Fractal adsorption characteristics of complex molecules on particles—A case study of dyes onto granular activated carbon (GAC)

The isothermic and kinetic adsorption processes of three dyes onto granular activated carbon (GAC) were studied in this paper. Langmuir fractal equation was chosen to fit the adsorption isotherm data. The exponent m in the equation is a function of surface fractal dimension (Ds) of particles and cross-section area (α0) or radius (r0) of dye molecules, which can be approximately estimated according to the relation between the first order term of molecular connective index 1χ and the total surface molecular area (TSA). Based on the modeling results, Ds of the GAC was estimated to be 2.59, indicating the fractal adsorption characteristics of GAC.To elucidate the adsorption kinetics of complex molecules onto fractal surfaces, the relationships of m, kinetic parameter h and fractal spectral dimension (ds) were developed, and the derivative relation of ds and surface fractal dimension Ds was achieved. Adsorption kinetic results showed that the kinetic process had fractal-like characteristics. The instantaneous rate coefficient exhibited power-law relation with reaction time. Although h was larger than one in this study, both the fractal spectral dimension (ds) and the order of reaction could be obtained, and the corresponding ds values were less than two. The effective reaction order x was related to ds, Ds and adsorbate concentration, and it was found that the order of diffusion-controlled adsorption reaction was fractional in most cases. The h or ds values calculated here implied that the reciprocating shake was not always effective to eliminate the dimensional constraints.