Parameters from a new kinetic equation to evaluate activated carbons efficiency for water treatment

Abstract

The fractal dimension of some commercial activated carbon (AC) was determined in the micro-, meso- and macropore range using mercury porosimetry and N 2 adsorption data. We studied the kinetic of adsorption of phenol, tannic acid and melanoidin on those ACs. The typical concentration–time profiles obtained here could be very well fitted by a general fractal kinetics equation q n , α ( t ) = q e [ 1 - ( 1 + ( n - 1 ) ( t / τ n , α ) α ) - 1 / ( n - 1 ) ] deduced from recently new methods of analysis of reaction kinetics and relaxation. The parameter n is the reaction order, α is a fractional time index, q e measures the maximal quantity of solute adsorbed, and a “half-reaction time”, τ 1 / 2 , can be calculated, which is the time necessary to reach half of the equilibrium. The adsorption process on AC is clearly a heterogeneous process, taking place at the liquid–solid boundary, and the diffusion process occurs in a complex matrix with a fractal architecture as demonstrated here. In fact, these systems belong to what has been called “complex systems” and the fractal kinetic, which has been extensively applied to biophysics, can be a useful theoretical tool for study adsorption processes.