Statistical optimization, kinetic, equilibrium isotherm and thermodynamic studies of copper biosorption onto Rosa damascena leaves as a low-cost biosorbent

Abstract

In this study, Rosa damascena leaf powder was evaluated as a biosorbent for the removal of copper from aqueous solutions. Process variables such as the biosorbent dose, pH, and initial copper concentration were optimized using response surface methodology. A quadratic model was established to relate the factors to the response based on the Box–Behnken design. Analysis of variance (ANOVA) was used to assess the experimental data, and multiple regression analysis was used to fit it to a second-order polynomial equation. A biosorbent dose of 4.0 g/L, pH of 5.5, and initial copper concentration of 55 mg/L were determined to be the best conditions for copper removal. The removal of Cu²⁺ ions was 88.7% under these optimal conditions, indicating that the experimental data and model predictions were in good agreement. The biosorption data were well fitted to the pseudo-second-order and Elovich kinetic models. The combination of film and intra-particle diffusion was found to influence Cu²⁺ biosorption. The Langmuir and Dubinin–Radushkevich isotherm models best fit the experimental data, showing a monolayer isotherm with a q_max value of 25.13 mg/g obtained under optimal conditions. The thermodynamic parameters showed the spontaneity, feasibility and endothermic nature of adsorption. Scanning electron microscopy, energy-dispersive X-ray spectroscopy, and Fourier transform infrared spectroscopy were used to characterize the biosorbent before and after Cu²⁺ biosorption, revealing its outstanding structural characteristics and high surface functional group availability. In addition, immobilized R. damascena leaves adsorbed 90.7% of the copper from aqueous solution, which is more than the amount adsorbed by the free biosorbent (85.3%). The main mechanism of interaction between R. damascena biomass and Cu²⁺ ions is controlled by both ion exchange and hydrogen bond formation. It can be concluded that R. damascena can be employed as a low-cost biosorbent to remove heavy metals from aqueous solutions.

Introduction

With the development of agriculture, industrial activities, and other human activities, various heavy metals have been released into water, and water resources have been severely contaminated¹. Heavy metal pollution has been a commonly researched topic for a long time because heavy metals are difficult to remove and are highly toxic². Copper and its composites are the most frequent heavy metal contaminants in the environment, according to the Environmental Protection Agency³. Wastewater from mining companies, tanneries, metal plating plants and refineries is the most prevalent source of copper⁴.

Copper is a trace metal that numerous enzymes require for catalysis in living organisms. High quantities of copper, however, may be highly poisonous and cause major health concerns. Ingestion of high levels of copper causes the copper to accumulate in the liver, which can lead to anemia, gastrointestinal issues, and renal difficulties⁵. As a result, research into low-cost alternatives to presently available processes has been required by the need for safe, more effective and less expensive approaches for removing copper ions from wastewater. Several strategies for the removal of heavy metals from wastewaters have been developed in recent years. Some of these approaches include solvent extraction, membrane filtration, chemical reduction and precipitation, coagulation and ion exchange. The primary drawbacks of these procedures include the need for significant amounts of chemicals, residual metal solubility, costly capital investment, high operating costs, and the formation of a large quantity of sludge⁶. Adsorption is a potential approach to processing and treating wastewater due to its cost and efficiency⁷. Recent research has shown that a variety of typical agricultural waste products, microorganisms, algae, and natural polymers are excellent biosorbents for heavy metal removal^8–10. Different parts of plants and their wastes are available and are more affordable than chemically modified products. As a result, the majority of adsorption research has focused on untreated plant products and wastes^11,12.

Roses are shrubs that are commonly cultivated worldwide. These decorative plants are also utilized in medicine, fragrances, and scented products. Rose water, rose oil, and rose waste biomass are the three major products of rose distillation¹³. Rose flower biomass has been examined as a biosorbent after distillation in a number of studies^13–16.

However, to the best of our knowledge, rose leaves have not been reported for use as waste biomass for the biosorption of copper ions. Therefore, in this study, Rosa damascena leaf powder was employed as a cost effective biosorbent to examine its efficiency in removing copper ions from aqueous solutions. A response surface methodology (RSM) was used to optimize the process variables and to analyze the influences of different factors on the examined response, providing significant advantages, as this methodology saved time, effort, and resources. In addition, RSM is more applicable since it can be used to predict and evaluate the interactive influences of different factors and depict their influence on a process^17–19. Three independent factors, including biosorbent dose, pH, and initial Cu²⁺ concentration, were optimized to maximize copper removal by Rosa damascena leaf powder. Furthermore, we assessed the efficiency of immobilized Rosa damascena biomass as a Cu²⁺ ion biosorbent. Kinetic, equilibrium, and thermodynamic investigations were carried out to study the nature of the biosorbent and the biosorption process. The biosorbent was characterized by SEM, EDX and FTIR.

Results and discussion

Effect of metal concentration

The initial metal concentration is a critical factor that influences the driving force of biosorption systems¹⁷. The data in Fig. 1a depict the influence of different metal concentrations (30–150 mg/L) on Cu²⁺ biosorption of onto the R. damascena biomass. The data showed that as the concentrations of Cu²⁺ increased from 60 to 150 mg/L, the copper removal declined from 84.0 to 46.3% (Fig. 1a) because at low Cu²⁺ concentrations, all active sites on the surface of R. damascena are vacant, but at high concentrations of Cu²⁺ ions, the number of binding sites is restricted. These binding sites are filled quickly, resulting in a significant reduction in Cu²⁺ biosorption. Several researchers have reported similar findings^20,21.

Figure 1.

Effect of (a) Initial Cu²⁺ concentration, and (b) Temperature on the biosorption of Cu²⁺ ions onto R. damascena leaves. Data is presented as average ± SE of three replicates.

Effect of temperature

The influence of temperature on Cu²⁺ ion removal by R. damascena leaf biomass was studied at three different temperatures (25, 35, and 45 °C; Fig. 1b). The data show that the removal of Cu²⁺ ions increased from 84.0 to 90.1% as the temperature was increased, showing that the biosorption process is endothermic. The highest removal of Cu²⁺ (90.1%) occurred at a high temperature (45 °C), which may be regarded as optimal for Cu²⁺ biosorption. Increases in adsorbate affinity for the surface of adsorbent, increases in adsorbent pore size, and increases in driving force to overcome the mass transfer resistance of the adsorbate between the adsorbent surface and aqueous solution may all contribute to the increased biosorption at higher temperatures²².

Box–Behnken experimental design

A Box–Behnken design (BBD) was utilized to decrease the number of tests and predict the best conditions for copper removal by R. damascena leaf powder. Seventeen experiments were carried out using a BBD with varied combinations of three parameters at three levels to maximize the removal of Cu²⁺ ions from aqueous solution. Table 1 illustrates the actual and predicted removal percentages of Cu²⁺ for the 17 runs of the design matrix. The results showed that the copper removal varied greatly depending on the independent parameters. The copper removal by R. damascena leaves varied between 44.25 and 87.68%. In run 4, with a biosorbent dose of 5 g/L, pH of 6, and initial Cu²⁺ concentration of 60 mg/L, the maximum copper removal was obtained with a value of 87.68%. Based on the Box–Behnken design results, a second-order polynomial equation was created to characterize the relationship between the independent parameters and the response, and the final model generated by backward elimination of insignificant parameters is as follows (Eq. (1)):

$${\text{Cu}}^{2+}\text{removal percentage}=57.2+10.54A+5.13B-4.28C+5.71A^2,$$ 1

where A, B and C are the biosorbent dose, pH and initial concentration of copper ions, respectively.

Table 1.

Box–Behnken design factors with coded and un-coded factors and data of the experimental response.

Run	Factor 1 A: biosorbent dose (g/L)	Factor 2 B: pH	Factor 3 C: initial Cu2+ conc. (mg/L)	Response: Cu2+ removal (%)	Predicted values
1	1 (− 1)	2 (− 1)	60 (0)	44.25	47.28
2	5 (+ 1)	2 (− 1)	60 (0)	64.03	68.36
3	1 (− 1)	6 (+ 1)	60 (0)	51.67	57.53
4	5 (+ 1)	6 (+ 1)	60 (0)	87.68	78.62
5	1 (− 1)	4 (0)	30 (− 1)	56.80	57.22
6	5 (+ 1)	4 (0)	30 (− 1)	77.90	78.31
7	1 (− 1)	4 (0)	90 (+ 1)	56.90	47.58
8	5 (+ 1)	4 (0)	90 (+ 1)	64.34	68.67
9	3 (0)	2 (− 1)	30 (− 1)	62.97	56.93
10	3 (0)	6 (+ 1)	30 (− 1)	68.43	67.18
11	3 (0)	2 (− 1)	90 (+ 1)	50.91	47.29
12	3 (0)	6 (+ 1)	90 (+ 1)	55.39	57.54
13–17*	3 (0)	4 (0)	60 (0)	60.20	57.24

*Mean value of five center point assays.

Table 2 summarizes the results of the analysis of variance (ANOVA) of the established model. The model was highly statistically significant, as evidenced by the high F value (10.26) and low p value (˂ 0.001). Furthermore, the F value of the lack of fit was 1.69, suggesting that the lack of fit is not significant (as the p value is larger than 0.05) in comparison to the true error, so the model validity may be affirmed²³.

Table 2.

Analysis of variance (ANOVA) of the response surface quadratic model of the biosorption of Cu²⁺ ions onto R. damascena.

Source	SS	df	MS	F value	p value Prob > F
Model	1423.4	4	355.8	10.26	0.0008*
Residual	416.4	12	34.70	–	–
Lack of fit	321.4	8	40.18	1.69	0.321**
Pure error	95.0	4	23.74	–	–
Correlation total	1839.8	16	–	–	–
R2 = 0.87	Adj. R2 = 0.80	Pred. R2 = 0.70	Adeq. precision = 9.8	CV% = 8.83	Mean = 59.92

Df degree of freedom, SS squares sum, MS mean sum of squares, CV Coefficient of variation.

*Significant at p ˂ 0.05.

**Not significant at p > 0.05.

The determination coefficient (R²) and adjusted R² were used to assess the model’s fit. The R² values ranged between 0 and 1.0, with values of approximately 1.0 indicating that the model is more accurate. However, under certain conditions, a larger R² value indicates that the model has a large number of insignificant variables, which indicates a poor response. As a result, the adjusted R² was developed, which adjusts the value of R² based on the number of variables and sample size in the model. The high R² value (0.87; Table 2) in this investigation implies that the actual and expected values are well correlated, and the model can explain 87.0% of the variability in the response. The adjusted R² of 0.80 agrees well with the R² value of 0.87, indicating that the model is valid. The actual and expected results were highly correlated, with the adjusted R² value being high and close to the predicted R² value (Table 2).

Moreover, the value of the variation coefficient as an estimate of the standard error was less than 10%, indicating that the model was reproducible²⁴. The signal-to-noise ratio indicated adequate precision. In this investigation, a ratio of 9.8 (higher than 4) was found to be sufficient²⁵. As a result, the model may be utilized to explore the design space. Therefore, biosorption studies may be conducted using this model.

Effect of interactive variables

In order to understand the impacts of the interactions of factors on the investigated response, 3-D response surface plots were made using the second-order Eq. (1) (Fig. 2). Each plot depicts the impact of two independent factors on the response within the examined ranges, while all other factors were held constant.

Figure 2.

3-D response surface plots for Cu²⁺ removal showing the interaction influences of (a) biosorbent dose and pH, (b) biosorbent dose and initial copper concentration, and (c) pH and initial copper concentration.

In Fig. 2a, 3-D plots depict the reciprocal interaction between the biosorbent dose and pH on Cu²⁺ removal by R. damascena leaf biomass. The data revealed that raising the biosorbent dose and pH improved Cu²⁺ biosorption by R. damascena leaves. The ANOVA findings also demonstrated that the biosorbent dose was significant and had a positive influence on the efficiency of copper removal (p = 0.0003; Table 3) in linear term. The number of active binding sites for the biosorption process is determined by the biosorbent dose²⁶. As the biosorbent dose was increased, the number of binding sites on the surface of R. damascena leaves rises, resulting in a higher percentage of copper removal²⁶. The elimination of copper by R. damascena leaves is also pH-dependent. The speciation of ions in aqueous solution and the dissociation state of biosorbent’s superficial functional groups are both affected by pH¹⁷. The pH exhibited a significant positive influence on the removal of copper by R. damascena leaves in linear term, according to the ANOVA results (Table 3). When the pH was raised from 2.0 to 6.0, the biosorption of Cu²⁺ increased. However, copper biosorption onto R. damascena leaves was minimal at lower pH. However, when the pH was 6.0, the maximum removal efficiency was observed because the surface charge of the biomass is positive at lower pH, which limits cation biosorption. Additionally, H⁺ ions compete with copper ions for active sites, leading to reduced biosorption. The competitive impact of H⁺ ions and electrostatic repulsions between cations and surface sites reduced as the pH was increased. As a result, metal biosorption also increased²⁷. Fawzy²⁰ stated that a pH of 5.0 was the most effective pH for copper removal by Codium vermilara.

Table 3.

Analysis of variance (ANOVA) for the coefficients of the quadratic model of the biosorption of Cu²⁺ ions onto R. damascena.

Model term	CE	df	SE	F value	p value Prob > F
Intercept	57.24	1	1.96	–	–
A-Biosorbent dose	10.54	1	2.08	25.63	0.0003
B-pH	5.13	1	2.08	6.06	0.03
C-initial Cu2+ conc.	− 4.82	1	2.08	5.36	0.039
A2	5.71	1	2.86	3.98	0.069

CE coefficient estimate, df degree of freedom, SE standard error.

Figure 2b depicts the mutual impacts of the biosorbent dose and initial copper concentration on the effectiveness of copper removal by R. damascena leaves.

When the biosorbent dose was increased from 1 to 5 g/L, the copper removal efficiency increased. More binding sites on the surface of R. damascena leaves become available to the copper ions as the biosorbent dose increases, resulting in enhanced removal efficiency. At a biosorbent dose of 5 g/L, the optimal removal effectiveness of 79% could be achieved. Generally, a higher biosorbent dose and lower copper concentrations improved the biosorption process²⁸.

As a result, raising the concentration of copper ions had a significant negative impact on Cu²⁺ ion removal (Table 3). Because more copper ions from the solution connected with the binding sites at lower copper concentrations, the biosorption of Cu²⁺ ions gradually increased; however, as the concentrations of copper were increased, biosorption was reduced due to biosorbent site saturation, and a large number of ions competed for the residual binding sites in the biosorbent.

The joint influence of pH and initial Cu²⁺ concentrations on metal ion removal was also investigated in the pH range of 2–6 and initial copper concentrations of 30–90 mg/L, as shown in Fig. 2c. The findings revealed that the removal of copper ions decreases as the pH is decreased. ANOVA revealed that the biosorbent dose was the most statistically significant factor that influenced the removal of copper (p = 0.0003), followed by pH (p = 0.03) and initial copper concentration (p˂ 0.05; Table 3).

Validation of the optimized variables

The goal of the optimization was to optimize the independent parameters of Cu²⁺ ion elimination by R. damascena leaf powder. The aim was to optimize the copper removal efficiency to achieve the maximum rate of Cu²⁺ removal. The average Cu²⁺ removal efficiency was compared to the expected value through experiments conducted in triplicate under optimized conditions. With a biosorbent dose of 4.0 g/L, pH of 5.5, and initial copper concentration of 55 mg/L, the highest expected Cu²⁺ elimination by R. damascena biomass was achieved. The experimentally observed copper removal efficiency (88.7%) was found to be in accordance with the expected value (87.4%) calculated by the design expert software, implying that the optimized conditions were ideal.

Effect of contact time and kinetic models

The impact of contact time on Cu²⁺ ion biosorption was used to evaluate the kinetics. Copper biosorption was examined under the optimal conditions of a 4.0 g/L biosorbent dose, pH 5.5, and an initial Cu²⁺ concentration of 55 mg/L by varying the biosorption time from 0 to 150 min (Fig. 3a). In the first 30 min, the rate of Cu²⁺ ion elimination was obviously fast. However, after equilibrium was reached, the biosorption efficiency increased until it was steady, and within 90 min, over 85.5% of the total metal was eliminated. The rates of adsorption and desorption were in dynamic equilibrium, and no additional biosorption was observed after this optimal equilibrium duration²⁹. Because copper ions came into contact with unoccupied surface biosorption sites, the biosorption of copper was initially quicker; however, after adsorption proceeded at equilibrium for 90 min, the biosorption sites became saturated, and no further biosorption occurred³⁰.

Figure 3.

(a) Effect of contact time, (b) Pseudo-first-order plot, (c) Pseudo-second-order plot, (d) Elovich plot, (e) Intra-particle diffusion plot, and (f) film diffusion plot for the biosorption of Cu²⁺ ions onto R. damascena leaves. Data is presented as average ± SE of three replicates.

Various kinetic models can be used to explain the mechanism and rate of metal ion sorption³¹. The biosorption kinetics of copper ions on R. damascena leaf biomass was studied using the pseudo-first-order, pseudo-second-order, Elvoish, intra-particle and film diffusion models.

Pseudo-first-order kinetic model

This model describes the adsorption of one adsorbate molecule onto one active site of the biosorbent. It is expressed as follows:

$$Log\left(q_e,-,q_t\right)=Log{q}_e-\frac{K_{1}t}{2.303},$$ 2

where q_e and q_t (mg/g) represent the quantity of copper ions absorbed by the biomass of R. damascena at equilibrium and at any time, respectively, and K₁ (min⁻¹) represents the rate constant of the pseudo-first-order model.

The constants K₁ and q_e were estimated from the slope and intercept by plotting log (q_e − q_t) vs. time, respectively (Fig. 3b).

The high value of the determination coefficient (R² = 0.980) indicates that the experimental results accurately fit the pseudo-first-order model for describing copper ion biosorption kinetics. However, high ∆q_e and X² values (23.3 and 1.02, respectively; Table 4) suggested that the pseudo-first-order kinetic model does not exhibit good regression. In addition, the difference between the copper ion quantity biosorbed onto the R. damascena surface estimated by experiments (q_{e exp}.; 17.1 mg/g) and the modeled value (q_{e calc}.; 13.4 mg/g) were larger. This result suggests that the biosorption process involved both the copper ions and biosorbent³². Therefore, the pseudo-first-order model is unable to describe the experimental data of Cu²⁺ biosorption onto the R. damascena biomass. The sorption kinetics of various metal ions onto various adsorbents has been described with similar findings^15,33,34.

Table 4.

Kinetic model parameters of the biosorption of Cu²⁺ ions onto R. damascena.

Parameters		Values
Experimental data	qe (exp.) (mg/g)	17.1
Pseudo-first order	qe (cal.) (mg/g)	13.4
	k1 (min−1)	0.029
	∆qe	23.3
	X2	1.02
	R2	0.980
Pseudo-second order	qe (cal.) (mg/g)	18.6
	k2 (g/mg min)	0.005
	h (g/mg min)	1.55
	∆qe	12.25
	X2	0.12
	R2	0.983
Elovich	α (g/mg min)	1.30
	β (g/mg)	0.303
	∆qe	3.53
	X2	0.192
	R2	0.971
Intra-particle diffusion	Ki (mg/g min0.5)	0.22
	Ci (mg/g)	6.25
	R2	0.801
Film diffusion	Df	0.001
	R2	0.821

The rate constant of pseudo-first-order (K₁ = 0.029 min⁻¹; Table 4) is not a quantifiable value that can clarify the rapid equilibrium of the biosorption of Cu²⁺ ions onto the R. damascena leaf surface reported within 30 min. As a result, this model was shown to be inadequate for accurately modeling copper biosorption by R. damascena biomass.

Pseudo-second-order kinetic model

In the pseudo-second-order kinetic model, chemical adsorption, which includes the exchange or sharing of electrons between the adsorbate and the adsorbent, controls the process of adsorption. This model can be described as follows:

$$\frac{t}{q_t}=\frac{1}{K_2{q}_e^2}+\frac{t}{q_e},$$ 3

where K₂ is the pseudo-second-order rate constant (g/mg min), which may be used to calculate the initial rate of biosorption (h; g/mg min).

$$h=K_2{q}_e^2.$$ 4

The kinetic constants K₂ and q_e were calculated from the intercept and slope of t/q_t against t plot, respectively (Fig. 3c).

The rate constant of pseudo-second-order (K₂) and the initial rate of adsorption (h) were 0.005 and 1.55 g/mg min, respectively (Table 4). At the beginning of the biosorption process, the h value indicated the rapid biosorption of copper ions. The high determination coefficient (R² = 0.983) and the low values of ∆q_e and X² (12.25 and 0.12, respectively; Table 4) indicated that the pseudo-second-order model best fit the experimental data for Cu²⁺ ion biosorption on the R. damascena leaf surface. Additionally, the experimental q_e (17.1 mg/g) was relatively similar to the calculated q_e (18.6 mg/g). Therefore, the pseudo-second-order model was chosen because it had the best fit, demonstrating significant interactions between the adsorbate and the adsorbent and indicating the occurrence of copper chemisorption on the surface of the R. damascena leaves. The results of several studies support the pseudo-second-order model for the adsorption of copper ions onto different biosorbents, including studies on the adsorption of Cu²⁺ onto activated rubber wood sawdust³⁵, Tectona grandis leaf³⁶, sour orange residue³⁷, banana trunk fiber³⁸, sulfur-modified bamboo powder³⁹, and Platanus orientalis leaf powder⁴⁰.

Elovich model

The Elovich model is utilized to explain the kinetics of chemical adsorption of a gas onto solid adsorbents, but it has been proven to be effective in describing various types of adsorption. The Elovich model can be represented by the following equation:

$$q_t=\frac{1}{\beta }\ln \left(\alpha \beta \right)+\frac{1}{\beta }\ln \left(\mathrm{t}\right),$$ 5

where α (mg/g min) represents the initial rate of sorption, and β (g/mg) is a constant that represents desorption.

To study the mechanism of Cu²⁺ biosorption, the experimental data were fitted to the Elovich kinetic model (Fig. 3d). A graph of q_t versus lnt was plotted, and the Elovich constants (α and β) were determined from the intercept and slope, respectively. The extent of chemisorption is proportional to the value of α. The high value of the Elovich constant (α = 1.3 g/mg min; Table 4) implies that chemisorption is the rate-limiting stage and biosorption proceeded via a pseudo-second-order mechanism.

The lower the value of the Elovich constant β is, the lower the chemisorption activation energy, implying that adsorption occurs quickly⁴¹. In the current investigation, the β value was fairly low (0.303 g/mg), suggesting a low activation energy of chemical adsorption. In addition, the high value of the determination coefficient (R² = 0.971) and the low ∆q_e and X² values (3.53 and 0.192, respectively; Table 4) show that the experimental data fit the Elovich kinetic model well.

From the previous data, it can be concluded that, the ∆q_e and X² values were found to be smaller for the pseudo-second-order and Elovich kinetic models; with higher R² values than to those of the pseudo-first-order. Thus, the pseudo-second-order and Elovich kinetic models are the best fit models for the biosorption of copper ion onto the R. damascena leaves.

Intra-particle and film diffusion models

The mechanism of diffusion influencing the Cu²⁺ biosorption process was also evaluated by intra-particle and film diffusion models⁴².

The intra-particle diffusion kinetic model is related to adsorbate diffusion to the inner pores as the rate-controlling step, which is represented by Eq. (6):

$$q_t=K_i{t}^{1/2}+C_i,$$ 6

where K_i denotes the intra-particle diffusion rate constant (mg/g min^0.5) and C_i denotes the intercept.

The film diffusion model is represented by the following Eq. (7):

$$-\log (1-\left(\frac{q_t}{q_e}\right)=D_f·t,$$ 7

where D_f is the film diffusion rate constant (min^-1).

The trendline of the linear plot in Fig. 3e does not pass through the origin, proposing that intra-particle diffusion is not the sole rate-limiting stage of biosorption. Figure 3e also exhibited the multilinearity of the plot, which has two sections. The first section shows that Cu²⁺ ions are transferred from the solution to the external surface of the R. damascena biomass via film diffusion. Moreover, the film diffusion plot of − log (1 − (q_t/q_e)) against time (Fig. 3f) nearly passes through the origin with an intercept of approximately zero, demonstrating that film diffusion plays a significant role in Cu²⁺ ion biosorption onto the surface of R. damascena leaves. The second part describes the additional Cu²⁺ ion biosorption on the internal pores of the R. damascena leaf surface, where intra-particle diffusion is the rate-limiting stage⁴³. This result revealed that external diffusion in the film controls the biosorption of copper ions onto R. damascena biomass, followed by the intra-particle diffusion model. The high value of the intercept (C_i, 6.25 mg/g; Table 4) might be due to increased boundary layer thickness, increased internal mass transfer, and reduced external mass transfer³⁰.

Equilibrium isotherms

Under certain experimental conditions, the adsorption isotherm represents the equilibrium correlation between the amounts of ions adsorbed by the biosorbent and the metal ion concentration in the solution⁴⁴.

Biosorption equilibrium isotherms were obtained under optimized conditions by BBD. The Langmuir, Freundlich, Temkin, Dubinin–Radushkevich and Jovanovic isotherm models were used to describe and estimate the experimental data of copper biosorption.

Langmuir model

This model implies that metal ions are adsorbed by monolayer adsorption on a homogeneous surface with no interaction between the adsorbed metal ions. The Langmuir model is represented in linear form as follows:

$$\frac{C_{\mathit{eq}}}{q_e}=\frac{1}{q_{\mathit{max}}b}+\frac{C_{\mathit{eq}}}{q_{\mathit{max}}},$$ 8

where q_max is the maximal sorption quantity (mg/g) required to produce full monolayer coverage on R. damascena’s surface at a high ion equilibrium concentration (C_eq; mg/L) and b is the constant of the Langmuir model, which is associated with binding site affinity⁴⁵.

The high value of R² (0.979; Table 5) indicates that the Langmuir model suitably describes the biosorption process, which is based on the homogeneous distribution of active sites on the surface of the R. damascena leaf.

Table 5.

Isotherm model parameters of the biosorption of Cu²⁺ ions onto R. damascena.

Isotherms	Parameters	Values
Langmuir	qmax (mg/g)	25.13
	b (L/mg)	0.095
	RL	0.062–0.201
	R2	0.979
Freundlich	1/n	0.313
	Kf (L/mg)	5.98
	R2	0.735
Temkin	A (L/mg)	1.9
	b (J/mol)	551.4
	R2	0.807
Dubinin–Radushkevich	qo (mg/g)	21.1
	β × 10–6(mol2/J2)	6.0
	E (KJ/mol)	9.13
	R2	0.926
Jovanovic	qmax (mg/g)	11.17
	KJ (L/g)	0.01
	R2	0.589

When C_eq/q_e was plotted versus C_eq, a straight line was formed, and the slope and intercept were used to determine the q_max and b values, respectively (Fig. 4a). The greater value of the Langmuir constant (b = 0.095 L/mg) suggested a stronger interaction with the functional groups on the R. damascena leaf surface. Furthermore, R. damascena biomass had a maximum biosorption capacity (q_max) of 25.13 mg/g. A similar pattern was achieved by using numerous equilibrium isotherm models, with the Langmuir model having the best fit^34,46.

Figure 4.

Biosorption isotherms of copper ions onto R. damascena leaves, including (a) Langmuir, (b) Freundlich, (c) Temkin, (d) Dubinin–Radushkevich and (e) Jovanovic models. Data is presented as average ± SE of three replicates.

A dimensionless separation factor (R_L) may be used to determine the shape and favorability of the biosorption process, which can be computed using Eq. (9):

$$R_L=\frac{1}{1+b{C}_0},$$ 9

where C_o is the metal ion concentration (mg/L). The type of Langmuir isotherm was determined by the R_L value, which was either unfavorable (R_L > 1), linear (R_L = 1), irreversible (R_L = 0) or favorable (0 ˂ R_L ˂ 1)⁴⁰. A value of R_L between 0 and 1 indicates that adsorption is favorable. In the current study, the R_L value was determined to be 0.062–0.201, showing that copper biosorption onto the leaves of R. damascena is favorable (Table 5).

Freundlich isotherm model

The adsorption of ions on an energetically heterogeneous surface is described by the Freundlich isotherm model. The following equation represents the linearized Freundlich model (10):

$$\text{ln}{q}_e=\text{ln}{K}_f+\frac{1}{n}\text{ln}{C}_{\mathit{eq}},$$ 10

where K_f is the Freundlich isotherm constant, which reflects the sorption capacity, and n is the Freundlich constant correlated to the adsorption intensity.

The intercept and slope of the plotting of ln q_e against lnC_eq are used to calculate the K_f and 1/n values, respectively (Fig. 4b). The greater the K_f value, the more biosorbent may be loaded. In addition, adsorption is favorable when the 1/n value is between 0.1 and 1.0⁴⁷. In this study, the value of 1/n was lower than 1.0 (0.313; Table 5), indicating that biosorption of copper ions by R. damascena leaves is favorable. The low value of the determination coefficient (R² = 0.735) suggested that the Freundlich model is not appropriate for describing the experimental data of the biosorption process (Table 5).

Temkin model

The Temkin model represents adsorption with a uniform distribution of binding energies up to the maximal binding energy, as shown in the following equation⁴⁸.

$$q_e=B\text{ln}A+B\text{ln}{C}_{\mathit{eq}},$$ 11

$$B=\frac{\mathit{RT}}{b},$$ 12

where A (L/mg) represents the equilibrium binding constant, b (J/mol) is the constant of the Temkin isotherm model, and B (J/mol) is the heat of sorption constant.

The Temkin model constants (A and b) were determined using the intercept and slope of the q_e versus lnC_eq plot (Fig. 4c). The high b value (551.4 J/mol; Table 5) indicates that the adsorbate and biosorbent surface interact strongly⁴⁹. The Temkin model fails to fit the results reported for copper biosorption by R. damascena leaves, as the R² value was low (0.807; Table 5).

Dubinin–Radushkevich model (D–R)

The D–R model describes whether biosorption occurs via a chemical or physical process and the mean sorption energy of the process. The D–R model is calculated from the following equations:

$$\text{ln}{q}_e=\text{ln}{q}_0-\beta {\epsilon }^2,$$ 13

$$\epsilon =RT\left(1,+,\frac{1}{C_{\mathit{eq}}}\right),$$ 14

$$E=\sqrt{1/2}\beta ,$$ 15

where q_o is the theoretical maximum capacity (mg/g), β is the constant of the D–R model associated with the mean free energy (mol²/J²), ε is the Polanyi potential, T (K) is the absolute temperature, R (8.314 J/mol K) is the gas constant, and E (kJ/mol) is the mean adsorption energy.

Table 5 shows the values of the D–R model parameters. The mean adsorption energy of the system (E) was determined using the parameter β (Eq. (15)). In addition, the chemical and physical characteristics of the adsorption process may be assessed by the mean adsorption energy.

Physical sorption is defined as a value of E less than 8 kJ/mol, whereas chemical sorption is defined as a value of 8 to 16 kJ/mol³⁰. The value of E (9.13 kJ/mol) indicates that R. damascena removed copper ions mostly by chemisorption. This result is also consistent with predictions from the pseudo-second-order and Elovich kinetic models. D–R isotherm model may best describe the experimental data of copper ion biosorption onto the R. damascena leaf surface, according to the R² value (0.926; Fig. 4d; Table 5).

Jovanovic model

The Jovanovic model is an approximation for localized monolayer adsorption without lateral contacts that is comparable to the Langmuir model. This model is determined as follows:

$$\text{ln}{q}_e=\text{ln}{q}_{\mathit{max}}{-K_{J}C}_{\mathit{eq}},$$ 16

where K_J: the Jovanovic isotherm constant. The values of q_max and K_J were calculated from the intercept and slope of linear plot of lnq_e versus C_eq (Fig. 4e).

The maximum biosorption capacity determined from the Jovanovic equation (q_max = 11.17 mg/g; Table 5) differs from the experimentally measured value (q_max = 23.18). Furthermore, the lower determination coefficient (R² = 0.589) found in this investigation revealed that there is a lateral interaction and no mechanical contact between the R. damascena leaf biomass and Cu²⁺ ions. As a result, Jovanovic isotherm model has a lower approach to saturation compared to Langmuir model as stated by Al-Ghouti and Da’ana⁵⁰.

Thermodynamic studies

The Gibbs free energy (∆G), enthalpy (∆H) and entropy (∆S) are all thermodynamic parameters that describe the spontaneity of a biphasic adsorption process⁵¹.

The following equations demonstrate the relationship between the thermodynamic parameters and the absolute temperature (T)⁵².

$$\mathrm{\Delta }G=\mathrm{\Delta }H-T\mathrm{\Delta }S,$$ 17

$$\mathrm{\Delta }G=-RT\text{ln}{K}_C,$$ 18

$${\mathit{LnK}}_C=\frac{\mathrm{\Delta }S}{R}-\frac{\mathrm{\Delta }H}{\mathit{RT}},$$ 19

where Kc is the thermodynamic equilibrium constant.

At the experimental temperatures, the values of ∆G were negative (Table 6), indicating that biosorption was feasible and spontaneous⁵⁰. Furthermore, a reduction in the values of ∆G with rising temperature indicates that adsorption became more feasible, resulting in the strengthening of bonds established between the binding sites on the R. damascena leaf surface and the Cu²⁺ ions¹⁹.

Table 6.

Thermodynamic values of Cu²⁺ ion biosorption onto R. damascena.

Temperature (K)	ΔG (KJ/mol)	ΔH (KJ/mol)	ΔS (KJ/mol)	R2
298	− 1.39	21.7	0.077	0.982
308	− 2.00
318	− 2.94

The changes in enthalpy and entropy were evaluated from the slope and intercept of the ln K versus 1/T plot, respectively (Fig. 5).

Figure 5.

Plot of 1/T against lnK for copper ion biosorption onto R. damascena.

The positive ∆H of 21.7 kJ/mol for copper biosorption by R. damascena leaves indicates that the biosorption process was endothermic. This result indicates that higher temperatures promote biosorption. In addition, the positive ∆S indicated that the biosorption of copper ions onto the R. damascena leaf surface occurred as a result of randomization at the adsorbate-biosorbent interface⁵³.

Characterization of R. damascena leaf surface

Scanning electron microscopy (SEM)

The morphology of the R. damascena leaf surface before and after Cu²⁺ biosorption was examined by SEM (Fig. 6). SEM micrographs demonstrated that the surface morphology of the R. damascena leaf before and after Cu²⁺ biosorption was different.

Figure 6.

SEM images of R. damascena leaves (a) before and (b) after Cd²⁺ biosorption.

The SEM micrographs of the R. damascena leaf surface before copper biosorption revealed a rough surface with substantial porosity (Fig. 6a). This rough flaky surface allowed copper ions to adhere more easily, improving biosorption. The biosorbent's porosity also enables it to interact with the adsorbate more quickly⁵⁴. However, the SEM images collected after the biosorption of copper revealed a flatter biosorbent surface, appearance of discrete lumps and fewer large spaces (Fig. 6b). These morphological alterations verified the interaction of copper ions with the functional groups on the R. damascena leaf surface²⁰.

Energy dispersive X-ray spectroscopy (EDX)

EDX analysis was used to determine the adsorbent surface composition and to confirm the presence of copper ions on the R. damascena leaf surface. Figure 7 displays the EDX spectra of R. damascena biomass. The EDX spectra showed that the R. damascena leaves consist mostly of C and O, with traces of additional elements, including Na, Mg, Cl, K, Si and Ca that were exchanged or removed during biosorption (Fig. 7a,b). This result shows that the biosorption of Cu²⁺ ions was caused by ion exchange. After biosorption, the EDX spectra of R. damascena biomass exhibited an additional Cu²⁺ peak (1.09%) on the R. damascena leaf surface, demonstrating that the biomass of R. damascena participates in the biosorption of Cu²⁺ ions from solution (Fig. 7b). In this regard, El-Naggar et al.⁵⁵ observed that a distinctive copper peak appeared following contact with copper.

Figure 7.

EDX images of R. damascena leaves (a) before and (b) after Cd²⁺ biosorption.

Analysis of the Fourier transform infrared spectra (FT-IR)

The functional groups found on the surface of biosorbent biomass play a significant role in the process of adsorption. Heavy metal biosorption has been related to various functional groups, such as sulfonate, sulfhydryl, amine, carboxyl, hydroxyl, carbonyl, and others⁵⁶. Figure 8a,b displays the FT-IR spectra of R. damascena leaves before and after copper biosorption.

Figure 8.

FTIR spectra of R. damascena leaves (a) before and (b) after Cd²⁺ biosorption.

The presence of a wide absorption peak at approximately 3421–3425 cm⁻¹ is allocated to O–H stretching of hydroxyl radicals of polysaccharides or water⁵⁷ and to N–H stretching of proteins (amide A)⁵⁸. Functional groups such as O–H and N–H are commonly present in natural cellulose and proteins found in plant cell walls⁵⁹. The O–H stretching vibration of the carboxylic acid might be represented by the bands at 2921 cm⁻¹ and 2922 cm⁻¹⁵⁹. These bands indicate the presence of an acidic group, such as –COOH, in the biosorbent cell wall; this group serves as a hyperchemical group for the adsorption of various multivalent metal ions⁶⁰. The absorption bands at 2852 cm⁻¹ and 2853 cm⁻¹ are attributed to stretching of C–H, more specifically to the C–H stretching vibrations of lipids⁶¹. The C=O stretching of amide I, which is related to proteins, is shown by the absorption peak at approximately 1654 cm⁻¹⁶². The appearance of new absorption bands at 1546 cm⁻¹ and 1460 cm⁻¹ after copper was biosorbed onto the surface of the R. damascena leaf might be due to C=O stretching vibrations of different carboxylic and amide (I, II) groups, respectively⁶³. The protein band spectrum identified at 1240 cm⁻¹ on the leaf surface was caused by the P=O asymmetric stretching vibration⁶⁴. The absorption peak at approximately 1160 cm⁻¹ detected only on the R. damascena leaf surface following copper biosorption is related to C–O–C stretching of polysaccharides from carbohydrates⁵⁷. Furthermore, after copper biosorption, the peak at 878 cm⁻¹ shifted to 893 cm⁻¹, indicating the binding of copper ions to the amine group on the leaf surface. The bands found only at 670 and 593 cm⁻¹ on the R. damascena leaf surface after copper biosorption may be associated with the compounds of organic halide⁵⁶. From Fig. 7, it can be observed that the R. damascena leaf biomass included several functional chemical groups, such as carbonyl groups, acids, phosphates, amides, hydroxyl groups, halides, carboxyl groups, and amine groups. They might compensate for the biosorption of copper ions from the aqueous solution onto the R. damascena leaf surface.

Copper removal by immobilized R. damascena biomass

The results in Fig. 9 show that the Ca-alginate-immobilized R. damascena leaves removed 90.7% of copper ions after 120 min under the conditions optimized by BBD, including the biosorbent dose (4 g/L), pH (5.5) and initial copper concentration (55 mg/L); this removal was higher than the removal achieved when a nonimmobilized biosorbent was used (85.3%). Various studies have found that immobilized biosorbents are a more straightforward approach for recovering and removing heavy metals from wastewater than free biosorbents^65,66. For example, Ansari et al.¹⁵ reported that immobilized rose waste is more effective at absorbing Pb²⁺ from aqueous solutions than free biomass. Ca-alginate-immobilized Fucus vesiculosus is also an effective biosorbent for copper, lead, and cadmium according to Mata et al.⁶⁷, and it occasionally has greater biosorption efficacy than free alga or even alginate alone. According to Davis et al.⁶⁸, the metal ion affinity for alginate is proportional to the quantity of guluronic acid and other uronic acids present. These acids are responsible for the biosorption of heavy metals since they include the majority of the carboxyl groups in alginate. Furthermore, the “egg-box” structure of the gels, as well as the crosslinking between the carboxyl groups and metal ions, have been linked to alginate’s metal selectivity. This selectivity is determined by the stereochemical environment created by the structure of the gel. Therefore, R. damascena immobilized in Ca-alginate has great potential to adsorb heavy metals from wastewater.

Figure 9.

Copper ion removal by Ca–alginate-immobilized R. damascena.

Mechanisms of biosorption

The mechanisms of biosorption for heavy metals include surface precipitation, chelation, complexation, ion exchange, electrostatic interaction, or a combination of these mechanisms depending on the biosorbent used and the conditions of solution⁶⁹. Ion exchange was suggested as a main mechanism for copper ion biosorption onto the R. damascena biomass⁷⁰. Light metal ions such as Ca²⁺, Mg²⁺, Na⁺ and K⁺ were described to be involved in the process of ion exchange owing to a poor connection with the biomass of R. damascena in comparison to the heavy metals⁷⁰. Moreover, functional groups containing oxygen and/or nitrogen, such as COOH, OH, and NH₂, help biosorb Cu²⁺ ions by forming hydrogen bonds between the surface of R. damascena biomass and Cu²⁺ ions. These findings were supported by the FT-IR analysis because of the shift in the wavenumbers of the COOH, OH, and NH₂ groups following Cu²⁺ ion biosorption (Fig. 8a,b). The intermolecular hydrogen bonding between the biomass of R. damascena and Cu²⁺ ions enhances the biosorption process. The formation of complexes with functional groups on the biosorbent through electrostatic interactions and ion exchange is also a possible mechanism for the biosorption of Cu²⁺ on R. damascena biomass.

SEM and EDX analyses were obtained after adsorption to acquire a better understanding of the Cu²⁺ biosorption mechanism by the biomass of R. damascena. The SEM analysis displays that the biomass of R. damascena is porous with numerous rough pores. The biosorption of Cu²⁺ takes place in the pores of the R. damascena biomass. In a comparison of the EDX analyses of R. damascena before and after Cu²⁺ ion biosorption (Fig. 7a,b), significant alterations were found along with the appearance of an additional Cu²⁺ peak, indicating that the R. damascena biomass was transformed after adsorption. As a result, all of these findings suggest that the biosorption of Cu²⁺ onto R. damascena biomass can be accomplished by ion exchange and hydrogen bond formation mechanisms.

Comparison of biosorption capacity

The maximum biosorption capacity of Cu²⁺ ions by various biosorbents was compared with that observed in the current investigation. Table 7 shows that R. damascena leaves have a higher biosorption capacity for copper removal than most of the biosorbents previously described in the literature^{20,34,71–77}. The wide availability of Rosa damascena leaf wastes and their low cost are added advantages for their selection by numerous industries.

Table 7.

Maximum biosorption capacity of Cu²⁺ ion by low-cost sorbents.

Biosorbent used for Cu(II)	qmax (mg/g)	References
Codium vermilara	14.4	20
Bael flowers	23.14	34
Sago waste	12.4	71
Myriophyllum spicatum	10.37	72
Wheat shell	10.84	73
Caulerpa lentillifera	5.57	74
Lentil shell	8.98	75
Cinnamomum camphora	16.76	76
Coconut shell	19.89	77
Neem leaves	17.49	77
Rosa damascena leaves	25.13	Present study

Conclusions

Heavy metals, such as copper, are present in high concentrations in certain industrial effluents, posing serious health and environmental risks. Biosorption is a biotechnological approach to heavy metal ion removal from contaminated aquatic environments. The aim of the current investigation was to optimize the process variables for maximal copper removal from aqueous solution using statistical design. The Box–Behnken experimental design combined with response surface methodology has been shown to be an effective method for maximizing the removal of copper ions from solution using R. damascena leaves because they require a decreased number of experimental tests, result in the most efficient conditions, and maintain the accuracy of the predicted response. ANOVA, with its low P value, high F value, and determination coefficient, showed that the developed model represents the experimental data with high accuracy. The maximum removal percentage of Cu²⁺ ions (88.7%) was reached under the optimal conditions of a biosorbent dose of 4.0 g/L, pH of 5.5, and initial copper content of 55 mg/L. The pseudo-second-order and Elovich kinetic models were best fit to the experimental data. In addition, the liquid film diffusion model initially describes copper biosorption onto the R. damascena surface, followed by the intra-particle diffusion model. Equilibrium isotherm studies demonstrated that the Langmuir and D–R isotherm models could describe Cu²⁺ biosorption better than the Freundlich, Temkin and Jovanovic models, with the highest monolayer biosorption capacity of 25.13 mg/g, suggesting chemical interactions between the metal ions and biosorbent. Thermodynamic parameters such as Gibbs free energy, enthalpy, and entropy showed that the biosorption process is spontaneous, feasible and endothermic. After biosorption, SEM and EDX spectroscopy indicated noticeable alterations in the properties of the R. damascena leaf surface. In addition, FT-IR spectroscopy revealed the existence of functional groups, such as carbonyl groups, acids, phosphates, amides, hydroxyl groups, halides, carboxyl groups, and amine groups, in the R. damascena leaf biomass, all of which are likely to be involved in the biosorption of copper ions. Immobilization was shown to be a promising method for producing efficient adsorbents that can be used to sequester metal ions from wastewater. Therefore, R. damascena leaves can be used as a low-cost biosorbent to remove copper ions from aqueous solutions.

Materials and methods

Preparation of biosorbent

Rosa damascena Miller var. trigintipetala Dieck was collected from Taif rose farms in the Al-Shafa highland, Taif region, Saudi Arabia. Voucher specimens were deposited and identified by staff members of the herbarium at Taif University, Taif, Saudi Arabia. The rose leaves were removed from the plants, washed under running water to eliminate any impurities or pollutants, and then dried at room temperature for two weeks. Until further investigation, the leaves were crushed into a fine powder and stored in an airtight container.

Preparation of copper solutions

Approximately 3.93 g of copper sulfate (CuSO₄·5H₂O) was dissolved in 1000 mL distilled water to prepare the Cu²⁺ stock solution. All of the chemicals used in this investigation were of analytical grade and obtained from Sigma–Aldrich, including CuSO₄·5H₂O, HCl, NaOH, Na-alginate and CaCl₂.

Batch biosorption experiments

Impact of individual factors

The impact of different variables on biosorption by R. damascena leaf biomass was investigated using batch experiments. The effect of the initial Cu²⁺ concentration (30–150 mg/L), temperature (25–45 °C) and contact time (0–150 min) was examined. The biosorption tests were carried out in 250 mL conical flasks with 100 mL of copper solution, and the mixture was agitated at 170 rpm in a shaker. Deionized water was used to prepare the solutions, and the pH was adjusted using 0.1 M HCl or 0.1 M NaOH.

Each experiment was repeated three times, with the average results provided. The biosorbent was removed from the solutions at the end of the biosorption procedure by centrifugation for 5 min at 4000 rpm.

The concentration of copper in the filtrate was determined by inductively coupled plasma–optical emission spectrometry (ICP–OES) (Perkin Elmer Optima 2000 DV). The following equation was used to calculate the biosorption of copper ions onto R. damascena leaf biomass (q_e; mg/g).

$$q_e=\frac{V\left(C_i,-,C_{\mathit{eq}}\right)}{W},$$ 20

where C_i and C_eq (mg/L) are the copper ion concentrations before and after the equilibrium contact time, V (mL) is the volume of copper solution, and W (g) is the weight of R. damascena leaf powder.

The removal percentage of Cu²⁺ ions by R. damascena leaves was calculated by Eq. (21):

$$\mathrm{Removal}\left(\%\right)=\frac{\left(C_i,-,C_{\mathit{eq}}\right)}{C_i}\times 100.$$ 21

Optimization of Cu²⁺ removal by Box–Behnken statistical design (BBD)

Response surface methodology is a multivariable optimization approach that fits experimental results to a second-order equation to determine the optimal response of a process that is a function of numerous independent factors. Designing an experimental matrix, developing a mathematical model, and optimizing the response are the three key processes of RSM⁷⁸. Experiments were developed to determine the optimal copper biosorption onto R. damascena leaves using Box–Behnken Design and RSM (Stat-Ease Inc., Minneapolis, USA). The design included 17 runs with three independent factors, biosorbent dose (1, 3, 5 g/L), pH (2, 4, 6) and initial copper concentration (30, 60, 90 mg/L), at three coded levels (− 1, 0, + 1) (Table 1).

The sorption experiments were carried out with a fixed contact time of 90 min at 25 °C and 180 rpm, and the remaining concentration of Cu²⁺ ions was then determined as previously described.

The following equation is a second-order polynomial equation that includes the independent factors and the dependent response.

$$Y={\beta }_0+\sum {\beta }_i{X}_i+\sum {\beta }_{\mathit{ii}}{X}_i^2+\sum {\beta }_{\mathit{ij}}{X}_i{X}_j+\epsilon ,$$ 22

where Y is the expected response, β₀ is the intercept term, β_i, β_ii and β_ij are the linear, quadratic, and interaction impacts, respectively, X_i and X_j are the independent variables, and ε is the error.

The optimized conditions obtained from BBD were used to determine the kinetic biosorption models at various time periods (0–150 min) and to estimate isothermal models at various initial Cu²⁺ concentrations (30, 60, 90, 120 and 150 mg/L) and a contact time of 90 min at 25 °C. Thermodynamic investigations of Cu²⁺ ion biosorption were also examined, with the biosorption process being tested under optimal conditions at different temperatures (25, 35, and 45 °C).

Validity of kinetics models

The applicability and validity of the biosorption kinetic models was established by determining the normalized standard deviation (NSD) and chi-square (X²).

The lower the NSD and X² values for a given kinetic model are, the more likely the experimental data are to be valid⁷⁹.

The mathematical equations of NSD and X² are given as follows:

$$\mathrm{\Delta }{q}_e\left(\%\right)=100\sqrt{\left[\frac{\left(q_{exp.},-,q_{cal.}\right)/q_{exp.}}{N-1}\right],}$$ 23

$$X^2=\sum _{i=1}^n\frac{{\left(q_{exp.},-,q_{cal.}\right)}^2}{q_{cal.}},$$ 24

where N is the number of data points.

Statistical analysis of the data

It has been stated that three-dimensional response surface plots can be used to analyze the principal and interaction impacts of two parameters while all other variables are held constant. The regression model was used to produce the 3D response surface plots for the copper removal percentage by keeping one factor at the center level. The experimental design and statistical analysis were performed in Design Expert version 7. Multiple regression analysis and ANOVA were used to assess the experimental data, and significance was determined at probability levels using the F test (p ≤ 0.05). The Duncan’s multiple range tests were performed to compare the means using the SPSS statistical package (version 16.0).

Characterization of R. damascena leaves

A scanning electron microscope (SEM-JEOL JSM-6510 L. V operated at 30 kV) with energy-dispersive X-ray spectroscopy (EDX, JEOL JEM-2100 (HRTEM) operated at a voltage of 200 kV) was used to examine the surface morphology of the R. damascena leaves. The functional groups on the R. damascena leaf surface were determined using Fourier transform infrared radiation spectroscopy (FTIR, Thermo Fisher Scientific model FT-IR is 10, USA) before and after biosorption process.

Biosorbent immobilization

Rosa damascena leaves were immobilized for 30 min at 60 °C under continuous stirring by the dissolution of 4 g of Na-alginate in 100 mL distilled water⁸⁰. In the Na-alginate solution, 4 g/L R. damascena leaf powder was added. This mixture was then added to a 2% CaCl₂ solution using a 3 mL syringe to form beads. For full gelation, the spherical beads (3 mm) were maintained for 2 h in a 2% calcium chloride solution. The beads were then rinsed in distilled water to eliminate any excess CaCl₂ and stored in the refrigerator until they were needed again. The biosorption experiment was performed as previously described using immobilized R. damascena leaves and non-immobilized biosorbent as a control under the optimum conditions obtained by BBD at a temperature of 25 °C and over various time intervals (0–150 min).

All methods were performed in accordance with relevant guidelines and regulations.

Author contributions

M.A.F.: Investigation, formal analysis, writing—original draft. H.M.A., T.M.G.: Writing—original draft, supervision, project administration, funding acquisition, writing—review & editing. M.A.F., R.Z.H., T.G.A.: Methodology, supervision, writing—review & editing. S.H.A.H., E.F.A.: Methodology, writing—review & editing.

Competing interests

The authors declare no competing interests.