Journal of Nuclear and Radiochemical Sciences, Vol. 9, No.1, pp. 1-6, 2008

ArticlesThermodynamics Study for the Sorption of 134Cs and 60Co Radionuclides from Aqueous
Solutions
E. Metwally,* T. El-Zakla, and R. R. Ayoub
Hot Laboratory Center, Atomic Energy Authority, P.O. 13759, Cairo, Egypt
Received: April 26, 2007; In Final Form: December 25, 2007
The removal of cesium and cobalt radionuclides from aqueous chloride solutions using hydrous titanium oxide
was investigated. The influence of initial ion concentration, pH, and temperature has been reported. The dataobtained have been correlated with Langumir, Freundlich, and Dubinin-Radushkevich (D-R) isotherm models.
The effect of temperature on the equilibrium distribution values has been investigated. The thermodynamic
parameters such as free energy (∆G o), enthalpy (∆Ho) and entropy (∆S o) have been calculated. Maximum ion
exchange capacity and the mean free energy of each studied ion have been determined using D-R isotherm
model.

1. Introduction
A number of activities and events have caused significant
radioactive contamination of different areas, these include:
inadequate practices for the management and disposal of radioactive waste, the intentional or accidental discharge of radioactive material to the environment, nuclear accidents, testing of
nuclear weapons, etc. Such contamination may present a hazard to human populations and the environment.1 Cesium andcobalt radionuclides are released into radioactive waste solutions from different radioactivities. They have a relatively long
half-lives and are considered as hazardous elements for theenvironment.2 Large amounts of cesium and cobalt radionuclides have been released to the subsurface from the Hanfordsite waste storage tanks.3, 4 New type of material is needed forthe selective removal and safe storage of 134Cs and 60 Co from
nuclear waste solutions and from groundwater. The radionuclide wastes are generally present in low concentrations and areassociated with an assortment of other cations.5 The cationicradioisotopes, present in the liquid effluents of low and intermidiate level liquid wastes, can be removed by the ion exchange
process. The inorganic ion exchanger materials possess highexchange capacity, possible selectivity and specificity, andgood resistant to radiation and heat.6-8 Thermodynamic modeling of metal-ligand interactions in high ionic strength NaClsolutions of Co2+ -oxalate system has been studied.9 Studies of
the kinetic and thermodynamic for the sorption of cesium(I) on
hydrous silica has been determined.10 Also the adsorption andthermodynamic behavior of some radionuclides as uranium(VI)on bentonite composite adsorbent has been determined.11 Ion
exchange properities of hydrous titanium oxide have been
receiving great attention, specially for application in radioactive liquid waste treatment.12-17 Adsorption of some elements
such as ferous ions on porous nanocrystalline TiO2 surface has
been conducted by the oxidation of ferous ions using photoelectrochemical process.18 Some adsorption studies of titaniumoxide ion exchanger has been determined such as the adsorption of cobalt on model catalysts consisting of Pd nanoparticles
on the surface of TiO2 using a thermal molecular beam.19 An
external gelation process has been conducted for developing
and preparation of TiO2 –SiO2 mixed gel spheres suitable forstrontium adsorption.20 Also, TiO2 –SiO2 mixed gel spheres*Corresponding author. E-mail: emetwally3@yahoo.com

prepared via sol–gel method was used for the sorption studies
of cesium radionuclides.21 Sorption of Cs + and Sr 2+ ions onhydrous titanium dioxide from chloride medium was studied,22
where, it showed a good ion exchange capacity for both metal
cations in neutral medium. The application of this study
towards column technique was tested.22 Also, hydrous titaniumoxide and sodium titanate was used for removal of cesium
radionuclides from aqueous solution.23 It was reported that anincrease in Cs concentration, temperature and pH at the studied
conditions apparently enhanced the uptake of Cs(I) on hydrous
titanium oxide.23
The objective of this study is to evaluate the use of hydrous
titanium oxide as an ion exchange material for the removal of134
Cs and 60Co from aqueous solution. The effect of temperature on the exchange process of each ion was studied to determine the relevant thermodynamic parameters. Freundlisch,
Langmuir, and Dubinin-Radushkevich (D-R) isotherms areapplied to the sorption data to calculate the different parameters and the best fitting achieved.
2. Experimental
2.1. Preparation and characterization of sorbent oxide.
All the reagents used were of AR grade chemicals. Stock solutions of the reagents were prepared by dissolving CsCl and
CoCl2.3H2O in double distilled water. Hydrous titanium oxide
was prepared by adding 150 cm3 of liquid TiCl4 to 450 cm3 of
distilled water followed by adding 2.5 M NaOH dropwisely
with vigorous stirring where the pH of the solution was
adjusted to 7. A white precipitate was formed. The precipitate
was filtered and washed several times with distilled water until
it was free of chloride ions and the washings were neutral. The
product was dried at 50 °C. The white precipitate of hydrous
titanium oxide was sieved to a particle size diameter < 370 µm
which was used in all experiments. Infrared spectra (IR), Xray diffraction analysis (XRD) and differential thermal analysis (DTA) studies for titanium hydrous oxide sample has been
determined and described in detail elsewhere.17 Also the specific surface area of the prepared hydrous titanium oxide sample has the value 216 m 2 /g, which was measured using
Micrometric type 2200 surface area analyzer. Pore size distribution analysis was carried out with high pressure Poresizer
9320, Micromeritics.
IR, XRD, and DTA curves for titanium hydrous oxide sample have been sumarized in Figure 1. As it is stated in© 2008 The Japan Society of Nuclear and Radiochemical Sciences
Published on Web 02/22/2008

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Metwally

J. Nucl. Radiochem. Sci., Vol. 9, No. 1, 2008

powder was shaken at 298, 308, and 335 K with 40 cm3 of different ion concentration of aqueous chloride solution in a thermostatic shaker for a specified period of contact time. Then, afixed volume (2 cm3) of the aliquot was withdrawn as a function of time and was applied for a radiometric measurement todetermine the concentration of the studied ions. Radiometricdetermination was achieved using NaI scintillation detector
connected to an ORTEC assembly (Nuclear Enterprises), USA.
The amount of metal ion retained in the solid phase, qe (µmol/g), was calculated from the expression:
Fig. 1aqe =(C0 –Ce)VW(1)

where Co and Ce are the initial and equilibrium concentrations(M) of metal ion in solution. V is the volume (L) and W is theweight (g) of the solid. It was observed that the uptake of each
ion was inhibited in the acidic medium, pH< 2.0. Where, thehighest uptake for cesium and cobalt ions was observed at pH
range 6.0–8.0. All sorption processs was achieved for sufficient long time up to 5 h and pH value of 6.0 for the studied
ions.
Fig. 1bFig. 1cFigure 1. a) Infrared spectra, b) X-Ray diffraction pattern, c)
Differential thermal analysis for titanium hydrous oxide sample.

Reference 11, IR spectrum of hydrous titanium oxide sample,
Figure 1a gives broad band at about 3700 – 2500 cm –1, which
belongs to the stretching vibrations of water molecules and OH
groups.24 The band at 1625.9 cm–1 is characteristic to the bending vibration of water molecules and the band near 1400 cm–1
is due to the bending vibrations of hydroxyl groups bounded totitanium atoms on the surface. 24 So, the surface hydroxyl
groups bonded to titanium atoms represent the adsorption
active sites, as the surface hydroxyl groups increase the capacity increase. The X-ray pattern, Figure 1b shows diffuse peaks
at the 2θ values 25.187, 37.936, and 62.755° corresponding to
the d-spacing 35.3, 23.67, and 14.79 nm. So, the preparedhydrous titanium oxide sample seems to be largely amorphousor microcrystalline. Thermogravemetric analysis (TGA),
Figure 1c shows a continuous loss in weight up to the maximum heating temperature used 800°C. The weight loss is due
to dehydration and its continuous nature is indicative of theabsence of definite hydrates of the prepared sample.24 Basedon these results, the chemical composition of the produced titanium oxide can be expressed as: TiO2. 0.82 H 2O as tentative
molecular formula and the percent of weight loss equal to18.4%.17, 25
2.2. Ion exchange measurements. Ion exchange behaviorof Cs + and Co2+ ions on hydrous titanium oxide sorbent wasstudied by applying batch technique. 0.1 g of the prepared

3. Results and Discussion
3.1. Ion exchange isotherm. Ion exchange isotherms ofCs(I) and Co(II) ions onto hydrous titanium oxide at different
temperatures are presented in Figure 2. Where a forward relation between C e and qe at 298, 308, and 325 K are obtained.
Langmuir isotherm of Cs (I) and Co (II) onto hydrous titaniumoxide at different temperatures are given in Figures 3a and 3b.
The isotherms are regular, positive. The initial rapid sorption
gives way to a slow approach to equilibrium at higher adsorbate
concentrations. These results reflect the scavenging efficiency
of hydrous titanium oxide for the removal of these metal ionsfrom wastewater in a wide range of concentrations. The
amount uptake increases with an increase in temperature forthe two ions thereby indicating the process to be endothermic
in nature.
Several common sorption isotherm models including
Langumir, Freundlich, and D-R isotherm models were
cosidered to fit the obtained isotherm data. These isotherm
models which were originally derived mainly for gas-solid systems have also been used successfully to represent sorption ofsolutes in liquid-solid systems.
Langmuir Isotherm
The Langmuir isotherm is given by the relation:26
qe =Qo bCe
1+bCe

Ce
1
1
=
+ o Ce .
qe
Qo bQ(Non-linear form)(2)(Linear form)(3)

Where Ce is the equilibrium solution phase concentration (µmol/L), qe is the equilibrium solid phase concentration(µmol/g), Qo is
the max concentration on the solid phase (µmol/g), b is the constant related to the free energy of the ion exchange (b ∝ e –∆G/RT).
The plot of Ce /qe against Ce, as shown in Figures 3a and 3b, islinear in the entire range of metal ion concentration at equilibrium. The numerical value of Langmuir constants Qo and b
evaluated from slope and intercept of the plot and the correlation
coefficient R2 are given in Table 1.
The good fit of the experimental data and the correlation
coefficients (R2) higher than 0.96 indicated the applicability ofThermodynamics Study for the Sorption of 134Cs and 60Co

J. Nucl. Radiochem. Sci., Vol. 9, No. 1, 2008othe langmuir isotherm model. The Langmuir constants Q andb increased with temperature showing that adsorption capacity
and intensity of adsorption are enhanced at higher temperatures and indicating the endothermic nature of adsorption. The
increase in adsorption capacity with temperature suggested thatthe active, surface centers available for adsorption haveincreased with temperature. Another reason may be due to thechange in pore size and enhanced rate of intraparticle diffusionof solute as diffusion is an endothermic process.27 Ce /qe values
for sorption of Cs(I) and Co(II) ions using hydrous titanium
100

100

Cs(I)

90

Co(II)

90

80

80

70

70

60

60

qe ( µmol /g)qe ( µmol /g)

3

50
40
30

10

40
30

298 K
308 K
325 K

20

298 K
308 K
325 K

20

50

10
0

0
0

5

10

15

0

20

5

10

Ce ( µmol /L)

15

20

Ce ( µmol /L)

Figure 2. Ion-exchange isotherms of Cs (I) and Co (II) on Hydrous titanium oxide at different temperatures.

0.5

1.0

Co(II)

Cs(I)

298 K
308 K
325 K

0.8

0.3

Ce/qe (g/L)

0.6

Ce/qe (g/L)

298 K
308 K
325 K

0.4

0.4

0.2

0.1

0.2
0.0

(a)

0.0

(b)

-0.1
0

5

10

15

0

20

5

10

15

Ce ( µmol /L)Ce ( µmol /L)
Figure 3. Langmuir isotherm of Cs (I) and Co (II) onto hydrous titanium oxide at different temperatures.

TABLE 1: Constant parameters and correlation coefficients calculated for Langmuir, Freundlisch, and D-R adsorption
models at different temperatures for Cs(I) and Co(II) adsorption onto hydrous titanium oxide
Cs(I)
Model

Co(II)

Parameters

Qo (µmol/g)
Langmuirb (L/µmol)
R2
KF (µmol/g)Freundlich
1/nR2
qm (mmol/g)
22
Dubinin-Radushkevich K (mol /kJ )E (kJ/mol)
(D-R)
R2

298 K
129.630.02990.99790.62370.84300.99600.6189–0.00340
12.1255
0.9959308 K
141.640.05370.99580.45820.7954
0.99310.4436–0.00304
12.8080.9933325 K
171.820.1196
0.99540.42970.74990.99050.4303–0.00271
13.5840.9905298 K
97.4650.04610.99501.17780.87100.9982
1.1795–0.00343
12.0636
0.9982308 K
169.770.1034
0.99172.45930.89970.98181.1052–0.00311
12.6828
0.9972

325 K
203.250.7761
0.96220.13060.5921
0.96371.7461–0.00223
14.9798
0.99604

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J. Nucl. Radiochem. Sci., Vol. 9, No. 1, 2008
2.0

2.0

Cs(I)

1.8

1.8

1.6

1.6

1.4

1.4

log qelog qeCo(II)

1.2
1.0

1.2
1.0

298 K
308 K
325 K

0.8

298 K
308 K
325 K

0.8

0.6

0.6
-6.5

-6.0

-5.5

-5.0

-4.5

-4.0

-8.5

-8.0

-7.5

-7.0

log Ce

-6.5

-6.0

-5.5

-5.0

-4.5

-4.0

log CeFigure 4. Freundlich isotherm of Cs (I) and Co (II) on hydrous titanium oxide at different temperatures.

oxide reach 0.3 (g/L) and 0.1 (g/L), respectively, at 298 K.
These values are higher than their corresponding values 4.5(mg/L), 2.5 (mg/L), 2.5 (mg/L), and 20 (mg/L) for sorption ofCs(I), Sr(I), Ca(II), and Mg(II) ions, repectively, using ZeoliteA sorbent.28 Adsorption capacity Qo for sorption of Co(II) ionsusing hydrous titanium oxide in the present work reachs 11.9
(mg/g), while in other work29 it reaches 0.919 (mg/g), 1.5 (mg/g), 4.38 (mg/g), 12.34 (mg/g), and 12.82(mg/g) for dikaolinite,
soil, marine bacterium, coir pith, and sluge sorbents, respectively.

layer. Whereas the solid surface reaches saturation while theFreundlich isotherm does not predict saturation of the solid
surface by the adsorbate, and therefore the surface coverage
being mathematically unlimited. In conclusion, Q o is themonolayer adsorption capacity while KF is the relative adsorption capacity or adsorption power.26
Dubinin –Radshkevich Isotherm (D–R Isotherm)
In order to study the nature of the sorption processes, the DR isotherm was also verified in the form:32, 33
2qe = qmax e–K' ε .

Freundlich Isotherm
The Freundlich isotherm is given by the relation:30
qe = KF C 1/ne(Non-linear form)(4)

log qe = log KF + 1/nlog Ce .

(Linear form)(5)

Where KF is the constant indicative of the relative ion exchange
capacity of the adsorbent (µmol/g) and 1/n is the constant indicative of the intensity of the ion exchange.
Plotting log qe versus log Ce as shown in Figures 4a and 4b
gives linear relation in the entire range of concentration atequilibrium. From the slope and intercept of the plot, numerical values of the Freundlich constants KF and 1/n and the correlation coefficient R2 can be determined as shown in Table 1.
It can be seen from these data that the Freundlich intensity
constant (n) are greater than unity for all studied ions. This has
physicochemical significance with reference to the qualitative
characteristics of the isotherms, as well as to the interactions
between metal ions species and hydrous titanium oxide. In ourcase for all metal ion species (n > 1), the hydrous titanium oxideshows an increase tendency for sorption with increasing solid
phase concentration. This should be attributed to the fact thatwith progressive surface coverage of adsorbent, the attractive
forces between the metal ion species such as van der Waals
forces, increases more rapidly than the repulsive forces, exemplified by short-range electronic or long-range Coulombic dipole
repulsion, and consequently, the metal ions manifest a stronger
tendency to bind to the hydrous titanium oxide site.31
Although the Freundlich and Langmuir constants KF and Qo
have different meanings, they led to the same conclusion about
the correlation of the experimental data with the sorption
model. The basic difference between K F and Q o is that
Langmuir isotherm assumes adsorption free energy independent of both the surface coverage and the formation of mono-(Non-linear form)(6)

Where qmax is the maximum concentration on the solid phase, i.e.,
ion exchange capacity (mmol/g), qe is the concentration in solid atequilibrium (mol/g), K' is the constant of the adsorption energy(mol2 /kJ2), and ε is the Polanyi potential (kJ/mol) and it is equaltoε = RT ln(1+1/Ce) .

(7)

Where R is the gas constant (kJmol –1 K–1), T is the absolutetemperature in degrees Kelvin, and Ce is the concentration insolution at equilibrium (mol/L).
The D–R isotherm can be linearized as:ln qe = ln qmax – K' ε 2 .

(Linear form)(8)

The D-R plots of ln qe versus ε 2 for all ions at different temperatures are given in Figures 5a and 5b. These linear plots
indicate that the D-R isotherm expression is followed for bothstudied metal ions. The D-R parameters, evaluated for sorptionof both studied ions at different temperatures, are presented inTable 1. The maximum sorption capacities (qmax) are in thesequence Co2+ > Cs +. These values are considerably less than
the theoretical exchange capacity (CEC) calculated from thechemical formula of hydrous titanium oxide (5.45 meq/g). This
could be due to the size window of the hydrous titanium oxide
and to the radius of all studied ions, which make difficult theion exchange and therefore the values determined experimentally were lower.34
The mean sorption energy E (kJ/mol), defined as the freeenergy change when one mole of ion is transferred to the surface of the solid from infinity in the solution, is calculated
according to the following equation:

Thermodynamics Study for the Sorption of 134Cs and 60Co
5.0

5.0

Cs(I)

4.5

298 K
308 K
325 K

4.5

Co(II)

298 K
308 K
325 K

4.0

4.0

3.5

ln qe

3.5

ln q e5

J. Nucl. Radiochem. Sci., Vol. 9, No. 1, 2008

3.0

3.0

2.5

2.5

2.0

2.0
1.5

1.5
26

28

30

32

34

36

38

40

42

26

44

28

30

32

�� �����

34

36

38

40

42

44

�� �����

Figure 5. The D-R isotherm of Cs (I) and Co (II) on hydrous titanium oxide at different Temperatures.
E = 1/ √ –2K' .

(9)

rized in Table 3.
Effect of temperature
The temperature has two major effects on the adsorption process. Increasing the temperature is known to increase the rateof diffusion of the adsorbate molecules across the externalboundary layer and in the internal pores of the adsorbent particle, owing to the decrease in the velocity of the solution. In
addition, changing the temperature will change the equilibrium
capacity of the adsobent for a particular adsorbate.36
Thermodynamics parameters, namely, Gibbs free energy(∆Go), enthalpy (∆Ho), and entropy (∆So) changes for the process
were also calculated using equations (10–12):

Where, K' is calculated from the D-R equation. The values ofE obtained from the slope of the D-R plots are given in Table 1.
The magnitude of E is useful for estimating the type of sorption reaction occurring. Calculated mean sorption energy forthe sorption of Cs + and Co2+ ions on hydrous titanium oxide
has the lowest value of 12.06 kJ/mol and has the highest valueof 14.97 kJ/mol, which are within the range of 8–16 kJ/mol
reported by Helfferich for ion exchange reactions.35
Among with the isotherm models tested and based on thecorrelation coefficient R2 values, the D-R approaches provided
a best fit over the entire range of concentration for all systems.
This suggests that some heterogenity in the surface or pores ofhydrous titanium oxide will play a role in the metal ion sorption.
The values of A, B1 and R2 used for fitting in the linear equation y = A + B1 × x, for the plots in Figures 3–5 are summa-∆Go = –RTln K1 ,
ln(

(10)

1
K1
∆H 1
)=–
( –
),
R T1 T2
K2(11)

TABLE 2: Thermodynamic parameters calculated for the adsorption of Cs(I) and Co(II) onto hydrous titanium oxide at
10 –5 M ion concentration
Cs(I)
T(K)

K
(L g–1)

298
308
325

K1=5.1510
K2 =7.6138
K3 =15.482∆G(kJ mol–1)–4.061–5.282–7.357o

Co(II)∆H(kJ mol–1)∆S(J mol–1K–1)

K(L g–1)32.961124.0822

K1=9.3670
K2 =17.5650
K3 =75.643

o

o

∆G
(kJ mol–1)–5.543–7.458–11.617o∆Ho(kJ mol–1)∆So(J mol–1K–1)

63.0511229.5121

TABLE 3: The values of A, B1 and R 2 used for fitting in the linear equation y = A + B1 × x for the plots in Figures 3–5
Model

LangmuirFreundlich

D-R

T (K)
298
308
325
298
308
325
298
308
325

A
0.194120.13134
0.06459
5.79500
5.661125.63318
13.33583
13.00286
12.97240Cs(I)B10.00582
0.00706
0.00773
0.84301
0.795400.74998–0.34007–0.30478–0.27095

R2
0.99799
0.99584
0.99549
0.99601
0.993130.99052
0.99599
0.99334
0.99055

A
0.10676
0.056930.013226.07108
6.39082
5.11601
13.9809
13.91561
12.07034

Co(II)
B1
0.00492
0.005890.010260.85109
0.89972
0.59216–0.34357–0.31084–0.22282

R2
0.99504
0.99177
0.962220.99827
0.98186
0.96379
0.99828
0.99720
0.99605

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J. Nucl. Radiochem. Sci., Vol. 9, No. 1, 2008

∆S = (∆H – ∆G )/T .
o

o

o

(12)

Where K is the apparent equilibrium constant corresponding to
the temperature which may be calculated from the product of
the Langmuir equation parameters Qo and b.37 So, the valuesof the constants K1, K2, and K3 corresponding to the temperatures of 298, 308, and 325 K, respectively, are given in Table 2.
Also, the values of the corresponding thermodynamic parameters (∆Go, ∆Ho, and ∆So) are given in Table 2.
The negative free energy values (∆Go) as shown in Table 2, foreach exchange ion, and its decrease with increasing exchange
temperature is connected with the higher affinity of hydrous
tita n ium oxide to these ions a nd with the cha nge ofthermodynamic stability of the hydrous titanium oxide
framework during the exchange process. Also, negative freeenergy values indicate the feasibility of the process and its
spontaneous nature. Based on the value of free energy deduced
from equilibrium isotherm data, the selectivity series is Co2+ >Cs+.
The values of enthalpy (∆Ho) as shown in Table 2 indicatethat the standard enthalpy of each exchange process does notdepend on the exchange temperature in the temperature range
from 298 to 325 K. The positive values of the standard
enthalpy show the process to be endothermic.
The values of entropy (∆So) as listed in Table 2 showed thatthe standard entropy of the exchange process does not dependon the exchange temperature in the temperature range from
298 to 325 K. Also, positive entropy reflects the affinity of theion exchange material for the metal ions under consideration.
4. Conclusion
The results of this study indicate that the prepared hydrous
titanium oxide sorbent can be successfully used for the recovery of cesium(I) and cobalt(II) radionuclides from aqueous
solutions under investigation. Thermodynamic parameters
were caculated for the adsorption process of Cs(I) and Co(II)radionuclides using hydrous titanium oxide at different temperatures. Equilibrium isotherms have been tested for different
isotherm expressions and the sorption data were successfullymodeled usi ng La ng u m i r, Freund l ich, a nd Dubi n i nRadushkevich (D-R) isotherms. The maximum ion exchange
capacity and the mean free energy of the studied cations havebeen determined using the D-R model expression. The
obtained thermodynamic data provide valuable information
about the exchange mechanisms for hazardous radionuclides
from waste solutions using hydrous titanium oxide.
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