*3.3. E*ff*ect of Initial Dye Concentration and Adsorption Isotherm*

The effect of initial dye concentration on the adsorption capacity was investigated in the 10–1000 mg L−<sup>1</sup> and 10–2000 mg L−<sup>1</sup> ranges for MB and CR, respectively. The systems were mixed at 25 ◦C and 120 rpm for 16 h and equilibrium was declared when there was no appreciable change in solution concentration with additional contact time. Concerning all adsorbents, at low dye concentration, adsorption increased dramatically with increasing concentration (Figure 6). The adsorption of MB reached a plateau when residual MB concentration was above 200 mg L−<sup>1</sup> in all cases. The final MB adsorption at equilibrium for CNF–GnP was 1207.5 mg g−<sup>1</sup> at the initial MB concentration of 1000 mg L<sup>−</sup>1. The adsorption of CR increased relatively slowly when the residual CR concentration was above 400 mg L−<sup>1</sup> in all cases. The final CR adsorption at equilibrium of CNF–GnP was 507.1 mg g−<sup>1</sup> at the initial CR concentration of 2000 mg L<sup>−</sup>1.

To further understand the mechanism of adsorption, the adsorbed quantities and residual dyes in the solution at equilibrium were fitted with isothermal models. The adsorption isotherm models describe the interaction between the adsorbate and adsorbent. Three models, Langmuir, Freundlich and Sips, were used to obtain the isotherm parameters for adsorption of dyes onto CNF, GnP, CNF–GnP.

The Langmuir isotherm equation is expressed as follows [46]:

$$q\_{\rm e} = \frac{q\_{\rm max} K\_{\rm L} \mathcal{C}\_{\rm e}}{1 + K\_{\rm L} \mathcal{C}\_{\rm e}} \tag{9}$$

where *q*<sup>e</sup> is the equilibrium adsorption amount per unit weight of the adsorbent (mg g−1), *C*<sup>e</sup> is the equilibrium concentration of adsorbate in the solution (mg L<sup>−</sup>1), *q*max is the maximum amount of the dyes adsorbed per unit weight of the adsorbent (mg g<sup>−</sup>1), which describes the complete single-layer coverage on the surface of the dye at a high equilibrium concentration of dyes, and *K*<sup>L</sup> is the Langmuir adsorption equilibrium constant related to binding site affinity (L g−1), representing the bonding energy of adsorbent and adsorption product. The Langmuir isotherm model is based on the monolayer sorption on a surface with a finite number of identical sites and uniform adsorption energies.

**Figure 6.** Adsorption of MB (**a**) and CR (**b**) to CNF, CNF–GnP and GnP. The Langmuir adsorption model was applied for data fitting.

The Freundlich isotherm equation is expressed as below [47]:

$$q\_{\mathfrak{e}} = K\_{\mathbb{F}} \times C\_{\mathfrak{e}}^{\frac{1}{n}} \tag{10}$$

where *K*<sup>F</sup> (mg g<sup>−</sup>1) and n are the Freundlich constants. The Freundlich isotherm model is an empirical equation for understanding the adsorption of heterogeneous surfaces with multiple adsorption layers. *K*<sup>F</sup> and n are related to adsorption capacity, adsorption strength and spontaneity, respectively. When the value of *n* is within the range of 1< *n* <10, it indicates a good adsorption process. The larger n value, the better the adsorption effect.

The Sips isotherm equation is given as follows [48]:

$$\frac{1}{q\_{\text{e}}} = \frac{1}{q\_{\text{max}}K\_{\text{s}}} \left(\frac{1}{\mathcal{C}\_{\text{e}}}\right)^{\frac{1}{n}} + \frac{1}{q\_{\text{max}}} \tag{11}$$

where *q*max is the Sips constant related to maximum adsorption capacity (mg g<sup>−</sup>1), *K*<sup>S</sup> is the isotherm constant of Sips related to adsorption energy (L g<sup>−</sup>1), and *n* is the heterogeneity factor. The Sips model is a combination of the Langmuir and Freundlich isotherms. As *K*<sup>S</sup> approaches 0, the Sips isotherm equation follows the Freundlich model. When *n* approaches or equals 1, the Sips isotherm equation is reduced to the Langmuir isotherm.

The fitting parameters of each model are listed in Table 2. According to the correlation coefficients (*R*2), both the Langmuir and Sips adsorption models could adequately describe the dye adsorption on each adsorbent, while the Freundlich isotherm model was the least suitable. Since the Sips model is derived from the Langmuir equation, employs one more fitting parameter, and yields similar correlation coefficients, it could be concluded that the Langmuir model is more appropriate to describe the adsorption behavior. The Langmuir fitting curves for the adsorption of MB and CR on the different adsorbents are shown in Figure 6. The binding constant *K*<sup>L</sup> is related to the adsorption energy between the adsorbent and the dye. MB displayed higher binding constants (GnP: 7.0 <sup>×</sup> 10−<sup>2</sup> L g<sup>−</sup>1, CNF: 8.3 <sup>×</sup> 10−<sup>2</sup> L g−1, CNF–GnP: 1.1 <sup>×</sup> 10−<sup>1</sup> L g−1) than CR (GnP: 7.1 <sup>×</sup> 10−<sup>3</sup> L g−1, CNF: 8.6 <sup>×</sup> 10−<sup>4</sup> L g−1, CNF–GnP: 3.8 <sup>×</sup> 10−<sup>3</sup> L g−1) regardless of the adsorbent nature, indicating a higher binding affinity to MB. Compared to the other dye-adsorbent complexes, the uptake of MB on CNF–GnP was the most favorable. The Langmuir model revealed that both MB and CR adsorbed as a monolayer on the CNF–GnP surfaces, with maximum adsorption capacities of 1178.5 mg g−<sup>1</sup> and 585.3 mg g−1, respectively. According to Equation (1) and the monolayer adsorption, the specific surface areas (SSA) of CNF and CNF–GnP were determined to be 3220.4 and 3036.1 m2 g<sup>−</sup>1, respectively. Theoretically, if CNF is assumed to be a perfect cylinder with a 1 nm diameter (cellulose density: 1.5 g/cm3), the surface area of CNF is 2667 m2/g. The high SSA determined by MB adsorption indicates CNFs contained a large number of micropores.


**Table 2.** Estimated adsorption parameters of Langmuir, Freundlich and Sips isotherms at room temperature.

Extensive research about the uptake of various dyes on carbon-based and cellulose/polysaccharide-based composites has been reported in the literature. Table 3 presents a comparison of the maximum dye adsorption capacity of different adsorbents. CNF–GnP was able to adsorb both cationic MB and anionic CR and yielded higher uptake values compared to recent studies using cellulose, activated carbon, graphene, and CNT-based composites.

**Table 3.** Comparison of adsorption capacity of different adsorbents.

