Concentration response constant flux

It is convenient from many points of view to assume that the constant value of the flux is unity, i.e., 1 mole of the diffusing species crossing 1 cm of the electrode-solution interface per second. This unit flux corresponds to a constant current density of 1A cm . This normalization of the flux scarcely affects the generality of the treatment because it will later be seen that the concentration response to an arbitrary flux can easily be obtained from the concentration response to a unit flux. 

The space and time variation of a concentration in response to the switching on of a constant flux has been analyzed. Suppose, however, that, instead of a constant flux, one switches on a sinusoidally varying flux. What is the resultant space and time variation of the concentration of the diffusing species ... 

The relationship (4.67) has been defined for a flux that has an arbitrary variation with time hence, it must also be true for the constant unit flux described in Section 4.2.10. The Laplace transform of this constant unit flux 7 = 1 is /p according to Appendix 4.2 and the Laplace transform of the concentration response to the constant unit flux is given by Eq. (4.60), i.e.. 

This is an important result Through the evaluation of y, it contains the concentration response to a constant unit flux switched on at f = 0. In addition, it shows how to obtain the concentration response to a flux/(t) that is varying in a known way. All one has to do is to take the Laplaee transform 7 of this flux7(r) switched on at time t = 0, substitute this 7 in Eq. (4.69), and get ,. If one inverse-transforms the resulting expression for c, one will obtain c, the perturbation in concentration as a function of X and t. 

In other words, the concentration response of the system to a 7 = A flux is a magnified-A-times version of the response to a constant unit flux. 

There is another important diffusion problem, the solution of which can be generated from the concentration response to a constant current (or a flux). Consider that in an eleetroehemieal system there is a plane electrode at the boundary of the eleetrolyte. Now, suppose that with the aid of an electronic pulse generator, an extremely short time eurrent pulse is sent through the system (Fig. 4.28). The current is direeted so as to dissolve the metal of the eleetrode hence, the effect of the pulse is to produee a burst of metal dissolution in whieh a layer of metal ions is piled up at the interface (Fig. 4.29). 

To ensure a constant-flux layer, one can simply move the measurement height closer to the surface. For the eddy correlation method, however, the response time of the instrument must be faster as the measurement height approaches the surface, because high-frequency turbulent eddies then contribute proportionally more to the concentration fluxes than at higher levels. On the other hand, fluxes measured very close to the surface may be less representative of those over the entire area for which the measurement is intended. For the gradient method, the requirement that z/zo 3> 1 (based on the requirements of similarity theory) constrains the minimum measurement height. Under very stable conditions, when turbulence may be intermittent, turbulent fluxes may become very small, and the constant-flux layer may be very shallow. Under conditions such as these, it can be quite difficult to determine the aerodynamic resistance term ra. 

In this section, microdisc electrodes will be discussed since the disc is the most important geometry for microelectrodes (see Sect. 2.7). Note that discs are not uniformly accessible electrodes so the mass flux is not the same at different points of the electrode surface. For non-reversible processes, the applied potential controls the rate constant but not the surface concentrations, since these are defined by the local balance of electron transfer rates and mass transport rates at each point of the surface. This local balance is characteristic of a particular electrode geometry and will evolve along the voltammetric response. For this reason, it is difficult (if not impossible) to find analytical rigorous expressions for the current analogous to that presented above for spherical electrodes. To deal with this complex situation, different numerical or semi-analytical approaches have been followed [19-25]. The expression most employed for analyzing stationary responses at disc microelectrodes was derived by Oldham [20], and takes the following form when equal diffusion coefficients are assumed ... 

From the voltammograms of Fig. 5.12, the evolution of the response from a reversible behavior for values of K hme > 10 to a totally irreversible one (for Kplane < 0.05) can be observed. The limits of the different reversibility zones of the charge transfer process depend on the electrochemical technique considered. For Normal or Single Pulse Voltammetry, this question was analyzed in Sect. 3.2.1.4, and the relation between the heterogeneous rate constant and the mass transport coefficient, m°, defined as the ratio between the surface flux and the difference of bulk and surface concentrations evaluated at the formal potential of the charge transfer process was considered [36, 37]. The expression of m° depends on the electrochemical technique considered (see for example Sect. 1.8.4). For CV or SCV it takes the form... 

During the desorption process in the presence of a flux of oxygen, the fall time is about a few seconds until 0.3/max then there is an almost exponential decay, whose time constant is about 1.5 min, under the condition shown in Fig. 13a, that returns the device to the original equilibrium condition. Figure 13b shows another typical response when an H2 concentration of 100 ppm is used. This time can be substantially lowered, for instance, by... 

Metabolic fluxes are responsible for maintaining the homeostatic state of the cell. This condition may be translated into the assumption that the metabolic network functions in or near a non-equilibrium steady state (NESS). That is, all of the concentrations are treated as constant in time. Under this assumption, the biochemical fluxes are balanced to maintain constant concentrations of all internal metabolic species. If the stoichiometry of a system made up of M species and N fluxes is known, then the stoichiometric numbers can be systematically tabulated in a... 

An example is the stationary state of an open chemically reactive system, where the intermediate concentrations, which are setded in the course of the internal processes, are time constant. The rate of changing these interme diate concentrations (fluxes of these parameters) equals zero. Evidendy, the stationary state is setded at a certain ratio of the rates of elementary reactions responsible for the formation and vanishing of the reactive intermediates. 

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