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

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### 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 findings20,21.

### 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)):

$${text{Cu}}^{{{2} + }} ;{text{removal percentage }} = { 57}.{2} + { 1}0.{54}A + { 5}.{13}B – { 4}.{28}C + { 5}.{71}A^{2} ,$$

(1)

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

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.

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.

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.

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.

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 qe and qt (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 qe were estimated from the slope and intercept by plotting log (qe − qt) 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 ∆qe 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 (qe exp.; 17.1 mg/g) and the modeled value (qe 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 findings15,33,34.

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 qe were calculated from the intercept and slope of t/qt 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 ∆qe 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 qe (17.1 mg/g) was relatively similar to the calculated qe (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:

$${q}_{t}=frac{1}{beta }mathrm{ln}left(mathrm{alpha beta }right)+frac{1}{beta }mathrm{ln}left(mathrm{t}right),$$

(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 qt 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 ∆qe 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 ∆qe 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 Ki denotes the intra-particle diffusion rate constant (mg/g min0.5) and Ci denotes the intercept.

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

$$-mathrm{log }(1-left(frac{{q}_{t}}{{q}_{e}}right)= {D}_{f}cdot t,$$

(7)

where Df 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 − (qt/qe)) 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 (Ci, 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:

$$frac{{C}_{eq}}{{q}_{e}}=frac{1}{{q}_{max}b}+frac{{C}_{eq}}{{q}_{max}},$$

(8)

where qmax is the maximal sorption quantity (mg/g) required to produce full monolayer coverage on R. damascena’s surface at a high ion equilibrium concentration (Ceq; 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.

When Ceq/qe was plotted versus Ceq, a straight line was formed, and the slope and intercept were used to determine the qmax 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 (qmax) of 25.13 mg/g. A similar pattern was achieved by using numerous equilibrium isotherm models, with the Langmuir model having the best fit34,46.

A dimensionless separation factor (RL) 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 Co is the metal ion concentration (mg/L). The type of Langmuir isotherm was determined by the RL value, which was either unfavorable (RL > 1), linear (RL = 1), irreversible (RL = 0) or favorable (0 ˂ RL ˂ 1)40. A value of RL between 0 and 1 indicates that adsorption is favorable. In the current study, the RL 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):

$$text{ln} {q}_{e}=text{ln} {K}_{f}+frac{1}{n} text{ln}{ C}_{eq},$$

(10)

where Kf 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 qe against lnCeq are used to calculate the Kf and 1/n values, respectively (Fig. 4b). The greater the Kf 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.

$${q}_{e}= Btext{ln}A+B text{ln}{C}_{eq},$$

(11)

$$B=frac{RT}{b},$$

(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 qe versus lnCeq 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).

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:

$$text{ln}{q}_{e}=text{ln}{q}_{0}-beta {varepsilon }^{2},$$

(13)

$$varepsilon =RTleft(1+frac{1}{{C}_{eq}}right),$$

(14)

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

(15)

where qo 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:

$$text{ln}{q}_{e}=text{ln}{q}_{max}{-{K}_{J}C}_{eq },$$

(16)

where KJ: the Jovanovic isotherm constant. The values of qmax and KJ were calculated from the intercept and slope of linear plot of lnqe versus Ceq (Fig. 4e).

The maximum biosorption capacity determined from the Jovanovic equation (qmax = 11.17 mg/g; Table 5) differs from the experimentally measured value (qmax = 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.

$$Delta G=Delta H-TDelta S,$$

(17)

$$Delta G=- RTtext{ln}{K}_{C},$$

(18)

$${LnK}_{C}=frac{Delta S}{R}- frac{Delta H}{RT},$$

(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.

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

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.

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.

### 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.

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 biosorbents65,66. 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.

### 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 literature20,34,71,72,73,74,75,76,77. The wide availability of Rosa damascena leaf wastes and their low cost are added advantages for their selection by numerous industries.