*3.2. E*ff*ect of Contact Time and Adsorption Kinetics*

The effect of CNF, CNF–GnP and GnP contact time (25 ◦C, 120 rpm) on dye removal was studied at low, medium and high initial dye concentrations (Figure 5). The initial MB concentrations were 10, 250 and 500 mg L−<sup>1</sup> and the initial CR concentrations were 10, 600 and 2000 mg L<sup>−</sup>1. The adsorption of MB dye onto CNF, CNF–GnP and GnP occurred rapidly during the first 30 min, then leveled beyond

60 min at all initial MB dye concentrations. The adsorption of CR dye onto CNF, CNF–GnP and GnP occurred at a lower speed compared to that of MB. The adsorption onto CNF and CNF–GnP slowed with adsorption time and reached a plateau beyond 90 min at all initial CR concentrations. However, the adsorption onto GnP still increased very slowly even after 120 min at all initial CR concentrations.

**Figure 5.** Effects of contact time on the dye removal efficiencies of MB and CR using CNF, CNF–GnP and GnP. Initial MB dye concentration: 10 mg L−<sup>1</sup> (**a**), 250 mg L−<sup>1</sup> (**b**), 500 mg L−<sup>1</sup> (**c**). Initial CR concentration: 100 mg L−<sup>1</sup> (**d**), 600 mg L−<sup>1</sup> (**e**), 2000 mg L−<sup>1</sup> (**f**). Pseudo-second-order adsorption kinetics was applied for all conditions in (**a**–**f**).

Adsorption kinetics models can be employed to predict the equilibrium adsorption capacity and elucidate the adsorption mechanism. During the adsorption process, the dye molecules migrated from the aqueous solution onto the surface of the adsorbent. MB molecules were adsorbed through electrostatic interactions. The electrostatic interactions occurred when the cationic dye MB was close enough to the adsorption sites (–COO−, –OH) on the adsorbent surface. CR molecules were adsorbed mainly through π–π bonding and hydrophobic interactions with carbon nanomaterials. Accompanying the increase in contact time, the accumulation of dye molecules on the adsorbent surface gradually increased and eventually reached equilibrium. The adsorption kinetics of MB and CR on different absorbents was evaluated using both the Lagergren's pseudo-first-order and the Ho's pseudo-second-order models. The Lagergren's pseudo-first-order kinetics is expressed as Equation (6) [41]:

$$q\_{\mathbf{t}} = q\_{\mathbf{t}} \left(\mathbf{1} - e^{-k\_{\mathbf{t}} \mathbf{t}}\right) \tag{6}$$

where *k*<sup>1</sup> is the rate constant (min<sup>−</sup>1), *q*<sup>t</sup> is the amounts of dye absorbed at a given time (mg g<sup>−</sup>1), and *q*<sup>e</sup> is the amount of dye adsorbed at equilibrium (mg g<sup>−</sup>1). Nonlinear regression analysis was used to assess the values of *q*e, *k*1. The Ho's pseudo-second-order kinetics was expressed as Equation (7) [42]:

$$\eta\_t = \frac{q\_e^2 k\_2 t}{1 + q\_e k\_2 t} \tag{7}$$

where *k*<sup>2</sup> is the pseudo-second-order rate constant (g mg−<sup>1</sup> min<sup>−</sup>1). Nonlinear regression analysis was used to assess the values of *q*e, *k*2. The initial adsorption rate *v*<sup>0</sup> at *t* = 0 could be calculated using Equation (8):

$$w\_0 = k\_2 \times q\_e^{\ast 2} \tag{8}$$

Regarding all adsorbents, the pseudo-second-order model was generally more applicable for describing the adsorption of MB, as demonstrated by the higher correlation coefficients (*R*2), compared to the first-order kinetics (Table 1). This result was consistent with previous reports of cationic dyes adsorbed onto pure CNF [22] and pure graphene [43]. The initial MB adsorption rate (*v*0) and MB dye adsorption capacity (*q*e) increased rapidly with increasing original dye concentrations from 10 to 250 mg L−<sup>1</sup> for all adsorbents. Further increasing of the original MB concentration from 250 mg L−<sup>1</sup> to 500 mg L−<sup>1</sup> resulted in an increase of *v*<sup>0</sup> for pure GnP, while *v*<sup>0</sup> did not change significantly in the cases of pure CNF and CNF–GnP hybrid. This phenomenon may be attributed to the limited amount of negatively charged adsorption sites on the CNF surface at longer contact times and higher MB concentrations. Although the adsorption of MB onto CNF–GnP sorbent was relatively slower than that on each component alone, the hybrid aerogel exhibited the highest theoretical MB adsorption capacity (*q*<sup>e</sup> = 1264.5 mg g<sup>−</sup>1) at a high initial MB concentration (i.e., 500 mg L−1).

The pseudo-second order kinetic model was also clearly a better fit for the adsorption of CR onto pure GnP, which is consistent with a previous study [44]. However, the sorption of CR onto pure CNF could be described as either pseudo first-order kinetics or pseudo second-order kinetics, as indicated by the similar *R*<sup>2</sup> (0.94–0.98) for both models. Occurring at neutral pH, both CR and CNF were negatively charged. Adsorption of CR onto CNF was relatively low and possibly resulted from hydrophobic interaction. The adsorption of CR onto the CNF–GnP hybrid also could be represented by either the first-order or second-order model and exhibited much higher uptake values than pure CNF. This result possibly indicates that in the hybrid material, CNF did not significantly affect the adsorption kinetics of GnP, even though the GnP content was relatively small. Both the CR adsorption rate (*v*0) and CR adsorption capacity (*q*e) increased with increasing the initial dye concentrations from 100 to 2000 mg L−<sup>1</sup> for all adsorbents. The augmentation of the initial concentration provided a greater driving force for the mass transfer and subsequent adsorption on the nanomaterials [45]. The theoretical *q*e value for CNF–GnP reached 648.5 mg g−<sup>1</sup> at a high initial CR concentration, 2.5 times higher than pristine CNF (182.4 mg g<sup>−</sup>1).


**Table 1.** Estimated kinetic parameters of the two adsorption models for methylene blue (MB) and Congo red (CR).
