### Response surface methodology

The highest dye removal observed and anticipated MB biosorption values, and the matrix of experimental design are listed in Table 4. In 60 min, 30 tests in total were conducted. *T. aestivum* had the highest dye removal rate (96%) compared to other combinations with 1.5 mg of biosorbent, 10 mg/L dye solution, pH 6, and a temperature of 25 °C. The link between the independent variables chosen and the biosorption of the MB dye is described by regression equations, which are used to express RSM. For this investigation, the regression equation is expressed in terms of coded values is shown as Eq. (11).

$$\begin{gathered} {\text{Dye Removal}} \left( \% \right) = 84.778 + 3.026 * A + – 0.951042 * B + 0.74097 * C \hfill \\ + – 0.843281 * D + 0.150187 * AB + 0.0474576 * AC + – 0.732874 * AD \hfill \\ + – 0.0578228 * BC + – 0.164211 * BD + 0.340879 * CD + – 0.12876 * A^{2} \hfill \\ + 2.29724 * B^{2} + 0.286968 * C^{2} + 0.926208* D^{2} \hfill \\ \end{gathered}$$

(11)

A, B, C, and D are the coded variables used in this RSM investigation. To forecast how each element will react to different phases, the equation can be utilised in conjunction with the coded variable. The standard notation for superior and subordinate status is + 1 and 1, respectively. Using this coding equation, the relative effects of the variables are ascertained after comparing the coefficients of the factors. Figure 3 illustrates that the predicted value of MB adsorption is plotted against the actual value from data, yielding an R^{2} value of 0.9945, which validates the models’ accuracy and can be used in the experiment.

### ANOVA analysis

ANOVA analysis used all the experimental findings for the full factorial response variable that was duplicated at the central and axial points (Table 5). A significant quadratic model contribution is shown in the ANOVA findings in Table 5 with a p-value of less than 0.01. The significant model in the current investigation is shown by the sample F-value of 193.32. This huge F-value may be caused by noise with a mere 0.01% probability. The values obtained using R^{2} = 0.9945 show a strong correlation between the experimental data currently available and the predicted values of the model put forth to describe the property of the polynomial model. This correlation is described by the calculation of the coefficient, the mean deviation across the model described, and the values themselves. The results with R^{2} = 0.9945 show that there is a strong correlation between the experimental data that is currently available and the predicted values of the model that is suggested to reflect the property of the polynomial model. The determination of the coefficient, the mean deviation throughout the described model, and the value all demonstrate this link. The value of F is 4.54 shows that there may be a 5.43% risk that the considerable prevalence of Fit F-value deficiency is because of noise, and the absence of Fit is not statistically significant.

Response surface plots show the MB biosorption efficiency (%) response to common parameters based on most values of alternative parameters for a certain set of components is shown in Fig. 4a–f. These 3D plots’ curves demonstrate how the process variables interact. The optimum scenario and interacting outcomes of the four evaluated factors are shown in the 3D aspect plots in Fig. 4a–f.

#### Effect of biosorbent dose

The availability and cost of biomass are the main deciding considerations when adopting it for large-scale industrial purposes. Biomass is one of the most exciting categories of biosorbents^{39}. In terms of getting rid of heavy metals from wastewater, agricultural biomass has a whole lot of benefits, which include being a cost-powerful renewable natural biomass, having an excessive metal elimination efficiency, having an excessive ability for absorption, and being capable of regenerating and reusing the biomass^{42}. Figure 4d demonstrates that the removal effectiveness of MB increases with increasing biosorbent dose and declines with decreasing dye concentrations. The primary cause for the simultaneous rise in MB’s biosorption capability and an increase in biosorbent concentration is the availability of many more open active sites on the surface of the biosorbent^{43}. On the other hand, Vijayaraghavan et al. discovered that the concentration of *T. aestivum* biomass increased together with the rate of MB biosorption from an aqueous solution^{44}. The reality that the dye’s biosorption per cent decreases as biomass attention increases demonstrates that the wide variety of dye molecules required to absolutely cowl all the lively adsorption sites in the biomass at excessive sorbent doses is insufficient^{1}.

#### Effect of MB concentrations

The relationship between the biosorbent dose and the concentration of MB dye is shown in Fig. 4a. The MB removal percentages increase with the increase of biosorbent dose and dye concentration. The biosorption process is also influenced by the initial MB concentrations. Growing the preliminary dye concentrations usually causes growth within the elimination percentage. The biosorption quantity of dye on the surface of adsorbents increases as the initial concentration of MB increases^{45}.

#### Effect of initial pH

The biosorption procedure may be motivated with the aid of using numerous variables, along with pH, preliminary concentration, and biosorbent dosage. Figure 4c describes the association between the pH and the temperature. While the initial pH level, MB concentration, and contact duration were retained at their zero levels, the three-dimensional surface plots (3D) in Fig. 4c show the simultaneous effects of pH and temperature on MB removal (%), respectively. The process of contaminant biosorption has been discovered to be most affected, among other things, by the initial pH level. pH levels influence a variety of processes, including the chemistry of metal solutions, the activity of functional groups in biomass, and the net charge on the surface of sorbent cells. Heavy metal ions and H^{+} may compete with one another for cellular active sites on the surface of biosorbent cells since the biosorption method for significant metals is usually potential of hydrogen ion concentration dependent^{46}. According to the study of experimental findings, the *T. aestivum* biomass can more efficaciously soak up the MB dye because the pH rises, with maximum biosorption happening at approximately pH 8. The *T. aestivum* surface appearing as a biosorbent and the protonation and deprotonation of the MB dye can each be used to provide an explanation for the outcome.

#### Effect of temperature

The biosorption process sensitivity to temperature can be used to determine a biosorbent sorption capacity. The impact of temperature on the removal of Basic Blue 41(BB41) through effective microorganism-primarily based total leaf compost was assessed at various temperatures between 25 and 45 °C^{47}. The outcomes of the experiment showed that a rise in temperature would result in a greater capacity for dye sorption (Fig. 4b). Figure 3e demonstrates that the slightly increasing the concentration at lower temperature the efficiency of dye removal also increases. Researchers have found that increasing temperatures increase the rate of solute diffusion, which has a significant impact on the sorbent’s ability to absorb solutes^{48}. However, the impact of temperature on biosorption is quite delicate and might be slightly increased at lower temperatures. The ability of the dye molecules to sustain contact with the biosorbent surface sites and the expansion of pore size with rising temperature were cited as the causes of this outcome. In general, a rise in temperature accelerates the rate of solute diffusion, which has a significant impact on the ability of biosorbents to bind to solutes^{48}.

### Isotherms model for biosorption

A fitting result of a linear line with a (C_{e}/q) intercept to the Langmuir equation is displayed as (C_{e}/q) versus (C_{e}) shown in Fig. 5A. According to Table 6, The Langmuir isotherm’s determined correlation coefficients were 0.9381. The biosorption’s deviation from linearity is considered when calculating the second Langmuir constant, R_{L}. In the current investigation, the equilibrium value of the dimensionless factor value, R_{L}, which ranges from 0 to 1, was 0.062 (Table 6), indicating favourable biosorption. That confirmed that *T. aestivum* and MB had favourable biosorption (Fig. 5A).

Figure 5B illustrates the values of 1/n and K_{f} determined from the intercept and slope of the linear plot of ln q_{e} versus ln C_{e}^{49}. The desired constants are provided with the regression equation as shown in Table 6. The favourable nature of biosorption was proved by the fact that n is between 0 and 1^{50}. The Langmuir and Freundlich biosorption isotherms best explain the equilibrium results, demonstrating that monolayer formation mediates biosorption on a homogeneous surface**.** Figure 5B shows a linear fit of the Freundlich equation using a line with an intercept of ln K_{f} and a slope of n^{49}.

#### Kinetic studies

The first-order kinetics’ calculated K_{1}, q_{e}, and R^{2} values are shown in Table 7. As shown in Fig. 6, pseudo-second-order graphs were made by plotting t/q_{t} vs. time. The second-order rate constants have been calculated using the charts. The second order’s calculated K_{2}, q_{e}, and R^{2} are supported by Table 7.

Pseudo-second-order kinetics’ correlation coefficients are becoming close to unity in contrast to pseudo-first-order kinetics. Therefore, it is evident that the pseudo-second-order model represents a biosorption that is more successful.

#### Thermodynamics study

As expected, the biosorption capacity of MB onto *T. aestivum* increases substantially while the temperature rises from 20 to 40 °C. The biosorption capability of *T. aestivum* is boosted through the biosorbent’s expanded pore length and the warming of the sorbent’s surface. Raising the temperature causes the big dye molecule to penetrate more deeply, which also enhanced the large dye ion’s potency, which lessens the impact of swelling^{16,51}. As a result, MB was able to absorb the *T. aestivum* more quickly at high temperatures. Gibbs free energy (\(\Delta\)G), enthalpy (\(\Delta\)H), and entropy (\(\Delta\)S), among other thermodynamic characteristics, have all been calculated for the extrusion^{28}. Furthermore, Table 8 also provides \(\Delta\)H, \(\Delta\)G, and \(\Delta\)S values for 20 mg/L preliminary MB dye concentrations.

The negative values of ΔG demonstrated the spontaneity and viability of the adsorption process for MB sorption on *T. aestivum*. Because there is less unpredictability at the solid/liquid interface when MB is adsorbing to *T. aestivum*, the value of entropy ΔS (− 10.11 kJ/mol K) is negative. The negative value of ΔH (− 12,300.04 kJ/mol for MB) supports the exothermic character of the reaction. Good interaction between *T. aestivum* and MB is indicated by high levels of ΔH. This led us to the conclusion that the sorption of the dye in T. aestivum is a process of chemical biosorption.

### Sticking probability

The sticking probability (S*) is a function of the adsorbate/biosorbent system under discussion, but it is temperature dependent and needs to fulfil the criterion 1 < S* < 1 for optimum biosorption. The value of sticking probability was calculated from experimental data. It was calculated using a modified Arrhenius- type equation.

$$S^{*} = \left( {1 – \theta } \right)e_{ RT}^{ – Ea}$$

(12)

The parameter S* represents the measure of an adsorbate’s capability to persist on the adsorbent indefinitely. The surface coverage (\(\theta\)) at different temperatures was calculated to assess the effects of temperature on the sticking probability over the temperature range from 288 to 308 K. The slope and intercept of the ln (1 − ϴ) against 1/T plot can be used to determine the value of Ea and S*. The negative value of Ea shows that methylene blue dye removal by adsorption onto *Triticum aestivum* is favoured by a lower solution temperature, and the biosorption process is exothermic in nature. This biosorbent has affinity for methylene blue, indicating that it is a superior biosorbent for removal of methylene blue, as shown by MB sticking probability of S* < 1 on the surface of biomass is presented in Table 8.

#### Artificial neural networks (ANNs) modelling

ANNs are used to generate new processes, analyse existing ones, and anticipate the result and performance of systems^{26}. The feed-forward neural network’s optimal topology consists of an output layer, a hidden layer, and four neurons each in the input and hidden layers (including one neuron).

The experiments designed by the CCD provided the input and output for training. After training, a neural network’s weights and biases are displayed in Table 9. The model’s logsig (log-sigmoid) transfer function provides the necessary information for anticipating the outcomes. Figure 7 displays the expected values of the ANN model. In terms of the number of learning epochs, Fig. 8 analyses the ANN model’s training, validation, and tests.

The RSM- predicted improved process conditions are also assessed using an ANN model. Biosorbent dose (2 mg), dye concentration (20 mg/l), dye solution pH (7) and temperature (20 °C) are used as input parameters for the ANN model. When the test error is lowest and the mean squared error has not changed for at least 1000 iterations, the training is terminated. The network is trained in this analysis for a total of 6 epochs. When the anticipated values from the ANN and RSM models are compared, it becomes evident that the values predicted by both models are considerably closer to the experimental results (Table 9).

#### Multiple response optimization

The experimental findings were optimised using Design-Expert software^{35}. The 93.51% biosorption efficiency was attained under the ideal conditions shown in Table 10^{25} and conducted a special batch experiment to demonstrate optimization under ideal circumstances for comparison under suitable circumstances between projected and actual results. The difference between the projected value and the actual value is 93.90% or 93.51% confirming that the anticipated and actual values are the same, yielding verified model results. According to the requirements listed in Table 10, model equation is developed to maximise MB removal efficiency. Predicted numerical optimization was obtained 2 mg biosorbent dose, 20 mg/L concentration, 7 pH and at 20 °C temperature with 93.90% MB dye removal efficiency. The percentage error between RSM prediction and optimized condition is 0.41% and error between RSM and ANN is 2.17%. Validation experiment conducted as same input value gave 93.51% MB removal efficiency & projected reactions are consistent with model predictions validated under these ideal process condition (Table 10).

#### Characterization of biosorbent

##### Surface modification analysis by FTIR

Using FTIR spectroscopy, surface alteration may be found, allowing the biosorption mechanism to be examined. Using the Perkin Elmer FTIR system, the FTIR spectrum data was Gathered. The surface of the biosorbent is visible with functional groups such as nitro, hydroxyl, carbonyl, carboxylic, phenol, and phenol groups in Fig. 9. FTIR spectra can be used to distinguish between the many functional groups that are present in biosorbent formations^{52}. Two distinct peaks at 1372 and 1371 cm^{−1} and 1512 and 1511 cm^{−1}, respectively, indicate the stretching vibration of the nitro-N–O groups, which were discovered to have been extended due to biosorption on biosorbent. The 1634 and 1632 cm^{−1} peaks are the stretches of C=C. The C–O stretch of various moieties and the carboxylic group have been implicated as the cause of the numerous strong, sharp peaks that were observed between the levels of 1100 and 1330 cm^{−1}^{24}. The hydroxyl functional group’s O–H stretching vibration and the band at 3200–3600 cm^{−1} had previously been linked (Fig. 9). The stretching of the carboxyl groups in C=O is responsible for the peak around 1700–1800 cm^{−1}. The surface charge differential may change due to positive or negative surface charges depending on the pH of the solution^{2,6,53}. In a solution with a lower pH value, the system will operate more frequently and develop a positive surface charge. The hydroxyl group is indicated by the height increase at 3340 cm^{−1} caused by the MB absorbed on *T. aestivum*, as well as by the prolonged robust sharp top at 1034 cm^{−1}. Peaks in the range of 1327–1372 cm^{−1} were caused by the interaction of MB and Nitro companies in *T. aestivum*^{54,55,56}.

##### SEM evaluation

The surface topography and properties of *T. aestivum* can be directly scanned using a scanning electron microscope (SEM) examination. SEM images are displayed Before and after MB biosorption, the biomass of *T. aestivum* (Fig. 10A,B). The biomass made of untreated *T. aestivum* had a rough and irregular surface, as seen in Fig. 10A. The look of fresh, shining particles absorbed on the surface of *T. aestivum* was depicted in Fig. 10B. Another distinguishing quality had been demonstrated (Fig. 10B). The surface area of polymeric *T. aestivum* has been reduced due to possible cross-linking between positively charged ions and negatively charged chemical functional groups in the cell wall. The surface of *T. aestivum* is rough and undulated, which increases the surface area exposure of the active biosorption sites and leads to MB’s enhanced bio-absorption efficacy.