Adsorption Isotherms And Kinetic Models For Fluoride Biology Essay

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Abstract: The adsorption of fluoride ion onto plasma modified CeO2/Al2O3 composites was systematically studied,which was investigated in a batch adsorption system, including both equilibrium adsorption isotherms and kinetics. Equilibrium adsorption data were analyzed using Langmuir, Freundlich and Dubinin-Radushkevich isotherm models,In order to understand the nature of adsorption, thermodynamic parameters such as ΔGθ,ΔSθ,ΔHθ and Ea were calculated. Results showed that the adsorption data was found to be well described by Langmuir model. The pseudo-first-order, pseudo-second-order and intraparticle diffusion models were applied to test the kinetic data, and the results revealed the pseudo-second-order kinetic reaction as the "surface reaction" was dominated and controlled adsorption stage. The ΔSθ increased from 78.42 J/mol K to 93.42J/mol K, the Ea decreased from 57.52kJ/mol to 49.94 kJ/mol and the ΔGθ was also decreased in fluoride ion adsorption onto plasma modified adsorbents in comparison with unmodified adsorbents. These confirmed that the adsorption occurred on plasma modified adsorbents was favorable.

Keywords: CeO2/Al2O3; plasma; adsorption kinetic; thermodynamic; isotherms

Introduction

CeO2 is making a positive effort for to environmental protection as environmental material, which was widely used as environmental degradable material, environmental engineering material, and environmental substituting material. In recent years, considerable attention has been focused on the study of defluoridation by rare earth metals from drink water, traditional treatment methods was rare earth metals loaded onto other materials, such as lanthanum incorporated chitosan beads[1], mixed rare earth oxides[2] and so on, most of studies were about synthesize material for fluoride remove[3-5], but less of them about material surface modification. Therefore, how to enhance the surface properties of materials is a timely task from both in lab and clinical viewpoints.

It is well known that plasma treatment can alter the surface properties of materials[6-11]. The plasma processing can modify the material's surface energy, permeability, surface conductivity, biocompatibility and adhesion to other materials without affecting the bulk of the materials [12]. Many researchers were reported that the modification of polymer materials[13-15], however, its application to adsorbents has not been well explored, there is still need(It is still needed ) for further scientific (to make an )efforts to study material surfaces modified by plasma, such as the thermodynamic parameter of activation energy change.

The thermodynamics and the kinetics determines the efficiency of adsorption, An appropriate isotherm for representing the equilibrium state of an adsorption,which can expresses the relation between the amounts of adsorbate removed from solution at equilibrium by unit of mass of adsorbent at constant temperature. The study of adsorption kinetics is highly relevant to the design of an adsorption system because it provides beneficial information in the reaction pathway, rate of adsorption and adsorption mechanism of adsorbate onto adsorbent, and it provides important information for designing and modeling the processes. hence, it is necessary to study the thermodynamics and kinetics of CeO2/Al2O3 composites remove fluoride from aqueous solution.

In this study, low temperature plasma was used to modify the surface state of CeO2/Al2O3 composites, the adsorption equilibrium and kinetic of fluoride onto CeO2/Al2O3 composites by different adsorption isotherm and kinetic models were investigated. Thermodynamic parameters were calculated by the adsorption isotherms.

Materials and methods

2.1. Reagents and instruments

NaF, Al2(SO4)3·18 H2O, Ce(NO3)3·6H2O, NaNO3, C6H5Na3O7·2H2O,NaOH, HCl, NH3·H2O, Total ionic strength adjustment buffer solution (TISAB), 200mg/L fluoride ion stock solution.

Fluoride ion selective electrode (pF-1), pH meter(pHS-3C), plasma generator(CTP-2000K).

2.2. Adsorption experiments

In our previous work, CeO2/Al2O3 composites have been synthesized by chemical coprecipitation method, The optimal calcination temperature conditions was 250℃, Ce /Al mol ratio of 1:20 has a high adsorption capacity. In this paper, 0.1 g of the adsorbent materials were added into 50mL of sodium fluoride at different initial concentrations. The adsorption capacity was calculated from following equation:

qt= (1)

(where qt is the adsorption capacity (mg /g) at any time, C0 and Ct are the initial fluoride concentration and the concentration of fluoride at time (mg/L), respectively, V is the volume (mL) of solution and m is the weight(g) of adsorbent used.)

2.3. Thermodynamic experiments

The equilibrium adsorption isotherm was determined using (to do )batch studies. 0.1g adsorbent materials and 50mL fluoride solution of various initial concentrations 20-200mg/L were poured into the beaker. The time required to reach equilibrium as determined in equilibrium studies was 24 h. A series of isotherms were determined at the temperatures of 303K, 318K, 333K, 348K, 363K, respectively.

2.4. Kinetic experiments

Adsorption experiments with modified CeO2/Al2O3 composites and pristine composites were performed at temperatures of 208K,298K, 308K, 318K. The concrete plan was made by well-stirred 0.3g composites added into 200mL sodium fluoride at different initial concentrations.

Results and discussion

Adsorption isotherms

For any adsorption investigation most of important parameters required to understand the behaviour of the adsorption process in the adsorption isotherm. The adsorption isotherms of fluoride ion onto CeO2/Al2O3 composites were investigated under the temperatures of 303K, 318K, 333K, 348K, 363K are shown in Fig. 1 and Fig.2. It should be noticed that an increase in initial concentration of fluoride leads to an increase in the adsorption capacity of fluoride by CeO2/Al2O3 adsorbents. It was also indicated that adsorbents adsorption capacity increased with increasing temperature. The increase in the adsorption capacity at increased temperature indicated that adsorption process of CeO2/Al2O3 composites was nature endothermic. Similar results were observed in the literature of other rare earth adsorbent materials[1]. For the fluoride initial concentration of 120mg/L, the temperature from 303K to 363K resulted the increases the adsorption capacity from 37.14mg/g to 46.59mg/g. The defluoridation experiments were also investigated using adsorbents of plasma modified. Fig. 2 illustrates adsorption capacity of adsorbent materials by plasma modified and pristine, the surfaces modification led to a further adsorption of the fluoride. For the fluoride initial concentration of 120mg/L, the adsorption capacity increased from 40.85mg/g to 44.0mg/g with the temperature of 333k. It was due to the availability of adsorption sites increased on adsorbent surfaces by plasma modified.

Fig.1. Adsorption isotherms of fluoride ion adsorption onto CeO2/Al2O3 composites

Fig.2. Adsorption isotherms of fluoride onto plasma modified and pristine CeO2/Al2O3 composites

Equilibrium modeling

The shape of an isotherm not only expresses the specific relation between the concentration of sorbate and adsorption capacity of adsorbents for adsorption, but it also reflects the possible mode for adsorbing fluoride ion. In order to adequately correlate the experimental data, adsorption experimental data were fitted to several isotherm models, such as Langmuir, Freundlich and Dubinin-Radushkevich equations[16-22].

3.2.1. The Langmuir equation is valid for monolayer sorption and is apply to homogeneous sorption on a surface. The equation of the Langmuir isotherm as:

qe= (2)

The linear representation of the Langmuir adsorption equation is

= (3)

The Langmuir constants were calculated from linear regression of Ce/qe versus Ce.

Dimensionless parameter of the equilibrium or adsorption intensity (RL) often use for the further analysis of Langmuir equation. The values of RL were calculated using the following equation

= (4)

The value of RL indicates the type of the isotherm of the following adsorption characteristics: RL>1 for unfavourable adsorption; RL=1 for linear adsorption; 0<RL<1 for favourable adsorption and RL=0 for irreversible adsorption.

As can be seen from Table.1 the experimental data can be fitted well the Langmuir model, It indicates fluoride has a strong intermolecular attraction to the surface of the adsorbent as a chemical interaction. It is also noticed that value of KL increased after plasma modified as evidenced the adsorptive capacity increased. On the other hand, the Langmuir constant KL increased from the temperature 303K to 363K showing the process to be endothermic as Fig.1and Fig.2 shown. All the calculated RL values were between 0 and 1, it is indicated that the adsorption of fluoride was favourable at the conditions being studied.

Table.1. Langmuir isotherm model constants and correlation coefficients for adsorption of fluoride onto adsorbents at different temperature

Temperature (K)

Unmodification

Plasma modification

KL (L/mg)

R2

KL (L/mg)

R2

303

0.065754

0.9772

0.067101

0.9594

318

0.084222

0.96831

0.109528

0.95889

333

0.126255

0.9841

0.152894

0.97477

348

0.132537

0.9909

0.164061

0.99052

363

0.208239

0.9928

0.307472

0.99734

3.2.2. Freundlich isotherm is an empirical equation is based upon the assumption of multilayer formation of adsorbate onto a heterogeneous surface adsorbent and assumes that the stronger binding sites are occupied first and that the binding strength decreases with the increasing degree of site occupation. The Freundlich isotherm is commonly presented as:

q­e = KFCe1/n (5)

A linearised form of the equation is followed by

Ln q­e= lnKF+lnCe (6)

Freundlich constants were obtained from linear regression of ln qe versus ln Ce. The magnitude of the exponent 1/n is the heterogeneity factor, which gives an indication of the favorability and capacity of the adsorption as the values n > 1 represent favorable.

The results are presented in Table.2. The isotherms were not to be linear as evidenced from the values of correlation coefficients (R2) obtained in the range 0.68-0.96. It is evident (that)from the table(of) the adsorption equilibrium data do not exactly fit the Freundlich model of adsorption. Thus, it is inferred that fluoride adsorption onto adsorbent materials was not multilayer adsorption, the monolayer adsorption showed that was chemisorption occurred in the adsorbent surface, the fact was further supported by Dubinin and Radushkevich isotherm as shown in Table.3.

Table.2. Freundlich isotherm model constants and correlation coefficients for adsorption of fluoride onto adsorbents at different temperature

Temperature (K)

Unmodification

Plasma modification

KF(mg/g (L/mg)1/n)

R2

n

KF (mg/g (L/mg)1/n)

R2

n

303

4.905711

0.9657

1.836986

4.645505

0.94786

1.640555

318

3.854495

0.94632

1.482492

3.717792

0.96914

1.418239

333

8.209483

0.91284

2.0924

7.742077

0.8802

1.754632

348

10.24377

0.72605

2.800414

11.99956

0.6813

2.94655

363

13.89599

0.74634

3.308629

13.74273

0.70761

2.962787

3.2.3 The Dubinin and Radushkevich isotherm widely applied sorption isotherm, which was proposed by Dubinin and Radushkevich. From the model, the characteristic adsorption curve is related to the porous structure of the adsorbent, so it does not assume a homogeneous surface. It may be represented as follows:

Ln qe = lnqmax -βε2 (7)

As shown in Table.3, the correlation coefficients given by the Dubinin and Radushkevich model(Table.3) confirmed that the model did not fit satisfactory experimental data. It is another way to illustrated that the adsorption was a monolayer chemisorption.

Table.3. The correlation coefficients of Dubinin-Radushkevich models for adsorption at different temperature

Temperature (K)

Unmodification R2

Plasma modification R2

303

0.91304

0.89581

318

0.96773

0.96544

333

0.94985

0.93086

348

0.78948

0.73729

363

0.78557

0.76401

Adsorption thermodynamics studies

To estimate the effect of temperature on the adsorption,the free energy change (â-³Gθ)and entropy change (â-³Sθ) which should be considered. The Gibbs free energy change of adsorption is defined as[23-24]:

ΔGθ=-RTln b (8)

The effect of temperature on the equilibrium constant is determined as follows

= (9)

ΔGθ=ΔHθ-TΔGθ (10)

After integration and necessary rearrangements, Equation. (11) gives

=-+ (11)

(where b is the constant obtained from Langmuir plots.)

ΔHθandΔSθwere calculated from the slope and intercept of the van't Hoff plots of ln K versus -1/T as shown in Fig.3. The values ofΔHθ,ΔGθandΔSθ are listed in Table 4. Positive values of ΔHθsuggest the endothermic nature for the adsorption of fluoride. The adsorption mechanism of defluoridation is mainly F- and -OH exchange, the desorption of -OH attached to active sites on the surface and need some sorption energy to leave the surface.This might explained the endothermic nature of the adsorption process. Physisorption and chemisorption can be classified by the magnitude of the enthalpy change.Generally speaking, ΔHθfor chemical adsorption similar to chemical reaction heat, compared to that of physical adsorption is exothermic, As shown in Table.4, the ΔHθwas The positive value, this would suggested that the adsorption process might be considered as chemisorption. The negative values of ΔGθconfirmed the feasibility of the adsorption process and also indicated that the adsorption of fluoride onto adsorbents were a spontaneous process. The positive value of ΔSθ suggested that both enthalpy and entropy are responsible for making theΔGθ negative, it was showed the increasing randomness at the solid- solution interface during the adsorption. Table. 4 also showed that the adsorption of fluoride on plasma modified adsorbents was more endothermic than pristine adsorbents asΔHθ 21.65kJ/mol and 25.86kJ/mol, respectively. ΔGθwas more negative andΔSθ was more positive with plasma modified adsorbents, which suggested that plasma modification facilitates the adsorption. It can be concluded surface energy was changed by plasma modified, Parts of sdsorption sites were activated on the surface of materials after plasma treatment.

Fig. 3. Van't Hoff plot for the adsorption of fluoride onto plasma modified and pristine CeO2/Al2O3 composites.

Table.4. Thermodynamic parameters for the sorption of fluoride onto plasma modified and pristine CeO2/Al2O3 composites

Unmodification

Plasma modification

Temperature (K)

ΔHθ

(kJ/mol)

ΔGθ

(kJ/mol)

ΔSθ

(J/mol K)

ΔHθ

(kJ/mol)

ΔGθ

(kJ/mol)

ΔSθ

(J/mol K)

303

21.64593

-2.11827

78.4209736

25.858025

-2.45184

93.4219

318

-3.29471

-3.85332

333

-4.47116

-5.2548

348

-5.64761

-6.65628

363

-6.82405

-8.05775

Adsorption kinetic studies

The kinetic of adsorption describes the rate of fluoride adsorb on adsorbents, which controls the equilibrium time and influences the adsorption mechanism. For a adsorption process, are typically considered as three major steps at the solid-liquid interface:

the diffusion through the film surrounding the solid adsorbent particles, called also"external diffusion";

the diffusion in the pores of the adsorbent or"intra-particle diffusion";

the reaction of adsorption (and desorption) itself or"surface reaction"[25].

The"external diffusion" is not often decisive, especially when the experimental system is well agitated[25]. In this paper, three kinetic adsorption models will be used to describe the experimental data. The pseudo-first order equation and pseudo-second order equation as "surface reaction"were tested, the intraparticle diffusion model was also discussed[26].

Effect of contact time and initial concentration

The effect of contact time and initial concentration was investigated under equilibrium conditions are presented in Fig.4. It can be seen that the adsorption of fluoride increases with an increase in agitation time and attains equilibrium earlier for solutions with lower initial concentrations. The adsorption capacity increased with increasing initial fluoride ions concentration. It was also observed that adsorption was rather quick, and after 1.5 hour, complete adsorption equilibrium was obtained. For next kinetic studies the tests were carried out for more than 1.5 hour.

Fig.4. Effect of contact time and initial concentration.

3.4.2. Kinetic models

The pseudo-first-order kinetic model[27-28] was called Lagergren model, has been widely used to predict the adsorption kinetics.

=k1(qe-qt) (12)

Integrating the Equation.(12) for the boundary conditions of t=0 to t=t and qt=0 to qt=qt, gives a linear expression:

㏑(qe-qt)=㏑qe-k1t

The values of k1 can be obtained from the slope of the plot of ㏑(qe-qt)versus t.

The pseudo-second-order equation[27-29] based on the equilibrium adsorption is expressed as:

=k2(qe-qt)2 (13)

Integration for boundary conditions of t=0 to t=t and qt=0 to qt=qt followed by rearrangement gives:

qt= (14)

or equivalently,

=+ (15)

Equation. (15) shows that the plot of t/qt versus t should be a line with slope and intercept of 1/qe and 1/(k2qe2), respectively.

In the process of the adsorption of fluoride ions on adsorbents. There is the possibility of intraparticle diffusion[23, 27], which could be described as:

qt=kpt1/2+C (16)

According to Equation.(16), if the adsorption mechanism follows the intraparticle diffusion processes a plot of qt versus t1/2 should be a straight line with a slope Kp and intercept C.

From the slope and intercept of the straight line obtained, the correlation coefficient values were determined, as listed in Table.5. In(on) contrast, the experimental data of kinetic model fitted well with the pseudo-second-order. Tables.5 indicates that the correlation coefficient for the linear plots from the pseudo-second-order equation are higher than the other kinetic models, This is generally in agreement with other research's result that the pseudo-second-order model was able to describe properly the kinetic process of other adsorbents for fluoride adsorption[26, 30]. This means that the "surface reaction" was dominated and controlled adsorption stage and other steps was instantaneous occured at the solid-liquid interface. The fact was also supported by adsorption isotherms as fit the Langmuir equation. The rate-limiting step may due to chemisorption involving valence forces through sharing or exchange of electrons[27].

Table.5 Correlation coefficient (R2) of the three models

Unmodification

Plasma modification

Model

Solution temperature (K)

Correlation coefficient R2

Solution temperature (K)

Correlation coefficient R2

Pseudo-first-order

288

0.97916

288

298

0.89644

298

0.76878

308

0.94967

308

0.89009

318

0.81336

318

0.84228

Pseudo-second-order

288

0.99916

288

298

0.99959

298

0.99995

308

0.99994

308

0.99998

318

0.99999

318

0.99999

Intraparticle diffusion

288

0.72069

288

298

0.71066

298

0.5139

308

0.67189

308

0.51415

318

0.51669

318

0.58942

Estimation of activation energy

The pseudo-second-order rate constants for fluoride adsorption at different temperature were calculated and listed in Table.5. An increase in temperature results in slightly increasing the rate constant. According to the Arrhenius's equation[31-32]:

k=Ae-Ea/RT (17)

Equation.(17) can be rearranged to obtain the following form:

㏑k= (18)

From the slopes of the linear plots of ㏑k versus -1/T, the apparent activation energy of adsorption can be calculated and presented in Fig.5. The calculated activation energy values were 57.52kJ/mol and 49.94 kJ/mol of fluoride adsorption onto pristine and plasma modified adsorbents, respectively. The activation energy for physical adsorption is usually no more than 42 kJ/ mol, since the forces involved in physical adsorption are weak[32]. Therefore, the adsorption capacity should largely depend on the chemisorption. It can be presumed rise in temperature favor the adsorption. The activation energy decreased as plasma treatment,This could be attributed to the adsorbent material's surface was activated.

Table.6. Pseudo-second-order rate constants for the fluoride adsorption

Unmodification

Plasma modification

Tmperature (K)

288

298

308

318

298

308

318

rate constants k2

0.012046

0.023461

0.054348

0.113278

0.032434

0.057842

0.115433

Fig.5. Plot of ln k versus -103/T for the fluoride adsorption.

Conclusion

This paper deals with the adsorption of fluoride onto plasma modified CeO2/Al2O3 Composites, including the equilibrium isotherms and kinetic of the adsorption. The Langmuir model was demonstrated to provide the best correlation for the sorption than the Freundlich and Dubinin-Radushkevich model. After the plasma treated on the surface of adsorbent, The ΔSθ increased from 78.42 J/mol K to 93.42J/mol K, the Ea decreased from 57.52kJ/mol to 49.94 kJ/mol and the ΔGθ was also decreased in fluoride ion adsorption onto plasma modified adsorbents. It was clearly indicated that the adsorption occurred on plasma modified adsorbents was favorable. The positive value of ΔHθand the negative of ΔGθindicated the endothermic and spontaneous nature of adsorption process on the surface of adsorbent materials. The pseudo second-order kinetic model agrees very well with the dynamical behaviour for the adsorption, and the "surface reaction" was dominated and controlled adsorption stage.

Appendix: Abbreviations and notations

Nomenclature

qe

the amounts of fluoride ions adsorbed at equilibrium (mg/g)

qt

the amounts of fluoride ions adsorbed at at time t (mg/g)

t

time (min)

V

volume of the solution (mL)

m

mass of adsorbents used (g)

C0

initial concentration (mg/L)

Ct

concentration at time t (mg/L)

Ce

equilibrium concentration (mg/L)

KL

Langmuir isotherm constant (mL/mg)

KF

Freundlich's constant (mg/g) (L/g)1/n

1/n

Freundlich exponent

qmax

maximum adsorption capacity (mg/g)

ε

film thickness (cm)

R2

correlation coefficient

â-³Gθ

Gibbs free energy (kJ/mol)

T

temperature (K)

ΔHθ

enthalpy of adsorption (kJ/mol)

ΔSθ

entropy of adsorption (kmol-1K-1)

k1

pseudo-first-order kinetic model constant (1/min)

k2

pseudo-second order kinetic model constant (gmg-1min-1)

Ea

the activation energy (kJ/mol)

A

the temperature independent factor (g mg-1min-1)

kp

intraparticle diffusion kinetic model constant (gmg-1 min-0.5)

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