The pseudo-first order, pseudo-second order and intra-particle diffusion kinetic plots are given in Fig. 2a–c respectively. In the pseudo-first order, the K 1 and q e values were 0.0582 (min−1) and 1.2103 (mg/g) respectively with a correlation coefficient (R 2) of 0.9586. In the pseudo-second order, the K 2 and q e values were 0.1104 (min−1) and 3.2362 (mg/g) respectively with a correlation coefficient (R 2) of 0.9989. The intra-particle diffusion, a plot of solute sorbed against square root of contact time, should normally yield a straight line passing through the origin but the line in the present case, did not pass through the origin and the values of K int and C were 0.1341 (mg/g min½) and 2.0427 (mg/g) respectively with a correlation coefficient (R 2) of 0.8942. From the experiments, q e obtained was 3.1308 mg/g which is suggestive that the adsorption of copper by DNES–CH composite could be by chemisorption, appropriately explained by the pseudo-second order model.
Fig. 2  a Pseudo-first order kinetics for adsorption of copper using DNES–CH composite. b Pseudo-second order kinetics for adsorption of copper using DNES–CH composite. c Intra-particle diffusion kinetics for adsorption of copper using DNES–CH composite