## 4 Discussion
The q\({}_{\rm max}\), which corresponds to the saturation capacity of the adsorbent material estimated by Langmuir plotting was around 2.50 mg g\({}^{-1}\) (chestnut) to 4.82 mg g\({}^{-1}\) (walnut) lower than the values obtained by [5; 47], around 50 mg g\({}^{-1}\) for _Punica granatum_ peel and 44.90 mg g\({}^{-1}\) for protonated rice bran, respectively. Nevertheless, the values are higher than the ones reported for the adsorption of nickel ions onto coal fly ash with just 0.30 mg g\({}^{-1}\)[30]. The \(n\) value from Freundlich isotherm varied from 2.41 to 4.72 which shows the good ability of these lignocellulosic adsorption materials since a good adsorption has been reported to be with \(n\) values ranging from 1 to 10 as reported before [17; 47; 48]; a similar result was found by [5] with \(n\) around 2.31 or by [30] with 2.57 for \(n\). the adsorption process includes membrane diffusion and surface adsorption and can also describe the mechanism in a more realistic way [46]. In relation to adsorption kinetics, the pseudo-second order reaction was the model that best represented the sorption process for all materials under evaluation. The R\({}^{2}\) values were between 0.998 for pine wood and 1.00 for walnut shell and chestnut shell. However, PFO showed a correlation greater than 0.90, but with lower values than those indicated by PSO. PFO was shown to be valid to describe the process only at the initial stage of adsorption [46]. There are two different phases, one until about 100 min with a higher slope and another one after that. Similarly, the adsorption of Ni by Bael tree leaf powder [49], protonated rice bran [5] and mesoporous rice husk ash [9] obeys the pseudo-second order kinetics with correlation values around 0.988, 1.00 and 0.999, respectively. A preference for PSO over PFO has generally been found in studies where a comparison of the two equations is made [29]. Elovich equation is known to describe chemisorption well. Many works assumed that the equation had a relation with strong heterogeneity at the adsorbent surface [46]. Elovich equation is known to describe chemisorption well as stated before, so the occurrence of chemical reactions between the surface and the adsorbate cannot be discharged specially for the shells used in this study. Nevertheless, the differences between the R\({}^{2}\) of both models are small and therefore no conclusions can be drawn about their importance in practical adsorption filters. Intraparticle diffusion is characterized by the transport of the adsorbate in solution to the active sites of the adsorbent by mass transfer. In some cases, the intraparticle diffusion may not be involved in the whole adsorption process [11] but rather explains only part of it, which seems to be happening here in nickel adsorption by lignocellulosic materials. The development of good adsorption includes three or four main steps: first, the external diffusion, which is the transportation of adsorbate to the external surface of adsorbent which, according to some authors, is divided into transport to the boundary layer and diffusion through the boundary layer to the external surface of the particle [50]; then, the intraparticle diffusion, which is the transference from the external surface into the pores; finally, the surface reaction, which is the attachment of adsorbate in the surface of the material [27; 46; 50; 51]. The biosorption of cadmium and nickel ions using _Spirulina platensis_ was reported to be well explained by the intraparticle diffusion model [44], which these authors stated is composed of more than one sorption process. Physisorption is a consequence of attractive forces between adsorbate and sorbent, whereas chemisorption provides a stronger connection as it involves the transfer or sharing of electrons between compounds. The monolayer capacity is the capacity to accommodate a single layer of adsorbed species on the adsorbent surface.