Response surface optimization for cadmium biosorption onto the pre-treated biomass of red algae Digenia simplex as a sustainable indigenous biosorbent

Algal biomass preparation

Samples of the native red marine macroalga Digenia simplex (Wulfen) C. Agardh were obtained from the Red Sea shores in Jeddah, Saudi Arabia. The samples were washed with deionized water in order to get rid of epiphytes, sand and impurities. The algae were then dried in an oven at 45 °C, ground into particles of 100–200 µm, and placed in air tight bottles at room temperature until required.

Pretreatment with calcium chloride

Dried D. simplex samples were treated with 0.2% calcium chloride (CaCl₂) at a ratio of 1 g:100 ml to improve the biosorption capacity of the algal biomass and then stirred with a magnetic stirrer at 25 °C for 2 h. Subsequently, the algae samples pretreated with CaCl₂ (DSC) were filtered, washed with deionized water, and dried in an oven at 45 °C until their weight remained constant (Omar, El-Gendy & Al-Ahmary, 2018).

Algal biomass characterization

Digenia algae pretreated with CaCl₂ were characterized before and after cadmium biosorption using two instrumental techniques, one of them is FTIR spectrometry (FTS, 3000 MX; Bio-Rad, Hercules, CA, USA), which is helpful in determining the type of functional groups present on the surface of the biosorbent. For sample preparation, a certain amount of biosorbent was thoroughly mixed with 0.4 g of KBr, and the mixture was analyzed in the spectral range of 4,000–400  cm⁻¹. The other technique is scanning electron microscopy (SEM, JSM-5400 LV; JEOL), attached to energy-dispersive X-ray spectroscopy (EDX, JSM-IT 200; JEOL), which enables the examination of morphological structure and elemental composition of the algae surface. EDX analysis was carried out using a silicon drift detector (SDD) at a working distance of 15 mm, an accelerating voltage of 20 kV, and live acquisition duration of 60 s.

Biosorption studies

Batch biosorption investigations were performed in 250 mL conical flasks containing 100 mL of distilled water and the required cadmium concentration. Appropriate amounts of CdSO_4.8/3H₂O were dissolved in 1,000 mL of deionized water for preparing a stock solution of cadmium with varying concentrations. In this study, different independent variables at different levels were used in order to maximize the Cd²⁺ ion removal efficiency. These factors included exposure time between 0 and 150 min, Cd²⁺ ion concentrations between 10 and 50 mg/L, and temperature of 25, 35, and 45 °C. The factors to be examined were varied while retaining the other conditions (pH 6, Cd concentration 30 mg/l, pretreated biomass concentration five g/l, and exposure time 60 min). The solutions were stirred at a fixed temperature of 25 °C and a speed of 170 rpm. The initial pH was adjusted with NaOH and/or H₂SO₄ (0.1 M). Each trial was repeated three times. After the experiment was completed, the algae biomass was removed from the aqueous solution by centrifugation at 4,000 rpm for 5 min. The cadmium concentration in the solution was then evaluated using an atomic absorption spectrometer (Buck Scientific 210VGP, Inc., East Norwalk, CT, USA).

The cadmium removal percentage (R, %) and biosorption capacity (q_e) were calculated from Eqs. (1) and (2) as follows: (1)${\displaystyle {\mathrm{q}}_{\mathrm{e}}\left(\mathrm{mg}/\mathrm{g}\right)=\frac{\mathrm{V}\left({\mathrm{C}}_0-{\mathrm{C}}_{\mathrm{f}}\right)}{{\mathrm{X}}_{\mathrm{m}}}}$ (2)${\displaystyle \left(\mathrm{R}\text{\%}\right)=\frac{{\mathrm{C}}_0-{\mathrm{C}}_{\mathrm{f}}}{{\mathrm{C}}_0}\times 100}$

where C₀ is the initial Cd²⁺ concentration (mg/L), C_f is the final Cd²⁺ concentration at any time (mg/L), X_m is the weight of algal biomass (g/L), and V is the volume of Cd²⁺ solution (mL).

Experimental design using RSM and BBD

The combined influences of different factors on the cadmium removal percentage by DSC were tested and modeled by RSM involving a Box–Behnken Design (BBD). The independent variables in the design were pH (3, 6, 9), initial cadmium concentration (10, 30, 50 mg/L), and algal dose (one, five, nine g/L). The quadratic model consisted of 15 experiments with three replicates to quantify experimental error. The BBD used a three-level design with test parameters at low, medium, and high (0, −1, and +1, respectively). The experiment was designed using Stat-Ease design expert v7.0 (Stat-Ease, Minneapolis, MN, USA). The experiment was conducted at a constant temperature of 25 °C and a contact time of 60 min, and the remaining cadmium concentration was assessed as earlier described.

The impacts of each independent parameter and their interactions were analyzed using the following second-order equation: (3)${\displaystyle Y={\beta }_0+\sum {\beta }_{\mathrm{i}}{X}_{\mathrm{i}}+\sum {\beta }_{\mathrm{ii}}{X_{\mathrm{i}}}_2+\sum {\beta }_{\mathrm{ij}}{X}_{\mathrm{i}}{X}_{\mathrm{j}}}$

where Y is the expected Cd²⁺ removal, X_i and X_j describe the studied parameters, and β₀ represents the intercept. β_i, β_ii, and β_ij are the linear, quadratic, and interaction coefficients, respectively.

Validation of predictive model and optimized conditions

Derringer’s desirability function approach was used to identify the optimal conditions of cadmium removal efficiency. Three experiments were carried out under these circumstances. The optimization was confirmed at an optimal pH of 5.78, an initial Cd concentration of 24.79 mg/L, and an algal dose of 6.13 g/L, with a contact time of 60 min at a temperature of 25 °C. The applicability and accuracy of the quadratic model were determined by comparing the experimental results with the expected results.

Kinetics, isotherms, and thermodynamic biosorption studies

For the kinetic experiments, 100 mL of cadmium solution (30 mg/L) was mixed with five g/L macroalgae concentration (DSC) in a 250 mL conical flask at 25 °C and pH 6. The mixture was then shaken at 170 rpm on a rotary shaker. Samples were taken from the cadmium-containing solution at intervals of 0–150 min, filtered, and the cadmium concentration was determined as mentioned previously. The kinetics of cadmium adsorption using CaCl₂-pretreated Digenia were analyzed by intraparticle diffusion (Eq. (4)), pseudo-first-order (Eq. (5)), and pseudo-second- order (Eq. (6)) as follows: (4)${\displaystyle q_t=K_i{t}^{0.5}+C_i}$ (5)${\displaystyle \mathrm{Log}\left({\mathrm{q}}_{\mathrm{e}}-{\mathrm{q}}_{\mathrm{t}}\right)=\mathrm{Log}{\mathrm{q}}_{\mathrm{e}}-\frac{{\mathrm{K}}_1\mathrm{t}}{2.303}}$ (6)${\displaystyle \frac{\mathrm{t}}{{\mathrm{q}}_{\mathrm{t}}}=\frac{1}{{\mathrm{K}}_2{\mathrm{q}}_{\mathrm{e}}^2}+\frac{\mathrm{t}}{{\mathrm{q}}_{\mathrm{e}}}}$

where q_t (mg/g) is the amount of cadmium adsorbed on the algae surface at any time (t), C_i is the boundary thickness, K_i (mg/g min^1/2), K₁ (1/min) and K₂ (g/mg min) are the rate constants of intra-particle, pseudo-1st -order, and pseudo-2nd-order, respectively.

For isothermal experiments, five g/L algal dosage (DSC) was added to 100 ml of cadmium solution with concentrations ranging from 10 to 50 mg/L, pH 6, and temperature 25 °C for 60 min. The mixture was shaken at 170 rpm, and then the residual cadmium concentration was determined. In order to evaluate the most appropriate biosorption isotherm for the biosorption of cadmium on the pretreatment algae, the Freundlich, Langmuir, and Dubinin–Radushkevich isotherm models were calculated as follows:

Freundlich model: (7)${\displaystyle ln{\mathrm{q}}_{\mathrm{e}}=ln{\mathrm{K}}_{\mathrm{f}}+\frac{1}{\mathrm{n}}ln{\mathrm{C}}_{\mathrm{eq}}}$

Langmuir isotherm model: (8)${\displaystyle \frac{{\mathrm{C}}_{\mathrm{eq}}}{{\mathrm{q}}_{\mathrm{e}}}=\frac{1}{{\mathrm{q}}_{\max }\mathrm{b}}+\frac{{\mathrm{C}}_{\mathrm{eq}}}{{\mathrm{q}}_{\max }}}$ (9)${\displaystyle {\mathrm{R}}_{\mathrm{L}}=1/\left(1+\mathrm{b}{\mathrm{C}}_{\mathrm{o}}\right)}$

Dubinin–Radushkevich isotherm model: (10)${\displaystyle {\mathrm{lnq}}_{\mathrm{e}}={\mathrm{lnq}}_0-\beta {\varepsilon }^2}$ (11)${\displaystyle \varepsilon =\mathrm{RT}ln\left(1+\frac{1}{{\mathrm{C}}_{\mathrm{eq}}}\right)}$ (12)${\displaystyle \mathrm{E}=\sqrt{1/2}\beta }$

where C_eq (mg/L) represents the equilibrium metal concentration after the biosorption process, n and K_f are Freundlich constants, b and q_max represent the affinity constant and maximum adsorption capacity of the Langmuir isotherm model, respectively, R_L is the dimensionless separation factor, C₀ (mg/L) represents the initial concentration of Cd²⁺ ions. β (mol²/J²) and q₀ (mg/g) are the mean biosorption energy and the biosorption capacity of Dubinin–Radushkevich, respectively, ɛ is the Polanyi potential, T (K) and R (8.314 kJ/mol) are the absolute temperature and universal gas constant, respectively, and E (kJ/mol) represents the average free energy of biosorption.

Finally, thermodynamic investigations were carried out at different temperatures (25, 35, and 45 °C). For this purpose, five g/L DSC was added to 100 ml of 30 mg/L cadmium solution (pH 6) and stirred for 60 min. The cadmium concentration was then measured as earlier described. Thermodynamic parameters were calculated using the following equations: (13)${\displaystyle K_C=\frac{Cs}{C_{eq}}}$ (14)${\displaystyle ln{K}_C=\frac{\Delta S^o}{R}-\frac{\Delta H^o}{RT}}$ (15)${\displaystyle \Delta G^o=\Delta H^o-T\Delta S^o}$

where Kc and Cs are the equilibrium constant and equilibrium cadmium concentration in the algal biomass, respectively. ΔG^o, ΔS^o, and ΔH^o are the free energy change, entropy change, and enthalpy change of biosorption, respectively.

Removal of cadmium from wastewater in Wady Al-Arj district

The real wastewater sample was obtained from the Wady Al-Arj district of Taif, Saudi Arabia. The temperature, pH, total dissolved solids (TDS), electrical conductivity (EC), and Cd²⁺ ion concentration of the sample were evaluated. The biosorption experiment was carried out under the optimal conditions according to the Box–Behnken Design (BBD). As the concentration of cadmium ions was found in a low amount, a definite concentration of Cd²⁺ was added to the effluent to adjust the initial concentration of Cd²⁺ at 24.79 mg/L which was determined by BBD.

Statistical analysis

The experimental data were analyzed using Stat-Ease Design Expert v7.0. Multiple linear regression was used to calculate the regression coefficients for linear and quadratic parameters and term interactions. The statistical significance of each regression coefficient was determined by computing the t-value of the pure error replicates at the center point. The statistical evaluation of the quadratic model was performed using analysis of variance (ANOVA).

Surface characterization

FT-IR analysis

FTIR analysis of Digenia pretreated with CaCl₂ was performed to estimate the type and number of functional groups on the algae surface involved in Cd²⁺ biosorption. FTIR spectra of Digenia algae before and after cadmium biosorption revealed a considerable number of functional groups on the algae surface that can bind Cd²⁺ ions in aqueous solution (Figs. 1A, 1B).

The peak observed at 3,424 cm⁻¹ is associated with the vibrations of N–H bonds, O–H bonds, and hydrogen bonds linking to amide group, showing the existence of proteins within the algae structure. This validates the role of hydrogen bonding in the biosorption process (Oke & Mohan, 2022). Other bands found at 2,923–2,927 cm⁻¹ can be associated with -CH bending vibrations of CH₂ and CH₃ groups (Smith, 2021). Furthermore, the bands observed at 1,750–1,747 cm⁻¹ before and after cadmium biosorption by D. simplex are connected with carboxylate ions (-COO-) (Madadgar et al., 2023). The peaks at 1,643–1,640 cm⁻¹ can be associated with the bending vibrations of the C=O bonds in the carboxylic and carboxyl functional groups, showing their participation in the biosorption process owing to electrostatic attraction (Oke & Mohan, 2022).

Some peaks appeared only after the biosorption of cadmium ions on the biosorbent surface, and significant changes in the intensity and position of the bands were detected in the algal biomass. These alterations confirmed the biosorption of cadmium by the chemically modified D. simplex. After Cd adsorption, the band in the biosorbent altered from 1,034 cm⁻¹ to 1,073 cm⁻¹. This shift shows the effective participation of CO groups in the biosorption process (Ciobanu et al., 2023). The bands at 1,160–1,153 cm⁻¹ before and after Cd²⁺ biosoprtion showed the presence of S=O groups. In addition, the biosorption of cadmium changed the intensities of the absorption bands at 467 cm⁻¹, 533 cm⁻¹, 713 cm⁻¹, 858 cm⁻¹, and 875 cm⁻¹ to 466 cm⁻¹, 493 cm⁻¹, 712 cm⁻¹, 857 cm⁻¹, and 874 cm⁻¹, respectively. These changes reflect the interaction of Cd²⁺ ions with D. simplex. The absorption bands at the wavelength 1,469–1,470 cm⁻¹ (O–H stretching vibration) are due to the coordinated H₂O molecules and the new peak at 1,252 cm⁻¹ (O–H stretching vibration) observed following Cd biosorption shows the O–H groups on the algae surface (Saberzadeh Sarvestani, Esmaeili & Ramavandi, 2016). After the biosorption process, a new weak absorption band at 770 cm⁻¹ was observed due to the N–H stretching vibration of primary and secondary amines (Wang et al., 2013). According to Lu et al. (2014), the peaks at 800 cm⁻¹ and 400 cm⁻¹ correspond to metal oxides (CdO₂).

The presence of these groups on the surface of the pretreated Digenia biomass is likely to provide high ion exchange capacity to the biosorbent (Mohseni-Bandpei, Ramavandi & Kafaei, 2019). Additionally, the decrease in band intensities following Cd²⁺ biosorption on the surface of biosorbent demonstrates that the aforementioned functional groups are effective in the biosorption process.

Analyses of SEM-EDX

SEM and EDX analyses were used to investigate the surface morphology and elemental alignment of the DSC biosorbent before and after cadmium biosorption and provide important information about the impact of adsorption on pretreated D. simplex. Significant alterations in the surface morphology of the algal biomass could be detected (Figs. 2A, 2B). The SEM image of the chemically modified D. simplex biomass (Fig. 2A) indicated the cell surface’s porous structure. This structure increased the sorbent’s surface area, hence facilitating the biosorption of cadmium. The presence of smooth pores with a flat shape after the biosorption process could be due to the accumulation of Cd ions on the surface of the pretreated Digenia biomass caused by electrostatic interactions (Fig. 2B) (Isam et al., 2023). Our findings also demonstrated that some changes in the morphology of the algal biomass occurred after Cd biosorption.

The elemental composition of the DSC biomass before and after cadmium biosorption was examined by EDX spectroscopy. The algal biomass was found to contain carbon, oxygen, sodium, magnesium, silicon, sulphur, chloride, calcium, and cadmium (Figs. 3A, 3B). The appearance of the cadmium band in the spectrum indicates that algal biomass efficiently collects metal ions from the aqueous solution (Fig. 3B). Furthermore, the decrease and/or disappearance of sodium, potassium, chloride, and magnesium in the analysis may be due to the complexation and/or ion exchange of Cd²⁺ with monovalent or divalent cations of the algal biomass, which are liberated by Cd²⁺ (Fawzy et al., 2022b). Aloufi et al. (2024) and Michalak, Mironiuk & Marycz (2018) described similar biosorption mechanisms.

Batch adsorption studies

Effect of exposure time

Contact time is a key parameter affecting the biosorption process. Figure 4A displays the impact of exposure time on the removal efficiency (%), and biosorption capacity of Cd ions. Algal biomass is distinguished by its rapid biosorption of cadmium from aqueous solutions. In Fig. 4A, it can be noticed that after 10 min of treatment time, more than 97% of Cd²⁺ ions was biosorbed on the pretreated D. simplex biomass, which is attributed to the strong concentration gradient and the availability of additional free active sites on the surface of the pretreated Digenia biomass. Moreover, a quick equilibrium time of approximately 20 min was achieved. These findings are significant since equilibrium time is a major factor for cost-effective wastewater treatment applications (Al-Zaban et al., 2022). After this equilibrium time, the biosorption efficiency of Cd decreases or relatively uniform biosorption occurs due to the decrease of biosorption sites on the algal surface (Fig. 4A) (Jabri et al., 2023). The equilibrium time recorded in this study is shorter than that commonly observed for cadmium adsorption on other materials. Several investigations on biosorption showed that most algae achieved maximum ion removal within times ranging from 30 to 90 min (Ibrahim, 2011; Amro & Abhary, 2019; Sayadi, Rashki & Shahri, 2019). As a result, the agitation period for the other biosorption experiments was set at 60 min to ensure complete equilibrium.

Analysis of Box–Behnken design

Evaluation of polynomial quadratic model and statistical analysis

The Box–Behnken design (BBD) is a statistical method used to design, model, and optimize cadmium removal by pretreated D. simplex (DSC). In this investigation, 15 runs were carried out to explore the impacts of three independent parameters such as pH, cadmium concentration, and algae dose on cadmium removal by D. simplex biomass. Table 1 shows that the percentage of Cd²⁺ removal ranged from 81.55% to 99.48% (93.84% on average). The highest Cd²⁺ biosorption percentage of pretreated D. simplex biomass was greater than the value reported by Fawzy et al. (2022a) for the maximum cadmium removal.

The second-order quadratic equation for cadmium removal efficiency by algal biomass is presented as follows: (16)${\displaystyle \text{\%}\text{Cd removal}=98.88042-1.15\text{A}-2.15\text{B}+3.72\text{C}+5.17\text{BC}-3.13{\text{A}}^2-6.32{\text{C}}^2}$ where A, B, and C represent pH, Cd²⁺ concentration, and algal dosage, respectively.

In this study, ANOVA was performed to examine the relationship between the studied factors and their impacts on the efficiency of cadmium removal by the biosorbent (Alsawalha, 2023). The data in Table 2 show that the quadratic RSM model was statistically significant with Prob. > F-value less than 0.05. The value of lack of fit was above 0.05, demonstrating that the model for Cd removal efficiency was also statistically significant (Table 2). Furthermore, the R² (0.90) and adjusted R² (0.83) values were close to each other, indicating a strong correlation between actual and expected values.

Table 1:

Experimental design of RSM quadratic model.

Trial	Independent variables				Dependent variable
	A pH	B Metal conc. (mg/L)	C Algal dosage (g/L)		Removal efficiency of Cd2+ (%)
1	3 (−1)	10 (−1)	5 (0)		98.76
2	9 (+1)	10 (−1)	5 (0)		96.97
3	3 (−1)	50 (+1)	5 (0)		93.85
4	9 (+1)	50 (+1)	5 (0)		96.63
5	3 (−1)	30 (0)	1 (−1)		87.13
6	9 (+1)	30 (0)	1 (−1)		81.55
7	3 (−1)	30 (0)	9 (+1)		95.23
8	9 (+1)	30 (0)	9 (+1)		90.61
9	6 (0)	10 (−1)	1 (−1)		98.35
10	6 (0)	50 (+1)	1 (−1)		82.05
11	6 (0)	10 (−1)	9 (+1)		94.33
12	6 (0)	50 (+1)	9 (+1)		98.70
13	6 (0)	30 (0)	5 (0)		99.48
14	6 (0)	30 (0)	5 (0)		98.17
15	6 (0)	30 (0)	5 (0)		95.80

DOI: 10.7717/peerj.19776/table-1

Table 2:

ANOVA data of the RSM quadratic model for Cd²⁺ removal by DSC biosorbent.

Model term	Sum of squares	df	Mean squares	F-value	p-value Prob. >F
Model	440.45	6	73.41	12.42	0.0011
A-pH	10.59	1	10.59	1.79	0.2175
B-metal conc.	36.88	1	36.88	6.24	0.0371
C-Algal dose	110.97	1	110.97	18.78	0.0025
BC	106.78	1	106.78	18.07	0.0028
A2	36.33	1	36.33	6.15	0.0382
C2	148.50	1	148.50	25.13	0.0010
Residual	47.28	8	5.91	–	–
Lack of fit	40.33	6	6.72	1.94	0.3791
Pure error	6.95	2	3.47	–	–
Correlation total	487.73	14	–	–	–
R2 = 0.90	Adj. R2= 0.83	Pred. R2=0.62	Adequate  precision = 10.71	Variation  coefficient % = 2.59	Mean = 93.8

DOI: 10.7717/peerj.19776/table-2

The data of this investigation were also analyzed to determine the suitability of the polynomial quadratic model. Figure 5A depicts a diagnostic scatter plot of the studentized residuals against the expected values for Cd²⁺ adsorption on algal biomass. The random distribution of the residuals for the expected values of Cd²⁺ biosorption along the central line shows that the actual values are consistent with the expected values. Furthermore, the range of the data points is ±3, showing that the design does not require a response transformation (Isam et al., 2023). Plotting the experimental results against the expected data shows an appropriate distribution along the straight line, indicating a satisfactory correlation (Fig. 5B). Since a large number of points are relatively close or centered on the diagonal line, this validates the model’s applicability. As a result, the findings indicate that the RSM model utilized in this study is capable of identifying appropriate and accurate information about the relationship between the actual and the expected data. Another diagnostic plot is shown in Fig. 5C, indicating that the entire run residuals range are between values +3.29 and −2, and no pattern traces are expected.

Interpretation of RSM quadratic model

Response surface curves were plotted to better comprehend the correlation between the parameters and evaluate the optimal concentration of each parameter to obtain the maximum response. Figure 6A depicts the impact of simultaneous changes in pH and cadmium ion concentration on the efficiency of the biosorption behavior of chemically modified D. simplex in the uptake of cadmium using 3-D and contour graphs. The graphs show that pH alterations had no significant influence on the percentage of cadmium biosorption (p > 0.05; Table 2); but increasing the initial Cd²⁺ concentration resulted in a significant decrease in the efficiency of cadmium removal by D. simplex. It is notable that the maximum removal efficiency was achieved at pH 6. The increase in Cd²⁺ biosorption percentage at pH 6 can be attributed to the deprotonation of carboxyl, hydroxyl, and other negatively charged groups on the algal surface, which results in electrostatic interactions between the algal biomass and the positively charged Cd²⁺ ions (Ofudje et al., 2020). FT-IR analysis confirmed these findings, which showed that cadmium biosorption primarily involves electrostatic interactions and ion exchange, and that the surface of D. simplex is composed of potential functional groups such as carbonyl, carboxyl, hydroxyl, and amide groups, which play a significant role in the interaction with cadmium ions. Similar maximum cadmium removal efficiencies at pH 6 was stated for Cystoseria indica (Khajavian et al., 2019), Chlorella vulgaris (Goher et al., 2016), and Hypnea valentiae (Rathinam et al., 2010).

Figure 6B shows the combined impacts of biomass dose and initial Cd²⁺ level on the cadmium removal efficiency of D. simplex. As illustrated in the figure, the removal efficiency of cadmium ions decreased significantly from 97.84% to 84.78% with increasing initial Cd²⁺ levels from 10 to 50 mg/L (p = 0.037; Table 2). The reason for this is the decrease in biosorption sites with increasing cadmium concentration for a fixed biomass of algae and increased intra-particle diffusion (Asgari, Ramavandi & Farjadfard, 2013). It is also worth mentioning that with increasing Cd²⁺ concentration, the ratio of metal ions to algal biomass also increased, resulting in a decrease in Cd removal. The graph also shows that increasing the algae concentration from one to five g/l resulted in a relative increase in the removal efficiency from 94.57 to 97.84% (Fig. 6B). ANOVA indicated that the increase in metal uptake was statistically significant (p = 0.002; Table 2), which was attributed to the increase in free binding sites on the algal surface, resulting in an increase in the elimination efficiency. When the biosorbent dose increased from five g/L to nine g/l, the percentage of cadmium biosorption decreased slightly from 97.84 to 91.31%. The reduction in the removal rate of cadmium at higher alga doses may be attributed to partial cell aggregation, which reduces the effective surface area available for the cadmium biosorption process (Kaparapu & Krishna Prasad, 2018). In this context, Moawad, El-Sayed & El-Naggar (2020) examined the Cd²⁺ biosorption on different doses of Cymodocea nodosa biomass and found comparable results.

Figure 6C depicts the combined influence of pH and algae concentration on the biosorption percentage of cadmium by D. simplex biomass. When the initial concentration of cadmium was fixed at 30 mg/L, increasing pH and algal dose resulted in an increase in cadmium removal efficiency, followed by a decrease in removal efficiency within the experimental range. The joint impact of pH and algae biomass concentration was estimated as maximum Cd biosorption (97.03%) at pH 6 and algal dosage of five g/L.

Evaluation of biosorption kinetics

Three kinetic models (intra-particle diffusion, pseudo-first and-second orders) were applied to examine the data and to estimate the best model that explains the mechanism of cadmium biosorption on the D. simplex surface.

In this study, the intra-particle diffusion kinetic model was applied to comprehend the role of the elementary diffusion stages in cadmium biosorption on Digenia biomass pretreated with calcium chloride. Figure S1 depicts the cadmium biosorption by DSC biosorbent, which can be divided into two stages. The first stage is characterized by diffusion of Cd²⁺ ions on the alga’s outer surface (film diffusion), whereas the second stage is characterized by cadmium ions diffusion via the internal pores of the biomass particles (intra-particle diffusion) (Bouabidi et al., 2018). As indicated in Table 3, the first sharper area displays an intra-particle diffusion rate constant (k_i1) of 0.332 mg/g min^1/2, related to quicker surface biosorption and external mass transfer. Nevertheless, the next gradual region indicates a slower diffusion rate with a k_i2 value of 0.0024 mg/g min^1/2, increasing the contact time needs to achieve equilibrium in the second step (Fig. S1A). It is clear that the elementary diffusion stage is significant in the biosorption process, but pore diffusion is not the rate-controlling stage for cadmium biosorption because the linear plot does not pass through the origin and the regression coefficient is low (R² = 0.805; Table 3). The deviation from the origin point can be attributed to the difference in mass transfer rates during the first and end stages of cadmium biosorption. This suggests a certain degree of boundary layer control and demonstrates that intraparticle diffusion is not the only rate-controlling stage. Chemical binding can also limit the biosorption rate, or both can occur concurrently. These findings are supported by the non-zero constant C_i values (Table 3), showing that film diffusion on the outer algal surface happens simultaneously with diffusion inside the pores (Fawzy et al., 2022a). Furthermore, it was found that cadmium ions more easily bind to the biosorbent’s functional groups. This reveals that the pretreated D. simplex biomass has a heterogeneous surface, as shown by SEM analysis, and the ease with which cadmium ions enter through the cracks on the algal surface depends primarily on its structural properties.

In the pseudo-first-order kinetic model, the reaction rate depends on the change between the adsorbate equilibrium concentration in the adsorbent’s solid phase and the instantaneous concentration in the solid phase. Table 3 shows that the measured equilibrium value (q_e exp. = 5.93) is inconsistent with the calculated value of the pseudo- first-order model (q_e cal. = 1.432). In addition, the regression coefficient is low (R² = 0.658; Fig. S1B), showing that Cd²⁺ biosorption on the pretreated Digenia biomass does not follow the pseudo-first-order model.

The pseudo-second-order model assumes that the rate-controlling phase is chemisorption. From Table 3 and Fig. S1C, it can be seen that the pseudo-second-order model with a regression coefficient close to 1.0 is in good agreement with the experimental results. Furthermore, the experimental q_e value (5.93 mg/g) was found to be quite similar to the calculated q_e value (5.672 mg/g), demonstrating that cadmium biosorption is controlled by chemical processes and indicates their charge specificity during equilibrium, such as covalent forces or electron exchange (Sahoo & Prelot, 2020).

From the previous data, it can be concluded that the pseudo-second-order model has higher regression coefficient value than the intra-particle diffusion model, indicating the presence of a chemisorption mechanism (Ciobanu et al., 2023). This validates that cadmium biosorption is a combination of surface chemical biosorption on the algal particle’s boundary layer and intraparticle diffusion.

Evaluation of biosorption isotherms

The adsorption isotherm is a significant parameter in the design of adsorption systems because it affects the adsorbent’s capacity and the interaction of the adsorbate with the adsorbent (Thomas et al., 2019). In the current investigation, the biosorption mechanism was studied using Freundlich, Langmuir, and D–R adsorption isotherm models (Khorshidi et al., 2016).

The Freundlich model assumes that the adsorption of metal ions occurs on heterogeneous surfaces via multilayer adsorption, which is mainly dominated by complexation through lateral interactions between metal ions present on the adsorbent surface. The heterogeneous nature of the algal biomass is expressed in terms of adsorption intensity (n), which is calculated from the curve (ln q_e) against ln C_eq (Fig. S2A). In this study, the 1/n value was within the range of 0 < 1/n < 1 (0.48; Table 4). Moreover, the value of parameter n is higher than 1.0, showing that biosorption of cadmium is favored and there is a strong affinity between Cd²⁺ ions and algal biomass, facilitating chemical biosorption. Due to the high regression coefficient (R² = 0.947), it can be concluded that the Freundlich model fits the data well and demonstrates the relationship between heterogeneous chemical multilayer adsorption and cadmium biosorption.

The Langmuir model assumes that the adsorption process occurs on a specific adsorption surface and that the attraction between ions reduces with increasing distance from the adsorption surface. It also indicates that the surface of biosorbent is homogenous. The regression coefficient for D. simplex was 0.997 (Table 4; Fig. S2B), demonstrating that the Langmuir model accurately predicted the cadmium biosorption on the pretreated Digenia biomass. Moreover, the calculated q_max value (11.16 mg/g) was relatively consistent with the experimental biosorption capacity of D. simplex (q_e = 9.40 mg/g). This suggests that the biosorption process on the homogeneous surface occurs mainly via ion exchange, resulting in monolayer coverage of the pretreated Digenia biomass surface with cadmium ions.

Table 5 compares the Langmuir maximum adsorption capacity with the data from other Cd²⁺ adsorption studies. It can be observed that the adsorption capacity of D. simplex is relatively comparable to or even greater than that of the other adsorbents. It can be concluded that DSC alga has a high potential for the removal of cadmium ions from wastewater. The structure of the red algae cell wall, composed of cellulose and sulfated polysaccharides, including carrageenan and agar, is responsible for this high capacity by binding metal ions to the algae biomass. Furthermore, the treatment of D. simplex with calcium chloride improved the binding sites for adsorption with cadmium ions (Ordóñez et al., 2023).

The dimensionless constant, termed the separation factor (R_L), describes the favorable biosorption process and is determined by the Langmuir isotherm constant (b) as described in Eq. (9). According to the value of the separation factor, the adsorption is favorable when 0 < R_L < 1, linear when R_L = 1, unfavorable when R_L > 1, or irreversible when R_L = 0. The values of the separation factor in this investigation were smaller than 1.0 (0.019−0.083) (Table 4), indicating that the Langmuir model fits the biosorption of cadmium ions on D. simplex biomass well (Abbou et al., 2021).

In this study, the Dubinin–Radushkevich (D–R) model was examined to distinguish between chemical and physical adsorption (Esvandi et al., 2020; Fig. S2C). The value of mean free energy (E), which is commonly used to determine the type of adsorption, was 31.62 kJ/mol (Table 4), which is higher than 16 kJ/mol (Aloufi et al., 2024). This shows that the biosorption process of cadmium ions in nature can be described as chemical biosorption. This result verifies previous data obtained from the Freundlich model and pseudo-second-order model.

In general, the R² values obtained by the Freundlich, Langmuir, and D–R models were all higher than 0.94. This indicates that the three isotherm models are in good agreement with the equilibrium results and verifies the efficiency of the pretreated D. simplex in eliminating cadmium ions from aqueous solutions.

Thermodynamic analysis

Thermodynamic investigations of Cd²⁺ biosorption on the surface of pretreated D. simplex were carried out at different temperatures in order to determine the resilience and feasibility of the adsorption process. Table 6 displays the values of the change in free energy (ΔG^o), entropy change (ΔS^o), and enthalpy change (ΔH^o). As shown in the table, the biosorption of Cd²⁺ ions at temperatures of 298, 308, and 318 K resulted in free energy changes of −2.12, −2.64, and −4.82 kJ/mol, respectively. The increase in temperature resulted in a reduction in the free energy change values, indicating a higher feasibility of cadmium biosorption (Fig. S3). Additionally, the negative ΔG^o values showed that the biosorption process of cadmium was feasible and spontaneous. Moreover, the positive value of ΔH^o showed that the endothermic class was responsible for the adsorption behavior of cadmium ions on the pretreated Digenia algae (Alharbi et al., 2022). This explains why the removal rate of cadmium ions increased with increasing temperature. According to Menezes et al. (2020), the values of ΔH^o between 80 and 200 kJ/mol, which represent the heat of chemical reaction, are commonly supposed to be comparable to values related to chemical adsorption processes. However, there is no specific standard associated with the values of ΔH^o to define the adsorption process. Therefore, the ΔH^o value (38.01 kJ/mol) in this investigation indicates that the Cd²⁺ biosorption process occurs through chemical biosorption rather than physical adsorption, which is consistent with the observations obtained previously. Additionally, the interaction between the active binding sites on the algal biomass and the cadmium ions is electrostatic (ion-exchange type), which is supported by the ΔH^o and ΔG^o values and the positive and low value of ΔS^o (0.134 kJ/mol K; Table 6). The positive ΔS^o value shows the degree of disorderliness at the solid-solution interface during the biosorption process (Gorzin & Bahri Rasht Abadi, 2018). This phenomenon is typical of ion exchange processes, in which a binding of cadmium ion happens concurrently with the release of another one into the aqueous solution (Kadiri et al., 2019).

Removal of cadmium from real wastewater

In this study, the removal of Cd²⁺ ions from real wastewater was also investigated under optimal circumstances achieved from BBD (pH 5.78, initial Cd²⁺ concentration 24.79 mg/L, and sorbent dosage 6.13 g/L), with a fixed contact time of 60 min and temperature of 25 °C. The characteristics of the effluent were evaluated as follows: temperature = 17 °C, pH of the solution = 8.74, TDS = 640.96 mg/L, and electrical conductivity = 1,001.5 µS/cm. Under the optimal conditions, the treatment of effluent with DSC biomass demonstrated high efficiency with 97.9% removal of Cd²⁺ ions. Treatment with CaCl₂ enhances the surface characteristics of D. simplex biomass by stabilizing and activating functional groups such as hydroxyl, carboxyl, and amide groups. These groups play an important role in cadmium ion binding through complexation and ion exchange mechanisms (Li et al., 2023). These results show that D. simplex biomass can effectively remove Cd²⁺ ions from wastewater.