Self-diffusion coefficients reactions

Mechanisms of micellar reactions have been studied by a kinetic study of the state of the proton at the surface of dodecyl sulfate micelles [191]. Surface diffusion constants of Ni(II) on a sodium dodecyl sulfate micelle were studied by electron spin resonance (ESR). The lateral diffusion constant of Ni(II) was found to be three orders of magnitude less than that in ordinary aqueous solutions [192]. Migration and self-diffusion coefficients of divalent counterions in micellar solutions containing monovalent counterions were studied for solutions of Be2+ in lithium dodecyl sulfate and for solutions of Ca2+ in sodium dodecyl sulfate [193]. The structural disposition of the porphyrin complex and the conformation of the surfactant molecules inside the micellar cavity was studied by NMR on aqueous sodium dodecyl sulfate micelles [194]. 

The experimental values of [l 1ltlcgral at 150, 200 and 250°C are listed in Table 1.4, together with their 0.95 confidence limits. These values represent the volume diffusivities of the Bi atoms in the NiBi 3 lattice in the course of reaction diffusion or, in other words, the reaction-diffusion coefficients of bismuth. The interconnection between the reaction- and self-diffusion coefficients of any component of a chemical compound will be discussed in the next section. 

Interconnection between the reaction- and self-diffusion coefficient of the components of a chemical compound... 

The experimental data available in the literature show large, if not to say huge, differences between the values of diffusion coefficients of the elements A and B in the ApBq chemical compound layer growing at the A-B interface and the values of diffusion coefficients of the same elements in a separate specimen of the same chemical compound. In other words, for the same component of the same compound the value of the reaction-diffusion coefficient is quite different from the value of the self-diffusion coefficient, with the difference amounting to a few orders of magnitudes. Note that the reaction-diffusion coefficient is always greater than the appropriate self-diffusion coefficient. Consider a few examples. 

Let us now continue an analysis of the ratio between the reaction- and self-diffusion coefficients. It is obvious that a mere recalculation using equation (1.70) and substituting into its denominator the total content, cA, of component A in the chemical compound instead of the concentration difference AcA, can hardly produce close values, for example, of the diffusion coefficient of aluminium in the growing Fe2Al5 layer on the one hand and in the non-growing one on the other because in this case ca/Aca 20. 

Seeing at these very small figures on the one hand and at very large values of the ratio of the reaction- to self-diffusion coefficient like those presented in Table 1.6 on the other, it only remains to assume that the relation179... 

When applying this relationship, one must be aware of (z) all diffusion mechanisms operative in a non-growing compound, (zz) the concentration of vacancies of a given component in this compound and (zzz) the value of its self-diffusion coefficient associated with the vacancy mechanism. In view of the lack of specially planned experiments aimed at obtaining all necessary data for the same compound, including reaction- and self-diffusion coefficients of its components, at present only calculations based on the results compiled from several works are possible. 

Table 1.6. Ratios between the reaction- and self-diffusion coefficients for some oxides with predominant oxygen diffusion at a temperature of 1000°C, calculated using the data from the book by P. Kofstad14...

In the case of non-stoichiometric compounds, the vacancy concentration is mainly associated with their deficiency parameters.14185 When comparing the reaction- and self-diffusion coefficients of iron cations in Fe3.504, satisfactory results can be obtained simply by setting cv 3/4 for the growing Fe3 s04 phase and cy 8 for the non-growing one. The value of 8 characterising the cation deficiency of the crystal structure of this phase is known to be around 1.0 xlO 2,14 160 185 considerably higher than the concentration of thermal vacancies. The Fe3.g04 layer grows mainly at the expense of diffusion of iron cations, while the value of their reaction-... 

It is worth mentioning that physicochemical considerations predict the opposite influence of the degree of deficiency of a chemical compound on the values of the reaction- and self-diffusion coefficients. The former must decrease with increasing compound deficiency, while the latter is known to increase with its increasing. This seems to be the case, for example, with oxides like FeO, Fe3C>4, MnO, CoO, etc., though complicating factors often mask these effects. 

The ApBq and A Bn layers are seen to grow parabolically, whereas the thickness of the ArBs layer will gradually decrease with passing time. Eventually, this layer will disappear. It is easy to notice that in this case the values of the diffusional constants k[A2 and kim can readily be determined from the experimental dependences x2- t and z2- t, respectively, using an artificially prepared specimen A-ApBq-ArBs-A iB,-B or A-A,B-B. It is essential to mention that both the ApBq and AtBn layers must be the first to occur at the A-B interface. The diffusional constant k[A2 thus obtained is the reaction-diffusion coefficient of the A atoms in the ApBq lattice, while the diffusional constant klB3 is the reaction-diffusion coefficient of the B atoms in the Afin lattice, to be compared with respective self-diffusion coefficients determined using radioactive tracers. 

The reasons for the great difference in values of reaction- and self-diffusion coefficients of the components of a chemical compound are analysed. For example, in the case of Fe3 s04 the reaction-diffusion coefficient is two orders of magnitude greater than the self-diffusion coefficient of iron ions. For other compounds (A1203, Fe2Al5, Pd2Si, AlSb, etc.) this difference varies from five to ten orders of magnitude. After the normalisation to the same vacancy concentration the values of reaction- and self-diffusion coefficients of the same component become close, if not identical, as it should be from a physical viewpoint. 

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... 

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]. 

In the past, attempts to prepare such ternary nitrides by reaction of the respective binary nitrides always have failed because the binary nitrides do not melt congruently and also because of the low self-diffusion coefficients of these materials. However, for the synthesis of SiPNj a molecular precursor Cl3SiNPCl3 has been proven to be specifically useful [5]. In this compound the required structural element of two vertex sharing tetrahedra centered by phosphorus and silicon and connected via a common nitrogen atom is pre-organized on a molecular level. The precursor compound is obtained (Scheme 3) in a three-step synthesis starting from ((CH3)3Si)2NH which is commercially available. 

Conclusions about a rate limiting stage of methanol chemisorption on the micropo-rous Xerogel were performed by Mertens and Fripiat [62] from the comparison of a self-diffusion coefficient of physically adsorbed methanol (D = 1.5 10 cm s at 25°C or 1.5 10 cm - s at 150°C) with a range of its reaction rate constants on the... 

To what extent does macroscopic friction , as indicated by solvent viscosity or by inverse self-diffusion coefficient, really reflects the microscopic friction experienced by the reaction coordinate ... 

---