. This results in the formation of two polymer molecules. Both chains have one initiator-derived end. One chain has an unsaturated end, the other has a saturated end (Scheme 5.1). 

The reactivity of macromonomers in copolymerizalion is strongly dependent on the particular comonomer-macromonomer pair. Solvent effects and the viscosity of the polymerization medium can also be important. Propagation may become diffusion controlled such that the propagation rate constant and reactivity ratios depend on the molecular weight of the macromonomer and the viscosity or, more accurately, the free volume of the medium. 

The field of modified electrodes spans a wide area of novel and promising research. The work dted in this article covers fundamental experimental aspects of electrochemistry such as the rate of electron transfer reactions and charge propagation within threedimensional arrays of redox centers and the distances over which electrons can be transferred in outer sphere redox reactions. Questions of polymer chemistry such as the study of permeability of membranes and the diffusion of ions and neutrals in solvent swollen polymers are accessible by new experimental techniques. There is hope of new solutions of macroscopic as well as microscopic electrochemical phenomena the selective and kinetically facile production of substances at square meters of modified electrodes and the detection of trace levels of substances in wastes or in biological material. Technical applications of electronic devices based on molecular chemistry, even those that mimic biological systems of impulse transmission appear feasible and the construction of organic polymer batteries and color displays is close to industrial use. 

The fact that the quenching limits of upward propagating rich limit flames are much wider in comparison with those moving downward can be explained in terms of preferential diffusion. When the molecular diffusivity of the deficient reactant is higher than the thermal diffusivity of the mixture and when the flame is stretched (upward propagating convex flames... 

In the so-called "wrinkled flame regime," the "turbulent flame speed" was expected to be controlled by a characteristic value of the turbulent fluctuations of velocity u rather than by chemistry and molecular diffusivities. Shchelkin [2] was the first to propose the law St/Sl= (1 + A u /Si) ), where A is a universal constant and Sl the laminar flame velocity of propagation. For the other limiting regime, called "distributed combustion," Summerfield [4] inferred that if the turbulent diffusivity simply replaces the molecular one, then the turbulent flame speed is proportional to the laminar flame speed but multiplied by the square root of the turbulence Reynolds number Re. ... 

For the catalytic oxidation of malonic acid by bromate (the Belousov-Zhabotinskii reaction), fimdamental studies on the interplay of flow and reaction were made. By means of capillary-flow investigations, spatio-temporal concentration patterns were monitored which stem from the interaction of a specific complex reaction and transport of reaction species by molecular diffusion [68]. One prominent class of these patterns is propagating reaction fronts. By external electrical stimulus, electromigration of ionic species can be investigated. 

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