Journal of Materials Science and Engineering with Advanced Technology Volume 13, Number 1, 2016, Pages 1-12 Available at http://scientificadvances.co.in DOI: http://dx.doi.org/10.18642/jmseat_7100121569

Keywords and phrases: chemical adsorption, rare-earth, optical materials, dysprosium, crystalline compounds, mathematical models. Received October 30, 2015

2016 Scientific Advances Publishers

INVESTIGATION OF RARE-EARTH TEMPERATURE-DEPENDENT PHYSICAL AND CHEMICAL

ADSORPTION PROCESS: CASE OF DYSPROSIUM ION

A. YUMAK

Department of Physics Marmara University Göztepe Kampus 34722 Kadiköy Istanbul Turkey e-mail: ayumak@marmara.edu.tr

ipwbp@yahoo.fr

Abstract

In this paper, chemical adsorption kinetics of rare-earth elements inside regular crystalline materials are discussed. An approximate analytical expression of the non-steady-state doping concentrations is deduced by using the Boubaker polynomials expansion scheme (BPES). Results concerning the particular case

of dysprosium ion +3Dy are discussed and compared to some other results concerning optical performance and which were presented in the recent literature.

A. YUMAK 2

Nomenclature

fk : Forward pseudo-first-order-rate constant.

rk : Reverse pseudo-first-order-rate constant.

eK : Temperature-dependent ratio r

fk

k .

Q : Mean interacting interfacial area.

V : Host lattice unitary volume.

[ ]( )SDy : Incorporated dysprosium concentration in the matrix.

[ ] ( )l3Dy + : Dysprosium cation concentration in the solution.

( )[ ] ( )SIIIDy : Trivalent dysprosium concentration in the interfacial area.

Λ : Constant.

( )tz : Dimensionless dysprosium concentration.

1. Introduction

Semiconductor compounds doped with lanthanides have been of increasing interest in the last decades’ literature [1-3]. Particularly, trivalent rare earth elements have very stable emissions, due to the 4-f electrons which are deeply buried and hence well shielded from the outer shells. This property of the rare earth elements enables their incorporation into various hosts with different lattices. Among several

trivalent lanthanides, dysprosium +3Dy ions have been incorporated into

several crystals and microstructures [4, 5] in order to bi-colour luminescent devices. Dysprosium-doped solid-state systems can be quite easy excited by the common UV or blue lasers, because their excitation spectra exhibit several 4f-4f electronic bands located in the lower part of the visible spectrum.

INVESTIGATION OF RARE-EARTH TEMPERATURE- … 3

In the present work, analytical solutions to the differential equations systems governing the kinetics of dysprosium adsorption within particular hosting edifices are presented. In the recent literature, many studies have been published in this context. Zhang et al. [1] studied dysprosium-t thenoyltrifluoroacetone (TTA) modified silica gel sorbent. They analyzed two certified reference materials of GBW07401 soil and GBW07301a sediment in order to determine races of Dy(III) in environmental samples with complicated matrix. Prasad et al. [2] achieved ion-selective electrode (ISE) by dispersing the dysprosium(III) IIP particles in 2-nitrophenyloctyl ether plasticizer and successfully demonstrated the performance of this compound for the determination of fluoride in mouth wash solution. On the another hand, Biju et al. [3] and

Zhang et al. [4] prepared +3Dy doped compounds using employing copolymerization of styrene monomers and a cross-linking agent divinyl-benzene in the presence of dysprosium(III)-5,7-dichloroquinoline-8-ol-4-vinyl pyridine ternary complex and modified vertical Bridgman methods, respectively. Their achieved lifetime measurements demonstrated the relevance of electric dipole-dipole interaction for energy transfer processes as well and the efficiency of as grown compounds for near-UV excitation-based white light-emitting devices. Magnetic study reveals also that these obtained surfaces exhibit ferromagnetism. Earlier, Fang

et al. [5] synthesized +3Dy doped calcium magnesium chlorosilicate materials by high-temperature solid-state reaction in air. Experimental

results indicated that +3Dy concentration not only affected emission intensity, but also altered colour coordination, colour temperature and

preferentially selected +3Dy site within host matrix.

The paper is arranged as follows: In Section 2, rare-earth elements adsorption patterns inside hosting structures are presented along with some structures and incorporation details. Section 3 presents adsorption chemical kinetics governing equations. In Section 4, results and related plots using the Boubaker polynomials expansion scheme (BPES) are detailed. Discussion and comparison are presented in the Section 5 while a recapitulating conclusion is formulated in Section 6.

A. YUMAK 4

2. Rare-Earth Elements Adsorption inside Hosting Structures

Many hosting structures are suitable for incorporating rare-earth elements (Figure 1). Rare-earth elements are naturally incorporated into the carbonate and silicate phase of natural samples, they are also experimentally incorporated into ternary alloys to achieve lower melting points and lower vapour pressures.

Figure 1. Some hosting crystalline structure.

The disparity in size between the atoms inside the structure leaves relatively large open spaces and allows incorporation of rare-earth atoms, i.e., lanthanum, scandium, dysprosium, ytterbium, and yttrium [6-9] (Figure 2).

INVESTIGATION OF RARE-EARTH TEMPERATURE- … 5

Figure 2. Rare-earth incorporation inside a crystalline structure.

3. Adsorption Chemical Kinetics Governing Equation

Adsorption and separation of REEs from initial aqueous solution can be carried out by using several techniques. Chemical precipitation, ion exchange, membrane separation, extraction chromatography, and reverse osmosis are most known efficient and tested techniques. Among these techniques, ion exchange has received a considerable attention in recent years because it is simplicity and low-cost [10, 13].

It is commonly known that dysprosium is a rare earth element that has a metallic, bright silver luster. Dysprosium performs a high magnetic strength especially at low temperatures with a simple ferromagnetic ordering at temperatures below 85K, which turns to a disordered paramagnetic state at 179K. Batch and column experiments were widely performed to test the feasibility of removal and recovery of dysprosium(III)

+3Dy from aqueous solution by using resins or similar materials.

A. YUMAK 6

The simplified energy level diagram of dysprosium is presented in Figure 3.

Figure 3. Dysprosium simplified energy level diagram.

Some factors affecting adsorption, such as pH of solution, initial concentration of dysprosium(III) contact time and temperature were examined. Kinetics and isotherm adsorption experiments should be explained in terms of possible and selective transition.

In fact, the primary excited state in dysprosium decay processes

relating to the ( )m25.1~HH 15/26

7/26 µ→ transition. Lower excitation

wavelength ( )m81.0~ µ and ( )m91.0~ µ which correspond to the levels

5/26 F and ,F7/2

6 respectively, seem to be entirely quenched by

multiphonon emission and low quantum (luminescence) efficiencies.

Luminescence spectrum of +3Dy consists of two relatively intense bands

in the visible spectral region that correspond to the 15/26

9/24 HF →

(blue) and 13/26

9/24 HF → (yellow) transitions, respectively. An

appropriate combination of these two luminescence bands leads to generation of white light, and the relative intensities of the

INVESTIGATION OF RARE-EARTH TEMPERATURE- … 7

13/26

9/24 HF → transition to the 15/2

69/2

4 HF → transition can be

modulated by varying host properties, chemical composition, excitation wavelengths range, ion concentration, and heat treatment.

Thermodynamic parameters of adsorption for +3Dy and mechanism

of incorporation of +3Dy and similar rare-earth ions inside some crystalline structure, i.e., XO matrix, have been thoroughly studied, i.e., by Low [14] and Thronley [15], but an important part of the process is still unexplained. The relatively simple shell electronic structure of dysprosium excludes excited-state absorption and also a variety of detrimental quenching processes. In this case, we can expect, in concordance with analyses presented elsewhere [11, 15], the following reactions:

( ) ( ) ,3Cl2Dy2DyCl 2Sl3 +↔ (1)

( ) ( ) ,3O6X6XO 2SS +↔ (2)

( ) ( ) ( )[ ] .3OIII4DyO2Dy3ODy4 2SS322S +→→+ (3)

Under the presumption that adsorption can be treated as a pseudo-order reversible reaction with respect to the metal cation, dysprosium incorporation is governed by the following equation:

[ ]( ) [ ]( ) ( )[ ] ( )( ).IIIDyDyDy

Sl3S

rf kkVQ

dtd

−=− + (4)

By introducing the temperature-dependent ratio :eK

( )[ ]( )( )

[ ]( )( )( )[ ] ( )

[ ]( ).

DyIIIDy

Dy

IIIDy

l3

SEq.l

3

.EqS

++≈==

r

fe k

kK (5)

Assuming that

[ ]( )[ ] ( ) [ ]( )( )

,DyDy

Dy.init

l3

3S

3

0l3 ++ +Λ−=

dt

d (6)

A. YUMAK 8

where 0Λ is a constant, and finally, by considering boundary conditions,

we obtain the system:

( ) ( ( ( ) ))

( )

( )[ ] ( )( )

[ ]( )( )

( ) ( )

=′=

=

−=Φ

+′′′Λ×Φ=′−

+

.00;00

,Dy

Dy,

,1

.initl

3S

0

zz

ttz

Kk

tzVQtz

ef (7)

4. Resolution of the Main Equation using the BPES

A solution to Equation (7), for a given temperature, is proposed by using the Boubaker polynomials expansion scheme (BPES) [16-29]. The resolution protocol, starts from attributing the following expression to the solution:

( ) ( ) ( ),21

41

.sol0

0

kk

N

kk rxBNxz ××λ= ∑

=

(8)

where kB4 are the 4k-order Boubaker polynomials, kr are kB4 minimal

positive roots, 0N is a prefixed integer, and ( )01

.solNkk …=λ are unknown

pondering real coefficients.

The main advantage of this formulation (Equation (8)) is the evidence of verifying the boundary conditions expressed in Equation (7), in advance to problem resolution thanks to the properties of the Boubaker polynomials [19-27]:

( )

( )

=

=/−=

==

==

∑

∑

;0

;02

14

014

qrx

N

qq

x

N

qq

xB

NxB

(9)

INVESTIGATION OF RARE-EARTH TEMPERATURE- … 9

and

( )

( )

( )

[ ] ( )

( ) ( )

+

×−

==

=

=

+

=

===

==

∑

∑∑

∑

.4

24

:with

;

;0

314

1

24

2

4

11

4

01

4

nrn

n

n

qqnn

nnn

N

qq

rx

N

q

q

x

N

q

q

rB

rBrr

rBH

HdxxdB

dxxdB

n

q

(10)

Thanks to the properties expressed by Equations (9) and (10), boundary conditions are trivially verified in advance to resolution process. The system (7) is hence reduced to

( ) ( ( ) ) .0121

21

34

3

100

4

10

00=+×λΛ×Φ−

×λ− ∑∑== dx

xrBdNdx

xrdBN

kkN

kk

kkN

kk

02VNQ

(11)

The BPES solution is obtained by determining the non-null set of coefficients

01~

Nkk …=λ that minimizes the absolute difference :0NΨ

( )

( )

+×ΛΦ=Λ′

×=Λ

Λ′×λ−

Λ×λ=Ψ

∫

∫

∑∑==

.1

,

:with

;~2

1~2

1

1

034

30

1

024

2

1010

00

0

dxrxdx

Bd

dxrxdx

Bd

NN

kk

k

kk

k

k

N

kkk

N

kkN

02VNQ

(12)

A. YUMAK 10

5. Results and Discussion

Figure 4 presents the solutions obtained for different temperatures.

Figure 4. Solutions plots.

Observable patterns in Figure 4 show a significant temperature gradient is observed while an exponential parabolic time-dependent behaviour is recorded. This result is confirmed by the results presented in the relevant literature [1-11]. These results show also that there is no reaction below a temperature limit. This feature refers to the energy required to promote a 4f electron to the valence band of metallic dysprosium, as stated earlier by Bukietynska et al. [30] and Karabulut et al. [31].

INVESTIGATION OF RARE-EARTH TEMPERATURE- … 11

6. Conclusion

In this paper, the Boubaker polynomials expansion scheme (BPES) has been used for solving a boundary-valued differential equation presented as a governing tool to a chemical process. The scheme has been successfully applied to the model of adsorption of dysprosium inside a given XO-type matrix. Solutions have been plotted in the time-temperature t-T planes and compared to some other results. A further investigation will clarify whether this mechanism is also applicable for other lanthanides, such as lanthanum, neodymium, samarium, and europium.

Conflict of Interest Statement

The authors of the manuscript, declare that they do not have conflict of interest with any financial organization or other regarding what was discussed in the manuscript.

References

[1] N. Zhang, B. Hu and C. Huang, Analytica Chimica Acta 597 (2007), 12-18.

[2] K. Prasad, R. Kala, T. Prasada Rao and G. R. K. Naidu, Analytica Chimica Acta 566 (2006), 69-74.

[3] V. M. Biju, J. Mary Gladis and T. Prasada Rao, Analytica Chimica Acta 478 (2003), 43-51.

[4] Y. Zhang, J. E. Xu and B. Lu, Journal of Alloys and Compounds 582 (2014), 635-639.

[5] Y. Fang, W. Zhuang, Y. Hu, X. Ye and X. Huang, Journal of Alloys and Compounds 455 (2008), 420-423.

[6] C. Liu, B. S. Zou, A. J. Rondinone and Z. J. Zhang, J. Am. Chem. Soc. 122 (2000), 6263.

[7] E. F. Schloemann, J. Magn. Magn. Mater. 209 (2000), 15-20.

[8] G.-L. Sun, Jian-Bao Li, Jing Jing Sun and Xiao Zhan Yang, J. Magn. Magn. Mater. 281 (2004), 173-177.

[9] N. Rezlescu, E. Rezlescu, C. Pasnicu and M. L. Craus, J. Phys.: Condens. Matter 6 (1994), 5707.

A. YUMAK 12

[10] O. M. Hemeda, M. Z. Said and M. M. Barakat, J. Magn. Magn. Mater. 224 (2001), 132-142.

[11] F. Cheng et al., J. Appl. Phys. 85 (1999), 2782.

[12] K. Kamala Bharathi, G. Markandeyulu and C. V. Ramana, J. Phys. Chem. C 115 (2011), 554.

[13] S. Bachir, J. Kossanyi, C. Sandouly, P. Valat and J. C. Ronfard-Haret, Journal of Physics and Chemistry 99 (1995), 5674.

[14] W. J. Low, Phys. Soc. Japan 17, Suppl. B-I 440 (1962).

[15] J. H. M. Thronley. Phys. Soc. 88 (1966), 325.

[16] J. Ghanouchi, H. Labiadh and K. Boubaker, International Journal of Heat and Technology 26 (2008), 49-53.

[17] S. Slama, J. Bessrour, K. Boubaker and M. Bouhafs, Eur. Phys. J. Appl. Phys. 44 (2008), 317.

[18] T. Ghrib, K. Boubaker and M. Bouhafs, Modern Physics Letters B 22 (2008), 2893.

[19] K. Boubaker, The Boubaker polynomials, a new function class for solving bi-varied second order differential equations, F. E. Journal of A Math. 31 (2008), 299.

[20] B. K. Ben Mahmoud, Cryogenics 49(5) (2009), 217.

[21] K. B. Ben Mahmoud and M. Amlouk, Materials Letters 63(12) (2009), 991.

[22] M. Dada, O. B. Awojoyogbe and K. Boubaker, Current Applied Physics 9(3) (2009), 622.

[23] S. Tabatabaei, T. Zhao, O. Awojoyogbe and F. Moses, Int. J. Heat Mass Transfer 45 (2009), 1247.

[24] A. Belhadj, O. Onyango and N. Rozibaeva, J. Thermophys. Heat Transf. 23 (2009), 639.

[25] P. A. Barry, Hennessy, Journal of Integer Sequences 13 (2010), 1.

[26] M. Agida and A. S. Kumar, El. Journal of Theoretical Physics 7 (2010), 319.

[27] A. Yildirim, S. T. Mohyud-Din and D. H. Zhang, Computers and Mathematics with Applications 59 (2010), 2473.

[28] A. S. Kumar, Journal of the Franklin Institute 347 (2010), 1755.

[29] A. Milgram, J. of Theoretical Biology 271 (2011), 157-158.

[30] K. Bukietynska and B. Radomska, Chem. Phys. Lett. 79 (1981), 162.

[31] Y. Karabulut, A. Canimoglu, Z. Kotan, O. Akyuz and E. Ekdal, Journal of Alloys and Compounds 583 (2014), 91-95.

g