doi.org/10.26434/chemrxiv.5899393.v2

A New Kinetic Model for Multicomponent Adsorption in Batch Systemsyongson hong, Kye-Ryong Sin, Yong-U Ri, Jong-Su Pak, Yung Jon, Chol-Sik Kim, Chol-Su Jang, Hye-RyonJu, Sung-Hwan Ri

Submitted date: 21/03/2018 • Posted date: 21/03/2018Licence: CC BY-NC-ND 4.0Citation information: hong, yongson; Sin, Kye-Ryong; Ri, Yong-U; Pak, Jong-Su; Jon, Yung; Kim, Chol-Sik; etal. (2018): A New Kinetic Model for Multicomponent Adsorption in Batch Systems. ChemRxiv. Preprint.

In many of kinetic studies on binary component adsorption, the kinetic models for unary component adsorptionwere used although binary adsorption process were more complex than unary ones. We proposed a newkinetic model for multicomponent adsorption in batch systems. This model, using the deactivation kineticsmodel(DKM) for the noncatalytic heterogeneous reaction, is represented by a set of simultaneous ordinarydifferential equations, the characteristic is to calculate the concentration of adsorbates and the overalldeactivation degree of the adsorbent with time together. The multicomponent adsorption kinetic model wassolved with ODE function of MATLAB and the kinetic parameters were estimated by the nonlinear leastsquares fitting. The results of nonlinear fitting to the previous experimental data show that the proposed kineticmodel can be useful for kinetics modeling of multicomponent adsorption in batch systems.

File list (1)

download fileview on ChemRxivChemRxiv-2018-3-21-A New Multicomponent Adsorption ... (1.30 MiB)

1

A New Kinetic Model for Multicomponent Adsorption in

Batch Systems

Yong-Son Hong,*,,2 Kye-Ryong Sin, **,1 Yong-U Ri,1 Jong-Su Pak,2 Yung Jon, 3 Chol-Sik Kim,2 Chol-Su

Jang,3 Hye-Ryon Ju,1and Sung-Hwan Ri1

Department of Physical Chemistry, Faculty of Chemistry, 1 Kim Il Sung University, 2 Kim Hyong Jik Normal University, 3 University of Science, Pyongyang, Democratic People’s Republic of Korea

AUTHOR INFORMATION

Corresponding Author

* yongsonhong77@yahoo.com , ** ryongnam9@yahoo.com

ABSTRACT

In many of kinetic studies on binary component adsorption, the kinetic models for unary component

adsorption were used although binary adsorption process were more complex than unary ones. We

proposed a new kinetic model for multicomponent adsorption in batch systems. This model, using the

deactivation kinetics model(DKM) for the non-catalytic heterogeneous reaction, is represented by a set

of simultaneous ordinary differential equations, the characteristic is to calculate the concentration of

adsorbates and the overall deactivation degree of the adsorbent with time together. The

multicomponent adsorption kinetic model was solved with ODE function of MATLAB and the kinetic

parameters were estimated by the nonlinear least squares fitting. The results of nonlinear fitting to the

previous experimental data show that the proposed kinetic model can be useful for kinetics modeling

of multicomponent adsorption in batch systems.

TOC GRAPHICS

KEYWORDS

Binary Adsorption, Competitive Adsorption, Deactivation Kinetics Model, Heterogeneous Reaction , Kinetic Parameter

t=0, X=0

X t= , X≦1 ∞

C B

A

2

Introduction

The study of adsorption kinetics is important to design industrial reactors and operation of adsorption equipment. Many unary component adsorption kinetic models have been proposed and used during about 120 years.1-5 The development of the kinetic model progressed in a direction to agree with the experimental data closely. 6-11 The pseudo-second-order(PSO) model(eq. 1) was the widely used equation for modeling of unary adsorption kinetics at the solid/solution interface and the linear form of model was used. 12-15

22 )( qqk

dt

dqe

(1)

where q and qe are the grams of solute adsorbed per gram of sorbent at any time(t) and at equilibrium,

respectively, and k2 is the PSO rate constant of sorption. Almost all kinetic models of unary adsorption are rate equations for q with time.

In many of the kinetic analysis of binary adsorption processes, the kinetic models for unary adsorption are used ignoring the interaction between adsorbates and adsorbent.16-20, 34-36 The binary adsorption process are more complex than the unary system and those should be considered. Binary adsorption kinetic models21-28 considered the interaction were already proposed.

Nitta et al.21 derived the multisite Langmuir model using a statistical thermodynamic method and Sircar22 derived it simply from the classical Langmuirian kinetics. The mass action law was used to describe the reversible multicomponent adsorption process. The sorption rate of component i in a multicomponent system was written as eq. 2

siidi

an

j

siiiaisii qqkqqCk

dt

qqdi

//1)/(

1

(2)

where qi and qsi are adsorption site concentration at time t and total adsorption site concentration in an adsorbent according to multisite Langmuir isotherm(g∙mol∙cm-3) , kai and kdi are specific adsorption and desorption reaction rate constants for component i, respectively, Ci is the gas-phase concentration(g∙mol∙cm-3), n is total component numbers and a is a adsorption sites occupied by each adsorbate molecule in the adsorbed phase.

Qinglin et al.23 presented the model equations for integral uptakes in adsorbent particles of a differential adsorption bed experiments using the multisite Langmuir model and introducing an imaginary gas-phase concentration24 under eight assumptions.

Gu et al.25 proposed eq.3 for multicomponent systems.

sidi

n

j

sjijiiaisi CkCCCkt

C

1

(3)

where Csi , Ci and Ci∞ are the dimensionless concentration in the solid phase of the particles,

concentration in the stagnant fluid phase inside particle macropores and adsorption saturation capacity(based on unit volume of particle skeleton) for component i, respectively, θij (0<θij ≤1, θij= Ci

∞/ Cj

∞, adsorption saturation capacity of component i is smaller than component j) are discount factors for extended multicomponent Langmuir isotherm, those θij values are obtained from experimental correlation. They had demonstrated the phenomena of peak reversal and crossover of breakthrough curve for the chromatographic process by using their model.

Suen et al.26 presented the following kinetic equation(eq. 4) for binary solute competitive adsorption behavior,

3

222102222

112101111

)(

)(

sdssas

sdssas

CkCCCCkdt

dC

CkCCCCkdt

dC

(4)

where subscript 1 indicates the solute with lower saturation capacity, whereas subscript 2 denotes the solute with higher saturation capacity, C , Cs and C0 are solute concentration in solution , adsorbed solute concentration and adsorption saturation capacity based on the solid volume(mol dm-3), respectively, ka and kd are adsorption and desorption reaction rate constants, θ= C01 /C02. This binary-solute Langmuir kinetic model(eq. 4) were used to calculate the values of association rate constants. Their results showed that when the rate constants were increased or decreased, the shapes of the association curves were significantly changed.

The commonality of the multicomponent adsorption kinetic models21-28 are that the Langmuir kinetic model was used and the adsorbent fraction that can be occupied by all adsorbates were taken into account. What is important in the use of these equations is to assess accurately the adsorbent fraction for all adsorbates, which is not easy to obtain those experimentally or theoretically.

The purpose of this study are to establish the new model of multicomponent adsorption kinetics by using the deactivation kinetics model(DKM) for the non-catalytic heterogeneous reaction and to prove its usefulness through calculation of previous experimental data.

We proposed the DKM in 201429 and used it for the kinetic analysis of H2S removal over mesoporous LaFeO3 /MCM-41 sorbent during hot coal gas desulfurization in a fixed-bed reactor. In 2017,30 we verified the validity of DKM through kinetic analysis for other experimental data. DKM has not considered the detailed characteristic parameters of the solid sorbent in such a microscopic way as unreacted shrinking core model(SCM)37 or random pore model (RPM)38 but in a macroscopic way. The change of fractional conversion with time in solid phase was expressed as a deactivation rate, as shown in eq 5:

)1(A XCkdt

dXd (5)

where X is a fractional conversion of the sorbent(0≦X≦1, dimensionless), kd is a deactivation rate

constant of the sorbent (L∙mol-1∙min-1), CA is a concentration of A component at any time (mol∙ L-1) and α

is a reaction order. The deactivation rate represents the senescence rate of solid adsorbent.

In order to establish the model of multicomponent adsorption kinetics by using the DKM, we assumed the following. First, X (deactivation degree of adsorbent)is 0 in the initial state and 1 in the saturated

adsorption state, i.e. X=0 at t=0, X=1(saturation) or X<1(unsaturation) at t=∞. Second, adsorption and

desorption are equilibrium every moment, therefore, the rate constants are apparent rate constants including both adsorption and desorption processes.

We proposed the model equations for unary(eq. 6), binary(eq. 7) and ternary(eq. 8) component adsorption kinetics.

)1(

)1(

A

AAA

XCkdt

dX

XCkdt

dC

d

(6)

4

)1)((

)1(

)1(

BA

BBB

AAA

XCCkdt

dX

XCkdt

dC

XCkdt

dC

d

(7)

)1()(

)1(

)1(

)1(

CBA

CCC

BBB

AAA

XCCCkdt

dX

XCkdt

dC

XCkdt

dC

XCkdt

dC

d

(8)

where subscript A, B and C indicate the adsorbates, kd are deactivation rate constants of the adsorbent (L∙mol-1∙min-1), k are adsorption rate constants of the adsorbates(min -1), C are concentration of adsorbates at any time (mol∙ L-1) and X are deactivation degree of the adsorbents(dimensionless). In fact, eq. 8 is a comprehensive model that includes eq. 7 and eq.6 as owner -special cases. The eq. 8 is equal to eq. 7 at CC=0 in the initial state(t=0) and is equal to eq. 6 at t=0, CB=CC=0. The multicomponent adsorption kinetic models are solved with ODE function of MATLAB, which solve initial value problems for ordinary differential equations and the programming are also simple. The kinetic parameters are calculated using the nonlinear least-squares fitting of the adsorbates concentration obtained by solving ordinary differential equations(eq. 6~8) to the experimental data. The input data required for the nonlinear optimization are only the change of non-dimensionalized concentration(C/C0) of the adsorbates with time, and X is automatically evaluated in the calculation process. The differentiation of our kinetic models from other kinetic models are to calculate the change rate of adsorbate concentration and adsorbent deactivation degree simultaneously in an adsorption system. Also, instead of the adsorbent fraction that should be occupied by every adsorbates in a competition adsorption, the overall deactivation degree of adsorbent is introduced by using DKM.

The changes in C/C0 of adsorbates and X of adsorbents calculated at different kinetic parameters were shown in the Figure 1(unary system, using eq. 6) and Figure S1(binary system, using eq. 7).

Figure 1. C/C0 and X calculated at different kinetic parameters for unary system(a-various kA, b-various kd)

5

As shown in Figure 1a, the larger the adsorption rate constant kA, the more steep the kinetic curve was obtained. Also the deactivation rate of adsorbent was affected by the adsorption rate of adsorbate despite the deactivation rate constant kd=1. This means that the adsorption rate of adsorbate directly affects the deactivation rate of the adsorbent. In the case of kA=0.5, at equilibrium, the adsorbate remained but the adsorbent was already saturated. In the case of kA=1.5, the adsorbate was adsorbed entirely but the adsorbent was not saturated yet. As shown in Figure 1b, the larger the deactivation rate constant kd, the more steep the kinetic curve was obtained and likewise the adsorption rate of adsorbate was affected by the deactivation rate of adsorbent. If the adsorbent is insufficient in the adsorption system, kA becomes smaller and kd becomes larger. Therefore, in this state, C/C0 and X are calculated as the curves of kA = 0.5 in Figure 1a and the curves of kd = 1.5 in Figure 1b. That is, the adsorbent is saturated when the adsorbate remains in the system. Conversely, if the adsorbent is excessive in the adsorption system, the adsorbate is adsorbed wholly and the adsorbent is unsaturated, so C/C0 and X are calculated as the curves of kA = 1.5 in Figure 1a and the curves of kd = 0.5 in Figure 1b. Figure S1 are the kinetic curves calculated using eq. 7 at different kinetic parameters in binary system. What we know from the Figure S1 are that the rate change of one component in competitive adsorption affects the rate of each component.

We used the proposed adsorption kinetic model for the kinetic analysis of the previous experimental data.31-35

Krishna et al.31 investigated the adsorption for the removal of heavy metal Cr (VI) on the powder of mosambi fruit peelings(PMFP) in a batch system. They also studied the effect of initial Cr (VI) concentration and adsorbent size on the adsorption process and reported that it was the pseudo first order. The fitted curves and calculated kinetic parameters using eq. 6 were presented in Figure 2 and Table 1. As shown in Figure 2 and correlation coefficient of Table 1 , and calculated results agreed well with the experimental data. Adsorption rate constants kA and deactivation rate constants kd decreased with increase in initial concentration (Table 1). This trend may be attributed to decrease in the readily available vacant sites as the adsorbate concentration is increased. In order words, once the easily available sites are occupied the excess adsorbate in solution find remote sites inside the pores of PMFP with difficulty, which makes the rate to decrease as the initial concentration is increased. While, the adsorption rate constants kA and deactivation rate constants kd decreased with increase in adsorbent size (Table 1). The reason is that the larger the particle size, the smaller the adsorption surface area.

Figure 2. The curves fitted using eq. 6 for Cr(VI) adsorption on PMFP:(a- various initial concentration and b- various adsorbent size).

Table 1. Kinetic parameters for Cr(VI) adsorption on PMFP .

initial Cr (VI)

concentration

kA

(min-1

)

kd

(L∙mg-1 ∙min

- R2

particle sizes

of PMFP

kA

(min-1

)

kd

(L∙mg-1 ∙min

- R2

6

(mg∙L-1

) 1) (mm)

1)

10 0.0187 0.0591 0.9985 0.6 0.0196 0.0624 0.9992

20 0.0131 0.0486 0.9991 0.8 0.0157 0.0561 0.9988

30 0.0083 0.0315 0.9952 1.7 0.0125 0.0505 0.9993

Lin et al.32 investigated the adsorption for the removal of heavy metal Cr (VI) on hyperbranched polyamide modified corncob(HPMC) in a batch system. The fitted curves and calculated kinetic parameters using eq. 6 were presented in Figure S2 and Table S1. Just as in Table 1, adsorption rate constants kA snd deactivation rate constants kd decreased with increase in initial concentration (Table S1) and calculated results agreed well with the experimental data.

Marczewski et al.33 investigated the temperature effect for 3- bromophenoxypropionic acid (3- BrPP) adsorption on activated carbon in a batch system and reported that the adsorption process was described as multi-exponential equation.6 We used eq. 6 to calculate the experimental data(Figure S3 and Table 2). As shown in Figure S3 and Table 2, rate constants increased with temperature of system and calculated results agreed well with the experimental data. We also calculated apparent activation energies by linear regression of Arrhenius equation, which were EA=33.6(activation energy of adsorbate adsorption) and Ed=26.6(activation energy of adsorbent deactivation) kJ∙mol-1, respectively. The calculated EA=33.6 kJ∙mol-1 was very close to 31.8 kJ∙mol-1 reported by them.33

Table 2. Kinetic parameters for 3-BrPP on activated carbon .

Temperat

ure(℃) kA×10

-2

(min-1

) kd

(L∙mmol-1 ∙min

-1)

R2

5 0.0876 0.0795 0.9964

15 0.1255 0.1039 0.9981

25 0.1982 0.1603 0.9984

35 0.2678 0.2074 0.9994

45 0.3997 0.2752 0.9998

55 0.9404 0.4982 0.9999

Activation energy

33.6(kJ∙mol-1

) 26. 6(kJ∙mol-1

)

Farhade et al. 34 investigated competitive adsorption of methylene blue(MB) and rhodamine B(RB) on natural zeolite and reported that their adsorption experimental data were following PSO in the binary component system. The eq. 6 and eq. 7 were used for kinetic analysis of their experimental data, rate constants were calculated for both unary and binary systems using eq.6 and binary system using eq.7(Table 3). As shown in Table 3, if eq. 6 was used for competitive adsorption of binary components, although there was only one adsorbent in a system, two deactivation rate constants were calculated. Since the deactivation rate constant is a kinetic concept that represents the senescence rate of solid adsorbent, we think there must be one deactivation rate constant for one adsorbent in one system. As shown the results for binary system using eq.7( in Table 3), it can be seen that the adsorption rate of MB is 5.8 times faster than RB at 25℃ and 7.4 times at 55℃. Furthermore, the adsorption rate of RB

decreases and is retarded by MB in competitive adsorption with increasing temperature. These calculation results can’t be obtained using PSO or eq. 6. The curves fitted using eq. 6 and eq. 7 were shown in Figure 3. As shown in Figure 3 and correlation coefficient of Table 3, calculated results agreed well with their experimental data.

Table 3. Kinetic parameters calculated using eq. 6 and eq. 7 for adsorption of RB and MB on natural zeolite in unary and binary component systems at 25℃ and 55℃.

Model → PSO34 Unary eq.6 Binary eq. 7

Parameter → k2 ×106

(mol ∙g-1∙h

-1)

qe×10-6

(mol ∙ g-

1)

R2 kA

(min-1

)

kd

(L∙ mol -1

∙min-1

)

R2 kA

(min-1

)

kB

(min-1

)

kd

(L∙ mol -

1 ∙min

-1)

R2

RB(Un.) 1.08

(7.08)# 7.51

(7.45) 0.9998 (1.000)

0.0008 (0.0017)

0.0340 (0.0678)

0.9971 (0.9999) A – RB

B – MB MB(Un.)

0.0275 (0.0260)

55.5 (63.5)

0.9982 (0.9998)

0.0006 (0.0009)

0.0393 (0.0689)

0.9983 (0.9999)

7

RB(Bin.) 2.48

(13.7)

4.92

(3.93)

0.9994

(0.9997)

0.0018

(0.0023)

0.0107

(0.0116)

0.9918

(0.9920) kA

0.0010 (0.0009)

kB 0.0058

(0.0067)

kd 0.0305

(0.0344)

0.9951

(0.9998)

MB(Bin.) 0.664

(0.155)

28.4

(28.8)

1.0000

(0.9999)

0.0047

(0.0065)

0.0508

(0.0685)

0.9991

(0.9998)

0.9984

(0.9998) # The data in parentheses are values in unary and binary systems at 55℃

Conditions: initial concentration of 6×10-6mol/L, 0.2 g/L zeolite , 150 mL of the solutions in unary and binary systems at 25 and 55℃

Figure 3. The curves fitted using eq. 6 and eq. 7 for RB and MB adsorption on natural zeolite: (a- at 25 ℃ and b- at 55 ℃).

Zolgharnein et al.35 studied simultaneous removal of binary mixture of brilliant green(BG) and crystal violet(CV) by surfactant-modified alumina(SMA) and reported that the adsorption process were following PSO. As above, their experimental data35 were analyzed kinetically using eq. 6 and eq. 7. The fitted curves were shown in Figure 4 and calculated kinetic parameters were shown in Table 4. αin

Figure 4 is a reaction order of DKM(See eq. 5). The reaction order related to the mechanism is an empirical quantity obtained from the experimental data and rate equation.39 As shown in Figure 4 and

Table 4, the fitted curves ofα=0.5 agreed better with their experimental data than α=1 in unary system

but the curves fitted atα=1 agreed well in binary system. From these results, it can be seen that the

unary adsorption and the binary adsorption occur due to different mechanisms. Considering the reaction order, we can get more information about the adsorption process.

Figure 4. The curves fitted using eq. 6 and eq. 7 for BG and CV adsorption on SMA

Table 4. Kinetic paramers calculated using eq. 6 and eq. 7 for dye adsorption on SMA in unary and binary systems

8

Model → PSO35 Unary eq.6# Binary eq 7&

Parameter →

k2 ×10-3

(g∙mg -

1∙min -1)

qe

(mg∙g-1

) R2

kA

(min-1

)

kd

(min-1

) R2

kA

(min-1

)

kB

(min-1

)

kd

(L∙ mg -1

∙min-1

)

R2

BG(Un.) 4.17 91 0.999 0.2126 0.1630 0.9990 A – BG B – CV CV(Un.) 5.26 100 0.999 0.1134 0.0985 0.9980

BG(Bin.) 2.44 83.3 0.997 0.3636 0.2494 0.9999 kA 0.2146

kB 0.3000

kd 0.1559

0.9964 CV(Bin.) 3.80 90.9 0.999 0.1984 0.1528 0.9990 0.9993

# : dX/dt= kdCA(1-X)0.5 in Unary Model eq. 6, & : a ll orders are 1 in Binary Model eq. 7 Conditions: 10 mL solution, pH=4,T=25℃ and 0.05 g of SMA for BG (400 mg/L) and CV (338 mg/L) in unary and binary systems.

In conclusion, we established the new model of adsorption kinetics using DKM for the non-catalytic heterogeneous reaction. This kinetic model is distinguished from other kinetic models by calculation for the change rate of adsorbate concentration and adsorbent deactivation degree simultaneously in an adsorption system and this has been extended to multicomponent adsorption system. Also, instead of the adsorbent fraction that should be occupied by every adsorbates in a multicomponent adsorption, the overall deactivation degree of adsorbent is introduced by using DKM. The validity is verified through calculation of previous experimental data.

AUTHOR INFORMATION

ORCID

Yong-Son Hong: 0000-0002-0566-6632 Kye-Ryong Sin: 0000-0003-4084-8703

Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to

the final version of the manuscript.

Notes

The authors declare no competing financial interests.

REFERENCES

(1) Lagergren, S. Y. Zur Theorie der sogenannten Adsorption gelöster Stoffe Kungliga Svenska Vetenskapsakademiens. Handlingar 1898, 24, 1–39.

(2) Ritchie, A. G. Alternative to the Elovich equation for the kinetics of adsorption of gases on solids. J. Chem. Soc. Faraday Trans. I 1977, 73, 1650–1653.

(3) Chien, S. H.; Clayton, W. R. Application of Elovich equation to the kinetics of phosphate release and sorption in soils. Soil Sci. Soc. Am. J. 1980, 44, 265–268.

(4) Ho, Y. S.; McKay, G. Pseudo-second order model for sorption processes. Process Biochem. 1999, 34, 451–465.

(5) Azizian, S. Kinetic Models of Sorption: A Theoretical Analysis. J.Colloid Interface Sci. 2004, 276, 47−52.

(6) Marczewski, A. W. Application of Mixed Order Rate Equations to Adsorption of Methylene Blue on Mesoporous Carbons. Appl. Surf. Sci. 2010, 256, 5145−5152.

(7) Yang, X.; Al-Duri, B. Kinetic modeling of liquid-phase adsorption of reactive dyes on activated carbon. J. Colloid Interface Sci. 2005, 287, 25–34.

(8) Brouers, F.; Sotolongo-Costa, O. Generalized fractal kinetics in complex systems, Physica A 2006, 368, 165−175.

9

(9) Azizian, S.; Fallah, R. N. A new empirical rate equation for adsorption kinetics at solid/solution interface. Appl. Surf. Sci. 2010, 256, 5153–5156.

(10) Haerifar, M.; Azizian, S. Fractal-Like Adsorption Kintetics at Solid/Solution Interface. J. Phy. Chem.C 2012, 116, 13111−13119.

(11) Haerifar, M.; Azizian, S. Mix Surface Reaction and Diffusion- Controlled Kintetic Model : A New Empirical Rate Equation for Adsorption at Solid/Solution Interface. J. Phy. Chem.C 2013, 117, 8310−8317.

(12) Plazinski, W.; Rudzinski, W.; Plazinska, A. Theoretical models of sorption kinetics including a surface reaction mechanism: A review. Adv. Colloid Interfac. 2009, 152 , 2–13.

(13) Largitte , L.; Pasquier, R. A review of the kinetics adsorption models and their application to the adsorption of lead by an activated carbon. Chem. Eng. Res. Des. 2016, 109, 495–504.

(14) Wang, L.C.; Nia, X. J.; Cao, Y. H.; Cao, G.Q. Adsorption behavior of bisphenol A on CTAB-modified graphite. App. Sur. Sci. 2018, 428, 165–170.

(15) Wu, Y.H.; Ming, Z.; Yang, S.X.; Fan, Y.; Fang, P.; Sha, H.T.; Cha, L.G. Adsorption of hexavalent chromium onto Bamboo Charcoal grafted by Cu2+-N-minopropylsilane complexes: Optimization, kinetic, and isotherm studies. J. Ind. Eng. Chem. 2017, 46, 222–233.

(16) Ghaedia, M.; Rozkhoosh, Z.; Asfaram, A.; Mirtamizdoust, B.; Mahmoudi, Z.; Bazrafshan, A.A. Comparative studies on removal of Erythrosine using ZnS and AgOH nanoparticles loaded on activated carbon as adsorbents: Kinetic and isotherm studies of adsorption. Spectrochim. Acta A, 2015, 138, 176–186.

(17) Zeinali, N.; Ghaedi, M.; Shafie, G. Competitive adsorption of methylene blue and brilliant green onto graphite oxide nano particle following: Derivative spectrophotometric and principal component-artificial neural network model methods for their simultaneous determination. J. Ind. Eng. Chem. 2014, 20, 3550–3558.

(18) Hajati, S.; Ghaedi, M.; Karimi, F.; Barazesh, B.; Sahraei, R.; Daneshfar, A. Competitive adsorption of Direct Yellow 12 and Reactive Orange 12 on ZnS:Mn nanoparticles loaded on activated carbon as novel adsorbent. J. Ind. Eng. Chem. 2014, 20, 564–571.

(19) Freitas,E.D.; Carmo, A.C.R.; Almeida, N. A.F.; Vieira, M.G.A. Binary adsorption of silver and copper on Verde-lodo bentonite: Kinetic and equilibrium study. Appl. Clay Sci. 2017, 143, 69-76.

(20) Dastkhoona, M.; Ghaedi, M.; Asfarama, A.; Hossein, M. ;Azqhandib, A.; Purkait, M. K. Simultaneous removal of dyes onto nanowires adsorbent use of ultrasound assisted adsorption to clean waste water: Chemometrics for modeling and optimization, multicomponent adsorption and kinetic study. Chem. Eng. Res. Des. 2017, 124, 222–237.

(21) Nitta, T.;Shigetomi, T.;Kruo-oka,M.;Katayama, T. An adsorption isotherm of multisite occupancy model for homogeneous surface. J.Chem. Eng. Jpn. 1984, 17, 39-43.

(22) Sircar, S. Influence of adsorbate size and adsorbent heterogeneity on IAST. AIChE J. 1995, 41, 1135.

(23) Qinglin, H.; Farooq,S.; Karimi,I. A. Binary and Ternary Adsorption Kinetics of Gases in Carbon Molecular Sieves. Langmuir 2003, 19, 5722-5734.

10

(24) Hu, X.; Do, D. D. Multicomponent adsorption kinetics of hydrocarbons onto activated carbon. Chem. Eng. Sci. 1993, 48, 1317.

(25) Gu, T. Y.; Tsai, G.J.; Tsao, G. T. Multicomponent Adsorption and Chromatography with Uneven Saturation Capacities. AIChE J. 1991, 37, 1333-1340.

(26) Suen, S.Y. A Comparison of Isotherm and Kinetic Models for Binary-solute Adsorption to Affinity Membranes. J . Chem. Tech. Biotechnol. 1996, 65, 249-257.

(27) Burde, J. T. ; Calbi, M. M. Early Removal of Weak-Binding Adsorbates by Kinetic Separation. J. Phys. Chem. Lett. 2010, 1, 808–812.

(28) Gaulke, M.; Guschin, V.; Knapp, S.; Pappert, S.; Eckl, W. A unified kinetic model for adsorption and desorptione Applied to water on zeolite. Micro. Meso. Mater. 2016, 233, 39-43.

(29) Hong, Y. S.; Zhang, Z. F.; Cai, Z. P.; Zhao, X. H.; Liu, B. S. Deactivation Kinetics Model of H2S Removal over Mesoporous LaFeO3 /MCM-41 Sorbent during Hot Coal Gas Desulfurization. Energy Fuels 2014, 28, 6012−6018.

(30) Hong, Y.S.; Sin, K.R.; Pak, J. S.;Kim, C. J.; Liu, B.S. Kinetic Analysis of H2S Removal over Mesoporous Cu−Mn Mixed Oxide/SBA-15 and La−Mn Mixed Oxide/KIT‑ 6 Sorbents during Hot Coal Gas Desulfurization Using the Deactivation Kinetics Model . Energy Fuels 2017, 31, 9874−9880.

(31) Krishna, R. H.; Swamy, A.V.V. Studies on the Removal of Ni(II) from Aqueous Solutions Using Powder of Mosambi Fruit Peelings as a Low Cost Sorbent. E-J.Chem. 2012, 9(3), 1389-1399.

(32) Lin, H.; Han, S.K.; Dong, Y.B.; He, Y.H. The surface characteristics of hyperbranched polyamide modified corncob and its adsorption property for Cr(VI). Appl. Surf. Sci., 2017, 412, 152–159.

(33) Marczewski, A. W.; Seczkowska, M.; Deryło-Marczewska, A. ; Blachnio, M. Adsorption equilibrium and kinetics of selected phenoxyacid pesticides on activated carbon: effect of temperature. Adsorption, 2016, 22, 777–790.

(34) Farhade, J. Z.; Aziz, H. Y. Competitive Adsorption of Methylene Blue and Rhodamine B on Natural Zeolite: Thermodynamic and Kinetic Studies. Chin. J. Chem. 2010,28, 349-356.

(35) Zolgharnein, J.; Bagtash, M.; Shariatmanesh, T. Simultaneous removal of binary mixture of Brilliant Green and Crystal Violet using derivative spectrophotometric determination, multivariate optimization and adsorption characterization of dyes on surfactant modified nano-c-alumina. Spectrochim. Acta A, 2015, 137, 1016–1028.

(36) Freitas,E.D.; Carmo, A.C.R.; Almeida Neto, A.F.; Vieira, M.G.A. Binary adsorption of silver and copper on Verde-lodo bentonite: Kinetic and equilibrium study. Appl. Clay Sci. 2017, 143, 69-76.

(37) Do, D. D. On the validity of the shrinking core model in noncatalytic gas solid reaction. Chem. Eng. Sci. 1982, 37, 1477−1481.

(38) Bhatia, S. K.; Perlmutter, D. D. A random pore model for fluidsolid reactions: I. Isothermal kinetic control. AIChE J. 1980, 26, 379−386.

(39) Atkins, P.; Paula, J. Physical Chemistry; W. H. Freeman and Company: New York, 2006; pp 798−810.

download fileview on ChemRxivChemRxiv-2018-3-21-A New Multicomponent Adsorption ... (1.30 MiB)