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

The fractal dimension of some commercial activated carbon (AC) was determined in the micro-, meso- and macropore range using mercury porosimetry and N2 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 qn,α(t)=qe[1-(1+(n-1)(t/τn,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, qe measures the maximal quantity of solute adsorbed, and a “half-reaction time”, τ1/2, 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.