Randomly distributed arrays

We now turn our attention to randomly distributed arrays of microdisc electrodes as illustrated in Figure 10.5 though they are not as commonly encountered as regularly distributed microdisc arrays, techniques do exist for their fabrication [22] and so here we consider the simulation of such arrays. Though the specific example of a randomly distributed microdisc array is of limited utility, the techniques for generating a random distribution of particles are applicable to a range of electrochemical problems. 

We assume that each disc is of the same radius the simulation of randomly distributed arrays of particles of different sizes is beyond the scope of this text. 

Using this approach it would take approximately N times longer to simulate a single randomly distributed array than it would to simulate a regular array, which is clearly impractical, as N is likely to be very large. 

Streeter I, Compton RG (2007) Linear sweep voltammetry at randomly distributed arrays of microband electrodes. J Phys Chem C 111 15053-15058... 

Randomly distributed Addressable High-density Sensor Array ... 

Note that Eq. (9.1) applies to pore arrays as well as to randomly distributed pores. For simple orthogonal or hexagonal arrays of macropores with one pore per unit cell of the pattern, the porosity can be defined locally as the ratio between the cross-sectional area of the pore AP and the area of the unit cell AU as shown in Fig. 9.15 a ... 

The special electrical properties of a-AgI inevitably led to a search for other solids exhibiting high ionic conductivity preferably at temperatures lower than 146°C. The partial replacement of Ag by Rb, forms the compound RbAgJs. This compound has an ionic conductivity at room temperature of 25 S m , with an activation energy of only 0.07 eV. The crystal structure is different from that of a-AgI, but similarly the Rb and T ions form a rigid array while the Ag ions are randomly distributed over a network of tetrahedral sites through which they can move. 

A microelectrode array consists of a series of microelectrodes separated by an insulating material [36]. The microelectrodes can be regularly or randomly distributed (in the latter case the term ensemble is also used). Arrays containing hundreds or even thousands of microelectrodes wired in parallel have been... 

Fig. 5 In-situ TEM view for initial oxidation of Fe-25 Cr-20 Ni (T = 650°C, pO = 10 torr) with time. Small oxides are arrayed along metal grain boundaries and randomly distributed within the grains.

Clearly, situations intermediate between perfect order and random distributions occur in arrays of absorbing chromophores, and a treatment is required that allows expression of the orientational distribution of structural units such as crystallites or segments which may be fluorescent in a bulk sample having uniaxial or biaxial symmetry. A complete mathematical approach using a herical harmonic expansion technique has been developed which expresses the distribution as spherical harmonics of various orders in terms of the Euler angles which specify the orientation of the coordinate system in a fixed structural unit with respect to the coordinate system in the bulk sample This is of use in solid systems, where time dependence is not observed. 

The sign of AH gives no indication of the spontaneous direction of a reaction. We see from Equation 45 that even if AH is positive, AG can still be negative if AS is positive enough. For example, if we mix certain solid salts with water, we observe a marked decrease in the temperature as the salt dissolves. Heat has been absorbed. AH is positive (heat must be added to keep the temperature of the system constant). The salt spontaneously dissolves, therefore AG is negative. The TAS term is positive—the ions of the salt that were originally in a highly ordered crystalline array are now randomly distributed in solution. 

In equipoint spinels (TiMg204) half of the B + ions occupy tetrahedral holes in the array of O -ions the other half, along with the Anions, are randomly distributed in half the octahedral sites. 

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