Analytical modeling and interpretation of ultrasound-assisted adsorption mechanism of fuchsine dye on MgZnFeO nanocomposites

Abstract An efficient co-precipitation followed by ultrasonication process is used for the synthesis of trimetallic MgZnFeO nanocomposites (MZFONCs) and further characterized by FE-SEM, FT-IR, XRD, EDX, etc. spectroscopic techniques. The adsorption process is applied for the removal of toxic cationic Basic Fuchsine (BF) dye using batch experiments. To enhance removal efficiency, the effect of deviation in parameters including shaking time; adsorbent dose; pH; etc. are studied. Q max obtained by Langmuir is found to be 250 mg/g for BF on the MZFONCs surface, at pH = 6.5; 40 min of agitation time, and a small dose of nanoparticles. The best match for the adsorption of BF on MZFONCs is a double-layer method which also describes the adsorption mechanism. The ‘n’ parameter value (0.507–0.628) is obtained from the statistical physics model, which shows mixed-orientation type adsorption of BF molecules on MZFONCs adsorbents. The calculated energies for BF dye adsorption are found to be less than 30 KJ/mol, hence implying an endothermic and physical adsorption mechanism. Graphical Abstract


Introduction
The textile industry is the major consumer of dye and also a major source of discharge of dye wastewater.Dye water reduces the ability of photosynthesis which can affect whole aquatic ecosystems.Incomplete dye decomposition by bacteria (anaerobically) through toxic amine in sludge can also disrupt aquatic life.Potable water sources on the planet are limited, yet they are still insufficient. [1]Fuchsine dye can cause respiratory illness such as nasal inflammation and chronic contamination and can lead to bladder tumors.The disposal of wastewater and solid waste caused by the overuse of Fuchsine dyes pollutes the environment. [2,3]Jia Li et al.  (2014) have used ZnFe 2 O 4 magnetic hollow fibers for acid Fuchsine removal with a significant adsorption capacity of 150.37 mg/g.Mohammadine El Haddad (2016) successfully utilized biomass waste material from a mussel shell for the adsorption of BF.Likewise, Gupta et al. studied the feasibility of 'bottom ash' and 'deoiled soya' for BF uptake and the percent adsorption was found to be 83.75 and 94.25%, respectively.Mohamed Kadari (2016) eliminated BF using functionalized Zn/Al-DDPA with 90% uptake efficiency.Similarly, investigation of the uptake capacity of activated carbon for BF from simulated water was found to be 98% in the research study of Liyi Ye (2011).6][7][8] Recently studied Mg, Zn, and Fe metal oxides for dye removal are selected and produced as MgZnFeO nanocomposites (MZFONCs) for the rapid and efficient adsorption of dye pollutants from industrial wastewater.11][12] The data from the experiments are used to validate various kinetic models.In addition, the isotherms of Freundlich, Langmuir and Temkin model are also studied.This study reveals how Fuchsine dye is adsorbed on MZFONCs as well as the importance of understanding the adsorption process by determining their mechanism, thereby further improving the actual adsorption process.The conventional isothermal models are applied to interpret and describe the interactions between BF-MZFONCs.Though the parameters of these empiric models lack physical significance, therefore the implementation of these models are contributed to a narrow understanding of the adsorption process.Additionally, the isothermal study of adsorption of BF dye is proposed with the help of statistical models. [13]At the molecular level, this statistical theory is beneficial, because it gives physico-chemical significance and provides specific interpretations of the parameters that influence the adsorption process. [14,15]Lotfi Sellaoui et al. first time applied this model for tetrachlorethylene adsorption study at microscopic levels. [16]The thermodynamic parameters of the phenomenon of adsorption can be derived using this model.The non-linear regression method is applied to the computer-based software (MS Excel; 2007) to fit and derive the analytical parameters of the models.

Material
Ferric chloride (FeCl 3 anhydrous); zinc chloride (ZnCl 2 powder); magnesium nitrate and Fuchsine (Basic) are purchased from Merck, India.Sodium hydroxide pellets, Basic Fuchsine dye and hydrochloric acid (HCl) are obtained from Fischer Scientific, India and are used without further purifications.De-ionized (MilliQ) water is used throughout this work, including the synthesis of nanocomposites.

Ultrasound-assisted synthesis of MZFONCs
The MZFONCs are blended by using a co-precipitating agent, NaOH in the aqueous medium followed by sonication with heating.Firstly 1.45 mol of MgNO 3 , 1.0 mol of ZnCl 2, and 1.0 mol of FeCl 3 are added into 150 mL of de-ionized water (DW) while stirring for 5 min.The temperature is kept at 45 � C to warm the solution and 1 g of sodium lauryl sulfate (SLS) is added.The product is precipitated by adding 50 mL of NaOH (5 M) solution to the former solution.For smaller and more uniform particles, the solution is sonicated by using an ultrasound probe system for 2 h at 40 � C. The precipitate is then cooled and washed with DW, till the pH reached below 7.5.The precipitate is dehydrated after filtration at approximately 100 � C for about 8 h.The material is processed into a fine powder and then calcinated for 3 h at 400 � C.

Characterization techniques
It is difficult to get the maximum output without first understanding the material's attributes.So, the very important task of characterization of the materials is performed.Advanced sophisticated techniques are used to reveal the properties of synthesized nanocomposites.Details of properties and their instruments exploited are given in supplementary Table T1.
The spectrophotometric method is used to find out the concentration of BF (k max ¼545 nm) dye during the experiment using UV-Visible spectrophotometer (model UV-1800).

Experimental
Basic Fuchsine (BF) is chosen as a triphenylmethane representative dye for the experiments over synthetic MZFONCs.At primary level without using ultrasound adsorption of BF dye (Table 2) is investigated and it is found to be very less, i.e., 20-30% adsorption of dye on to MZFONCs.To increase the adsorption percentage ultrasonication treatment is applied.The process and outcome are given in next section.

Ultrasound-assisted adsorption experiments
Initially degradation of BF dye is studied without addition of nanocomposite and it is observed to be only 8-10% of dye is degraded.While, after addition of nanocomposites adsorption of dye increased.The detail study is as follows: 50 mg of MZFONCs is added in 50 mL of BF dye solution of known concentration and pH, in a 250 mL conical flask.At room temperature, the mixture of MZFONCs and BF dye solution is kept in an ultrasonic bath for 90 min.The sample is centrifuged and the final BF dye concentration is measured using a UV-Vis spectrophotometer at a wavelength of 545 nm.The various parameters are investigated, viz.sonication time (0-90 min); BF concentration (10-200 mg/L); pH (3-12) and MZFONCs amount (50-200 mg).The MZFONCs with BF dyes are isolated by centrifugation at the end of the adsorption tests. [17]he supplementary equation 1, calculates the adsorption capacity, q t (mg/g) at various time intervals: After 90 min, the dye concentration at equilibrium, q eation (mg/g) is measured as well as computed by using the supplementary equation 2.

Optimization of pH of the solution
To determine the optimal condition for maximum dye adsorption efficiency of MZFONCs, some preliminary testing is carried out.The adsorption of basic Fuchsine on MZFONCs is examined by adjusting the pH in the range of 3-12 in different Erlenmeyer flasks.Initially, 50 mL of 10 mg/L dye solution and 50 mg of MZFONCs are combined in an ultrasonic bath for 90 min.After reaching equilibrium, the amount of dye remaining is estimated by spectrophotometer (k max ¼ 545 nm).The pH profile is illustrated in supplementary Fig. S2.According to the pH plots the significant uptake of the dye takes place at pH ¼ 6.5.Hence, all the later studies are executed at pH 6.5.After the optimization of all the parameters, finally, the spectrophotometric method is exploited to determine the quantity of the remaining dye in the solution.

Optimization of contact time
50 mg of MZFONCs and 50 mL of 10 mg/L dye solution in the flask are mixed using a rotary shaker for different time slots at 250 rpm for 2-90 min at previously optimized pH ¼ 6.5.The significant uptake amount of the dye takes place at 90 min.Therefore, an optimum contact time of 90 min is set.

Optimization of adsorbent dose
Adsorbent dosages of 50, 100, 150, and 200 mg/L are introduced to four Erlenmeyer flasks, each holding 50 mL of 10 mg/L BF solutions.At room temperatures, the optimized experimental parameters are kept at their optimum conditions.A 200 mg/L dosage of adsorbent results in a large quantity of dye absorption.After that, 0.20 g/L is chosen as the optimal adsorbent dose.

Optimization of dye concentration
For a 200 mg/L adsorbent dose, a range of dye concentrations of 10-200 mg/L is utilized.All of the other parameters are kept at their optimal settings.At 200 mg/L adsorbent dosages, there is a large quantity of dye adsorption.As a result, 200 mg/L is chosen as the optimal dye concentration.

Statistical physics model for dye adsorption mechanism
An adsorption model is developed by using the assumptions of the statistical physics method. [18]A large number of molecules are connected to receptor sites (N M ) on the adsorbent (unit mass).So, in the general reaction, the adsorbate molecules (D) are adsorbed onto the adsorbent receptor site (R). [15] where n ¼ stoichiometric coefficient (may be an integer or not; lower than or greater than 1).When n < 1 (i.e., multi-anchorage adsorption involved), the fraction of molecule is adsorbed per site of adsorbent (supplementary figure S8) and if n > 1 (i.e., multi-molecular adsorption is assumed), means the single site is occupied by the number of molecules). [19]The isotherm may be represented within this theory by a single layer process or by modeling the formation of two or more layers.The experimental dye adsorption may be estimated by using a two-energy double-layer model.The suggested model which is based on statistical approaches may be seen here.The analytical model is utilized to evaluate the dye mechanism by assuming a multilayer system.The adsorption of BF dye onto nanoparticles is believed to occur through the development of multilayers of BF dye (adsorbate).The formation of the first layer (BF-MZFONPs interaction) and the second or more layers (N 2 ) (that entail BF-BF interaction) are both influenced by two energies viz.e 1 and e 2 , respectively.Advanced statistical models for the formalism of the mechanism of BF dye adsorption onto tested nanocomposites are presented for the assessment of operational parameters that impact the adsorption process.

Monolayer, double layer and multi-layer adsorption model
According to the monolayer adsorption model, [16] RHB dye molecules form a single layer with adsorption energy (e 1 ).Double layer adsorption, [20][21][22] in which the first layer must offer acceptor sites for an additional layer of dye molecules, resulting in two adsorption energies e 1 and e 2 as previously stated.If adsorption occurs by multilayer adsorption [23][24][25] with two distinct interaction energies e 1 and e 2 , the equations are as follows: We can determine n, N M , C 1 , C 2 , and the total number of dye molecules layers N t ¼ 1 þ N 2 using this approach.C 1 is the first layer and C 2 is the concentration of the remaining N 2 layers at half-saturation.

Desorption/reuse studies
The adsorbed dye is desorbed using a 2.5 mL methanolacetic acid combination at an 80:20 ratio as a desorption medium, to test the reusability of produced MZFONCs.In a flask, the BF-MZFONCs are exposed to this dispersion medium.After centrifugation, the mixture is shaken for 10 min.The dye is mostly desorbed and the regenerated nanocomposites are calcinated for 2 h at 60 � C and reused.The percentage of dye desorbed is calculated using the following formula: where C d is the concentration of dye at the end of desorption (in mg/L)

Characterization
Advanced sophisticated techniques revealed the properties of synthetic MZFONCs.The FE-SEM image (Figure 1a) shows MZFONCs with a medium particle diameter of 70 nm in similar shapes with different sizes.As shown in Figure 1b, the sample composition is verified using EDX analysis, and the results confirmed that the MZFONCs consist of Mg, Zn Fe, and Oxygen.The synthetic nanocomposite is found to be pure by EDX analysis, with weight amounts of 7.33, 14.59, 11.83, and 66.25%, respectively.Figure 1c

Effect of contact time
The time of interaction between the dye and the adsorbent is an important factor.The results of the time variation demonstrate that just 40 min of ultrasonication is required for dye adsorption (above 90% ±2) (supplementary Fig. S1).
Additional ultrasonication shows little effect on dye adsorption which remained steady.The reason for this is that the starting concentrations of both dye and adsorbent are high, resulting in rapid absorption.After 40 min, the active sites of the adsorbent are blocked by the dye adsorption and it is about to attain equilibrium.As a result, no additional dye is adsorbed, and the graph showed a straight line after 40 min (supplementary Fig. S1).

Effect of pH
The pH of the adsorption system is an important factor.The MZFONCs' point of zero charge is 5.9 (pH zpc ¼5.9).It indicates that when the pH of the system is above 5.9, the surface of the nanocomposites will be negatively charged, whereas when the pH is below 5.9, the surface will be positively charged.According to supplementary Fig. S2, considerable dye adsorption occurs above pH zpc , indicating that the adsorption is caused by electrostatic interaction between the negatively charged surface of MZFONCs and cationic dye molecules.At this pH, Basic Fuchsine is removed at a maximum of 97%±2.

Effect of adsorbent dose
For this experiment, different amounts of MZFONCs (0.05-0.20 g) are used as described in the experimental section.In light of the findings, it is noted that on increasing the quantity of MZFONCs the percentage of BF adsorption increases (supplementary Fig. S3).This behavior is attributable to a large number of dye-absorbing sites present on MZFONCs surface. [26]

Effect of dye concentration
When the percent adsorption of BF dye is plotted versus the concentration of the dye solution (supplementary Fig. S4), it can be seen that the percent adsorption of the dye decreases as the concentration of the dye solution increases.At increasing dye concentrations, the available active sites of the material will be utilized first then there are no active sites available resulting in a drop in dye adsorption. [26]

Adsorption kinetics and diffusion models
To understand the removal behavior of dye, the reaction kinetics, as well as factors that influence the removal rate, must be determined.(Pseudo) first-order (Eq.4) and (Pseudo) second-order (Eq.5) kinetics for BF elimination are investigated.supplementary Fig. S5 shows the linear plot of a second-order kinetic model.The second-order adequacy is validated by maximum R 2 ¼0.999 value which is compared to experimental and theoretical data originated from the (Pseudo) first-order (as seen in supplementary Table T3) which indicated that the concentration of BF dyes in aqueous solution decreased with reaction time. log Where the rate constants for pseudo-first-order and pseudo-second-order kinetics are K 1 (min À 1 ) and K 2 , respectively.The values are placed in supplementary Table T3.The pseudo-second-order kinetic experimental value of Q e (200 mg/g) corresponds to the theoretical value (q e ¼ 200 mg/g).At the deep level, the phenomenon intraparticle diffusion model co-exists along with the adsorption.This phenomenon affects the rate of adsorption and aids in finding the rate-determining step.This phenomenon is known as liquid film diffusion in physisorption and as mass transfer in chemisorption. [1]The rate-determining phase will adjust, depending on the quality of the adsorption. [1]For the acceptability of this model, the plot of q t vs. t 1/2 should have zero intercepts (i.e., pass through the origin), then it is assumed that diffusion inside the particle is the only mechanism for regulating the intensity of the adsorption. [1]owever, the plot of q t vs. t 1/2 (as shown in supplementary Fig. S6) does not have a zero intercept in the current experimental study.Hence, indicating that there should be a boundary layer effect, in addition to intraparticle diffusion, and therefore it would not be the only rate-controlling step for BF-MZFONCs system.Diffusion constant K id (mg g À 1 min À 1/2 ) is calculated using a plot of q t vs. t 1/2 (Eq.6).
It is shown in supplementary Fig. S6 that there is linearity after a certain period, but a full intercept is not obtained.It occurs due to the influence of the boundary layer. [1]

Adsorption isotherm
Isotherms are the equilibrium relationships between the concentration of solid-phase adsorbate and the concentration of the liquid phase adsorbates. [27]At a solution pH 6.0, adsorbent isotherms are tested with different initial dye (BF) concentrations (10-200 mg/L) and different adsorbent dosages (50-200 mg/L).The experimental data are fitted with adsorption isothermal models such as Langmuir and Freundlich isotherms.The isotherm parameters and R 2 values calculated from the linear fitting of experimental results are shown in supplementary Table T4.BF adsorption isotherms on MZFONCs are shown in supplementary Fig. S7.Adsorption isotherms provide information on the adsorbent's potential as well as on the nature of the interaction between the solute and the surface.
The adsorption potential of MZFONCs increases as the dye concentration increases. [27]The Langmuir isotherm is estimated to be monolayer adsorption of molecules on a homogenous surface and all the sites are equivalents. [27]upplementary equation 3 [27] is used to formulate the expression and the result are shown in supplementary Table T4.The Langmuir isotherm revealed that the BF-MZFONCs system is monolayer and that the experimental maximum adsorption potential (q max ) of MZFONCs is 250 mg/g (mg dye per gram of adsorbent).Freundlich isotherm is an analytical model that proposes that adsorption takes place on heterogeneous surfaces generated by the adsorption of different groups.The following equation represents Freundlich isotherm: [27] where K f is the adsorption capacity and is calculated by the intercept, and 1/n is the adsorption intensity or heterogeneity factor, which is derived by the slope of the linear plot of lnq e versus lnC e (supplementary Fig. S7).In addition, the numerical values are given in supplementary Table T4.All

Thermodynamic study
The Gibb's free energy (DG o ), entropy (DS o ), and enthalpy (DH o ) changes that were associated with the adsorption of BF dye onto MZFONCs were estimated using the Gibb's free energy and Vant Hoff equations (Supplementary equations 4-6).As indicated in supplemental Table T5, the values of Gibb's free energy are negative for BF dye adsorption on MZFONCs, and increase with increasing temperature.The enthalpy change (DH o ) value is positive, i.e., 0.215 ± 0.01 kJ/mol, indicating that the adsorption process is endothermic.Similarly, the value of entropy (DS o ) is positive 0.0325 ± 0.001 kJ/mol, indicating that randomness increases as a result of interactions.

Adsorption mechanism of BF dye onto the MZFONCs
As BF is a cationic dye, the electrostatic attraction between the MZFONCs and BF should be the reason behind this mechanism.At first, Cl À ions from the BF are attracted to the MZFONCs surface and are adsorbed initially due to the coordinating effect of Cl À ions generating a negative surface. [27,28]ationic BF is easily attracted to the negatively charged MZFONCs surface.Figure 2 illustrated the most probable mechanism.The maximum removal of BF is found to be at pH 6.5 as per the data collected during the study of pH influence on solution.It is noted that the adsorption capacity is less when the pH is higher or lower than the reported pH of 6.5.The solution turns colorless, indicating that the dye got adsorbed on the MZFONCs' surface.According to the above study, the good adsorption performance of MZFONCs is connected to its unique framework and a wide range of different surface spaces. [26]The adsorption process may be linked to the electrostatic attraction and the formation of an ion-association network. [27]The probable mechanism is illustrated in Figure 2a, b.

Interpretation of statistical parameters
For the assessment of experimental data, various computerized standard models are tested.Specifically, the analysis of the fitting of BF dye adsorption isotherm was studied using three statistical models as discussed earlier.
The estimated root mean square error (RMSE) and the well-familiar R 2 are chosen as the major criterion for selecting a good model.[35] The fitting graph of the double-layer model at temperature ranges from 298 to 318 K is presented in Figure 3.
The parameter 'n': It corresponds to the number of anchored BF unit species per functional group of tested nanocomposites and also provides the geometrical orientation of adsorbate molecules on the adsorbent surface at all temperatures studied (supplementary Fig. S8a).As depicted in Table 2, 'n' changes from 0.507 to 0.639.16,[20][21][22][23] This refers to the fact that dye molecules are subjected to many interactions.Remarkable thing is that no aggregation of dye molecules occurs since n < 1.This non-aggregation phenomenon is responsible for breaking of binding between adsorbate and receptor site and this leads to a decrease in the number of molecules per site.The rise in temperature causes a little increment in the values of 'n' as shown in Table 2.The thermal agitation causes the orientation as 'n' increases up to 0.639 at 308 K.

Interpretation of adsorption energies
To gain an accurate understanding of the adsorption behavior of the BF on adsorbent; the adsorption energy measurement is useful.The adsorption energies e 1 and e 2 associated with the formation of the two layers on MZFONCs adsorbents are measured using the expressions (8) and (9) at various temperatures with concentrations at half-saturation.The results are summarized in Table 2.This observation revealed that the adsorption process is endothermic.This is associated with the effect of temperature on the adsorption potential (supplementary Fig. S8d).
Where R is the ideal gas constant and Cs is the water solubility of BF dye.
The magnitude of e 1 is higher than e 2 confirming that the BF-MZFONCs interaction is stronger than the BF-BF interaction (supplementary Fig. S8d).44][45]

Reuse properties of the MZFONCs
After the adsorption experiment, the BF-MZFONCs system is regenerated by desorbing the dye in the desorbing media mixture of methanol and acetic acid and is further calcined at 60 � C for 2 h.The rejuvenated MZFONCs are reused and the performance is recorded which is displayed in the graphical format in supplementary Fig. S10 (as a function of the reuse cycle).The experimental adsorption capacity of 250 mg/g is considered to be 100%.There is no leaching of metal ion from the adsorbent is observed during the adsorption, desorption and reuse study.As the NCs are reused up to the fifth cycle, their % adsorption capacity decreases to about 85%.MZFONCs can still be reused for the following cycle, although it is not cost-effective.The comparision of MZFONCs adsorbent with the previously reported adsorbents for the Basic Fuschin dye is given in the Table 3.

Advantages and disadvantages of MZFONCs
We have found that this synthesized MZFONCs is chemically inert, environmentally friendly as there is no toxic element in the composite, economically viable and has good reusable properties (supplementary Fig. S9), No loss of electronic property after reuse, good adsorption capacity (supplementary Fig. S2).Similarly this nanocomposites have some disadvantages as it is less selective i.e., it is not only used for the removal of dye but also for toxic metals like Cr and it is having very limited binding sites as compared to functionalized adsorbents such as Fe/ZSM-5 (Table 3).

Conclusions
The synthetic MZFONCs have an excellent adsorption potential of 250 mg/g.The maximum adsorption occurred at optimized conditions of experimental parameters, viz.pH 6.5; 0.20 g/L adsorbent dosage, 10 mg/L dye concentration and 40 minutes of ultrasonication contacting time.The rate of adsorption was shown to be affected by both liquid film transfer and intraparticle diffusion.In this study, novel MZFO nanocomposite is first time synthesized and reported as an adsorbent for the removal of Basic Fuchsin dye from wastewater.This new nanocomposite is extremely effective (supplementary Fig. S2), efficient (supplementary Fig. S1), economically viable, and reusable (supplementary Fig. S9) nano adsorbents.This adsorption method is efficient, cheap and rapid for the removal of dyes.Synthesized MZFONC competing the convensional adsorbent as it having very good adsorption capacity as compared to previously reported adsorbent such as Fe-MgO/kaolinite (10.36 mg/g), Al/MCM-41 (54.44),YZnO nanoparticles (75.53 mg/g) and Starch-capped zinc selenide nanoparticles (222.7 mg/g).In particular, as compared to traditional adsorbents for the removal of hazardous dyes from water, these new composite nanoparticles are extremely effective, efficient, economically viable, and reusable nano adsorbents.

Disclosure Statement
We have no conflict of interest.
depicts the XRD results.The MZFONCs miller planes (200), (111), (002), and (111) are represented by the X-Ray peaks of 28.48 � , 31.61 � , 35.49 � , and 55.72 � , respectively.The sharp peak indicates a uniform surface with high specific surface area.XRD graph after desorption of dye and reuse of nanocomposite is exactly matched with earlier one that indicate the stability of nanocomposite.Peaks in FTIR spectrum in Figure 1d at 903, 875, and 835 cm À 1 are due to the characteristic metallic bonding M-O (M ¼ Mg, Zn, Fe) and also Peak at 1349 cm À 1 related to M-O modes.Bending and stretching vibrational modes of hydroxyl groups are observed at 1633 and 3398 cm À 1 .

Figure 1 .
Figure 1.(a) High-resolution FE-SEM image (b) EDX spectrum, (c) X-ray diffraction pattern before and after reuse of NCs and (d) FT-IR spectrum of MZFONCs.
of the values of correlation coefficient R 2 for the Langmuir model are greater than those for the Freundlich model, according to the experimental data.All the Langmuir model parameters indicate BF monolayer coverage on the surface of MZFONCs.

Figure 2 .
Figure 2. Illustrations of the possible mechanism for BF-MZFONCs system.

Figure 3 .
Figure 3. Non-linear fitting of model 2 at three different temperatures.

Table 3 .
Adsorption capacity of several adsorbents toward Basic Fuschin dye.