Smart nanocomposite of V/Pd-layer double hydroxide encapsulated with double-layer hydrogel for optimum adsorption of basic yellow 28 dye

2.1. Fabrication of the adsorbent

2.1.1. Fabrication of V/Pd-LDH

The process of synthesizing LDH supplies using the coprecipitation technique has been demonstrated in Figure 1. The procedure commenced with the dissolution of 2.7 mL (0.425 g) of Vanadium trichloride (VCl₃) in 50 mL of double-distilled water. Concurrently, a distinct beaker was employed to dissolve 6.077 mol (1.07 g) of palladium chloride (PdCl₂) in a 5% HCl solution [23]. The two-metal solution was mixed together. After that, a supplementary 50 mL of double-distilled water was added to dissolve 5 mmol of Na₂CO₃ alongside 16.20 mmol (0.6483 g) of NaOH to raise the metal solution pH using this alkaline solution. After modification, the pH of the solution was determined to be between 9 and 10. It was put in a nitrogen environment and left to agitate for a whole day at room temperature. The resultant precipitates were isolated as V/Pd-LDH powder through a series of centrifugations conducted at 5000 rpm for 10 min each, utilizing double-distilled water and EtOH to wash away superfluous ions. After this, the precipitates were dried in an oven set at 60°C to create the finished product.

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Figure 1.

V/Pd-LDH/CD-Alg hydrogel bead synthesis schematic diagram.

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2.2. Removal and batch analyses of BY28 via the hydrogel beads of V/Pd-LDH/CD-Alg

The study investigated the sorption capacity and effectiveness of V/Pd-LDH/CD-Alg hydrogel beads produced under ideal conditions for the adsorption of BY28. A concentrated standard solution of BY28 dye was formulated at a concentration of 1000 mg/L, which functioned as the precursor for generating additional diluted solutions with the use of double-distilled water. The pH levels of these resultant solutions were meticulously reformed using 0.01 M of HCl as well as NaOH to attain the specified levels of acidity or alkalinity. The batch adsorption investigates were conducted in 150 mL glass flasks, which were situated in a well-regulated water bath to ensure uniform experimental conditions throughout the study. An analysis was conducted to evaluate the influence of several sorption parameters [28,29]. The parameters examined encompassed a pH range of 2 to 12, solution temperatures between 20 and 45°C, variable adsorbent amounts from 0.02 to 0.50 g, initial dye concentrations fluctuating between 22 and 509 mg/L, and contact durations spanning from 0 to 100 min. By using appropriate dilutions, the concentration of BY28 in the filtrates gained after sorption studies was adapted to fall within the detectable range. The spectrophotometer was set at 433 nm in wavelength to measure the absorbance of the filtrates. The calculation of the sorption percentage and sorption capability was performed employing Eqs. (1) and (2). Within these equations, C₀ denotes the original concentration of the solutions, while C_e shows the final concentration. In addition, q_e (mg/g) quantifies the quantity of dye that has been adsorbed relative to each unit of adsorbent mass. Moreover, V (L) denotes the volume of the solution, while m (g) signifies the mass of the adsorbent employed in the procedure [24,30].

2.3. Experimental design

The RSM framework is used to build statistical models to address situations with several possible answers. Clarifying the relationships between the response variable and the independent experimental variables is the main goal. Additionally, this methodology makes it possible to enhance the entire process. RSM employs a methodical approach by implementing a series of carefully structured experiments that are specifically aligned with the unique attributes of the process, enabling the identification of the most effective course of action for the overall procedure [31]. One common technique used for process parameter optimization is CCD. Eq. (1) gives a quantitative measurement of the BY28 adsorption per gram of the adsorbent beads, with special attention to the VPd-LDH/CD-Alg over a range of time intervals (t). Conversely, Eq. (2) functions as an analytical instrument for assessing the efficiency of the elimination process [20,21]. Three factors have been recognized as critical constraints in the procedure: “adsorbent mass,” “contact time,” and “solution pH.” Their importance stems from their detrimental effects on the adsorption efficacy, as illustrated in Table S3.

A thorough summary of the upper and lower bounds for every specified parameter, as generated by the Design Expert Software, has been given in Table S3. The combinations of constraints and their accompanying results are systematically described in this table. It consists of 2n factorial runs, “2×n” axial runs, and central runs [18]. The number of controlled trials, which is influenced by the number of input factors, can be found using Eq. (3):

In this context, “N” signifies the number of procedure influences that affect the outcomes, while “p” refers to the number of investigational runs considered necessary. For this analysis, the parameter “m” is established as equal to 3 [32]. The CCD comprises three critical steps: initially, the calculation of the model’s constants; next, the development of the investigational setup; and finally, the forecasting of the model’s presentation, along with an evaluation of the results. After conducting these analyses, a practical model is generated that evaluates the function’s dynamics concerning changes in the input variables. As seen in Eq. (4), this procedure results in the development of a quadratic regression model.

Throughout this analysis, we identify “I” and “j” as the resistance and speed factors, respectively. According to a predetermined order, the constants for resistance, interaction, speed, and the term for a constant are represented as β₀, β_i, β_ii, and β_ij, individually. The effectiveness of the planned polynomial model calculation was assessed through statistical metrics R², R²_Adj, and R²_Pred. It is essential to highlight that a raised R² value demonstrates a greater precision of the equation in conforming to the empirical data collected from experimental procedures [33].

3.1. Characterization of V/Pd-LDH/CD-Alg

3.1.1. X-ray diffraction (XRD) Patterns

The incorporation of Vanadium (V) and Palladium (Pd) ions onto the surface has caused in an observable improvement in the crystallinity of the V/Pd-LDH that is encapsulated within β-cyclodextrin and alginate hydrogel beads [34]. The substance system featuring Vanadium and Palladium is identified as having a tetragonal crystal assembly, specifically categorized within the P4 space group. This classification has been confirmed through rigorous analysis employing the Foolproof besides Check Cell methodologies. The obtained limits provide insights into the magnitudes of the crystal, delineating them as follows: a = 10.927 Å, b = 10.927 Å, c = 9.727 Å. Additionally, the angular measurements are reported as α = 90°, β = 90°, and γ = 90°. Figure 2(a) clearly exemplifies that the diffraction peaks corresponding to the V/Pd-LDH/CD-Alg maintained their integrity after the adsorption process, which highlights the excellent stability of the crystalline framework. The information shown in Table S4 supports this observation even further.

Table S4

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Figure 2.

(a) XRD pattern of V/Pd-LDH/CD-Alg, (b) N₂ adsorption/desorption isotherm of V/Pd-LDH/CD-Alg and BY28-V/Pd-LDH/CD-Alg, (c) FT-IR of V/Pd-LDH/CD-Alg, (d) EDX of V/Pd-LDH/CD-Alg, (e) SEM of V/Pd-LDH/CD-Alg, and (f) SEM mapping of V/Pd-LDH/CD-Alg.

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3.1.6. X-ray photoelectron spectroscopy (XPS)

The C1s XPS spectrum of the V/Pd-LDH/CD-Alg displays three diverse peaks, which offer valuable information about the chemical environment of the carbon atoms within the sample (Figure 3). The detection of a peak at approximately 284.84 eV proposes the presence of C-C and C-H bonds, indicative of non-functionalized carbon atoms found within the aliphatic chains and cyclic structure of β-cyclodextrin. Conversely, the peak observed at about 288.08 eV corresponds to the presence of C-O and C-OH bonds [39]. These bonds are prevalent in both β-cyclodextrin and alginate, signifying the presence of hydroxyl groups that play a crucial role in imparting hydrophilic characteristics and functional attributes to the hydrogel. The observed peak at approximately 292.82 eV reveals C=O and COO bonds, which suggests the presence of carboxylate groups within the alginate hydrogel. Additionally, the existence of these peaks shows that alginate and β-cyclodextrin were successfully incorporated into the V/Pd-LDH framework. This integration underscores the material’s functional versatility, particularly in relation to its capabilities for adsorption and catalytic processes [40,41].

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Figure 3.

XPS of V/Pd-LDH/CD-Alg hydrogel beads.

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The XPS examination of the Ca2p region in V/Pd-LDH/CD-Alg identifies two significant peaks. These peaks are linked to the Ca2p^3/2 and Ca2p^1/2 spin-orbit components, providing in-depth insight into the calcium chemical environment within the hydrogel matrix. The primary peak located near 348 eV (Ca2p^3/2) indicates calcium existing in its ionic form (Ca²⁺), which engages with the carboxylate groups found in alginates. This particular interaction is crucial for the crosslinking of alginate chains, ultimately leading to the development of the hydrogel framework. A subsequent peak observed near 351.63 eV (Ca2p1/2) is linked to spin-orbit splitting, providing further confirmation of calcium’s presence in an ionic state. Moreover, this peak displays a notable energy difference of approximately 3.7 eV when compared to the adjacent peak [42,43].

The Cl2p XPS spectrum obtained from the V/Pd-LDH/CD-Alg reveals two significant peaks consistent with the Cl2p^3/2 and Cl2p^1/2 spin-orbit components. These features serve as critical indicators of the chlorine’s chemical state within the composite structure [44]. The detection of a peak at 201.26 eV, attributed to the Cl2p^3/2 level, highlights the principal binding energy associated with chloride ions (Cl⁻) that interact with the hydrogel matrix. This interaction is especially pertinent to the structural integrity of the LDH. The presence of chloride ions is crucial for maintaining charge neutrality within the positively charged layers that characterize the LDH framework. The detection of a secondary peak near 203.04 eV, representing Cl 2p^1/2, is linked to the phenomenon of spin-orbit splitting and corroborates the existence of chlorine in a similar ionic state. The energy disparity, approximately 1.78 eV, between these two peaks is consistent with the properties associated with chloride ions, thereby underlining their essential function in maintaining both the structural stability and charge neutrality of the material.

The XPS examination of the N1s area in the V/Pd-LDH/CD-Alg identified two notable peaks. These peaks, situated at binding energies of 402.61 and 400.53 eV, indicate the presence of distinct nitrogen chemical environments within the sample. The peak attributed to 402.61 eV is likely representative of nitrogen species associated with higher oxidation states. This observation underscores the significant role of encapsulation in shaping the chemical architecture. In contrast, the peak detected at 400.53 eV corresponds to nitrogen that exists in a bonding configuration characterized by lower energy levels. This proposes the potential of amine or amide functional groups within the structural composition of either β-cyclodextrin or alginate. The observed difference of roughly 2 eV between the peaks indicates the existence of various nitrogen functionalities, which confirms the encapsulation effect and highlights specific interactions between the hydrogel components and the V/Pd-LDH. Together, these peaks demonstrate the chemical complexity and heterogeneity inherent to the encapsulated system [23,31].

The O1s XPS spectrum for the V/Pd-LDH/CD-Alg revealed three distinct peaks, indicating the presence of different oxygen environments in the material (Figure 3). The peak detected at 529.87 eV, contributing 2.53% to the overall signal, corresponds to oxygen linked to metal-oxygen bonds within the lattice of the V/Pd-LDH framework. This observation implies the presence of a crystalline framework typical of the LDH structure. The detected peak at 531.54 eV, representing 23.45% of the overall spectral intensity, suggests a correlation with surface hydroxyl (-OH) groups or adsorbed water molecules. This observation points to the types of surface interactions that may facilitate hydrogen bonding or electrostatic forces between the LDH and the hydrogel matrix. The dominant peak identified at 532.92 eV, representing 74.02% of the overall data, is indicative of oxygen atoms associated with C-O and C=O functional groups. This finding can be attributed mainly to the organic components of β-cyclodextrin and alginate, which work in concert to facilitate the development of the encapsulating hydrogel matrix [45]. The XPS spectrum of Pd3d derived from the V/Pd-LDH/CD-Alg reveals four identifiable peaks, which suggest the presence of palladium in multiple chemical states and different environmental conditions [21,30]. The spectral feature identified at 341.75 eV, representing 8.99% of the overall signal, is reflective of the Pd3d^3/2 state linked to a higher oxidation state, most likely Pd(II). This observation implies a noteworthy interaction between palladium and oxygen-rich groups within the hydrogel matrix. In contrast, the peak observed at 340.02 eV, which contributes 23.74% to the total signal, represents the Pd 3d^3/2 state in a lower oxidation state, presumably indicating the presence of metallic palladium (Pd(0)). The detection of reduced palladium species is significant, highlighting their essential role in the catalytic activities demonstrated within the system. The dominant peak at 336.01 eV, representing 55.94% of the overall spectrum, is attributed to the Pd 3d^5/2 orbital corresponding to Pd(II). This observation implies that palladium may be integrated into the structure of the LDH or interact with the functional groups within the hydrogel, potentially resulting in complex formation. The peak identified at 333.62 eV, which constitutes 11.32% of the overall signal, resembled the Pd3d^5/2 state linked to metallic palladium (Pd(0)). This finding signifies that active palladium sites are successfully stabilized within the encapsulating matrix, as illustrated in Figure 3 [46].

3.2. Batch investigates

3.2.1. Results of the pH and point of zero charge

The initial pH values of the solutions were carefully modified within the range of 2 to 12 to examine the influence of pH on the adsorption characteristics of BY28 dye. The baseline pH acts as a noteworthy factor affecting the adsorption process [47]. Once the solution pH decreases below the point of zero charge (pH_pzc) of the V/Pd-LDH/CD-Alg hydrogel beads, particularly below the threshold of 5.56, it is anticipated that the surface characteristics of the sorbent will display a net positive charge, as illustrated in Figure 4(a). To optimize the efficacy of the V/Pd-LDH/CD-Alg in the context of cationic dye removal or targeted adsorption applications, a thorough investigation of how pH influences the adsorption mechanism is vital. As the pH increases, the adsorption capacity of BY28 dye increases, reaching a maximum at pH 8, as shown in Figure 4(b). This phenomenon can be analyzed through an examination of the chemical composition of the dyes alongside the pH_pzc of the V/Pd-LDH/CD-Alg, as both elements significantly contribute to this observed behavior. When the solution pH is lower than the pH_pzc of the V/Pd-LDH/CD-Alg hydrogel beads (notably at pH values below 5.7), it is expected that a positive net charge will exist on the surface of the sorbent. The existence of a net positive charge on the surface of the adsorbent leads to minimal adsorption of cationic dyes due to the occurrence of repulsive forces between the positively charged adsorbent surface and the cationic dye molecules. Conversely, it is feasible that the adsorbent’s surface may exhibit a net negative charge, which would enhance the adsorption of cationic dyes. However, it is important to recognize that this adsorption effect diminishes significantly when the solution pH surpasses the pH_pzc of the V/Pd-LDH/CD-Alg, particularly at pH levels exceeding 5.7 [48].

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Figure 4.

(a) Resolve of pH_zpc, (b) Result of pH, (c) Result of adsorbent dose, (d) Result of preliminary concentration, (e) Result of communication time, and (f) Result of temperature.

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In conditions where the pH exceeds 8, the presence of hydroxide ions (OH⁻) generates a competitive interaction between carboxylate anions (-COO⁻) and positively charged nitrogen sites (-N⁺). BY28 ion adsorption onto the adsorbent surface is improved by the competition. The electrostatic reaction, which happens when the negatively charged surface of the adsorbent attracts the positively charged regions of the dye particles, is the main mechanism causing this adsorption. Consequently, comprehending the role of pH in the adsorption mechanism is crucial for enhancing the efficacy of V/Pd-LDH/CD-Alg in the elimination of cationic dyes [34,35].

3.3. Adsorption isotherm

Understanding and improving the adsorption behavior of BY28 dye on V/Pd-LDH/CD-Alg requires the use of adsorption isotherm models. These models offer important insights into the properties of the system and the fundamental processes underpinning the adsorption process. Specifically, the Langmuir isotherm model asserts that adsorption happens as a monolayer by a homogeneous surface, which renders it particularly effective for determining the maximum adsorption capacity (Q_max) [56]. This property highlights how successful the particular adsorbent is. However, the Freundlich isotherm, which is suitable for heterogeneous surfaces, shows variations in surface energy and adsorption intensity (n) [57]. This characteristic effectively represents the non-ideal aspects of the system. The Dubinin–Radushkevich (D–R) model offers a methodological framework for distinguishing among physical besides chemical adsorption procedures through the computation of the mean free energy (E_a) [58]. This analytical method is especially useful for evaluating porous materials, like hydrogel beads, as it allows for a more thorough comprehension of their adsorption properties. The Temkin isotherm offers a better understanding of the heat produced during the adsorption process by accounting for the interactions between the adsorbate particles. This is mainly significant for systems considered by moderate interaction forces among the adsorbates. In contrast, the Jossens isotherm demonstrates superior capability in characterizing non-ideal and intricate adsorption phenomena, proficiently addressing heterogeneous systems that exhibit a range of interaction strengths [59]. When shared, these models enable a thorough examination of the adsorption procedure, clarifying the composite substance’s effectiveness, surface appearances, and underlying adsorption mechanisms (Table S5).

Adsorption isotherm models, in particular the Langmuir isotherm, are essential instruments for investigating the adsorption characteristics of BY28 dye onto V/Pd-LDH/CD-Alg. Critical attributes such as adsorption capability, affinities, and the overall viability of the adsorption procedure can be more easily evaluated thanks to these models, which offer insightful information on adsorption dynamics [56]. For systems with a monolayer of adsorption on a uniform surface, the Langmuir model offers a substantial benefit, as it can accurately measure the equilibrium constant (K_L) and the maximum adsorption capability (Q_max). In this instance, with K_L valued at 0.165 L/mg, the moderate K_L value suggests a reasonably robust interaction between the adsorbate and adsorbent. This dynamic offers a favorable balance between efficient adsorption and the potential for dye desorption when necessary [60]. The dimensionless separation factor (R_L) has been determined to be 0.63, categorizing it within the favorable spectrum (0 < R_L < 1). This designates that the adsorption process is both viable and effective under the experimental conditions analyzed. Such metrics not only validate the efficacy of hydrogel beads for removing BY28 dye but also establish a basis for potential scaling of the process and optimization of operational parameters for practical implementations (Figure 5a).

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Figure 5.

(a) Adsorption isotherms, (b) Adsorption kinetics, (c) Intraparticular diffusion, and (d) Schematic mechanism of the diffusion.

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The Freundlich isotherm and other adsorption isotherm models are vital for analyzing and improving the adsorption of BY28 dye on V/Pd-LDH/CD-Alg. This is chiefly relevant for systems considered by heterogeneous surfaces, where the complexities of adsorption behavior must be thoroughly evaluated. The Freundlich model demonstrates its utility in analyzing complex systems by accounting for a heterogeneous distribution of adsorption sites and differing affinities [61,62]. This property allows for a more sophisticated comprehension of adsorption processes that can take place over a variety of energy levels. In the analysis of this system, the Freundlich constant, denoted as K_F= 217.83 (mg/g) (L/mg)^1/n, shows a considerable potential for adsorption and acts as a gauge of both adsorption intensity and capacity [63]. Given that a number larger than one indicates high contacts between the adsorbent and the adsorbate as well as a significant affinity for the dye BY28, the measured value of n=6.33 suggests that the adsorption circumstances are favorable. Furthermore, the high value of n specifies that the adsorption procedure is both efficient and quick, highlighting the effectiveness of hydrogel beads as an adsorbent substance [57]. These parameters underscore the beneficial aspects of the Freundlich isotherm in representing the varied characteristics of the hydrogel beads’ surface. To advance the efficiency of dye removal techniques, they provide important information that can aid in the design, scaling, and optimization of adsorption processes (Table S6).

The adsorption kinetics of BY28 dye onto V/Pd-LDH/CD-Alg can be better understood using the models of adsorption isotherm, including the model of D–R. This is especially crucial for differentiating between chemical and physical adsorption processes. The D–R isotherm, rooted in the principles of adsorption energy and predicated on a Gaussian distribution of energy across the surface of the adsorbent, proves to be especially applicable to porous materials such as hydrogel beads [20,38,53]. Given their exceptional adsorption capacity (Q_DR=420.26 mg/g), these hydrogel beads appear to be highly effective at removing BY28 from aqueous solutions. With a mean free energy of adsorption, E_a, of 27.8 kJ/mol and an estimated K_DR of 1.113×10⁻⁶ mol²kJ⁻², it is clear that chemical interactions are the main force behind the adsorption process. The finding that an Ea value greater than 8 kJ/mol is typically suggestive of chemisorption taking place inside the system lends more credence to this. The evidence presented underscores the robust binding interactions exhibited by hydrogel beads with dye molecules, positioning them as a potentially effective adsorbent. The D–R model proves to be instrumental in offering mechanistic insights and quantifying energy parameters, thereby serving as an appreciated device for the optimization and design of efficient adsorption organizations aimed at the removal of industrial dyes [58].

Adsorption isotherm models, exemplified by the Temkin model, offer significant benefits for the examination of BY28 dye adsorption onto V/Pd-LDH/CD-Alg. The analysis of the communications among the adsorbate molecules and the surface of the adsorbent is very pertinent in this context. According to the Temkin isotherm, connections among adsorbates cause the heat of adsorption to decrease linearly as surface coverage rises. Because of this feature, the isotherm is especially important when examining systems in which these communications play a critical role. The adsorption energy in this analysis is represented by the Temkin constant, b_T = 67.17 J/mol, which shows a modest degree of contact strength. This suggests that stability and equilibrium are reached during the adsorption procedure. Additionally, the equilibrium binding constant K_T = 8.53 L/mol indicates that the hydrogel beads have a strong affinity for BY28 dye, supporting their effectiveness as an adsorbent material. A detailed examination of the adsorption process is made conceivable by the model’s ability to incorporate the impacts of adsorbate interactions in addition to the adsorption energy. This synthesis of factors contributes to the optimization of operational parameters and the enhancement of the adsorption system’s scalability, ultimately improving the efficacy of dye removal [64].

The Jossens adsorption isotherm model offers significant benefits when examining intricate adsorption processes, such as the adsorption of BY28 dye onto V/Pd-LDH/CD-Alg. This model is especially relevant in scenarios characterized by surface heterogeneity and various mechanisms of interaction [22,46,65]. The model incorporates considerations for non-ideal adsorption phenomena and offers a versatile structure for examining systems characterized by fluctuating adsorption energies. Within this framework, the equilibrium constant (K = 73.61) signifies a strong interaction between the hydrogel beads and the BY28 dye, pointing to a substantial adsorption efficiency. Meanwhile, the heterogeneity factor (J = 0.138) represents the degree of uniformity among the adsorption sites; a diminished J-value suggests an increased level of heterogeneity, a characteristic often observed in composite materials such as hydrogel beads. The specified parameters underscore the model’s efficacy in elucidating the complex adsorption processes of BY28 dye on the hydrogel interface. By integrating both equilibrium conditions and heterogeneity considerations, the Jossens model offers significant analytical insights into the underlying adsorption mechanisms. This characteristic renders it a crucial instrument for refining system performance in practical dye removal applications.

3.4. Adsorption kinetics

It is necessary to apply kinetic models of adsorption to clarify the processes and rate-limiting factors associated with the adsorption of BY28 dye onto V/Pd-LDH/CD-Alg. For processes primarily governed by physical adsorption mechanisms, the pseudo-first-order model is effective since it assumes that the rate of adsorption is exactly proportional to the number of available vacant adsorption sites. This makes it useful for exploratory studies [66]. The pseudo-second-order model, in contrast, shows better performance in situations when chemisorption processes are essential to the process [67]. The underlying assumption of this model is that the square of the number of available adsorption sites and the reaction rate are comparable. These perspectives proposals valuable insights into the mechanisms of chemical bonding and electron transfer. The intraparticle diffusion model examines the process by which dye molecules penetrate the pores of hydrogel beads. It determines the dominant mechanism, be it intraparticle diffusion, surface adsorption, or film diffusion, that regulates the rate of this diffusion [68]. Improving the adsorbent’s physical properties requires knowing which of these processes acts as the rate-limiting factor [36,60,69]. The Elovich model is specifically formulated for systems exhibiting heterogeneous surface characteristics and effectively characterizes chemisorption phenomena [70]. In this model, the rate of adsorption is observed to decline exponentially as surface coverage increases, which yields important insights into the heterogeneity of the substantial and the intricate dynamics of its interactions. When considered alongside other models, the Elovich model facilitates a detailed analysis of adsorption kinetics, allowing for the discernment of prevailing mechanisms and informing the optimization processes for hydrogel beads, thereby enhancing their efficiency and scalability in the removal of BY28 dye (Table S5).

The model of pseudo-first-order kinetics has many benefits when studying the adsorption of BY28 dye onto V/Pd-LDH/CD-Alg, especially when physical adsorption is more common. Because it accepts that the adsorption rate is directly comparable to the number of available adsorption sites, this model is especially well-suited for first evaluations of the basic adsorption mechanism. In this system, the rate constant (K₁ = 0.08 (min⁻¹)x10⁻²) is noted to be relatively low, which implies a moderate adsorption rate. This finding implies a slow shift toward equilibrium and shows a strong dependence on the dye’s initial concentration. The straightforward nature of this model, coupled with its capacity to generate preliminary rate predictions, makes it an important tool for assessing the adsorption properties and determining whether hydrogel beads are viable as adsorbents [66]. Additionally, it makes it easier to compare different adsorbent materials and improves empathetic of the adsorption dynamics, both of which are critical for system optimization and scalability Figure 5(b). The model of pseudo-second-order kinetics provides important information about how BY28 dye adsorbs onto V/Pd-LDH/CD-Alg, especially when chemisorption is the predominant mechanism [67]. According to this model, the rate of adsorption is directly correlated to the square of the number of available adsorption sites, which makes it especially suitable for systems with strong interactions involving the adsorbent and adsorbate. The rate constant (K₂ = 2.38×10⁻⁵ (g.mg⁻¹min⁻¹)x10⁻²) indicates a relatively gradual yet consistent adsorption rate. This finding implies that chemical bonding in combination with the sharing of electrons or exchange mechanisms is most likely a crucial component of the adsorption process. Because it offers crucial details on the kinetics and adsorption capacity of the process, the pseudo-second-order model offers several advantages. Additionally, it typically shows a superior fit to experimental data, especially in systems like the V/Pd-LDH/CD-Alg that have heterogeneous or chemically interacting surfaces. Thus, for efficient dye removal applications, this model is an essential tool for improving operating conditions and enabling the scaling of adsorption systems (Figure 5c).

There are many advantages to using the model intraparticle diffusion kinetics for the analysis of BY28 dye adsorption onto V/Pd-LDH/CD-Alg by elucidating the diffusion mechanism and pinpointing the rate-limiting steps. According to this model, the adsorption procedure happens in multiple steps, including the achievement of equilibrium adsorption on the surface, intraparticle diffusion, and external mass transfer (Table S7). The intraparticle diffusion rate constant (K_i = 50.78 (mgg⁻¹min^1/2)) functions as a metric for assessing the rate at which dye molecules enter the internal architecture of the hydrogel beads. This value signifies effective utilization of pores, while also implying a swift attainment of equilibrium. Conversely, the intercept (X=22.62 mg/g) indicates the boundary layer’s influence; a greater value suggests that significant surface adsorption takes place prior to the internal diffusion process. This model presents a significant advantage through its capability to differentiate various stages of diffusion and assess whether intraparticle diffusion is the singular rate-limiting factor or if additional influences, such as film diffusion or surface adsorption, contribute to the overall process. The model of intraparticle diffusion is a vital tool for optimizing the structure, arrangement, and functioning of hydrogel beads by providing a thorough examination of mass transfer mechanisms, which eventually enhances the effectiveness of dye removal [68].

There are several advantages to using the Elovich kinetic model to analyze BY28 dye adsorption on V/Pd-LDH/CD-Alg. hydrogel beads, particularly in scenarios characterized by heterogeneous surfaces. When surface coverage rises, the rate of adsorption decreases exponentially, suggesting a decrease in adsorption efficacy as accessible sites are employed. This model accurately depicts the dynamics of the processes of adsorption. The Elovich constant (β=58.77 g/mg) in this analysis represents the rate constant for desorption; a higher value indicates a slower desorption process, which is suggestive of strong connections among the adsorbent besides adsorbate. As the complex dynamics of contact found in the composite hydrogel beads are reflected in the initial adsorption rate parameter (α=0.0011 mg.g⁻¹min⁻¹), the technique of adsorption appears to be initiated gradually. The Elovich model presents a significant benefit in its capacity to accurately represent adsorption phenomena on adsorbent surfaces exhibiting high heterogeneity, such as V/Pd-LDH/CD-Alg. beads. In these instances, there is a notable variation in adsorption energies across the surface. This model offers crucial insights into the performance dynamics of the adsorbent overtime and assists in determining the optimal operational conditions to enhance efficiency [70]. The Elovich model offers a complete analysis of adsorption kinetics while emphasizing the impact of surface heterogeneity. This knowledge is essential for increasing hydrogel beads’ operational effectiveness and design, which will ultimately increase their efficacy and sustainability in dye removal applications [71].

3.5. Diffusion mechanism

The diffusion process, along with its rate-controlling phase, was elucidated through the application of diffusion theories to equilibrium data. This analysis reveals four distinct phases associated with the kinetics of adsorption. The film diffusion process mostly determines: (a) how the sorbate goes from most of the solution to the external surface. This phenomena demonstrates how mass transfer works, with the pace at which the sorbate moves across the surface’s surrounding boundary layer determining the transfer technique’s overall effectiveness; (b) dispersion throughout the outermost layer; (c) The procedure by which the sorbate goes from the outside to the inside of the sorbent material’s pores is known as intra-particle diffusion; and (d) The binding places are efficiently blocked by the adsorbent. The influence of diffusion across the boundary layer and the extent of binding region occupancy by the sorbate on the kinetics is comparatively less significant when contrasted with the consequences of both film and intra-particle diffusion [72]. Both surface and pore diffusion processes were investigated using an intra-particle diffusion model to determine the phase responsible for the rate shown in Figure 5(d).

3.6. Adsorption thermodynamics

Analyzing thermodynamic limits is essential for evaluating the spontaneity then enthalpy alterations involved in sorption processes. These limitations are computed using the equilibrium constant (K_c), which is obtained from the linearized Langmuir model [73]. Eqs. S9 and S10 of the van’t Hoff formula represent the link between temperature with the equilibrium constant. Within this framework, ΔH^o represents the enthalpy change, ΔS^o indicates the entropy change, and ΔG^o denotes the Gibbs free energy change, each playing a crucial role in understanding the dynamics of chemical reactions. The standards of ΔH^o and ΔS^o were extracted from the slope and intercept determined from the linear correlation formed between lnK_c and 1/T. An analytical examination of the thermodynamics associated with the biosorption process has yielded significant findings regarding its characteristics. The positive enthalpy change (ΔH^o = 95.08 kJ/mol) suggests that the procedure is characterized by an endothermic reaction, implying that it absorbs heat from its surroundings during the course of the reaction. This implies that the adsorption mechanism needs the absorption of heat energy to proceed, which could be connected to the robust interactions that take place between the dye particles and the surface of the sorbent. Furthermore, a positive change in entropy (ΔS^o = 328.5 J/mol.K) was noted, signifying a rise in disorder at the boundary between the solid and liquid phases throughout the adsorption procedure [74]. The rearrangement of the adsorbent and the adsorbate, along with the release of ions or water molecules from the sorbent’s surface during the adsorption process, are linked to the observed rise in entropy. Similarly, the change in Gibbs free energy (ΔG^o) exhibited a relationship with temperature, as shown in Figure 6, which indicated that a temperature rise was linked to a more negative value of ΔG^o. The values presented suggest that the process exhibits thermodynamic favorability and exhibits an increased spontaneity as temperatures rise (Table S5 and S8). This observation is consistent with the endothermic characteristics associated with the adsorption process, where elevated temperatures contribute to the spontaneity. The Van’t Hoff plot, showing an R² value of 0.986, indicates a strong correlation; however, it implies that the system might not entirely comply with the theoretical constraints put forth by the Van’t Hoff calculation. Numerous factors, including surface heterogeneity, multi-site sorption dynamics, and ion exchange interactions, can affect the equilibrium constant and are responsible for the phenomenon being studied. The adsorption process appears to have endothermic properties, which are more advantageous as the temperature rises, according to the thermodynamic variables. This hypothesis is further supported by the observed decrease in Gibbs free energy with increasing temperatures. However, the Van’t Hoff model’s weak correlation suggests that other variables may have an impact on the adsorption dynamics, requiring more investigation to fully elucidate the underlying mechanisms at work [75].

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Figure 6.

Van’t Hoff model of adsorption of BY28 onto V/Pd-LDH/CD-Alg.

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3.7. The interaction mechanism

The adsorption mechanism involving β-cyclodextrin and alginate-based particles can be understood through the intricate interactions among its principal constituents. The matrix formed by β-cyclodextrin and alginate serves as the primary active substrate, featuring crucial useful groups, specifically carboxyl (COO⁻) and hydroxyl (-OH) groups. Multiple connections to dye molecules, including pore-filling, hydrogen bonding, van der Waals forces, and electrostatic attraction, are made possible by the different functional entities. These interactions significantly affect the overall effectiveness of adsorption. Additionally, cross-linking agents like epichlorohydrin play a vital role in establishing covalent bonds among the chains of the alginate polymer [76]. This engagement results in the creation of a three-dimensional structure that advances the material’s mechanical strength in addition to chemical stability. The implementation of this framework effectively avoids the dissolution or gelation of β-cyclodextrin as well as alginate under acidic conditions. This enhanced stability ensures the physical integrity of the subdivisions is maintained while diminishing their swelling. As a result, this process optimizes both the surface area and accessibility of active places (Figure 5d).

The widely acknowledged principle of electrostatic attraction focuses on its capability to generate interactions between surfaces that carry opposing charges. The amount of charge carried by the contaminant under analysis and the acidity or basicity of the solution in question have a big influence on this phenomenon. The V/Pd-LDH/CD-Alg presents a negative charge, attributed to the deprotonation of reactive groups that are accessible in an alkaline situation. This phenomenon is maintained by the material’s point of zero charge (pH_pzc), which is measured at 5.56. This characteristic implies that the BY28 dye and negatively charged groups located on the V/Pd-LDH/CD-Alg hydrogel beads’ surface could create electrostatic relationships [49,77].

• A dipole-dipole communication known as a hydrogen bond (H-bond) is produced when binary atoms acting as hydrogen donors besides acceptors combined. To properly secure different organic molecules connected to V/Pd-LDH/CD-Alg, this type of bond frequently plays a crucial role. The hydrogen acceptors in this case are provided by BY28 dye, which primarily consists of nitrogen besides oxygen atoms, whereas the hydrogen donor is anticipated to come from the hydroxyl (-OH) groups found in the constituents. Strong correlations exist between the amount of hydrogen bonding in the V/Pd-LDH/CD-Alg and the percentage of oxygen as well as nitrogen in the detected BY28 dye [71].

• The process of BY28 dye adsorption onto V/Pd-LDH/CD-Alg can be interpreted as primarily driven by pore filling mechanisms. The important decrease in pore size, surface area, and volume shown both before then after adsorption lends credence to this conclusion. Such changes suggest that the adsorbent’s pores effectively accommodated a portion of the BY28 dye, indicating a successful engagement between the substrate and the dye [52,59].

• One possible process is the interaction of BY28 dye atoms with lone electron pairs, which are made possible by coordination bonds, with positive cations, namely V and Pd. The synthetic composite’s peak adsorption capacity at equilibrium, according to an examination of other materials, is 453.1 mg/g. This positions the composite as one of the more efficient materials for the adsorption of BY28 dye. Additionally, it is cost-effective since it eliminates the need for pricey ingredients such as zeolite imidazole frameworks or activated carbon [38,78].

3.8. Reusability

An investigation into the feasibility of conducting multiple tests was undertaken concerning the recyclability of V/Pd-LDH/CD-Alg. To facilitate this experimental inquiry, 0.02 g of the V/Pd-LDH/CD-Alg was placed into a 25 mL conical flask, which contained a solution of BY28 dye at a concentration of 200 mg/L. Upon thoroughly mixing the components until adsorption equilibrium was reached, the residual quantity of BY28 dye was quantitatively assessed. After conducting a series of washing and rinsing procedures using anhydrous ethanol, the adsorbent underwent treatment with a 0.1 mol/L solution of HCl, then EtOH. Eliminating BY28 dye particles that were sticking to the adsorbent’s surface was the goal of this treatment. To assess the adsorbent’s adsorption capability following each cycle of use, the procedure was repeated several times. As exposed in Figure 7(a), the results offer an analytical viewpoint on the possibility of eliminating BY28 dye from aqueous solutions on a wide scale and at a reasonable cost. Remarkably, after undergoing six iterations of testing, the adsorbent maintained a robust capacity for BY28 dye molecule adsorption, consistently surpassing 86.6%. These findings from the repeatability assessment suggest a significant potential for the reusability of the adsorbent. Following six testing cycles, an analysis of the XRD data showed that the adsorbent had maintained its structural integrity, as shown in Figure 7(b). The stability of the V/Pd-LDH/CD-Alg. Hydrogel beads were evaluated through XRD analysis, which indicated that the adsorbent preserves its structural form despite undergoing multiple regeneration processes [79].

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Figure 7.

(a) Renewal effectiveness of V/Pd-LDH/CD-Alg hydrogel beads, and (b) PXRD pattern of V/Pd-LDH/CD-Alg and renewed.

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Following six successive adsorption–desorption cycles, the adsorbent’s structural integrity and elemental consistency were carefully evaluated using SEM-EDX elemental mapping and point EDX spectral analysis (Figures S1 and S2). The SEM imagery indicates that the material’s flake-like microstructure remains fully intact, showing no apparent signs of fragmentation or morphological degradation, thereby confirming its notable mechanical stability. Elemental mapping reinforces this finding, revealing a uniform and consistent distribution of essential elements including calcium (Ca), chlorine (Cl), nitrogen (N), oxygen (O), carbon (C), palladium (Pd), and vanadium (V) throughout the surface, which reflects the even retention of the composite’s functional components. Furthermore, the associated pie chart and the EDX spectrum quantitatively illustrates the enduring presence of these major constituents: calcium (19.1%), oxygen (15.9%), chlorine (8.7%), carbon (8.7%), nitrogen (2.6%), Vanadium (2.6%), and Palladium (0.6%). The simultaneous maintenance of both the elemental composition and morphological integrity over six regeneration cycles emphasizes the material’s significant reusability and chemical resilience, highlighting its promising application in efficient and sustainable heavy metal removal.

3.9. Effect salinity

This study investigated the impact of various anions, specifically Cl⁻, SO₄²⁻, NO₃⁻, and HCO₃⁻, on the ability of V/Pd-LDH/CD-Alg to adsorb BY28 dye at a 200 mg/L concentration and a 50 mg/L salt concentration. The addition of chloride ions has been determined to significantly enhance the adsorption of BY28, reaching a notable efficiency of 94.2%, as depicted in Figure 8. In contrast, the presence of sulfate and nitrate ions exhibited a negligible impact on BY28 adsorption, resulting in a decreased removal efficacy of 80.2% and 82.4%, respectively [37]. Additionally, the presence of bicarbonate ions severely hindered the adsorption capacity, resulting in a removal efficiency of only 64.8%. This diminished adsorption capability may be attributed to an increase in solution pH, which can lead to the deprotonation of the adsorbent surface, thereby reducing its efficacy to adsorb due to increased repulsive forces. According to these results, BY28 competes with chloride, sulfate, nitrate, and bicarbonate ions for binding to the active sites on the surface of V/Pd-LDH/CD-Alg [36].

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Figure 8.

The impact of disruptive ions on BY28 adsorption onto V/Pd-LDH/CD-Alg.

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3.10. Comparison with other adsorbents

The sorbent V/Pd-LDH/CD-Alg has an impressive sorption capability of 453.1 mg/g, exceptional the performance of most adsorbents reported in the works to date. In addition to this high sorption capacity, the kinetics of sorption associated with these beads are particularly swift, suggesting their viability as an efficient and practical option for diverse applications (Table S9). The adsorbent demonstrates significant efficacy in wastewater treatment, particularly in scenarios where the contaminant is prevalent in aquatic environments. This is evidenced by its notable capability to bond with BY28 dye, particularly within wastewater contexts. In conclusion, there is significant promise for the V/Pd-LDH/CD-Alg as an adsorbent for the removal of BY28 dye from aqueous solutions [54,62]. Table S10 contrast table summarizing the performance of various LDH-based adsorbents with similar functionalities to your V/Pd-LDH/CD-Alg.

3.11. Response surface study and modelling of investigational designs

3.11.2. Model adequacy checking

To obtain an in-depth understanding of how the examined variables influence the removal of BY28 dye, three-dimensional surface response designs were employed to investigate the significant interactions among these variables. Figure 9(a) shows how the amount of V/Pd-LDH/CD-Alg and variations in pH levels affect the BY28 dye’s adsorption capacity. Each modification in the experimental conditions was maintained for a duration of 100 min, allowing for a comprehensive assessment of their effects. The information illustrated in Figure 9(b) reveals a notable correlation between the increasing pH levels, ranging from 2 to 8, and the enhanced adsorption efficiency of BY28 dye. This indicates that a rise in pH is associated with an augmentation in the dye’s adsorption capacity. An enhancement in the adsorption capacity was seen at a pH of 8. It was discovered that pH 8 and an adsorbent dosage of 0.02 g per 25 mL were the optimal values. The determination of pH 8 as the most favorable condition can be primarily linked to the positively charged nature of the BY28 dye, along with the pH_pzc value of the V/Pd-LDH/CD-Alg, which has been reported to be 5.56. Therefore, the adsorption process demonstrates an improvement when the pH is sustained above the threshold of 5.48. Figure 9(b) illustrates the impact that variations in the dosage and application timing of V/Pd-LDH/CD-Alg hydrogel beads have on the adsorption capacity for BY28. The findings indicate a relationship between the length of interaction and the adsorption efficiency, with the maximum absorption occurring at 0.02 g of the adsorbent and a continued contact time of 100 min. Variations in exposure times and pH levels have an impact on the adsorption capability of V/Pd-LDH/CD-Alg with respect to BY28 dye, as shown in Figure 9(c). The data indicate that as pH values increase, particularly in alkaline environments, the adsorption capacity demonstrates an initial rise when transitioning from pH 2 to pH 8, after which a decline is noted. Additionally, it was found that extending the contact time correlates positively with an increase in adsorption capacity [19,20].

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Figure 9.

(a-c) Analysis of the mutual interaction and desirability regarding the dye adsorption capacity of BY28 on V/Pd-LDH/CD-Alg derived from RSM-CCD: interactions between adsorbent amount and pH; adsorbent amount and duration; pH and duration.

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3.11.3. Cubic interaction and perturbation plot

The visual connection between predictable and measured values is illustrated in Figures 10(a) and (b). The V/Pd-LDH/CD-Alg served as the medium for the extraction of BY28 dye. To evaluate the effectiveness of this procedure, various analytical methodologies were employed, including an examination of residuals in relation to the number of runs, calculations of extremely studentized residuals, generation of the BOX-COX plot, and an analysis of agitation effects. The high degree of consistency between the expected values and the actual data found demonstrates the statistical dependability of the model, as shown in Figures 10(a) and (b). Additionally, Figures 10(c) and (d) provide a visual demonstration of the relationship between the residuals and the adsorption dynamics of BY28 dye [20]. The data points’ wide dispersion and aggregation close to zero speak to the model’s high level of dependability and effectiveness. By analyzing the response results to the actual values, one might find any unexpected or unforeseen values or trends that the model might not have considered. The Box-Cox curves, which serve as a helpful tool for determining the optimal power transformation objective for the response variable, are displayed in Figure 10(e). The Box-Cox graph’s smallest point indicates the ideal Lambda value, which is associated with the modified model’s least residual sum of squares. The ideal Lambda value, which yields the least residual sum of squares in the updated model, is thus represented by this lowest point on the Box-Cox graph [21,22]. The graphs demonstrating the suitability of the model demonstrate a high degree of performance. To properly evaluate the yield reply, one variable was changed while maintaining the same values for all other variables. The variables under analysis appear to have a favorable effect on the adsorption capability. The differences shown in the figure indicate that the duration, pH, and dosage have the most significant influence. Furthermore, the correlation between pH levels and adsorption process time demonstrates how rapidly these factors impact adsorption capability [84,85]. Figure 10(f) shows that the variables of duration, pH, and amount had a favorable impact on the process of adsorption. As shown in Figure 10(f), the parameters that produced the best adsorption efficacy were a pH of 8, a dose limit of 0.02 g, and a communication time of 100 min [86].

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Figure 10.

(a) Real values compared to predictable values, (b) Standard residual probability, (c) Residuals in relation to forecasts, (d) Residuals against iterations, (e) Box-Cox graph, and (f) Disturbance plot.

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Figure 11.

(a) There is an increasing attention in the best numerical solutions, (b) The appeal of each response is considered, and (c) A bar chart illustrating the attractiveness of each response is presented.

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