*4.1. Kinetics*

The adsorption kinetics helps in defining the rate of efficiency of adsorption. Kinetic parameters are useful for designing and modeling the bio-sorption processes. Several types of kinetic models have been proposed by researchers to study the mechanism and rate-regulating steps. The Lagergren's rate equation is one of the most commonly used models to explain the adsorption of an adsorbate from the liquid phase [143]. The linear form of the pseudo-first-order equation is given as [144]:

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

where, 'qt' and 'qe' are amount of adsorbed material (mg/g) at time 't' and at equilibrium, respectively. 'k1' (min−1) is the rate constant for the pseudo-first-order reaction. The pseudo-second-order kinetics explain the involvement of both the adsorbate and adsorbent in the rate-limiting step [113,144]. The equation for the linearized pseudo-second-order reaction is given as:

$$\frac{\mathbf{t}}{\mathbf{q}\_{\mathbf{t}}} = \frac{1}{\mathbf{k}\_2 \ \mathbf{q}\_{\mathbf{e}}^2} + \frac{\mathbf{t}}{\mathbf{q}\_{\mathbf{e}}} \tag{2}$$

where, 'k2 is the rate constant (g/mg−<sup>1</sup> min−1) of the second-order kinetics [113,145]. The initial adsorption rate 'h' (mg/g min−1) is defined as:

$$\mathbf{h} = \mathbf{k}\_2 \mathbf{q}^2 \mathbf{e} \tag{3}$$

the values of 'k2 and 'h' can be obtained from the intercept of the plot based on the secondorder equation [146]. The kinetics defined by Elovich's model is based on the principle that adsorption sites increase exponentially with progress in the adsorption process, suggesting multilayer adsorption [147]. The linear form of Elovich's equation is given as:

$$\mathbf{q}\_{\mathbf{t}} = \frac{1}{\beta} \ln(\alpha \beta) + \frac{1}{\beta} \ln \mathbf{t} \tag{4}$$

where, 'α' is the initial rate of adsorption (mg/g−<sup>1</sup> min−1) and 'β' is related to surface coverage (g/mg−1). Weber and Morris proposed an intra-particle diffusion model [117,148]. The equation for the linear form of this model is given as:

$$\mathbf{q}\_{\rm t} = \mathbf{k} \mathbf{t}^{1/2} + \mathbf{C} \tag{5}$$

where, 'C' is the intercept and 'k' is the intra-particle diffusion constant. The value of 'k' can be calculated from the slope of the linear plot of 'qt' vs. 't1/2'. If intra-particle diffusion is involved in adsorption, then there would be a linear plot for of 'qt' against 't1*/*2'. In cases where the line passes through the origin, it shows that intra-particle diffusion is the rate-controlling step [132].

### *4.2. Thermodynamic Observations*

Appropriate study and explanation of adsorption isotherms is very significant and crucial for the overall development of the adsorption mechanism and effective design of the adsorption system. It helps to explain the mechanism of interaction between adsorbate molecules with the adsorbent surface. There are many models and operational designs available to understand the batch adsorption system. The most commonly employed methods are Langmuir and Freundlich models. The Langmuir adsorption isotherm model explains monolayer adsorption equilibrium between the adsorbate and the adsorbent [149]. This model is suitable for explaining the chemisorption when there is covalent or ionic bond formation between the adsorbate and the adsorbent. Many systems followed the equation to explain the binary adsorption system. The Langmuir model in its linear form may be expressed as:

$$\frac{1}{\mathbf{q}\_{\rm e}} = \frac{1}{\mathbf{K}\_{\rm L}\mathbf{C}\_{\rm e}\mathbf{q}\_{\rm m}} + \frac{1}{\mathbf{q}\_{\rm m}}\tag{6}$$

In this equation, 'qe' is adsorption capacity (mg/g−1) at equilibrium, 'Ce' is the equilibrium concentration (mg <sup>L</sup>−1) of the adsorbate, 'qm' is maximum adsorption capacity (mg/g−1) and 'KL' is the Langmuir constant (L mg<sup>−</sup>1). The Freundlich isotherm explains

the multi-layered adsorption phenomenon. It is applicable for reversible adsorption of the adsorbate on the surface of the adsorbent [120,150]. It states that the surface of the adsorbent should be heterogeneous in nature for multilayer adsorption [115,145]. This model states that the surface of the adsorbent has a diverse binding energy spectrum. The linear form of the Freundlich isotherm equation can be expressed as:

$$
\log\_{\mathbf{q}\_{\mathbf{p}}} = \log \mathbf{K}\_{\mathbf{F}} + \frac{1}{\mathbf{n}} \log \mathbf{C}\_{\mathbf{c}} \tag{7}
$$

where, 'KF' is the Freundlich isotherm constant (mg<sup>1</sup>−1/n L1/n g<sup>−</sup>1), and shows the adsorption efficiency of per unit mass of adsorbent. The 1/n value expresses the heterogeneity factor.

Thermodynamic parameters, e.g., entropy change, enthalpy change and standard free energy, are signification parameters to assess and evaluate the viability of the adsorption process along with the nature of adsorption. The negative value of change in enthalpy (Δ H◦) shows the exothermic nature of the adsorption process, while the positive value of change in entropy ( ΔS◦) stipulates the increased randomness of the process at the interface. It explains that the process is entropy-driven. The Gibbs free energy change of the adsorption process is subsequent to 'Kc' and given by the following equation:

$$
\Delta \mathbf{G}^{\circ} = -\mathbf{R} \mathbf{T} \ln \mathbf{K}\_{\mathbf{c}} \tag{8}
$$

 Here, 'Kc' can be expressed as shown in the following equation:

$$
\ln \text{K}\_{\text{c}} = \frac{\Delta \text{S}^{\circ}}{\text{R}} - \frac{\Delta \text{H}^{\circ}}{\text{RT}} \tag{9}
$$

Standard free energy ( Δ G◦), enthalpy change ( Δ H◦) and entropy change ( ΔS◦) can be determined by using the following equation:

$$
\boldsymbol{\Delta G}^{\circ} = \boldsymbol{\Delta H}^{\circ} - \boldsymbol{\Gamma} \boldsymbol{\Delta S}^{\circ} \tag{10}
$$

where, 'R' is universal gas constant (8.314 J.mol−<sup>1</sup> <sup>K</sup>−1), 'T' is temperature in Kelvin and 'Kc' is equilibrium constant. Change in enthalpy ( Δ H◦) and entropy ( ΔS◦) can be calculated from the slope of the plot of ( Δ G◦) vs. T. Reported values of Δ H◦ for physical adsorption range from −4 to −40 kJ.mol−1. Bhatnagar et al. has calculated thermodynamic parameters to check the adsorption nature of cobalt using lemon peel as a bio-sorbent. The value of ΔH ( −21.2 kJ.mol−1) found in the range shows the physical adsorption [119]. The value of ΔG calculated indicates the spontaneity in the process. A thermodynamic study of the biosorption of methylene blue from *C. sinensis* bagasse was observed by Bhatti et al., and the calculated value of Δ H◦ (51.9 kJ/mol) shows a similar physical adsorption in the process as a purely physical or chemical one [132]. The role of physisorption can be explained on the basis of the heat involved, which is >40 kJ.mol−1, whereas, for chemisorption, it is reported in a range of 80–200 kJ.mol−1. Similar results have been reported for the adsorption of Reamzol Brilliant Blue using an orange peel adsorbent [137]. The process was efficient as the negative value of free energy denotes the feasibility of the process. Additionally, the positive values of ΔH and ΔS shown are in favor of the adsorption process. These results also show the affinity of the adsorbent towards the dye. However, the adsorption of dyes has been reported as an exothermic phenomenon in many studies. Bio-sorption of La and Ce using peels of *Citrus reticulata* was also found to be a thermodynamically feasible and spontaneous process. It is shown to be a process of endothermic nature in the temperature range of 293–323 K, and the overall entropy increases due to the exchange of the metal ions with more mobile ions [107]. Malachite green dye adsorbed by *Citrus grandis* peels revealed the change in Δ G◦ from −21.55 to −24.22 kJ.mol−1, in the temperature range of 303 to 333 K, indicating enhanced spontaneity at high temperatures [140]. Similar results were also observed during the removal of fluoride using a *Citrus limetta* peels adsorbent activated with FeCl3 [56]. A thermodynamic study for the removal of methylene blue dye

using *Citrus limetta* peel waste exhibited Gibbs free energy (ΔG◦) values in favor of the process [48] (Table 5). Kaffir lime peels were used to reduce graphene oxide to prepare reduced graphene oxide (RGO), and applied for the absorption of methylene blue [151]. Several kinetic models fitted for the citrus peel as adsorbent have been shown in Table 5.

**Table 5.** Thermodynamics and kinetics studies of various dyes and ions on citrus peel as adsorbents.


### **5. Design of Experiments**

Response surface methodology (RSM) is a very popular tool for the optimization of process variables. It has been adopted in various studies for the design and analysis of the experiments. Principally, it is a mathematical and statistical technique for the design of experiments using relations between a cluster of controlled experimental variables and the measured properties, created on one or more selected conditions [156]. Numerical or physical experimental data are calculated by an expression that is generally a loworder polynomial. Usually, a second-order polynomial equation is fitted to analyze the experimental data by means of RSM, which can be represented as:

$$\mathbf{Y} = \mathbf{b}\_0 + \sum\_{\mathbf{i}=1}^{n} \mathbf{b}\_{\mathbf{i}} \mathbf{x}\_{\mathbf{i}} + \left(\sum\_{\mathbf{i}=1}^{n} \mathbf{b}\_{\mathbf{i}\mathbf{i}} \mathbf{x}\_{\mathbf{i}}\right)^2 + \left(\sum\_{\mathbf{i}=1}^{n-1} \sum\_{\mathbf{j}=\mathbf{i}+1}^{n} \mathbf{b}\_{\mathbf{i}\mathbf{j}} \mathbf{x}\_{\mathbf{i}} \mathbf{x}\_{\mathbf{j}}\right) + \varepsilon \tag{11}$$

The results are obtained as 2D contours and 3D plots. This method is very competent, and uses the experimental data and interactions between the factors [157,158]. This process

is based on three key steps, which involve statistically designed experiments, determination of the coefficients through estimation of response via mathematical modeling and investigating the competency of the model [159]. The ANOVA program is used to calculate the statistical parameters along with the optimization of independent parameters and dependent output responses. Dutta et al. analyzed the result of each run and correlated the responses with three individual factors for preparation of an adsorbent using an empirical second-degree polynomial, as shown above. Optimized conditions obtained as responses for carbonization of citrus fruit peel were weight ratio of the peel to the activating agent, temperature of carbonization and time of carbonization, which have the values of 3:1, 798 K and 0.75 h, respectively (Table 5) [72]. An experimental design for the removal of MB dye by charred citrus fruit peel has also been attained. Numeric parameters selected were initial concentration of MB, amount of adsorbent and pH of the solution, and results obtained from statistical design were maintained during the experiment and found to be fitted for the removal of dye [72]. The model adequacy of the Cr(VI) adsorption by Musambi peels was also found to be statistically viable [152]. In recent years, RSM modeling has been applied and reported in several adsorbent-based materials. It is an efficient and useful procedure which can help maximize the performance along with responses based on combinations of variables. Therefore, RSM offers an extensive scope for modeling the parameters' optimization along with the percent removal of heavy metal/dye by citrus peel waste-based adsorbent materials. Some of the experimental models applied for citrus peel adsorbents are recorded in Table 6.



### **6. Summary and Conclusions**

Biotransformation of citrus waste into valuable compounds and adsorbent substrate materials for the purpose of adsorption of heavy metals, dyes and toxic chemicals from industrial wastewaters is among hugely adopted research projects around the world. Hazards of pollution in water are not only restricted to the aquatic ecosystem but are also found to spread to the underground water tables, crops and crop products, human/livestock/birds' health and microbial ecosystems on the land. Adsorbents from citrus wastes can be developed by a number of methods, namely physical processes, chemical methods, thermal and thermo-chemical techniques. Protonated adsorbents have demonstrated efficiencies better than native peel bio-sorbents. In addition, chemically treated bio-sorbents exhibit several advantages, such as greater chemical and mechanical stabilities in the test solution. Furthermore, they help in improving the surface properties with additional functional groups or active adsorption sites and enhance the adsorptive capacities of the resultant sorption materials. Thermochemical activation gives rise to activated carbon materials, which show enhanced porosity to facilitate physisorption along with chemical adsorption. The sorption process is governed by a number mechanisms, such as physical adsorption on the adsorbent surface by van der Waals forces of attraction, hydrogen bonding, dipoleinduced dipole moments and electrostatic attraction between charged species, i.e., cationic charges on heavy metal ions and polyanionic charges on the bio-sorbent surface. Two main methods of carrying out sorption processes are popular and widely adopted in experiments: batch adsorption tests and fixed-bed adsorption columns. The latter has an advantage of installing an additional number of columns in order to increase the length of the adsorption bed for enhanced capacity of removal of pollutants from wastewater. Theoretical studies, including kinetics, thermodynamics, simulation and modeling, add a greater in-depth understanding of the adsorption mechanism. Bio-sorbents derived from citrus wastes, the largest fruit crop grown on the planet, provide an inexpensive, natural, renewable and sustainable means of obtaining resourceful as well as fruitful products.

**Author Contributions:** This work was completed with the contributions of 8 authors. N.M. and P.A. designed and wrote the manuscript; M.S. and A.D. contributed to analyzing recent studies on the valorization of citrus waste and synthesis of bio-adsorbents from citrus peel waste; P.A. compiled the theoretical studies reported in this subject area; B.P. and D.M. contributed to the summary and interpretation of reports and relevance to the current research progress issues; M.K.T. and S.A. performed the final proof-reading of the manuscript; N.M. carried out the final editing, revision and supervision of the project to bring it to its final format. All authors have read and agreed to the published version of the manuscript.

**Funding:** Authors acknowledge support from the National Research Foundation of Korea (NRF) Korean Government (Ministry of Science and ICT) (NRF-2020R1G1A1015243).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.
