Sustainable and Green Synthesis of Carbon Nanofibers from Date Palm Residues and Their Adsorption Efficiency for Eosin Dye

Abstract

This work investigates the prospective usage of dried date palm residues for eosin Y and eosin B (ES-Y and ES-B) dye removal from an aqueous solution. A green synthesis route is utilized to prepare carbon nanofibers (CNFs) from date palm residues. We study the characteristics of carbon nanomaterials based on their composition and morphology. The characterization includes different types of instruments such as a Fourier-Transform Infrared Spectroscopy (FTIR), Brunauer Emmett Teller (BET), and Scanning Electron Microscopy (SEM). Batch mode experimentations are conducted and studied utilizing various significant factors such as the dose of the adsorbent, solution pH, contact time, and the initial quantity of eosin molecules as a pollutant. The dye adsorption capability improves with an increasing adsorbent dose of up to 40 mg of CNFs. The adsorption of dyes onto CNFs achieves equilibrium in around 60 h, whereas the optimal starting dye concentration in this study is 50 ppm. Further, to study the under-investigated toxic molecules’ adsorption process mechanism on the nanomaterials’ active sites, we introduce kinetic models involving pseudo-first-order, pseudo-second-order, and models based on intra-particle diffusion. Langmuir and Freundlich’s isotherms are considered to study the equilibrium isotherms, and the Langmuir isotherm model deals considerably with the attained experimentation results.

1. Introduction

The Qassim area of Saudi Arabia contributes almost 25 percent of the kingdom’s overall output of dates. With more than 7 million palm trees [1], Khalas, Sukkari, Anbara, Ajwa, Ruthana, Barhi, Segae, and Ruzeiz are the most noteworthy [2]. This region has seen a substantial rise in data losses. As a result, it is a national priority to develop the procedures for the exploitation of dates and palm trash for their further valorization into innovative and sustainable goods. Lost dates with flaws, excessive hardness, poor texture, or microbial and fungal contamination are unfit for human eating [3,4]. These discarded dates are abundant in biodegradable sugars [5], which could be used to make ethanol biofuels [6]. They are mainly used to manufacture fragrances, cosmetics [7], cleansers [8], pharmaceuticals [7], paints [8], and vinegar [9]. Sugars, starches, and lignocelluloses are the three main types of feedstocks for ethanol synthesis [10]. Researchers look at date fruits as raw materials for making ethanol [11,12]. On the other hand, according to the literature, ethanol is a potential reagent for the synthesis of carbon nanotubes (CNTs) [13,14], which are produced by the pyrolysis of alcohol vapor since alcohol is a cheap, harmless, abundant reagent and can also be applied as a fuel in fuel cell [15].

Water resource contamination by various contaminants is now one of the most significant worldwide environmental challenges [16,17]. The leftover dyes from many resources, such as fabrics, polymeric materials, paper, foodstuff, leather, and pharmaceuticals, are believed to be an unhealthy danger and pollution to water supplies. The textile sector is the second-largest polluter of the world’s water supplies, next to agriculture [18]. Removing dyes from textile effluent presently is a significant problem [19]. Over the years [20,21], various separation methods have been used to study dye removal from wastewater, including dripping filters, functioning slurry, agglomeration, optical degradation, adsorption via different substances, and membrane filtering. Over time, however, adsorption has been regarded as a better separation technique [22,23]. The ability to reuse and recycle the adsorbent and the low creation of residues are the primary advantages of this technology [24]. Furthermore, coagulation and adsorption procedures are effective [25,26]. Therefore, researchers are always searching for novel low-cost sorbent materials that might provide more valuable outcomes [27]. Several adsorbents exist to remove the dye from aqueous solutions, including zeolite, modified sawdusts, and different types of modified and unmodified chitosan [28,29].

Eosin Y, ES-Y (anionic dye, C₂₀H₆Br₄Na₂O₅) with an IUPAC designation 2-(2,4,5,6-Tetrabromo-6-oxido-3-oxido-3H xanthenes-9-yl) benzoate disodium salt, is enormously dissolved in aqueous solution and is a luminescent dye. It has an excellent capacity for powerful adsorption through red blood cells, and its red hue enables its use in gram stains to distinguish between species of bacteria [30]. Due to how dangerous it is, the U.S. government has banned the use of dyes in food [31]. The ES-Y indicates neurotoxic dangers as well, including significant skin disorders with burning and discomfort [32], and consumption has detrimental consequences, especially on essential organs such as the liver, kidney, etc. [33,34] and severe corneal damage through the destruction of retinal ganglion cells [34]. It also destroys DNA inside live organisms’ digestive systems, causing several illnesses [35,36]. Following breakdown by heat, oxidizing chemicals, and light, the metabolites of dyes are also extraordinarily poisonous and carcinogenic [37]. Considering the toxicity of ES-Y, it has been deemed necessary to create a cost-effective and rapid technique for removing it from wastewater. Various wastewater treatment technologies, including chemical methods [38], oxidizing agents [39], ozonolysis [40], photochemistry process [41], and foaming extraction [42], have emerged over many years. Adsorption, with its well-known benefits over the techniques mentioned above [43], may effectively remove hazardous compounds without generating byproducts that degrade water quality. Utilizing inexpensive, eco-friendly, and highly active surface porous materials to enhance the economic and expenditure of the procedure [44,45] has been the focus and subject of numerous efforts to date. In this context, concurrent analysis and optimization parameters are a demanding need for achieving a cost-effective and widespread treatment for wastewater.

Eosin B, ES-B (anionic dye, C₂₀H₈Br₂N₂O₉), 2-(4,5-dibromo-2,7-dinitro-6-oxido-3-oxo-3H-xanthen-9-yl) benzoate disodium salt, is a widely used and indispensable organic dye in the fabric and sanitary sectors that is tremendously poisonous because of its aromaticity [46]. Biological processes, coagulation, adsorption, etc., are employed to remove organic and pigmented pollutants [47,48]. Nevertheless, a few adsorbents, mainly several modified and unmodified activated carbon, were utilized over decades to remove ES-B (Acid Red 91) from aqueous systems [49,50]. ES-B has a somewhat bluish hue [51]. Graphene oxide in aqueous solutions eliminates a variety of dyes. Various studies demonstrate that graphene oxide is an efficient adsorbent for removing these pigments from aqueous environments [52,53]. In aqueous solutions, graphene oxide can remove ionic dyes. Nevertheless, it is hindered by regional issues [54].

Adsorption is one of the efficient chemical, physical, and biological strategies for removing pigments from wastewater. Adsorption is a superior technology with tremendous significance owing to the simplicity of procedures and comparably inexpensive deployment costs [55]. This presents an appealing option for treating polluted water, mainly if the sorbent is affordable and its deployment does not need extra preparation [56]. Activated carbon is a regularly used adsorbent with suitable dyes and chemical removal capability [57,58]. Its downsides, however, are the high cost of treatment and the difficulty of replenishing the adsorbent, which raises the expense of wastewater treatment. For the adsorption process to be economically feasible, there is a need for more adsorbents composed of affordable and locally accessible materials. Researchers have investigated the viability of low-cost adsorbents, including several natural compounds. Health, productivity, and expense are addressed while deciding between several strategies for treating wastewater polluted with dye. Previous work briefly outlines the different advantages and disadvantages of the various methods [59]. The eosin class dyes also irritate the eyes and skin, inhibit protein-protein interaction, and cause human genotoxicity. Consequently, these dyes containing effluent must be thoroughly treated before discharge. Adsorption, utilizing carbon or graphene materials, is a standard physicochemical method for treating wastewater containing stains due to its ease of use and operational efficiency. Recently, researchers discussed the benefits of using different materials for wastewater treatment [60,61]. Furthermore, commercial activated carbon and graphene are expensive. As a result of this obstacle, researchers have investigated feasible and less costly adsorbents to replace these materials, designing various eco-friendly materials for ecological treatments, including removing dyes [62,63]. Herein we introduce an efficient route for the adsorption of vital dyes from an aqueous solution using the synthesized CNFs from palm residues Scheme 1. We have designed and produced novel materials of dispersed CNFs using a green synthesis technique. This technique introduces new nanomaterials and studies the material adsorption characteristics. The prepared nanomaterials offer a high adsorption ability. Therefore, this research investigates the potential of CNFs for water treatment from dangerous pollutants involving toxic eosin dye removal. The influence of diverse factors, such as adsorbent concentration, dye molecules content, and contact time, on adsorption efficiency were investigated. Lastly, the proper conditions of the experiment series, kinetics, and the isotherm (Langmuir and Freundlich) equations are investigated.

2. Materials and Methods

2.1. Materials

All the reagents are of analytical grades; hydrochloric acid (HCl. 37%) was purchased from Sharlau, Spain. S. bayamus yeast strains were obtained from Laboratoire Oenotechnique, Clermont-L’Herault, France, and used for submerged fermentation. The discarded dates (date samples), which are mushy and have a terrible texture, are unsuitable for human consumption, were employed as samples for this research. These dates combined all date cultivars cultivated in Saudi Arabia (Al-Qassim area).

2.2. Preparation of Alcohol

In a particular machine, date samples were cleaned and combined with deionized water. This machine cooked the date–water combination at 80 °C for 30 min and then mechanically separated the seeds. The blended seedless date solution was transferred to a 20-L-capacity tank for mixing and allowing it to stand at room temperature in the tank. The extracted date was then decanted, refined, and microfiltered. Seventeen liters of clarified and microfiltered date juice was poured into a fermenter, 5 g of S. ba’atnus was added, and the mixture was agitated vigorously for 48 h at 30 °C. The fermented date juice was distilled at 78.5 °C [64].

2.3. Preparation of CNFs

The CNFs were produced by precipitating date ethanol vapor in a tube furnace’s interior stainless-steel layer at 680 °C. The black soot was collected. Then, 10 g of the contents was purified using 100 mL of concentrated HCl and boiled for one h. The products were filtered, washed until neutral, and dried in an oven at 40 °C for 12 h.

2.4. Batch Biosorption Experiments

Using batch-mode procedures, the adsorption effectiveness of ES-Y and ES-B onto CNFs was influenced by many variables, including adsorbent dosage, contact duration, solution pH, and starting concentration. Experiments on the adsorption of ES-Y and ES-B by CNFs were conducted using 50-mL conical stoppered flasks using a batch technique. 50 mg of CNFs were soaked in 50 mL of an aqueous solution comprising varying concentrations of ES-Y and ES-B, and the resulting mixes were mechanically stirred at room temperature. Investigations on the adsorption of ES-Y and ES-B by CNFs have been conducted at twenty, forty, sixty, eighty, hundred, and one hundred twenty intervals. At the same time, sorbent dose, pH, and starting ES-Y and ES-B concentrations were held constant. The impact of the adsorbent dose was studied by shaking for 60 h a known quantity of CNFs ranging from 0.01 to 0.1 g with a solution in water that has a 0.01 g/l ES-Y and ES-B. To explore the influence of the starting content of ES-Y and ES-B, batch sorption experiments were conducted at varying concentrations of ES-Y and ES-B (10, 50, 100, 150, 200, 250, and 300 mg/L). At the same time, additional variables involving sorbent dose and contact duration remained unchanged.

The proportions are collected from the main stock at predetermined times and filtered utilizing a 0.45 m filter paper (GF/C Whatman, Maidstone, UK) prior to colorimetric measurement of the residual concentrations of ES-Y and ES-B using a VIS/UV Spectrophotometer-19 (SCO-Tech, Dingelstädt, Germany). To minimize the errors, tests were done thrice for 60 h at 298 °K, and the results were utilized for supplementary computations. Assurance controls were concurrently conducted to measure ES-Y and ES-B ion elimination throughout adsorption in the absence of adsorbent. A quantity that adsorbed ES-Y and ES-B at equilibrium, q_e (mg/g), into CNFs was determined by subtracting the initial and equilibrium concentrations using the formula below [65].

$${\mathrm{q}}_{\mathrm{t}}=\frac{\left({\mathrm{C}}_{\mathrm{o}}-{\mathrm{C}}_{\mathrm{t}}\right)\mathrm{V}}{{\mathrm{m}}_{\mathrm{s}}}$$

(1)

while

q_e = adsorbed dye at equilibrium (mg·g⁻¹),

C₀ = initial concentrations (mg·L⁻¹)

C_t = contaminant concentrations (mg·L⁻¹) in the liquid phase at equilibrium and time t

V = the total volume, and m_s is the mass of CNFs.

Based on the given formula, the percent of adsorption (E%) in CNFs was calculated as:

$$\mathrm{E}\%=\left[\frac{{\mathrm{C}}_{\mathrm{o}}-{\mathrm{C}}_{\mathrm{e}}}{{\mathrm{C}}_{\mathrm{o}}}\right]\times 100$$

(2)

where:

C_o = Concentration of ES-Y and ES-B at the investigation start (mg/L) and

C_e = Concentration of ES-Y and ES-B at equilibrium (mg/L).

2.5. Adsorption Capacity Analysis

The adsorption capacities of CNFs were calculated using the following equation

$${\mathrm{q}}_{\mathrm{t}}=\frac{\left({\mathrm{C}}_{\mathrm{o}}-{\mathrm{C}}_{\mathrm{t}}\right)\mathrm{V}}{{\mathrm{m}}_{\mathrm{s}}}$$

(3)

where:

q_t = amount of ES-Y and ES-B adsorbed by the silica nanoparticles (mg/g),

C_o = initial ES-Y and ES-B concentrations (mg/L),

C_t = equilibrium ES-Y and ES-B concentrations (mg/L) of ES-Y and ES-B solutions,

V = volume of ES-Y and ES-B in litre, and

m_s = CNFs mass in gram.

2.6. Equilibrium Biosorption Isotherm Models

To analyze the equilibrium interactions among contaminants with adsorbent materials, Freundlich and Langmuir isotherm models have been employed to characterize how ES-Y and ES-B interact with CNFs and their equilibrium concentrations in solution at a constant temperature. These formulas provide the linear version of the Langmuir and Freundlich isotherms:

$$\mathrm{Langmuir}\mathrm{formula}:\frac{{\mathrm{C}}_{\mathrm{e}}}{{\mathrm{Q}}_{\mathrm{e}}}=\frac{1}{{\mathrm{Q}}_{\max }{\mathrm{K}}_{\mathrm{L}}}+\frac{{\mathrm{C}}_{\mathrm{e}}}{{\mathrm{Q}}_{\max }}$$

(4)

$$\mathrm{Freundlich}\mathrm{formula}:{\mathrm{Log}\mathrm{Q}}_{\mathrm{e}}={\log \mathrm{K}}_{\mathrm{f}}+\frac{1}{\mathrm{n}}{\mathrm{Log}\mathrm{C}}_{\mathrm{e}}$$

(5)

where Q_e is the equilibrium adsorption mass of ES-Y and ES-B per unit mass of adsorbent (mg/g) and the concentration of ES-Y and ES-B at equilibration is denoted by C_e (mg/L). Q_max is the maximum absorption specificity at saturation of the monolayer (mg/g). K_L is the Langmuir constant, while K_f is the Freundlich constant. n is an empirical variable that varies based on the heterogeneity of the adsorbent’s surface.

3. Results

3.1. Characterization of Sorbents

The SEM images of CNFs are shown in Figure 1a,b, respectively. The SEM micrographs were obtained using a JEOL JSM-5400 LV SEM (JEOL Ltd., Akishima, Japan). An acceleration voltage of 5 kV was conducted for the measurements. The magnifications ranged from 100 to 2000×. Images depict a thick proliferation of homogeneous cylinders CNFs of various sizes. These data demonstrate that the inner surface of a commercial stainless-steel tube may facilitate the formation of CNFs at a temperature of 680 °C without the need for additional catalysis. As moderate oxidation settings were maintained to prevent damage to the CNFs, amorphous carbon residues resistant to oxidation remained attached to the CNFs’ surfaces. Moreover, FTIR analysis was carried out for the synthesized CNFs, as shown in Figure 1b.

In addition, CNFs were characterized through XRD (Figure 2). The patterns show a distinct, sharp, and high-intensity peak around 2-theta 26.53, 35.45, 43.76, and 50.87, thereby confirming the presence of highly crystalline graphitic CNFs. These results agree with the recent works [66,67]. Further, the BET value was measured for CNFs and found to be 335 m²/g. This indicates the extreme surface area of the synthesized CNFs.

3.2. Effect of Adsorbent Dosage

The influence of the adsorbent dosage, which establishes the adsorbent’s capability for a specific ES-Y and ES-B concentration, is one of the critical parameters in ES-Y and ES-B removal investigations. Figure 3 illustrates how such an adsorbent dosage affects how effectively ES-Y and ES-B are removed through an aqueous medium. Different adsorbent concentrations of the CNFs dose ranged from 10 to 100 mg for the 50 mL, 50 ppm ES-Y and ES-B solutions. In the initial phases, the data demonstrate that the percent of ES-Y and ES-B clearance increases with the increase in adsorbent dosage; however, no substantial improvement was seen afterward. The removal efficiency, which seems dependent on CNFs, is 62.0% to 86.0% for ES-Y and 53.5% to 83.0% for ES-B, correspondingly. This means that there is 40 mg of CNFs uptake 43.0 ppm for ES-Y and 41.5 ppm for ES-B from an aqueous solution containing 50 ppm of phenol concentration. The adsorption efficiency of ES-Y and ES-B ions is enhanced based on the adsorbent dosage of 0.040 g. After this dose, the adsorption is peripheral and steady [68,69]. Therefore, it is concluded that 0.8 g/L of CNFs is the ideal concentration for this experiment. Our findings concur with those findings [70].

3.3. Contact Time

After the adsorbent dose, the influence of shaking duration is the second-most-critical factor in determining the biosorption equilibrium time in batch biosorption studies [71]. The shaking time required to establish an optimum outcome was influenced by the surface properties of CNFs and their accessible adsorption sites. Figure 4 depicts the influence of contact time on the removal efficiency of ES-Y and ES-B from aqueous solutions. The effect of shaking time on the biosorption of ES-Y and ES-B onto CNFs was investigated as a function of contact time ranging from 20 to 120 h at neutral medium, 278 ± 1 °K, and 150.0 round per minute. The graph displays ES-Y and ES-B removal efficiencies for CNFs varying from 50% to 84.0 for ES-Y and 43% to 80% for ES-B, respectively. During the earliest phases, the adsorption effectiveness of ES-Y and ES-B on CNFs increases dramatically, suggesting an abundance of active binding sites that are easily accessible. The curve eventually reaches a plateau, indicating that the absorbent is saturated at this level. According to the graph, the ES-Y and ES-B removal efficiencies for both CNFs achieve equilibrium after 60 h. With the steady occupation of active binding sites, a prolonged interaction period does not significantly improve. After equilibrium, ES-Y and ES-B adsorption uptake does not vary substantially with time [72]. This demonstrates that the optimal shaking duration is 60 h, which is adequate to achieve equilibrium for the most significant removal efficiency of ES-Y and ES-B ions from aqueous solutions by CNFs.

3.4. Effect of Initial Dye Concentration

The impact of starting concentration (50–250 mg/L) on the removal efficiency of ES-Y and ES-B from aqueous solution by CNFs at neutral medium, 278 ± 1 °K, 50 mg biosorption dosage, 60 h, and 150 round per minute of shaking speed is depicted in Figure 5. When the adsorption of ES-Y and ES-B ions on CNFs diminishes as ES-Y and ES-B concentrations increase. The ES-Y and ES-B removal efficiencies for CNFs range from 83 to 49% for ES-Y and 79 to 41%, for ES-B. The CNFs may have more active adsorption sites than ES-Y and ES-B ions in the solution at lower initial ES-Y and ES-B concentrations, which could lead to the increased absorption. At the same time, the lower uptake at higher initial ES-Y and ES-B concentrations indicates the formation of monolayer coverage of the ions. The ES-Y and ES-B removal efficiency decreases on the outer surface of the CNFs because the time required to reach the adsorption equilibrium point on CNFs was expected to be longer at a higher initial ES-Y and ES-B concentration than at a lower initial concentration [73]. Consequently, it is deduced that this study’s optimal beginning ES-Y and ES-B concentration is 50 mg/L.

3.5. Effect of pH

ES-Y and ES-B adsorption on CNFs is pH dependent, as established in (Figure 6). The pH of a solution is a critical factor governing the adsorption capacity of ionic organics onto an adsorbent [74]. Ji et al. anticipate that an increase in the pH of the adsorbate might split hydrophobic neutral adsorbate molecules into hydrophilic, negatively charged species, hence diminishing the hydrophobic interaction [75]. Wang et al. also postulate that an increase in electrostatic repulsion as the pH of the adsorbate increases would decrease the electrostatic interaction between oppositely charged adsorbate and adsorbent [76]. A change in pH may also benefit the adsorbate’s ability to transfer electrons, boosting the interaction between electron donors and acceptors [77]. The impact of pH was evaluated by evaluating the dye absorption of 0.04 g adsorbent at pH values ranging from 2 to 10, using hydrochloric acid or sodium hydroxide to alter the pH and 50 ppm concentration of eosin dyes. The reaction was left overnight at room temperature. As seen in Figure 6, the removal efficacy of CNFs decreases considerably at pH values over six. It is usual for anionic dyes such as ES-Y and ES-B to be negatively charged in an acidic medium. Consequently, it encourages an electrostatic interaction between the positively charged adsorbents and the anionic groups of the dye. At higher pH levels, the anionic bromide groups of eosin dyes compete with the system’s excess OH^– ions for adsorption sites on adsorbents, lowering the adsorbent’s removal efficiency.

Little removal in the pH zone above 7 indicates that electrostatic attraction is not the predominant adsorption mechanism. Other processes, such as hydrophobic interactions between the dye and the adsorbent, interactions involving hydrogen bonding and Van der Waals force, and pore trapping, are also at work during adsorption at this pH [78].

Ethanol was used as the desorption solvent for the reusability of the CNFs. The polar nature of ethanol helps to release dyes from adsorption onto CNFs [79]. The removal efficiency of dyes from CNFs surface barely decreases for consecutive cycles to reach about 81–77% for ES-Y and ES-B, respectively, after five cycles.

3.6. Adsorption Isotherms

The adsorption isotherm describes the equilibrium concentration of the adsorbate in the solid phase, which is statically bonded to the surface of the adsorbent, and in the liquid phase as a soluble component. The research was conducted at a constant temperature throughout the adsorption process. [80]. The findings of these models reveal the adsorbate molecules’ maximal adsorption capability. Following the sorption phenomena of ES-Y and ES-B molecules on CNFs surfaces, two major isotherm models incorporating Langmuir and Freundlich isotherms are presented here. Figure 7 depicts the adsorption characteristics of isotherm models for the ES-Y and ES-B molecule adsorption processes. The monolayer adsorption process is described by the Langmuir model [81]. The adsorption process achieves equilibrium and ceases when the active surface sites of adsorbent molecules are saturated with adsorbate molecules. The Langmuir isotherm data validate the experiment results with regression coefficients of 0.995 and 0.998 for ES-Y and ES-B, respectively.

In addition, the Qmax value is slightly greater for ES-Y than ES-B, indicating that the number of CNFs active sites accessible for the adsorption process remains consistent. Freundlich’s experimental model is supplied and used on a heterogeneous adsorbent surface for the multilayer adsorption isotherm. The values of K_f and n indicate a greater affinity for adsorption, suggesting that the adsorption capacity and intensity are better. KF and n values computed from the intercept and slope of the plot are shown in

Table 1. Parameters of Langmuir and Freundlich adsorption isotherm models.

Adsorbent.	Langmuir			Freundlich
	Qmax (mg/g)	KL (L/mg)	R2	n	KF	R2
ES-Y	168.634	0.0323	0.995	1.7449	10.3767	0.951
ES-B	165.017	0.0209	0.998	1.6899	8.30001	0.941

. (Figure 7). Based on CNFs, the R² values for ES-Y and ES-B are 0.951 and 0.941, respectively. The R² of the Langmuir isotherm is determined to have the lowest values. The greater the value of n than one, the greater the affinity between the adsorbate molecules and active sites of adsorbent molecules based on chemisorption.

In addition, the Langmuir isotherm regression coefficients R² are closer to one than those derived for the Freundlich isotherm. Therefore, the Langmuir isotherm model is more consistent with the experimental findings of ES-Y and ES-B adsorption on the surface of CNFs. According to the Langmuir equation, the maximum adsorption capacities of ES-Y and ES-B molecules by CNF surfaces at 298 °K are 168.634 and 165.017 mg/g. These findings indicate that CNFs effectively adsorb Es-Y and Es-B ions from an aqueous solution.

3.7. Kinetics of the Adsorption of ES-Y and ES-B onto CNFs

To identify the optimal mechanism and rate-determining step of ES-Y and ES-B molecule adsorption on CNFs surfaces, the influence of shaking duration on the adsorption process is examined (see Figure 8). In addition, the absorption of ES-Y and ES-B molecules on active sites of CNFs is commonly enhanced. After roughly twenty-four hours, the balance is reached. Figure 8 shows the interpretation of kinetic data using three distinct adsorption kinetic models, including pseudo-first order, pseudo-second order, and intra-particle diffusion based on the isotherm model, the rate of the adsorption process, which comprises the adsorption of ES-Y and ES-B molecules to the surface of the nanomaterials, was determined. Also explored are the performance and probable mechanism between ES-Y and ES-B molecules and CNFs adsorbent.

3.8. Pseudo-First Order

Equation (6) shows the pseudo-first-order [82]:

Log(q_e − q_t) = logq_e − k₁t

(6)

where

q_e (mg g⁻¹) = amount of ES-Y and ES-B adsorbed/wt of the CNFs at equilibrium and

q_t (mg g⁻¹) = adsorption capacity of ES-Y and ES-B at time t (min).

The rate constant of the pseudo-first-order was introduced as k₁ (min⁻¹). Figure 9 shows the linear plots of log (q_e − q_t) versus the time of the adsorption process (t).

Table 2. Pseudo-first-order and pseudo-second-order models using CNFs.

CNFs	Experimental Value qe (mg g−1)	First-Order			Second-Order
		K1	qe	R2	K2	qe	R2
ES-Y	9.2	0.0264	10.242	0.970	0.0102	9.5247	0.994
ES-B	9.1	0.0318	12.242	0.958	0.0077	9.3327	0.991

lists the values of the rate constants (K₁) and the theoretical adsorption capacities (q_e).

3.9. Pseudo-Second-Order Rate Model

Pseudo-second-order rate model is expressed as follows in Equation (7):

t/q_t = 1/k₂q_e² + t/q_e

(7)

The pseudo-second-order rate constant k₂ can be determined from the plot of t/q vs. time t for adsorption (g mg⁻¹min⁻¹). The plots of t/q_t vs. time (t) produce straight lines whose slopes and intercepts are proportional to the pseudo-second-order rate constants (k₂) and the maximal adsorption capacities (q_e) and (q_theo), respectively. The data from Figure 9 and Figure 10 are mentioned in Table 2.

Table 2 lists the correlation coefficients (R²) for the adsorption capacities (q_e) and theoretical capacities (q_theo) of the pseudo-first-order and pseudo-second-order models. The pseudo-second-order R2 is greater than the pseudo-first-order R². In addition, the q_e and q_theo values pertain to the outcomes of the adsorption trials. The second-order kinetics model represents the adsorption of ES-Y and ES-B molecules onto CNFs surfaces.

3.10. The Waber-Morris Model

This intra-particle diffusion model is used to investigate the adsorption mechanism of the ES-Y and ES-B molecules (adsorbate) to the surface of the CNFs. It detects the lowest step or the rate-determining step in the adsorption process. The intra-particle diffusion is shown as follows in Equation (8) [83]:

q_e = k_idt^1/2 + C

(8)

where:

q_e is the adsorption capacity (mg g⁻¹), t is the time (min) of the adsorption process, k_id (mg g⁻¹ min^−1/2) is the rate constant of the intra-particle diffusion (slope), and C is the thickness of the surface (intercept) respectively. As illustrated in Figure 11, the nonlinear plots of q_e versus t^1/2 are comprised of two stages. Firstly, the ES-Y and ES-B molecules take part in the adsorption process on the surface of the adsorbent molecules. The next stage involves diffusion within the pore of adsorbent molecules. The plots show that the intra-particle distribution is not the principal rate-controlling step, and the adsorption of ES-Y and ES-B onto CNFs is not easy to express using available isotherm models.

4. Conclusions

The conclusion of this project has revealed the synthesis of CNFs from palm wastes. In an aqueous solution, the CNFs display intriguing adsorption behaviors for ES-Y and ES-B. The adsorption of ES-Y and ES-B by CNFs is similarly dependent on the adsorbent dose, contact duration, and starting dye concentration. The results of this work have proven that CNFs may be produced from palm wastes. Langmuir’s isotherms and Freundlich’s isotherms were used to find where the eosin colors stick to the CNFs. The Langmuir isotherm model is mostly about how things work in the real world. The results of adsorption dynamics can be explained by three different models: pseudo-first-order, pseudo-second-order, and intra-particle diffusion. The results show the pseudo-second-order kinetic model for how adsorption happens on the surface of CNFs. Finally, we introduced CNFs with great potential for dye removal. They are versatile for promising industrial applications due to their high surface area-to-volume ratio, nanoscale diameter, and surface properties.