Macroscopic current

By tradition, electrochemistry has been considered a branch of physical chemistry devoted to macroscopic models and theories. We measure macroscopic currents, electrodic potentials, consumed charges, conductivities, admittance, etc. All of these take place on a macroscopic scale and are the result of multiple molecular, atomic, or ionic events taking place at the electrode/electrolyte interface. Great efforts are being made by electrochemists to show that in a century where the most brilliant star of physical chemistry has been quantum chemistry, electrodes can be studied at an atomic level and elemental electron transfers measured.1 The problem is that elemental electrochemical steps and their kinetics and structural consequences cannot be extrapolated to macroscopic and industrial events without including the structure of the surface electrode. 

The incorporation of discreet nucleation events into models for the current density has been reviewed by Scharifker et al. [111]. The current density is found by integrating the current over a large number of nucleation sites whose distribution and growth rates depend on the electrochemical potential field and the substrate properties. The process is non-local because the presence of one nucleus affects the controlling field and influences production or growth of other nuclei. It is deterministic because microscopic variables such as the density of nuclei and their rate of formation are incorporated as parameters rather than stochastic variables. Various approaches have been taken to determine the macroscopic current density to overlapping diffusion fields of distributed nuclei under potentiostatic control. 

Mehdizadeh et al. exploited the separability of current distribution on different scales to model the macroscopic current distribution on patterns made up of lines or points distributed over a large workpeice [136], They solved the secondary distribution of the superficial current density sup using a boundary condition which captures the density of small features but not their geometry. The boundary condition is based on a smoothly varying parameter representing the Faradaically active fraction of surface area. 

Critical current measurements have been made with a variety of techniques. The indirect technique, that of obtaining the critical current from the magnetization response is discussed in Chapter 18. Direct transport measurements, using attached current and voltage leads, and indirect measurements requiring macroscopic current circulation will be discussed. Critical currents are desired as a function of both temperature and applied magnetic field since a variety of theories discuss the functional relationship. And applications may require either or both of these data. 

In Fig. 22a, an example of a spin configuration with two spin vortices is depicted. Different current patterns are possible for the same spin configuration by different X. Although each loop current is rather localized around each center of the vortices, a macroscopic current can be generated as a collection of loop currents if the number of loop currents is large enough (Fig. 22d). 

CatteraU You could probably do this with macroscopic currents. Knowing the answer for phenytoin, you could see what happens with macroscopic currents. 

Segal We did our studies using single channel recording in part because we worried that any persistent inward current that we would see by macroscopic current recording could be dismissed as an artefact of poor clamp control of the neuron. However, Chao Alzheimer (1995) did such a study of macroscopic currents while we were doing our single-channel studies and they found a similar... 

The relationship between single-channel currents and macroscopic currents has been considered both experimentally and theoretically by Wyllie et al. (104), who give the general relationship that relates the two sorts of measurement. 

Figure 11.17. The predicted macroscopic current. The rate constants that have been fitted to results from equilibrium recordings (see Figs. 11.14-11.16) were used to calculate the macroscopic response to a 0.2-ms pulse of ACh (ImM), as in Colquhoun and Hawkes (44). This calculation predicts that the mutation will cause a sevenfold slowing of the decay of the synaptic current, much as observed (102). See color insert.

Figure 11.17. The predicted macroscopic current. The rate constants that have been fitted to results from equilibrium recordings (see Figs. 11.14-11.16) were used to calculate the macroscopic response to a...

The parameters that control the macroscopic current distribution (in the absence of substrate resistance) can be represented in terms of the Wagner number, defined by the ratio of the activation resistance of the surface reaction, (Ra), to the electrolyte ohmic resistance, (Rn) ... 

Here, k is the conductivity l is the characteristic length and dr Jd is the slope of the polarization line. A large Wagner number is indicative of a uniform macroscopic current distribution since it corresponds to a large activation resistance (which tends to level off the current) and a small ohmic resistance (which is geometry-dependent and usually causes non-uniformities). 

---