Alumina/Iron Oxide Nano Composite for Cadmium Ions Removal from Aqueous Solutions

Magnetic alumina nano composite (MANC) was prepared for combination of the adsorption features of nano activated alumina with the magnetic properties of iron oxides to produce a nano magnetic adsorbent, which can be separated from the medium by a simple magnetic process after adsorption. MANC was characterized using XRD, SEM, TEM, EDX and surface area (BET). Quantum design SQUID magnetometer was used to study the magnetic measurement. The present study was conducted to evaluate the feasibility of MANC for the removal of cadmium ions from aqueous solutions through batch adsorption technique. The effects of pH, adsorbent dose, temperature, contact time and initial Cd2+ concentration on cadmium ions adsorption were studied. Equilibrium data were fitted to Langmuir, Freundlich and Temkin isotherms. The equilibrium data were best represented by the Langmuir isotherm. The kinetic data were fitted to pseudo-first-order, pseudo-second-order, Elovich and intraparticle diffusion models, and it was found to follow closely the pseudo-second-order model. Thermodynamic parameters were calculated for the Cd2+ ion-MANC system and the positive value of ΔH° showed that the adsorption was endothermic in nature. Furthermore, a single-stage batch adsorber was designed for the removal of Cd2+ ions by MANC based on the equilibrium data obtained.


Introduction
Water is the most precious natural resource that exists on our planet although we as humans recognize this fact; we discharged it by polluting our rivers, lakes and underground water. The release of heavy metals into the environment is a potential threat to water and soil quality as well as to plant, animal and human health. Heavy metals can be bioaccumulated through food chain transfers and unlike organic toxicants are not amenable to biological degradation [1]. Over the last two decades there has been a sharp rise in the global use of Cd for batteries and a steady decline in its use for other applications, such as pigments, polyvinyl chloride stabilizers, and plating. This trend in the use of Cd products and compounds has inspired a number of international agreements to manage and control the release of Cd to the environment and limit human and environmental exposure to Cd can cause kidney damage in mammals and humans [2,3]. Also, cadmium (Cd) is one toxic heavy metal of particular environmental concern, because it can be introduced into and accumulated in soils through agricultural application of sewage sludge, fertilizers, and/or through land disposal of Cd-contaminated municipal and industrial wastes. Cd is a known human carcinogen and may induce lung insufficiency, bone lesions and hypertension [4]. The high toxicity of cadmium has resulted in governments imposing ever tighter environmental legislation limiting wastewater discharge and the removal of heavy metals such as Cd from wastewater has been a major preoccupation of environmental professionals for many years. In particular, ever increasing world populations are likely to place increasing stress on a limited clean water resource placing a greater focus on clean up and reuse of contaminated wastewater streams [1]. Among the various methods proposed for this purpose adsorption proved to be of the most promising ones [5,6]. Several natural (e.g. natural zeolites, bentonites, metal oxides) and synthetic (e.g. synthetic zeolites, resins, metal phosphates and silicates, synthetic oxides/hydroxides/hydroxyoxides) materials have been investigated as sorbents for heavy metal removal from solutions achieving different levels of success [7][8][9][10][11][12][13]. Moreover, considerable research work has been done on various industrial waste materials in order to develop suitable sorbents for water treatment; so fly ash [14,15], blast fumace slug [16], biomass [17,18] and bagasse fly ash [19], among others have been tested as sorbents for heavy metal removal with various levels of success. Although, Adsorption processes are widely used for treatment of polluted surface and groundwaters and also play a significant role in advanced wastewater treatment. In adsorption, Adsorbents remove adsorbates by means of concentrating them on the large inner surface so that adsorbents with higher specific surface area possess superior adsorption capacity. A small particle size of the adsorbent can offer not only a greater specific surface area but also better mass transfer efficiency. However, a high pressure drop may be encountered with the compact adsorbent in a packed bed adsorption column if the particle diameter is smaller than 0.5 mm [5]. Because of the disadvantages caused by the small particle size, the batch stirred adsorption system with intensive mixing, which enhances the adsorption rate, is usually adopted for the use of powder adsorbents. However, the separation technology of ultra-fine particles, especially nano-scale particles, is still under development and presents difficulties to a certain extent. As a result of these disadvantages using such small particles as adsorbents, there is a great deal of interest in the preparation of nanosized magnetic particles and understanding of their properties, which are drastically different from those of the corresponding bulk materials [20]. The magnetic particle technology has a high potential to be applied in adsorption systems. In order to remove the target pollutants or compounds from the streams, the magnetic particles can be modified by the combination or modification of functional groups or inorganic compounds yielding magnetic adsorbents [21]. It is well known that porous ceramics are used in a wide range of applications including catalysts, effective absorbents, ionic conductors, filtering membranes, coatings and insulating aerogels [22][23][24][25]. Alumina is one of the most widely used ceramics due to its high specific surface area, very good thermal stability and amphoteric properties [26]. Due to these characteristics porous alumina is generally a very good candidate as a catalyst carrier as well as an adsorbent. Although alumina is used very fre-quently as a ceramic matrix for metal-composite materials, only a few works have been published concerning its participation in magnetic composites.
This work aims to evaluate the prepared magnetic alumina nano-composite (MANC) in removal of cadmium ions from aqueous solutions. The effects of various operating parameters such as solution pH, adsorbent dose, temperature, initial Cd 2+ concentration and contact time on cadmium ions adsorption were investigated. Also the effect of loading of alumina by iron oxide on cadmium ions adsorption was studied. Adsorption isotherms, kinetics and thermodynamics of the sorption process were studied. Further, a single-stage batch adsorber was designed for the removal of cadmium ions by MANC based on the equilibrium data obtained.

Preparation of Magnetic Alumina Nano Composite (Adsorbent)
The nano composite (MANC) was prepared from a suspension of activated alumina in 400 mL solution of FeCl 3 (7.8 g, 28 mmol) and FeSO 4 ·H 2 O (3.9 g, 14 mmol) at 343 K. A solution of NaOH (100 mL, 5 mol·L −1 ) was added drop wise to precipitate the iron oxides. The amount of activated alumina was adjusted in order to obtain the Activated Alumina/iron oxide with weight ratio of 3:1. The 3:1 weight ratio of activated alumina to Fe oxide was chosen to avoid a decreasing in adsorption capacity of the composites due the high content of iron oxide. The obtained materials were dried in a digital dryer of (Carbolite, Aston Lane, Hope Sheffield, 5302RP, England) at 373 K for 3 h.

Characterization of Magnetic Alumina
The adsorbent(MANC) was characterized by using X-ray diffraction analysis (XRD), Scanning electron microscopy (SEM), transmission electron microscope (TEM), Quantum design SQUID magnetometer and BET surface area. X-ray diffraction analysis was carried out using Xray diffractometer (Schimadzu-7000, USA) to evaluate the phase composition, XRD spectra were obtained with a 30 kW rotating anode diffractometer fitted with a copper target. XRD spectra were obtained between 20˚ and 80˚ (2θ) in continuous scan with 4 • /min using the stan-dard θ -2θ geometry. The morphology of the synthesized powders was studied using the SEM/EDX analysis which was performed using scanning electron microscope Jeol JMS 6360 LA, and the sample was prepared by coating with gold. Also, Jeol transmission electron microscope (TEM) with Max. Mag. 600 k× and resolution 0.2 nm was used to study the morphology of the prepared MANC. The samples were prepared by sonication for 30 min. Also the textural characteristics of MANC including surface area, pore size analyzer (BET) were determined using standard N2-adsorption techniques (Beckman Coulter, SA3100, USA). A quantum design SQUID magnetometer was used to obtain hysteresis loops of products at 25 • C and in fields up to 15 kOe nano composite.

Adsorbate
A stock solution of Cd 2+ was prepared (1000 mg·L −1 ) by dissolving required amount of, CdCl 2 ·2.5H 2 O in distilled water. The stock solution was diluted with distilled water to obtain desired concentration ranging from 100 to 1000 mg/L. pH was adjusted using 0.1 N HCl or 0.1 N NaOH. The remaining concentration of Cd 2+ in each sample before and after adsorption was determined by using prodigy prism high dispersion inductive coupled plasmaatomic emission spectroscopy (ICP-AES, USA).

Batch Mode Adsorption Studies
The effects of experimental parameters such as, pH (2 -9) using pH meter (Denver Instrument Co., USA), adsorbent dosage (0.25 -3.0 g·L −1 ), temperature (22 • C -55 • C), initial Cd 2+ ions concentration (100 -1000 mg·L −1 ) and contact time (0 -300 min) on the adsorptive removal of Cd 2+ ions were studied in a batch mode operation. For kinetic studies, 250 mL of Cd 2+ solution of known different initial concentrations and pH = 6 was taken in a 250 mL screw-cap conical flask with a fixed adsorbent dosage (1 g·L −1 ) and was agitated in a orbital shaker (yellow line OS 10 Control, Germany) for a contact time varied in the range 0 -300 min at a speed of 250 rpm at 295 K. At various time intervals, the adsorbent was separated and the concentration of Cd 2+ was determined. For adsorption isotherms, 250 ml of different initial Cd 2+ ion concentrations (100 -1000 mg·L −1 ) were agitated with 1 g·L −1 adsorbent dosage in an orbital shaker at 250 rpm for 240 min. The adsorbent was separated and the metal under consideration was determined as mentioned previously. The concentration retained in the adsorbent phase (q e , mg·g −1 ) was calculated by using the following equation where C o is the initial Cd 2+ concentration and C e is the Cd 2+ concentration (mg·L −1 ) at equilibrium, V is the volume of solution (L) and W is the mass of the adsorbent (g).

X-Ray Analysis and Microstructure
The X-ray diffractograph in Figure 1(a) represent the pattern of pure alumina used in the experimental work. Figure 1( where β is the FWHM of diffraction peak, λ is the wave length of X-ray (0.154 nm), L is the crystallite size, and θ is the Bragg peak position. The crystallite size was found to be 13.6 nm and 17.5 nm for both Al 2 O 3 and Fe 3 O 4 respectively.

Magnetic Properties
The magnetization curve obtained from the SQUID magnetometer is shown in Figure 2. The saturation magnetization Ms value is 12.12 emu/g, the remanance  Mr is 2.679 emu/g and the coericivity Hc is 44.89 Oe. This behaviour indicates that magnetic loaded alumina showed paramagnetic properties and its separation from treatment aqueous media can be achieved by applying magnetic field [27]. The magnetite content can be calculated on the basis of being the saturation magnetization of bulk magnetite is 94 emu/g. Because the magnetization of the produced composite is only due to Fe 3 O 4 , the mass percentage of Fe 3 O 4 in MANC can be estimated from the value of Ms considering the saturation magnetization of Fe 3 O 4 as reference saturation magnetization. So the content of Fe 3 O 4 in MANC is 12.12 weight percent.

Morphology and Microstructure
The SEM image of MANC was shown in Figure 3(a). The particles are nearly uniformly spherical and the particle size can be measured in the range of 25 -29 nm. In addition the energy dispersive X-ray spectroscopy (EDX) is shown in Figure 3(c), (EDX) shows the atomic percent of Al and Fe are 29.89 and 36.39 respectively. The EDX spectra reveal that the Fe 3 O 4 phase is abundant on the surface of MANC deduced from the high atomic ratio of iron.
Transmission electron microscope (TEM) was used to investigate the nature of magnetic nanoparticles in the produced composite. The produced composite showed uniform spherical nanoparticles with diameter range between 7 and 18 nm, the magnetite nanoparticles are finally divided and well distributed within the composite as shown in Figure 3(b). It was not possible to distinguish between the iron oxide and aluminium oxide phase's structure.

Textural Analysis
The surface area and the pore structure of MANC sample were determined from nitrogen isotherm analysis, as shown in Figure 4. MANC displayed a type-IV iso- therm, characteristic for mesoporous materials. Using these data, the specific surface area SBET was calculated to be 298 m 2 ·g −1 , the pore size 25 Å, and the total pore volume 0.29 mL·g −1 .

Effect of pH
Metal-ion adsorption is known to be dependent on the pH of solution. The effect of pH on the adsorption of Cd 2+ by MANC was studied by varying the initial pH of the solution over the range of 2 -9. The calculation from the solubility product equilibrium constant (Ksp) demonstrated that the best pH range of 2 -9 for Cd 2+ for adsorption [28]. Figure 5 illustrated that removal efficiency increased with increase pH. The uptake of Cd 2+ by MANC increased as the pH increased from 2 to 9. Although a maximum uptake was noted at a pH of 9, as the pH of the solution increased to >7, Cd 2+ started to precipitate out from the solution. Therefore, experiments were not conducted over pH 7 to avoid precipitation [29]. The increased capacity of adsorption at pH > 7 may be a combination of both adsorption and precipitation on the surface of the adsorbent. It is considered that MANC had a maximum adsorption capacity at a pH = 6, if the precipitated amount is not considered in the calculation. Therefore, the optimum pH for Cd 2+ was determined to be 6 and used in all experiments. The same trend has also been reported in the removal of Cd 2+ ions by other adsorbent materials such as Bamboo charcoal [30] and crosslinked carboxymethyl konjac glucomannan [31].  The metal ions in the aqueous solution may undergo salvation and hydrolysis. The process involved for metal adsorption is as follows [32]: The pK a value for Cd 2+ is 10.1. Perusal of the literature on metal speciation shows that the dominant species is M(OH) 2 at pH > 6.0 and M 2+ and M(OH) + at pH < 6.0. Maximum removal of metal was observed at pH 6 for adsorption. On further increase of pH adsorption decreases probably due to the formation of hydroxide of cadmium because of chemical precipitation [33][34][35].

Effect of Adsorbent Dosage
Adsorbent dosage is an important parameter because it determines the capacity of an adsorbent for a given initial concentration of the adsorbate. The effect of adsorbent dosage was studied on Cd 2+ ions removal from aqueous solutions by varying the amount of MANC from 0.25 to 3.0 g·L −1 , while keeping other parameters (pH, agitation speed, temperature, initial Cd 2+ ion concentration and contact time) constant. Figure 6 showed that the percent removal of Cd 2+ ion increased from 96.06% to 99.99% for MANC as the adsorption dosage was increased from 0.25 to 3 g·L −1 . On the other hand, the amount adsorbed per unit mass of the adsorbent decreased considerably. The decrease in unit adsorption with increase in the dosage of adsorbent was due to adsorption sites remaining unsaturated during the adsorption process [36]. For the rest of the study 1 g·L −1 adsorbent dosage is considered as optimum dosage for cadmium removal using MANC. Figure 7 shows the effect of contact time on the adsorbed amount of Cd 2+ by MANC from solutions with different initial concentrations of Cd 2+ (100 -1000 mg/ L) at 22 • C. The adsorption increased sharply with contact time in the first 40 min and attained equilibrium within 240 min. It is also clear from Figure 7(a) that by increasing the initial Cd 2+ ions concentration the percentage of Cd 2+ removal decreased, although the actual amount of Cd 2+ adsorbed per unit mass of MANC increased as shown in Figure 7(b). At low initial solution concentration, the surface area and the availability of adsorption sites were relatively high, and the Cd 2+ ions were easily adsorbed. At higher initial solution concentration, the total available adsorption sites are limited, thus resulting in a decrease in percentage removal of Cd 2+ ions. The increased in the equilibrium adsorption amount of Cd 2+ at higher initial concentration can beattributed to enhance the driving force. The equilibrium adsorption amount of Cd 2+ was found to increase from 100 to 501 mg·g −1 as the initial concentration increased from 100 to 1000 mg·L −1 .

Effect of Contact Time and Initial Cd 2+ Ions Concentration
The same trend has also been reported in the removal of Cd 2+ ions by Bamboo charcoal [30]. The higher adsorption capacity and rate of Cd 2+ on MANC indicated its suitability to treat wastewater polluted with Cd 2+ .

Effect of Temperature
Temperature plays key roles on the adsorption process [37]. First, increasing the temperature decreases the viscosity of the solution which, in turn, enhances the rate of diffusion of the adsorbate molecules across the external boundary layer of the adsorbent and resulted in higher adsorption. Second, changing the temperature may affect the equilibrium adsorption capacity of the adsorbent. For instance, the adsorption capacity will decrease upon increasing the temperature for an exothermic reaction; while it will increase for an endothermic one. Hence, a study of the temperature-dependent adsorption processes provides valuable information about the standard Gibbs free energy, enthalpy and entropy changes accompanying adsorption. In this study, a series of experiments were conducted at 22 • C, 35 • C, 45 • C and 55 • C to investigate the effect of temperature on Cd 2+ adsorption and determine thermodynamic parameters. Figure 8 shows the amount of Cd 2+ adsorbed onto MANC nano adsorbents at different temperatures. As seen in the figure, the amount of Cd 2+ adsorbed increases as the temperature increased. This increase suggests that the adsorption process is an endothermic one. The increase in the Cd 2+ adsorption with temperature may be due to the increase in ions mobility, which in turn increases the number of ions that interacted with active sites at the adsorbent surfaces. Similar trends are also observed by other researchers for aqueous phase adsorption [38,39].

Effect of Loading of Alumina by Iron Oxide
The adsorption tests showed that the magnetic alumina nano-composite possesses the same adsorption capacity as pure activated alumina, suggesting that the presence of Fe oxide in the composite is not inhibiting the adsorption of metals. Figure 9 compares the adsorption capacity of magnetic alumina nanocomposite and activated alumina. From this figure, the composites showed high adsorption capacities for the Cd 2+ in aqueous solution and, more important, no reduction of the adsorption was produced by the formation of the composite.

Adsorption Isotherms
Adsorption isotherms describe qualitative information on the nature of the solute-surface interaction as well as the specific relation between the concentration of adsorbate and its degree of accumulation onto adsorbent surface at constant temperature. Adsorption isotherms are critical in optimizing the use of adsorbents, and the analysis of the isotherm data by fitting them to different isotherm models is an important step to find the suitable model that can be used for design purposes [40]. There are several isotherm equations available for analyzing experimental sorption equilibrium data, the most famous adsorption models for single-solute systems are the Langmuir and Freundlich models. The experimental data obtained in the present work was tested with the Langmuir, Freundlich and Temkin, isotherm models. Linear regression is frequently used to determine the best-fitting isotherm, and the applicability of isotherm equations is compared by judging the correlation coefficients.

Langmuir Isotherm
The theoretical Langmuir sorption isotherm [41] is valid for adsorption of a solute from a liquid solution as monolayer adsorption on a surface containing a finite number of identical sites. The model is based on several basic assumptions: 1) the sorption takes place at specific homogenous sites within the adsorbent; 2) once a Cd 2+ occupies a site; 3) the adsorbent has a finite capacity for the adsorbate (at equilibrium); 4) all sites are identical and energetically equivalent. Langmuir isotherm model assumes uniform energies of adsorption onto the surface without transmigration of adsorbate in the plane of the surface. Therefore, the Langmuir isotherm model was chosen for estimation of the maximum adsorption capacity corresponding to complete mono-layer coverage on the sorbent surface. The Langmuir isotherm model is represented in the linear form as follows [41] ( ) where K L is the Langmuir adsorption constant (L·mg −1 ) and Q m is the theoretical maximum adsorption capacity (mg·g −1 ). Figure 10 shows the Langmuir (C e /q e vs. C e ) plot for adsorption of Cd 2+ ions. The value of Q m and K L constants and the correlation coefficient for Langmuir isotherm are presented in Table 1. The correlation coefficient was high (R 2 = 0.976) as shown in Table 1. This result indicates that the experimental data fitted well to Langmuir sorption isotherm with maximum adsorption capacity 625 mg/g. The essential characteristics of Langmuir dimensionless constant separation factor or equilibrium parameter, R L , which is defined by the following Equation [42]: where C o is the initial Cd 2+ ions concentration, mg/L. The R L parameter is considered as more reliable indicator of the adsorption. There are four probabilities for the R L value: 1) for favorable adsorption 0 < R L < 1, 2) for unfavorable adsorption R L > 1, 3) for linear adsorption R L = 1 and 4) for irreversible adsorption R L =0. In the present study, the values of R L ( Table 2) are observed to be in the range 0 -1, indicating that the adsorption process is favorable for MANC.

The Freundlich Isotherm
The Freundlich isotherm model is the earliest known relationship describing the sorption process [43]. The model applies to adsorption on heterogeneous surfaces with interaction between adsorbed molecules and the application of the Freundlich equation also suggests that sorption energy exponentially decreases on completion of the sorption centers of an adsorbent. This isotherm is an empirical equation which can be employed to describe heterogeneous systems and is expressed in the linear form as follows  where K F is the Freundlich constant (L·g −1 ) related to the bonding energy. K F can be defined as the adsorption or distribution coefficient and represents the quantity of Cd 2+ adsorbed onto adsorbent for unit equilibrium concentration. 1/n is the heterogeneity factor and n is a measure of the deviation from linearity of adsorption. Its value indicates the degree of non-linearity between solution concentration and adsorption as follows: if the value of n is equal to unity, the adsorption is linear; if the value is lower than unity, this implies that adsorption process is chemical; if the value is higher unity adsorption is a favorable physical process [44]. Figure 11 shows the plot of log(q e ) versus log(C e ) to generate the intercept value of K F and the slope of 1/n ( Table 1). The value of n is higher than unity, indicating that adsorption of Cd 2+ onto MANC is a favorable physical process [44]. The correlation coefficients, R 2 = 0.921. This result indicates that the experimental data did not fit well to Freundlich model. the Cd 2+ adsorption onto MANC because of the small correlation coefficient.

The Temkin Isotherm
Temkin isotherm model contains a factor that explicitly takes into account adsorbing species-adsorbate interactions [45]. This model assumes the following: 1) the heat of adsorption of all the molecules in the layer decreases linearly with coverage due to adsorbate-adsorbent interactions, and 2) adsorption is characterized by a uniform distribution of binding energies, up to some maximum binding energy. The derivation of the Temkin isotherm assumes that the fall in the heat of sorption is linear rather than logarithmic, as implied in the Freundlich equation. The Temkin isotherm has commonly been applied in the following form (Equation (9)) Table 1 summarizes all the constants and correlation coefficients, R 2 of the three isotherm models. The Langmuir model yielded the best fit with R 2 which were higher than 0.97. Confirmation of the experimental data into the Langmuir isotherm equation indicated the homogeneous nature of magnetic alumina nano-composite surface, i.e., each Cd 2+ ion/magnetic alumina nano composite (MANC) adsorption had equal adsorption activation energy. The results also demonstrated the formation of monolayer coverage of cadmium ions at the outer surface of MANC. The good correlation coefficients showed that Langmuir model is more suitable than Freundlich and Temkin for adsorption equilibrium of cadmium ions onto MANC. Values of the adsorption capacity of other adsorbents from the literature are given in Table 3 for comparison [46][47][48][49][50]. It is clear from this table that the adsorption capacity of MANC for Cd 2+ is higher than the other adsorbents. . A plot of q e vs lnC e at studied temperature is given in Figure 12. The constants obtained for Temkin isotherm are illustrated in Table 1. Examination of the data shows that the Temkin isotherm is not applicable to

Adsorption Kinetics
Kinetic models can be helpful to understand the mechanisms of metal adsorption and evaluate performance of the adsorbents for metal removal. The kinetics of Cd 2+ adsorption onto MANC is required for selecting optimum operating conditions for the full-scale batch process. The kinetic parameters, which are helpful for the prediction of adsorption rate, give important information for designing and modeling the adsorption processes. Thus, Lagergren pseudo-first-order [51], pseudo-second-order [52], Elovich [53][54][55] and intraparticle diffusion [56,57] kinetic models were used for the adsorption of Cd 2+ onto MANC. The conformity between experimental data and the model-predicted values was expressed by the correlation coefficients (R 2 , values close or equal to 1, the relatively higher value is the more applicable model).

The Pseudo First-Order Equation
The Lagergren pseudo-first-order model [51] is the earliest known equation describing the adsorption rate based on the adsorption capacity, which can be expressed in a linear form as where q e and q t are the amount of cadmium ions adsorbed (mg·g −1 ) on the MANC at the equilibrium and at time t, respectively, and k 1 is the rate of constant adsorp-  Natural corncobs 5.09 [46] Oxidized corncobs 55.2 [46] Alcaligenes eutrophus 122 [47] Leaves, platanus 110 [48] Soil, haldimand 99.9 [49] Yeast, baker's 91.74 [50] of ln(q e − q t ) versus t for different concentrations of the tion (min −1 ). Values of k 1 were calculated from the plots Cd 2+ ion as shown in Figure 13. The values k 1 and q e are given in Table 4.
The pseudo-first order equation was used to correlate the experimental data, based on the following mechanistic scheme: One cadmium ion was assumed to sorb onto one adsorption site of the MANC.
As noticed from Table 4 pseudo-first order kinetic predicts a lower value of the equilibrium adsorption capacity than the experimental value. Hence, this equation cannot provide an accurate fit of the experimental data.

The Pseudo Second-Order Equation
where k 2 is the rate constant of pseudo second-order adsorption (g·mg −1 ·min −1 ). The constants can be obtained Table 4. The pseudo first-order, second-order and Elovich kinetic parameters for Cd 2+ at different initial cadmium ions concentration by MANC.
1 st -order kinetic model 2 nd -order kinetic model Elovich kinetics model from plotting (t/q t ) versus t Figure 14. The values k 2 , q e and the initial adsorption rate h are given in Table 4.
The pseudo-second order model assumes that cadmium is sorbed onto two active sites: The equilibrium adsorption capacities, q e , obtained with this model are slightly more reasonable than those of the pseudo-first order when comparing predicted results with experimental data. Moreover, the values of R 2 also indicated that this equation produced better results ( Table 4) at all concentrations and adsorbent doses, R 2 values for pseudo-second-order kinetic model were found to be between 0.974 and 1. This indicates that the Cd 2+ MANC adsorption system obeys the pseudo-second order kinetic model for the entire sorption period.

Elovich Kinetic Equation
The Elovich equation is of general application to chem. isorptions kinetics. The equation has been applied satisfactorily to some chemisorption processes and has been found to cover a wide range of slow adsorption rates. The same equation is often valid for systems in which the adsorbing surface is heterogeneous, and is formulated as: where α (mg/g·min) is the initial adsorption rate and β is related to the extent of surface coverage and the activation energy involved in chemisorption (g/mg). The Elovich equation assumes that the active sites of adsorbent are heterogeneous [58], and therefore exhibit different activation energies for chemisorption. Teng and Hsieh [59] proposed that constant α is related to the rate of chemisorptions and β is related to the surface cover-age.
The Elovich equation is based on a general secondorder reaction mechanism for heterogeneous adsorption processes [58].
Plot of q t versus ln(t) should yield a linear relationship if the Elovich is applicable with a slope of (1/β) and an intercept of (1/βln(αβ) (Figure 15). The Elovich constants obtained from the slope and the intercept of the straight line reported in Table 4. The correlation coefficients R 2 are very wavy and ranged from low value to high value without definite role ( Table 4).

Intra-Particle Diffusion Model
The adsorption mechanism of adsorbate onto adsorbent follows three steps: film diffusion, pore diffusion and intra-particle transport. The slowest of three steps controls the overall rate of the process. Generally, intra-particle diffusion is often rate-limiting in a batch reactor, while for a continuous flow system film diffusion is more likely the rate-limiting step. In order to investigate the possibility of intra-particle diffusion resistance affecting the adsorption intra-particle diffusion model [56] was explored 0.5 t i where K i (mg·g −1 ·min −0.5 ) is the intra-particle diffusion rate constant. Figure 16 represents a plot of q t vs t 0.5 , it shows two separate regions the initial part is attributed to the bulk diffusion while the final part to the intra-particle diffusion. Values of I give an idea about the thickness of boundary layer (Table 5), i.e. the larger the intercept the greater is the boundary layer effect [60]. The data indicate that intra-particle diffusion controls the adsorption rate. Simultaneously, external mass transfer resistance cannot be neglected although this resistance is only significant for the initial period of time [61].   The data exhibit multi-linear plots, revealing that the process is governed by two or more steps (Figure 16). The first linear portion (phase I) at all concentrations, can be attributed to the immediate utilization of the most readily available sorbing sites on the sorbent surface. Phase II may be attributed to very slow diffusion of the Cd 2+ from the MANC surface site into the inner pores. Thus, initial portion of Cd 2+ ions sorption by MANC may be governed by the initial intra-particle transport of Cd 2+ controlled by surface diffusion process and the later part controlled by pore diffusion. The values of ki 1 and ki 2 (diffusion rate constants for phases I and II, respectively) obtained from the slope of linear plots are listed in Table  5.

Thermodynamics Studies
Thermodynamic parameters were evaluated to confirm the adsorption nature of the present study.
The variation in temperature, influencing the distribution of adsorbate between solid and liquid phases, was examined in the range 295 -328 ˚K. Moreover the increase in Cd 2+ sorption with a rise in temperature can be explained on the basis of thermodynamic parameters such as change in enthalpy (ΔH°), entropy (ΔS°) and free energy (ΔG°). The change in enthalpy (ΔH°) and entropy (ΔS°) are calculated by using the van't Hoff equation [62]. ; is the fraction adsorbed at equilibrium, while T is the temperature in degree K and R is the gas constant [8.314 (J/mol K)].
The plot of lnk c vs 1/T gives a straight line with acceptable coefficient (R 2 ) as shown in Figure 17. From the slope and the intercept of van't Hoff plots, the values of ΔH° and ΔS° were computed, while the Gibbs free enrgy change ΔG° was calculated using the following equation [63]: The thermodynamic parameters for the sorption of cadmium ions onto MANC at various temperatures were calculated and summarized in Table 6. The positive value of ΔH° indicates that the studied sorption processes are endothermic in nature. Furthermore the negative values of ΔG° demonstrate the spontaneous behavior of the sorption processes [63]. The decrease in the value of ΔG° with the increase of temperature shows that the reaction  is more spontaneous at higher temperature which indicates that the sorption processes are favored by the increase in temperature [64]. It is noteworthy that adsorption process with ΔG o values between −20 and 0 kJ/mol corresponds to spontaneous physical process, while that with values between −80 and −400 kJ/mol corresponds to chemisorptions [65,66]. From the ΔG o values obtained in this study, it can be deduced that the adsorption mechanism is dominated by physisorption. This also is supported by the fact that ΔH o < 40 kJ mol, indicating physical adsorption process [65]. Finally, the positive value of ΔS° suggest that the increased randomness at the solid-solution interface during the sorption process. The adsorbed solvent molecules which are displaced by the adsorbate species gain more translational entropy than ions lost by adsorbate, thus allowing for prevalence of randomness in the system [67]. Normally, adsorption of gases leads to a decrease in entropy due to orderly arrangement of the gas molecules on a solid surface. However, the same may not be true for the complicated system of sorption from solution [68].
Energy of activation was calculated and illustrated in Table 6 according to a relationship between E a and ΔH° for reactions in solution by the following equation [69]: Energies of activation below 42 kJ·mol −1 generally indicate diffusion-controlled processes and higher values represent chemical reaction processes [54]. In terms of E a , diffusion or transport controlled reactions are those governed by mass transfer or diffusion of the adsorbate from the bulk solution to the adsorbent surface and can be described using the parabolic rate law [70]. Conversely, the reaction is surface controlled if the reaction between the adsorbate and adsorbent is slow compared with the transport or diffusion of the adsorbate to the adsorbent. For surface controlled reactions, the concentration of the adsorbate next to the adsorbent surface is equal to the concentration of the adsorbate in the bulk solution and the kinetic relationship between time and adsorbate concentration should be linear [71]. In our study, the small value of the activation energy below 42 kJ·mol −1 confirms the fact that the process of the removal Cd 2+ using MANC is diffusion controlled.

Single-Stage Batch Adsorber
Adsorption isotherm studies can also be used to predict the design of single stage batch adsorption systems [72][73][74]. The schematic diagram for a single-stage adsorption process is shown in Figure 18. The solution to be treated contains V (L) of water and an initial Cd 2+ concentration C o (400 mg/L) which is to be reduced to C e in the adsorption process. In the treatment stage, the amount of adsorbent W (g) added is added to solution and the Cd 2+ ions concentration on the solid changes from q 0 = 0 to q e . The mass balance for the dye in the single stage is given by The Langmuir isotherm data may now be applied to Equation (19) since the Langmuir isotherm gave the best fit to experimental data.  Figure 19 shows a series of plots derived from Equation (20) for the adsorption of Cd 2+ ions on the adsorbent and depicts the amount of effluent which can be treated to reduce the cadmium ions content by 90%, 80%, 70%, 60% and 50% using various masses of the adsorbent.

Conclusions
The prepared Magnetic composite MANC was found to be in nano-scale with high surface area 298 m 2 ·g −1 and its magnetic behavior was paramagnetic, which makes its removal from treatment media by applying magnetic field possible. These properties made this composite an excellent candidate for removal of cadmium ions from water. Removal of cadmium ions on Magnetic alumina nano composite (MANC) is pH dependent and the maximum removal was attained at pH 6. The equilibrium adsorption is practically achieved through a time of 240 min. It was also a function of initial adsorbent dose and cadmium ions concentration, Also adsorption equilibrium data follows; Langmuir sorption isotherm with maximum adsorption capacity 625 mg·g −1 . The data indicate that the adsorption kinetics follow the pseudosecond-order model with intraparticle diffusion as one of the rate determining steps. The adsorption process was spontaneous and increased with increase in temperature showing endothermic nature of the adsorption.