Digital simulations diffusion coefficients

Axial and radial dispersion or non-ideal flow in tubular reactors is usually characterised by analogy to molecular diffusion, in which the molecular diffusivity is replaced by eddy dispersion coefficients, characterising both radial and longitudinal dispersion effects. In this text, however, the discussion will be limited to that of tubular reactors with axial dispersion only. Otherwise the model equations become too complicated and beyond the capability of a simple digital simulation language. 

Two general approaches have been used in low-temperature studies. In the first, the uncompensated resistance, electrode capacitance, diffusion coefficient, and kinetic and thermodynamic parameters describing the electrode reaction are incorporated in a master model, which is treated (usually by some form of digital simulation) to calculate the expected voltammetric response for comparison with experiment [7,49]. 

With a potentiostat the potential at the working electrode is linearly increased from 1.0 to 1.6 V and then decreased back to 0 V. In the first interval 1 is oxidized to the radical cation l+ with a peak potential of p.a = 1-38 V. 1 is stable in this solvent and is reduced in the reverse scan back to 1 at p,c = 1-32 V. The ratio of the current for reduction and oxidation ip c-ip.a = 1 indicates the stability of the radical cation. All of 1, that is formed by oxidation of 1 is reduced back to 1. This behavior is termed chemically reversible. Upon addition of 2,6-lutidine, the radical cation 1 reacts with the nucleophile to afford 2 , which is further oxidized to a dication, which yields the dication with 2,6-lutidine. This can be seen in the decrease of /p,c fp,a and an increase of due to the transition from an le to a 2e oxidation. From the variation of the ratio ip.c-ip,n with the scan rate, the reaction rate of the radical cation with the nucleophile can be determined [9]. This can also be aehieved by digital simulation of the cyclovoltammogram, whereby the current-potential dependence is calculated from the diffusion coefficients, the rate constants for electron transfer and chemical reactions of substrate and intermediates at the electrode/electrolyte interface [10]. With fast cyclovoltammetry [11] scan rates of up to 10 Vs- can be achieved and the kinetics of very short-lived intermediates thus resolved. 

Note that the above theoretical treatment is highly approximate the modern approach to data analysis would be via digital simulation allowing for depletion of Z and for variable diffusion coefficients, as well as for providing a rigorous (rather than approximate) solution of the coupled dilfusion-kinetic equations involved. 

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