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Porous Electrodes with Immobilized Enzymes: The Fractal-Percolation Properties of Supports Manufactured from Particles of Finely Divided Colloidal Graphite

“…The theory of fractals is rendered in [58][59][60][61][62][63] (good reviews of the theory of fractals may also be found in [64][65][66][67]). If we start calculating the dimensionality of porous formations by methods intrinsic to the theory of fractals, then this quantity, which carries the name "fractal dimensionality" D will not at all be rigorously equal to 2 or 3, which are dimensionalities of two-dimensional or three-dimensional euclidean space ( d = 2 for a surface and d = 3 for a volume).…”

“…The magnitude of J is defined by the nature of the selected enzyme and the magnitude of polarization, more complicated is the question of the magnitude of N A . We attempted to determine this quantity by a method of computer simulation [6] in [7][8][9][10][11], where we investigated AL of very diverse architecture, specifically, stochastic (all particles are distributed in space in a random fashion) and with partiallly (insertion of regular gas pores [9]) and completely regular structure [10,11]. We have demonstrated how important it is to create an effective porous support in AL for placing as large a number of active molecules of the enzyme on its surface as possible.…”

Porous Electrodes with Immobilized Enzymes: The Problem of Development of Nanocomposites with High Concentrations of Molecules of Active Enzymes

“…It is precisely these random fractal clusters that define all the major properties of a would-be AL. For example, the presence or, on the other hand, the absence in it of an "electron cluster" [4], which is a system of macroscopic dimensions consisting of particles of the support. Such a random fractal cluster connects the front and the rear sides of AL of the electrode and provides for the passing of an electric current through the porous electrode.…”

“…of all that makes an enzyme molecule a participant of the electrochemical process, and J is the current that is generated by one molecule of the enzyme. The way one should perform calculation of concentration N Ä , the difficulties that emerge here have comprehensively been discussed in a series of papers [4] where we examined multicomponent (with equidimensional particles) electrodes with enzyme laccase. The necessity of employing formula (4) instead of formulas (1) and (2) when performing estimates of the electrochemical activity of porous electrodes upon going to biofuel cells is their first peculiarity.…”

“…That is why we can speak now not of a finely divided support (relationships (1) and (2)) with molecules of an enzyme adsorbed on its surface, but of some composite comprising particles of the support and molecules of the enzyme, which has a complicated internal structure. Of course, for biofuel cells, too, it could probably have been possible to manufacture, out of nanosized particles, a macroscopic porous support, but then there would have emerged considerable difficulties with the insertion into its pores, and these must be small, of molecules of an enzyme and with their immobilization on the internal side of such a support [4]. If, on the other hand, one would try and prepare a porous support out of large particles of the support, purposely attempting to create broad pores in it, thus making it easier to land molecules of an enzyme onto its internal surface, then, if criterion (3) is fulfilled, it would also be difficult to hope to reach high values of concentration N Ä , because the major part of the volume of space occupied by the composite would be given to particles of the support.…”