Magnetic activated carbon nanocomposite from Nigella sativa L. waste (MNSA) for the removal of Coomassie brilliant blue dye from aqueous solution: Statistical design of experiments for optimization of the adsorption conditions.

The present work was carried out to evaluate the removal of Coomassie brilliant blue dye by adsorption onto a magnetized activated carbon nanocomposite (MNSA) prepared from Nigella sativa L. (NS) waste. Different techniques, including infrared spectroscopy, scanning electron microscopy, and nitrogen adsorption/desorption, were used to characterize MNSA to investigate its adsorption properties. Adsorption experiments were carried out by simultaneously optimizing four variables that usually present a strong effect in adsorption studies. A full 24 factorial design with 3 central points was used. The four independent variables were the initial pH of the dye solution (pH), the initial dye concentration (Co), the adsorbent mass (m), and the contact time (t). The sorption capacity (q) of the adsorbent and the percentage of dye removal (% Rem) from an aqueous solution were used as the responses of the factorial design. The results indicated that pH, Co, and m were essential factors for the overall optimization of both responses (q and % Rem) and that several interactions of two, three and four factors occurred. Based on the design of the experiments (DOE), the optimized conditions for adsorption were pH = 2.00, Co = 40.0 mg L-1, m = 30.0 mg, and t = 3.0 h. Under these conditions, both responses, q and % Rem, were maximized, with a desirability of 85.54%. The findings of this study could be useful for industrial wastewater treatment systems.

Introduction

Coomassie brilliant blue dye is a synthetic dye commonly used in the textile industry and represents a toxic and unmanageable organic pollutant [1]. This dye has several industrial applications due to its intense colour and simplicity of application. Effluents containing Coomassie dye have several adverse effects on the eco-aquatic system [2]. Water-soluble dyes are poorly biodegradable, and according to Sandhya et al. [3], 20–50% of the overall dye remains in effluents as a result of the manufacturing process. As legislation has become more stringent, considerable importance has been given to the treatment of dye-containing effluents [4]. Therefore, it is highly desirable to remove dyes in general and Coomassie brilliant blue in particular from wastewater. Since synthetic dyes are inherently prepared as stable and non-degradable molecules, conventional treatment methods are not suitable for removal of such dyes from the aqueous phase. Over the years, the possibility of techniques such as oxidative degradation, electrocoagulation, membrane-based separation and biochemical degradation have been exploited, but these methods have drawbacks due to their inapplicability to large-scale units along with their energy- and chemical-intensive nature [5].

Nevertheless, adsorption is an effective method for dye removal from the aqueous phase because of its simple operation, low initial cost of implementation, high tolerance to concomitant species, ability to treat concentrated wastewater contaminated with different dyes and the possibility of reusing the spent adsorbent via regeneration. Subsequently, a variety of activated carbon-based adsorbents derived from various materials have been investigated for their efficacy and efficiency in the removal of dyes. However, the large volume of wastewater with high dye concentrations has inspired the development of non-toxic, low-cost and efficient adsorbents with the possibility of regeneration for reuse. Unfortunately, activated carbons are difficult to isolate from solution and are discarded with processed sludge after use in water and wastewater treatment, causing secondary pollution [6]. Among several studied adsorbents, magnetized adsorbents have shown high efficiency for the removal of dyes from effluents owing to their easy control and fast separation by direct application of a magnetic field [7], [8], [9], [10], [11], [12], [13], [14]. The high adsorption capacity of magnetized adsorbents for dyes has been ascribed to the interactions of hydroxyl groups with the dye molecules [5]. In adsorption-based methods, it is desirable to know the process variables and their influence on the adsorption capacity to increase the contaminant removal efficiency of the adsorbent. The liquid-solid interface adsorption process is mainly affected by the initial concentration of the adsorbate, initial pH of the solution, adsorbent dose, surface area of the adsorbent, contact time, and temperature [15], [16], [17].

Optimization of the process variables is required to achieve the maximum adsorption capacity and removal efficiency of the adsorbent. The conventional method for the optimization of process variables requires a vast number of experiments to be performed, which increases costs and is time consuming. Additionally, the conventional approach does not verify the effects of interactions between the process variables on the dependent variables. The design of experiments (DOE) approach is a successful process for planning experimental runs. DOE generates an optimum experimental plan, decreasing the amount of chemicals used and the experimental time, thus leading to a better performance of experiments using less time [18]. The specific aims of the present study were to develop a novel magnetized activated carbon prepared from Nigella sativa L. waste and to apply a full factorial design with central points to obtain the maximum adsorption capacity of the developed magnetic nanocomposite for Coomassie brilliant blue dye removal from aqueous solution. This study consisted of examining the effects of four independent variables (initial dye concentration, initial pH of the dye solution, adsorbent dose, and contact time) and their interactions on the adsorption capacity of the magnetized carbon for Coomassie brilliant blue dye.

Material and methods

Preparation of the adsorbent

Magnetized carbon-iron oxide composite was prepared using carbon from Nigella sativa waste (NSW), an agro-waste material. NSW was obtained from a local factory in Egypt and treated with n-hexane followed by deionized water (DW) before oven drying at 100 °C to constant weight. The resulting material was then carbonized at 600 °C. The magnetized carbon-iron oxide composite derived from NSW was prepared following the procedure of Gupta and Nayak [19] with little modification. In 100 mL DW, ferric chloride (6.1 g) (Merck, Darmstadt, Germany) and ferrous sulfate (4.2 g) (Merck, Darmstadt, Germany) were dissolved and heated to 90 °C. Then, 10 mL of sodium hydroxide (2 M) (Merck, Darmstadt, Germany) and a solution of 1.00 g of NS carbon suspended in 200 mL of DW were quickly and consecutively added. The mixture was stirred for 30 min at 80 °C and then allowed to sitto reach room temperature. The black precipitate was filtered, washed and dried at 50 °C.

Characterization of the prepared adsorbent

The surface texture of the adsorbent was investigated using a JSM-6390LV instrument (JEOL Ltd, Tokyo, Japan) with a 3 kV accelerating voltage after drying the sample overnight at approximately 105 °C under vacuum before scanning electron microscopy (SEM) analysis. The surface functional groups on N. Sativa carbon and its magnetized carbon were studied using a Fourier transform infrared (FTIR) spectrophotometer (AVATAR 370 Csl, Thermo Nicolet Co., Massachusetts, USA) at a resolution of 4 cm−1 over the range of 500–4000 cm−1. The samples were examined as KBr pellets (Thermo Fisher Scientific, Geel, Belgium). The textural properties of surface areas (SBET) were determined from the Brunauer-Emmett-Teller (BET) method. The Barrett-Joyner-Halenda (BJH) method was used to calculate pore size. The textural characterization of the carbon material was obtained using nitrogen adsorption/desorption isotherms (Micromeritics Instrument Co., model TriStar II 3020- Atlanta, Georgia, USA). The surface area analyser was operated at −196 °C after drying the solid sample for 8 h at 150 °C at a pressure of < 2 mbar. The magnetic properties of magnetized Nigella sativa L. Activated carbon (MNSA) were confirmed using a Lake Shore7400 vibrating sample magnetometer (VSM) (California, USA).

Preparation of dye solutions

Stock solutions of the dye were prepared by dissolving the desired amount of Coomassie brilliant blue (C.I. 42660, Sigma-Aldrich, Switzerland) in DW. The pH of the test solution was adjusted using reagent-grade diluted hydrochloric acid.

Process variables and experimental design

Four variables (initial dye concentration (Co), initial pH of the dye solution (pH), mass of adsorbent (m), and contact time(t)) were identified to investigate their influence on the adsorption capacity of MNSA for Coomassie brilliant blue dye (C.I. 42660). A full factorial 24 design with 3 central points (total of 19 experiments) was adopted to verify the effect of the described variables on the percentage of dye removal (% Rem) and the adsorption capacity of the adsorbent (q). The selected variables with their values are given in Table 1.

Table 1

Experiments performed for the 24 full factorial design with 3 central points. The responses of this factorial design were% Rem and q. Values of responses are given with four significant digits.

Exp.	pH	Co (mg L−1)	Mass (mg)	Time (h)	% Rem	q (mg g−1)
1	2.00	40.00	30.0	1.00	81.18	54.12
2	4.00	40.00	30.0	1.00	9.760	6.520
3	2.00	80.00	30.0	1.00	30.20	40.20
4	4.00	80.00	30.0	1.00	20.77	27.68
5	2.00	40.00	50.0	1.00	60.00	24.00
6	4.00	40.00	50.0	1.00	3.560	1.420
7	2.00	80.00	50.0	1.00	62.60	50.00
8	4.00	80.00	50.0	1.00	9.800	7.800
9	2.00	40.00	30.0	3.00	85.88	57.25
10	4.00	40.00	30.0	3.00	5.580	3.710
11	2.00	80.00	30.0	3.00	58.70	78.25
12	4.00	80.00	30.0	3.00	1.240	1.680
13	2.00	40.00	50.0	3.00	76.47	30.59
14	4.00	40.00	50.0	3.00	0.000	0.000
15	2.00	80.00	50.0	3.00	30.69	24.55
16	4.00	80.00	50.0	3.00	0.000	0.000
17	3.00	60.00	40.0	2.00	25.03	18.77
18	3.00	60.00	40.0	2.00	19.30	14.50
19	3.00	60.00	40.0	2.00	26.10	19.50

The coded level −1 stands for the lowest value of the parameter, the +1 level stands for the highest value of the parameter, and 0 stands for the central point, that is, the median of the −1 and +1 values of each parameter.

It was hypothesized that the four independent variables and the experimental response data follow a linear equation, given in Eq. (1) [20]:where R is the predicted response (% Rem or q); X1 to X4 are the coded variables; βo is the constant coefficient; β1 to β4 are the linear term coefficients; β5 to β10 are the interaction coefficients between two variables; β11 to β14 are the interaction coefficients among three variables; β15 is the interaction coefficient among four variables; and ε is the experimental error [20].

Batch adsorption design

Batch experiments based on a 24 full factorial design plus 3 central points were conducted randomly to investigate the effect of the four pre-selected operating variables on q and % Rem with MNSA. For adsorption of the dye on the developed magnetic adsorbent, different amounts of adsorbent (30.0–50.0 mg) were added to 50.00 mL of solution initially containing 40.00 to 80.00 mg L−1 of the dye. Standard solutions of the dye were prepared by diluting the stock solution, and the pH was adjusted to 2.00–4.00 by using diluted hydrochloric acid. The adsorption experiments were conducted in a thermo-controlled (±1 °C) (Oxylab, São Leopoldo, Brazil) water bath shaker for different time intervals (1.00 to 3.00 h) at 50 rpm. The ranges of the initial pH of the solution were chosen according to previous experiments. Samples were removed and centrifuged after reaching equilibrium. The remaining concentration of dye in the solution was then determined using a visible spectrophotometer at a λmax of 551 nm (UV-1280 Shimadzu, Kyoto, Japan).

The adsorbed quantity expressed per unit mass of magnetic activated carbon and the percentages of dye removal are given by Eqs. (1), (2), respectively:where q is the amount of dye adsorbed by the adsorbent (mg g−1); C is the initial dye concentration in contact with the adsorbent (mg L−1); C is the dye concentration after the batch adsorption study (mg L−1); m is the mass of adsorbent (g); and V is the volume of the dye solution (L).

Results and discussion

FTIR spectral analysis of adsorbent

Fig. 1(A, B) illustrates the FTIR spectra of (A) N. sativa carbon (NSC) and (B) MNSA. The spectra revealed a broad and strong band at approximately 3406 cm−1, which is characteristic of the stretching vibration of O—H in the hydroxyl groups of hydrogen bonds [1]. The bands in the region between 1452 and 908 cm−1 could be assigned to C—O stretching vibrations [21]. The intense broadband positioned at1080 cm−1 in NSC, which was shifted to 1119 cm−1 in MNSA, could be attributed to C—O vibrations in secondary and primary R–OH groups in alcohols [1]. The small bands at 908, 717, and 611 cm−1 were attributed to the out-of-plane bending vibrations of C—H in benzene derivatives, and the medium-width intense band at 563 cm−1 is ascribed to O—H bending. The new peak at 591 cm−1 in the MNSA spectrum was assigned to Fe—O [22]. A comparison of the NSC and MNSA spectra indicated the disappearance, shifting, and emergence of individual peaks. Significant band shifts from 1452 cm−1 (OC—OH carboxyl stretching) and 1080 cm−1 (C—O stretching) on NSC to 1358 cm−1 and 1119 cm−1, respectively, on MNSA were also observed. In addition, a new peak appeared at 591 cm−1 in the MNSA spectrum, which was attributed to the formation of Fe—O. The peak shifts of the OC—OH of carboxyl and C—O of alcohol in NSC relative to their locations in MNSA were due to the interactions of iron compounds with these groups. The analysis of the FTIR spectra indicated the formation of MNSA [19].

Fig. 1

FTIR spectra of (A) N. sativa carbon (NSC) and (B) magnetized N. sativa (MNSA).

Scanning electron microscopy (SEM) analysis

SEM analysis was performed on both NSC and MNSA to study their surface porosity development. Fig. 2A shows an SEM micrograph of NSC, the surface of which had small pores; in contrast, the SEM micrograph of MNSA in Fig. 2B shows larger developed pores on the surface of MNSA, which enhanced the adsorption process and removal efficiency. This difference in pore size could be due to the contribution of iron oxide in the ash composite, which improved the surface morphology and surface properties of the material.

Fig. 2

Micrographs of (A) N. sativa carbon (NSC) and (B) magnetized N. sativa (MNSA) × 50,000.

Textural characteristics of the adsorbent material

The surface area and total pore volume of the magnetic carbon material were 106.4 m2 g−1 and 0.220 g cm−3, respectively, which are compatible with the previously reported properties of magnetic composites comprising carbon materials loaded with magnetic iron compounds [23], [24], [25], [26].

Magnetic properties of the adsorbent

The magnetic properties of MNSA were confirmed by hysteresis loops obtained from plots of magnetization against field strength, as shown in Fig. 3 [27].

Fig. 3

Magnetic moment of magnetic and nonmagnetic activated carbons.

Full factorial design

A factorial design is applied to minimize the total number of experimental runs to attain the optimization of a whole system [11], [15], [16], [17], [28], [29]. The design verifies the factors that have essential effects on a response and shows how the effect of a factor changes with the levels of other factors [30].

Dye adsorption by an adsorbent in a batch system typically depends on various factors, such as solution pH, adsorbate concentration, adsorbent mass, contact time, and temperature. The optimization of all these variables using a univariate procedure is tedious because each variable (factor) is optimized by varying just one specific factor and keeping the others constant. Then, the best value attained for that specific factor is fixed, and the other factors are varied in turn [31]. The drawback of this one-factor process is that the best conditions cannot be reached because the interactional effects of the factors are ignored; in addition, it is not possible to predict whether the same optimization would be attained if the levels of other variables were changed. Additionally, the total number of experiments to be performed in the univariate procedure is much higher than that when using a statistical DOE [31].

In this work, the factors monitored were pH (X1), initial dye concentration (X2), adsorbent mass (X3) and contact time between MNSA and dye (X4) to determine the maximum q and % Rem. The experiments in Table 1 (n = 19) were carried out to obtain the two responses of the system; q was expressed in milligrams of dye per gram of adsorbent, and % Rem was expressed as a percentage. The definitions of the factors and the levels used in the complete design are presented in Table 1. The main and interaction effects, model coefficients, standard deviations, and probabilities for the full 24 factorial design for the responses of q and % Rem are presented in Table 2, Table 3, respectively.

Table 2

Factorial Fit: q versus pH, Co, m, t and central point.

Term	Effect	Coefficient	SE of coefficient	P
Constant		25.49 (β0)	0.6750	0.001
Main factors
pH (X1)	−38.77	−19.38 (β1)	0.6750	0.001
Co (X2)	6.569	3.285 (β2)	0.6750	0.040
M (X3)	−16.38	−8.191 (β3)	0.6750	0.007
t (X4)	−1.964	−0.9820 (β4)	0.6750	0.283
2-way interaction
pH⋅Co (X1X2)	−0.1920	−0.09600 (β5)	0.6750	0.900
pH⋅m (X1X3)	8.789	4.394 (β6)	0.6750	0.023
pH⋅t (X1X4)	−7.544	−3.772 (β7)	0.6750	0.031
Co⋅m (X2X3)	1.600.10−2	8.000.10−3 (β8)	0.6750	0.991
Co⋅t (X2X4)	−3.336	−1.668 (β9)	0.6750	0.132
m⋅t (X3X4)	−5.057	−2.528 (β10)	0.6750	0.064
3-way interaction
pH⋅Co⋅m (X1X2X3)	−3.204	−1.602 (β11)	0.6750	0.141
pH⋅Co⋅t (X1X2X4)	−4.056	−2.028 (β12)	0.6750	0.095
pH⋅m⋅t (X1X3X4)	9.954	4.977 (β13)	0.6750	0.018
Co⋅m⋅t (X2X3X4)	−6.268	−3.134 (β14)	0.6750	0.043
4-way interaction
pH⋅Co⋅m⋅t (X1X2X3X4)	10.47	5.235 (β15)	0.6750	0.016
Central point (cp)		−7.900	1.700	0.043
S = 2.701	R2 = 0.9984	R2adj = 0.9858

Estimated effects and coefficients for q (coded units). Full 24 factorial design. The effects and coefficients are given in coded units. All values are expressed with 4 significant digits, except probability (P), which is expressed with three decimal places.

Table 3

Analysis of variance factorial fit: q versus pH; Co, m, t, and central point.

Source	DF	Contribution	Adj. SS	Adj. MS	F-value	P-value
Model	16	99.84%	9213.30	575.83	78.94	0.013
Linear	4	78.82%	7273.34	1818.33	249.28	0.004
pH	1	65.15%	6011.91	6011.91	824.19	0.001
Co	1	1.87%	172.62	172.62	23.67	0.040
m	1	11.63%	1073.38	1073.38	147.15	0.007
t	1	0.17%	15.43	15.43	2.11	0.283
2-way interaction	6	7.41%	683.55	113.93	15.62	0.061
pH.Co	1	0.00%	0.15	0.15	0.020	0.900
pH.m	1	3.35%	308.97	308.97	42.36	0.023
pH.t	1	2.47%	227.63	227.63	31.21	0.031
Co.m	1	0.00%	0.00	0.00	0.00	0.991
Co.t	1	0.48%	44.52	44.52	6.10	0.132
m.t	1	1.11%	102.28	102.28	14.02	0.064
3-way interaction	4	7.16%	660.38	165.10	22.63	0.043
pH.Co.m	1	0.44%	41.06	41.06	5.63	0.141
pH.Co.t	1	0.71%	65.81	65.81	9.02	0.095
pH.m.t	1	4.30%	396.35	396.35	54.34	0.018
Co.m.t	1	1.70%	157.16	157.16	21.55	0.043
4-way interaction	1	4.75%	438.55	438.55	60.12	0.016
pH.Co.m.t	1	4.75%	438.55	438.55	60.12	0.016
Central point (cp)	1	1.71%	157.48	157.48	21.59	0.043
Error	2	0.16%	14.59	7.29
Total	18	100.00%

For the response q (Table 2), all the main factors were significant with a probability level P ≤ 0.05, except (X4). All the main effects and interactions that presented probabilities lower than 0.05 were significant (see Table 2). Regarding the interaction factors, two interactions of 2 factors, two interactions of 3 factors and one interaction of 4 factors were significant at the 5% significance level (P ≤ 0.05). The fit model presented an adjusted squared determination coefficient (R2adj) of 0.9858, fitting the statistical model very well.

Thus, q could be expressed as Eq. (4):

In Eq. (4), the values of the factors are coded, and the levels are valid only in the intervals described in Table 1 (from −1 to + 1). The uncertainty of this equation is only 1.42%, based on the R2adj. Positive coefficients mean that an increase in the levels of the corresponding factor led to an increase in q; in contrast, negative coefficients led to a decrease in the response (q) when the corresponding levels were increased.

To better evaluate each factor and its interactions, Fig. 4A presents the normal probability plot of standardized effects. This graph is divided into two regions: the region where the factors and their interactions presented negative effects (pH, m, X⋅t, pH⋅t, Co⋅m⋅t) and the region where the factors and interactions had positive effects (Co, pH⋅m, pH⋅m⋅t, pH⋅Co⋅m⋅t). All of these factors and interactions, which were represented as squares, were significant, and the terms fell outside the central line that crosses the zero value at the abscissa at a 50% probability. A circle represents the effects along this line, corresponding to the estimated errors of the effects, which were not significant (p ≥ 0.05, see Table 2). The analysis of variance of the factorial fit of q versus pH, Co, m, and t gave the contribution of each factor and its interaction as a percentage (see Table 3). Additionally, all factors and interactions with a probability ≤5% (P ≤ 0.05) were significant at the 95% probability level.

Fig. 4

Normal probability plot of standardized effects for (A) adsorption capacity (q) and (B) percent removal (% Rem).

By analysing the graph in Fig. 4A and the values in Table 2 and Table 3, it can be inferred that pH was the most critical variable in the overall adsorption procedure (65.15%). The negative coefficient of pH means that the adsorbance of the adsorbate by MNSA was favoured at low pH values (pH 2.0). An increase in pH led to a remarkable decrease in dye adsorption by the magnetic adsorbent. These results are in agreement with Royer et al. [32] and da Silva et al. [33]. For further optimization experiments, the pH was kept at 2.0 to prevent the leaching out of iron from the magnetic adsorbent at lower pH values [31].

The next most important factor for overall optimization of the batch system was m (11.63%). An increase in m led to a decrease in q, as expected [34]. This correlation occurred because an increase in mat a preset volume and concentration of dye leads to the non-saturation of adsorption sites as adsorption progresses; furthermore, the decrease in q may be due to particle aggregation resulting from the high m. Such aggregation would lead to a reduction in the total surface area of the adsorbent and an increase in the diffusional path length [34].

The third most important factor for overall optimization of the adsorption system was the interaction of four factors (pH⋅Co⋅m⋅t) (4.75%), which was more significant than the main factor Co (1.87%). This result rationalizes the benefits of using a factorial DOE rather than a conventional univariate process for adsorption method optimization [31] because this interactive relationship would not be identified in univariate optimization of a batch adsorption system. This interaction had appositive coefficient. The fourth most important factor for the overall optimization of the batch contact adsorption system was an interaction of three factors (pH⋅m⋅t) (4.30%), followed by the fifth most important factor, which was the interaction of two factors (pH⋅m) (3.35%); both factors had a positive coefficient. The sixth most important factor was the interaction of two factors (pH⋅t) (2.47%), with a negative coefficient. The seventh most important factor was Co(1.87%), which had a positive coefficient and was followed by an interaction of three factors (Co⋅m⋅t) (1.70%), which had a negative coefficient and was ranked eighth in relation to the overall optimization of the response (q).

For the response of % Rem (Table 4 and Table 5), the main factors that were significant at the 5% significance level (P ≤ 0.05) were pH (75.83% overall response) and Co(4.71%). Regarding the interaction factors, there was one interaction of 2 factors (pH⋅Co) (7.22%), one interaction of three factors (Co⋅m⋅t) (1.59%) and one interaction of four factors (pH⋅Co⋅m⋅t) (2.65%).

Table 4

Factorial fit: % Rem versus pH, Co, m, t and central point.

Term	Effect	Coefficient	SE of coefficient	P
Constant		33.53 (β0)	0.9140	0.001
Main factors
pH (X1)	−54.38	−27.19 (β1)	0.9140	0.001
Co (X2)	−13.553	−6.776 (β2)	0.9140	0.018
m (X3)	−6.273	−3.136 (β3)	0.9140	0.075
t (X4)	−2.414	−1.207 (β4)	0.9140	0.318
2-way interaction
pH⋅Co (X1X2)	16.78	8.390 (β5)	0.9140	0.012
pH⋅m (X1X3)	0.2750	0.1380 (β6)	0.9140	0.894
pH⋅t (X1X4)	−6.854	−3.427 (β7)	0.9140	0.064
Co⋅m (X2X3)	4.318	2.159 (β8)	0.9140	0.142
Co⋅t (X2X4)	−5.771	−2.886 (β9)	0.9140	0.087
m⋅t (X3X4)	−4.786	−2.393 (β10)	0.9140	0.120
3-way interaction
pH⋅Co⋅m (X1X2X3)	−4.425	−2.213 (β11)	0.9140	0.137
pH⋅Co⋅t (X1X2X4)	0.3740	0.1870 (β12)	0.9140	0.857
pH⋅m⋅t (X1X3X4)	7.374	3.687 (β13)	0.9140	0.056
Co⋅m⋅t (X2X3X4)	−7.884	−3.942 (β14)	0.9140	0.050
4-way interaction
pH⋅Co⋅m⋅t (X1X2X3X4)	10.16	5.081 (β15)	0.9140	0.031
Central point (cp)		−10.05	2.300	0.049
S = 3.656	R2 = 0.9983	R2 (adjusted) = 0.9846

Table 5

Analysis of variance factorial fit: % Rem versus pH, Co, m, t and central point.

Source	DF	Contribution	Adj. SS	Adj. MS	F-value	P-value
Model	16	99.83%	15569.1	973.1	72.78	0.014
Linear	4	81.70%	12742.0	3185.5	238.26	0.004
pH	1	75.83%	11826.6	11826.6	884.59	0.001
Co	1	4.71%	734.7	734.7	54.95	0.018
m	1	1.01%	157.4	157.4	11.77	0.075
t	1	0.15%	23.3	23.3	1.74	0.318
2-way interaction	6	10.35%	1613.9	269.0	20.12	0.048
pH.Co	1	7.22%	1126.3	1126.3	84.24	0.012
pH.m	1	0.00%	0.3	0.3	0.02	0.894
pH.t	1	1.20%	187.9	187.9	14.05	0.064
Co.m	1	0.48%	74.6	74.6	5.58	0.142
Co.t	1	0.85%	133.2	133.2	9.96	0.087
m.t	1	0.59%	91.6	91.6	6.85	0.120
3-way interaction	4	3.49%	545.0	136.2	10.19	0.091
pH.Co.m	1	0.50%	78.3	78.3	5.86	0.137
pH.Co.t	1	0.00%	0.6	0.6	0.04	0.857
pH.m.t	1	1.39%	217.5	217.5	16.27	0.056
Co.m.t	1	1.59%	248.6	248.6	18.60	0.050
4-way interaction	1	2.65%	413.0	413.0	30.89	0.031
pH.Co.m.t	1	2.65%	413.0	413.0	30.89	0.031
Central point (cp)	1	1.64%	255.1	255.1	19.08	0.049
Error	2	0.17%	26.7	13.4
Total	18	100.00%

The model had an R2 of 0.9983, thus fitting the statistical model very well.

Estimated effects and coefficients for % Rem (coded units). Full 24 factorial design. The effects and coefficients are given in coded units. All values are expressed with 4 significant digits, except probability (P), which is expressed with three decimal places.

Thus, % Rem could be expressed as Eq. (5):

In Eq. (5), the values of the factors are coded, and the levels correspond to the levels described in Table 1. The uncertainty of this equation is only 1.54%, based on R2adj.

Analysis of the graph in Fig. 4B and the values in Table 4, Table 5 shows that pH is the variable that presents the most relevant influence on the overall optimization of % Rem. Additionally, the negative coefficient of this variable indicates that an increase in pH would lead to a decrease in% Rem. As stated before, further experiments were carried out at pH 2.0. The second most important factor for optimization of the response was the interaction of pH⋅Co, which was more relevant to the response than the main factor Co. This information is beneficial for the optimization of the batch contact adsorption system and would not be obtained using univariate optimization. A small negative error in pH in conjunction with a small error in Co would lead to an expected increase in % Rem, which the user would not perceive during the optimization of batch adsorption using univariate analysis.

In contrast, when using a full factorial design, information about the interactions of factors can be obtained, as observed in this work.

The third most important factor in the optimization of the response (% Rem) was Co, which had a negative coefficient, meaning that an increase in Co leads to a decrease in % Rem, as is usually expected for any batch adsorption system [33], [34]. The fourth most important factor in the optimization of the response was the interaction of the four factors pH⋅Co⋅m⋅t, which has a positive coefficient, and the fifth factor was an interaction of three factors (Co⋅m⋅t). The factors m and t only appeared in the overall optimization of % Rem as parts of interaction factors; however, in the response of q, m had a negative coefficient.

Considering that two responses were used in this work to obtain a maximum q and% Rem, the desirability function of the DOE was performed. The desirability function is an optimization method that considers both responses (q and % Rem) to furnish values of variables that would increase both responses. Therefore, the desirability function is an arrangement of values intended to maximize each independent response. Using the desirability function, the optimized conditions were as follows: pH = 2.00; Co = 40.0 mg L−1; m = 30.0 mg; and t = 3.0 h. The desirability function (D) presents a value of 0.8554, which corresponds to an overall optimization of the two responses by 85.54%.

Conclusions

Magnetized activated carbon nanocomposite (MNSA) was successfully prepared using Nigella sativa waste (NSW) and was examined as an adsorbent for Coomassie brilliant blue in aqueous solution under conditions optimized using the design of experiments (DOE). The optimum conditions obtained from the desirability function were as follows: initial pH of adsorption 2.00; initial dye concentration of 40.0 mg/L; adsorbent mass of 30.0 mg; and contact time between the adsorbent and adsorbate of 3.0 h. The results of the present work suggest that agro-industrial wastes could be turned onto valuable, efficient and cost-effective adsorbents for wastewater treatment; furthermore, by applying a full factorial design, information about the interactions of the factors that affect the optimization of a suggested method could be obtained, as observed in this work. To continue this work, adsorption experiments will be performed using the conditions described above and applied to real wastewater samples.

Conflict of interest

The authors have declared no conflict of interest.

Compliance with Ethics Requirements

This article does not contain any studies with human or animal subjects.