Abstract
This chapter presents a fractal analysis for the binding and dissociation of various environmental pollutants either in solution or in the gas phase to receptors immobilized on different biosensor surfaces. The fractal analysis is offered as an alternative way to improve the understanding of the kinetics in the heterogeneous case with diffusion-limited reactions occurring on structured surfaces. Binding and dissociation rate coefficients as well as fractal dimensions in the binding and in the dissociation phase are provided, and on the basis of prefactor analysis of aggregates, quantitative and predictive equations are developed for the binding rate coefficient k as a function of the fractal dimension Df or the toluene concentration in solution for the binding of toluene in solution to MC1061-pXylRS-lacZ; the binding rate coefficient k as a function of the fractal dimension Df for the binding of 3-methylbenzylchloride, 3-nitrotoluene, and nonane to the MC1061-pXylRS-lacZ biosensor; the binding rate coefficient k as a function of the molecular weight of the aromatic and non-aromatic compounds in solution; and the binding rate coefficient k as a function of xylene concentration in solution. The analysis demonstrates that the binding rate coefficient k is only mildly sensitive to the degree of heterogeneity or the fractal dimension present on the biosensor surface. The order of dependence on the fractal dimension Df is found to be –0.7958 for the binding of various concentrations of toluene in solution to the MC1061-pXylRS-lacZ electrochemical biosensor, and it is equal to 0.6470 for the binding of aromatics and non-aromatics (3-methylbenzylchloride, 3-nitrotoluene, and nonane) in solution to the MC1061-pXylRS-lacZ electrochemical biosensor.
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