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Arab Journal Of Nuclear Science And Applications, 46(2),(1-16) 2013
Equilibrium and Kinetic Sorption of Some Heavy Metals from Aqueous
Waste Solutions Using p (AAc-HEMA).
M. M. B. El -Sabbah *2 , El-Sayed A. H, E. Elnesr, F. H. Khalil, , B. El-Gammal * 1 , and T.
mansour
National Center for Radiation Research and Technology P.O.Box 29,Nasr city. Cairo, Egypt
* 1 Hot lab. Center-Inshas- Atomic Energy Authority
* 2 Chemistry Department, Faculty of Science, Alazhar university
Received: 4/1/2012 Accepted: 30/1/2012
ABSTRACT
Removal of heavy metals from aqueous waste solution using poly acrylic acid /
2-hydroxyethyle methacrylate ( p-AAc/ HEMA) was investigated. Experiments were
carried out as function of contact time, initial concentration , pH, partipcle size and
temperature . Adsorption data were modeled using the pseudo-first-order, pseudosecond-order
and intra-particle diffusion kinetics equations. It was shown that
pseudo-second-order kinetic equation could best describe the adsorption kinetics.
The results indicated that poly acrylic acid / 2-hydroxyethyle methacrylate ( p-AAc/
HEMA) is suitable as adsorbent material for adsorption of Sr 2+ , Co 2+ , Cd 2+ , Zn 2+ ,
Nd 3+ and Eu 3+ radio active nuclei from aqueous solutions.
Key words: polyacrylic acid - 2-hydroxyethyle methacrylate / europium/neodymium,
strontium/ cadmium/ zinc and cobalt.
INTRODUCTION
The removal of radioactive nuclei from aqueous waste solution is one of the most important
issues of environmental remediation. poly acrylic acid / 2-hydroxyethyle methacrylate ( p-AAc/
HEMA) was chemically synthesized and exploited as adsorbent material for the decontamination
study of Sr 2+ , Co 2+ , Cd 2+ , Zn 2+ , Nd 3+ and Eu 3+ radioactive nuclei from aqueous solutions under
simulated conditions using batch technique. The main sources of these elements are metal plating
industries, abandoned disposal sites, and mining industries (1) . The presence of toxic heavy metals in
water has caused several health problems with animals, plants, and human being [2] . Among toxic
heavy metals, cadmium is one of the most dangerous for human health [3] . Cadmium is an irritant to
the respiratory tract and exposure to this pollutant can lead to anaemia, renal damage, osseous disease
with effects similar to osteoporosis, and Itai-Itai disease (4,5) . However, cadmium has also practical
applications: e.g., it is highly corrosion resistant and is used as a protective coating for iron, steel, and
copper. The industrial uses of cadmium are increasing in plastics, paint pigments, electroplating,
batteries, mining, and alloy industries (6) , also, cadmium having several industrial applications are the
potential pollutants widely found in industrial wastewaters (7,8). The aim of this study was to synthesize
and characterize polymeric hydrogels and demonstrate its potential use in various practical
applications.
1

Materials:
Arab Journal Of Nuclear Science And Applications, 46(2),(1-16) 2013
EXPERIMENTAL
All chemicals and reagents were of analytical grade. Acrylic acid (CH2CHCOOH), / 2hydroxyethyle
methacrylate and Nitric acid (HNO3) were obtained from Porlabo, europium nitrate
[Eu(NO3)3] was obtained from Aldrich Chem. Co, cobalt chloride [Co(Cl)2], neodymium chloride
[Nd(Cl)3], strontium chloride [Sr(Cl)2], cadmium chloride [Cd(Cl)2], zinc chloride [Zn(Cl)2], were
purchased from Merck. The pH was adjusted by the addition of NH4OH.
Instrumentation:
Atomic absorption spectrophotometer (Buck Scientific) model 210 VGP, USA, was used to
analyze europium, neodymium, strontium, cadmium, zinc, and cobalt ions in the solution. For batch
investigation, a good shaking for the two phases was achieved using a thermostated mechanical
shaker. The hydrogen ion concentration of different solutions was measured using CG-820 Schott
Gerate pH meter, Germany. The samples were weighed on analytical balance produced by Bosch.
Preparation of the ion exchange material:
A known volume of AAc/HEMA comonomers of composition ratios (1:1) was dissolved in
water. Different amounts of HEMA are added to known volume of the prepared AAc, depending on
the required comonomers ratios. This mixture was then placed in test tubes and degassed by bubbling
of pure nitrogen gas for 5 minuets and subjected to 60 Co -Gamma irradiation. The prepared materials
were washed several times with bidistilled water and dried in oven at 50ºC for 24 hours. The product
was then grounded , and sieved to obtain the desired mesh size of 500μ.
Characterization:
Characterization of the prepared ion exchangers was carried out using the different analytical
techniques such as: Scanning Electron Microscope (SEM), Differential Scanning Calorimeter (DSC),
Fourier Transform Infrared Spectra (FTIR), Particle Size Analyzer (PSA) and Electron Spin
Resonance (ESR). The thermal analysis of materials was studied using Differential Scanning
Calorimeter (DSC); PERKIN ELMER DSC 7 at National Center of Radiation Research and
Technology.
The IR spectrum was measured using ATI MATTFON [ Genfis Series, Unicam, England ]
FTIR spectrometer. Each sample was thoroughly mixed with KBr as a matrix, the mixture was ground
and then pressed to give a disc of standard diameter. The electron spin resonance (ESR Spectroscopy)
of the prepared material was studied using EPR spectrophotometer ( X-pand ) BRUKUR Germany.
The morphology of the prepared material was studied using scanning electron microscopy. Samples
were washed, dried and mounting on support and then made conductive with sputtered gold. The
surface observations were made using JEOL JSM-5400 Scanning Electron Microscope.
Ion-exchange capacity:
The ion-exchange capacities of the Sr, Nd, Zn, Cd, Co and Eu ions on poly-acrylic
acid/Acrylonitrile (P-AAc/HEMA) were determined using batch experiment by shaking 10 ml of 10 -4
M sample solution with 0.05 g of exchanger at room temperature for 24 hours till reach the
equilibrium,. The liquid and the solid phases were separated and then the ion concentration was
measured in the liquid phase to calculate the percent uptake, ( eq. 1). Another 10 ml of sample solution
was added to the solid phase and by repeating these steps several times and calculating the percent
uptake in each case till no uptake was obtained. The ion exchange capacity was determined by
equation (2) (9,10) .
2

Arab Journal Of Nuclear Science And Applications, 46(2),(1-16) 2013
% Uptake = x 100 -------------- (1)
Capacity = x V/m x Co -------- (2)
Where Co , C are the initial and the measured concentrations of the tested ion,V is the volume
of solution (L), m is the weight of exchanger (g).
. Table (1) illustrates the values of capacity for Sr, Nd, Zn, Cd, Co and Eu ions, according to the
order: Eu3+ > Nd3+ > Sr2+ > Zn2+ >Co2+ > Cd2+ Co
- C
Co
Σ % uptake
100
.
Table (1): The capacities of the Sr 2+ , Co 2+ , Cd 2+ , Zn 2+ , Nd 3+ and Eu 3+ ions on P-AAc/ HEMA.
Factors affecting on the prepared materials:
Metal ion capacity, meq/g
Cd 2+ 3.01
Co 2+ 3.15
Zn 2+ 3.34
Sr 2+ 3.72
Nd 3+ 3.91
Eu 3+ 4.1
RESULTS AND DISCUSSION
To prepare the hydrophilic copolymers in the final forms there are different factors which
affect the preparation process such as:
i. Effect of Comonomer Concentration on The copolymerization process.
The influence of comonomer dilution in its solvent on the yield of copolymerization was
studied and represented in Figure(1). We noted from the figure, the copolymer yield increases with
increasing the comonomer concentration so that the maximum gel yields are produced using about
50% comonomers concentration.
ii. Effect of comonomer composition on the copolymer yield.
Figure (2) illustrates the effect of AAc/HEMA comonomers composition on the yield of
copolymers. The figure showed that the maximum degree of grafting obtained at comonomer
composition of (50:50).
3

Copolymer Yield
100
80
60
40
20
Arab Journal Of Nuclear Science And Applications, 46(2),(1-16) 2013
0
10 20 30 40 50
Comonomers Concentration %
Fig. (1) Effect of comonomers concentration
on the yield of copolymer, comonomer
composition 50/50, Irradiation Dose 20
kGy.
iii. Effect of irradiation dose on the copolymer yield.
Copolymer Yield
100
80
60
40
20
0
10 20 30 40 50
Irradiation Dose (kGy.
4
Copolymer Yield
100
95
90
85
20/80 40/60 50/50 60/40 80/20
Comonomers Composition %
Figure (3) illustrates the effect of irradiation dose on the yield of copolymers. The figure
showed that the yield of copolymers increases when the radiation dose increases; the highest
degree of copolymer (98%) is obtained at 50 kGy for 50% solution concentration.
iv. Infrared analysis (IR):
Fig. (2) Effect of comonomers composition on
the yield of copolymer , comonomer
concentration 50%, Irradiation Dose 20 kGy.
Fig. (3) Effect of irradiation doses on the yield of copolymer, comonomer
composition 50/50, comonomer concentration 50%.
Figure (4) illustrates the infrared analysis obtained Poly-acrylic acid/2-hydroxy
ethylemethacrylate (P-AAc/HEMA).The absorption band at 3400-3460 cm -1 is of O-H, also the
absorption band at 1720 cm -1 which corresponds to the carbonyl group in case of AAc is clear. The
spectra show the characteristic band around 2655-2950 cm -1 corresponding to methyl group.

Arab Journal Of Nuclear Science And Applications, 46(2),(1-16) 2013
v. Electron Spin Resonance (ESR):
Figure. (5) illustrates the Electron Spin Resonance (ESR) for P-AAc/HEMA which shows a
hyperfine structure that is having the g-value, 3.51 T, which is different from the free electron
indicating that participation of different atoms in a paramagnetic complex. This phenomena is
encountered in complexation of some transition metal elements with organic ligands
Intensity
300
200
100
0
-100
-200
-300
3400 3420 3440 3460 3480 3500 3520 3540 3560
vi. Differential Scanning Calorimeter (DSC):
Fig. (4) FTIR spectrum of P-AAc/HEMA.
[G] value
Fig. (5) Electron Spin Resonance of P-AAc/HEMA.
The differential scanning calorimeter (DSC) figure. (6) Showed that the melt enthalpy of P-
AAc/HEMA is observed at 222.5 °C
5

Arab Journal Of Nuclear Science And Applications, 46(2),(1-16) 2013
Fig. (6) Differential scanning calorimeter (DSC) of P-AAc/HEMA.
vii. Scanning Electron Microscope (SEM):
Scanning electron microscope of P-AAc/HEMA is investigated in figure. (7) from which it is
concluded that the particle size of the material is 3-9 μm and slit like porosity with width equals 1 μm
and 20 μm length.
Fig. (7) Scanning electron microscope (SEM) of P-AAc/HEMA.
Kinetic study
Effect of initial metal ion concentration and shaking time on the adsorption.
6

Arab Journal Of Nuclear Science And Applications, 46(2),(1-16) 2013
i. Effect of Metal Ion Concentration on adsorption:
The effect of metal ion concentration in the range from 10 -2 to 10 -4 M on sorption of metal
ions, under study, by poly-acrylic acid/2-hydroxyethylene methacrylate (P-AAc/HEMA) from 0.01 M
HNO3 medium, for 4 hours and V/m = 200 ml/g at room temperature was studied. The uptake
decreases by increasing the metal ion concentration for Zn 2+ , Cd 2+ ,Co 2+ , Sr 2+ , Nd 3+ and Eu 3+ onto P-
AAc/HEMA ions as shown in Figure (8).
% uptake
90
85
80
75
70
65
60
55
50
45
40
35
0.000 0.002 0.004 0.006 0.008 0.010
C (M)
Fig. (8) Effect of metal ion concentration on the % uptake in case
of P-AAc/HEMA at room temperature.
ii. Effect of Contact Time:
The effect of contact time on the uptake of 10 -4 M Sr 2+ , Co 2+ , Cd 2+ , Zn 2+ , Nd 3+ and Eu 3+ by
poly-acrylic acid/2-hydroxyethylene methacrylate (P-AAc/HEMA) as cation exchanger from aqueous
solution of 0.01 M HNO3 has been investigated batchwisely at room temperature. The percent uptake
increases sharply at the initial stages by increasing shaking time until the equilibrium is obtained,
91.51%, 85.3%, 78.8%, 77.9%, 75.41% and 74.6% for Eu 3+ Nd 3+ Sr 2+ , Co 2+ , Cd 2+ and Zn 2+ ions
respectively as shown the figure (9) which illustrates that the time required for equilibrium is within
60 minutes.
7
Sr
Nd
Eu
Co
Cd
Zn

Arab Journal Of Nuclear Science And Applications, 46(2),(1-16) 2013
iii. Effect of particle size
The effect of particle size using the size ranging 5 – 15 µm of Poly-acrylic acid/2-hydroxy
ethylemethacrylate (P-AAc/HEMA) on the removal of Eu3+ , Nd3+ , Sr2+ , Co2+ , Cd2+ and Zn2+ ions was
studied at room temperature. Figures. (10-1) : (10-6) show the effect of contact time at different
particle sizes. The capacity of aforementioned ions sorption at the equilibrium was calculated and
found to increase with the decrease of the adsorbent particle sizes indicating that the ions sorption
occurs by a surface mechanism, as shown in Table (2). It was also observed that the variation in
particle size affects on the equilibrium time. Thus, for particle size 5 µm, the time required to reach
equilibrium is about 50 minutes for metal ions. While for particle sizes 15 µm, the time necessary is
about 80 minutes for the metal ions. Consequently, increasing particle size increases the time needed
to reach equilibrium. These results suggest that the sorption kinetic of Eu3+ , Nd3+ , Sr2+ , Co2+ , Cd2+ and
Zn2+ ,ions by Poly-acrylic acid/2-hydroxyethylemethacrylate (P-AAc/HEMA) is largely determined by
the particle size.
Table (2) Effect of particle size of P-AAc/AN on the capacity of
Zn2+ , Cd2+ Co2+ , Sr2+ , Nd3+ and Eu3+ Fig.(9): Effect of contact time on the % uptake in case
of P-AAc/HEMA.
ions.
Metal ion Zn Cd Co
Particle size,
µm
Capacity,
meq/g
5 10 15 5 10 15 5 10 15
3.84 2.56 1.87 3.55 2.91 1.74 3.62 2.68 1.81
Metal ion Sr Nd Eu
Particle size,
µm
Capacity,
meq/g
% uptake
100
80
60
40
20
0
0 20 40 60 80 100 120
5 10 15 5 10 15 5 10 15
4.3 3.1 2.22 4 2.95 2.32 4.6 3.66 2.72
8
time, mint.
Sr
Nd
Eu
Co
Cd
Zn

% uptake
% uptake
% uptake
80
60
40
20
Arab Journal Of Nuclear Science And Applications, 46(2),(1-16) 2013
0
0 50 100 150 200 250 300
80
70
60
50
40
30
20
10
100
80
60
40
20
0
0 50 100 150 200 250 300
time, mint.
0.05mm
0.10mm
0.15mm
0
0 50 100 150 200 250 300
Sorption Kinetics Modeling
time, mint.
time, mint.
0.05mm
0.10mm
0.15mm
Fig. (10-1) Effect of particle size of P-
AAc/HEMA on removal of Eu 3+ ion.
Fig. (10-3) Effect of particle size of P-
AAc/HEMA on removal of Sr 2+ ion.
0.05mm
0.10mm
0.15mm
Fig. (10-5) Effect of particle size of P-
AAc/HEMA on removal of Cd 2+ ion.
9
% uptake
% uptake
Fig. (10-2) Effect of particle size of P-
AAc/HEMA on removal of Nd 3+ ion.
80
60
40
20
0
0 50 100 150 200 250 300
80
70
60
50
40
30
20
10
0 50 100 150 200 250 300
time, mint.
0.05mm
0.10mm
0.15mm
Fig. (10-4) Effect of particle size of P-
AAc/HEMA on removal of Co 2+ ion.
0
0 50 100 150 200 250 300
time, mint.
0.05mm
0.10mm
0.15mm
Fig. (10-6) Effect of particle size of P-
AAc/HEMA on removal of Zn 2+ ion.
As given in the previous section, for P-AAc/HEMA system, the sorption process was investigated
by studying some kinetic models, pseudo-first-order, pseudo-second-order and intra-particle diffusion.
% uptake
100
80
60
40
20
0
time, mint.
0.05mm
0.10mm
0.15mm

Arab Journal Of Nuclear Science And Applications, 46(2),(1-16) 2013
i. First-order kinetic model
The sorption kinetics of metal ions from liquid phase to solid is considered as a reversible reaction
with an equilibrium state being established between two phases. A simple pseudo first order model
(11,12,13,14) was therefore used to correlate the rate of reaction and expressed by the Lagergren equation
as follows:
k 1
log qe qt logq
e t
(2)
2.303
qe and qt are the amounts adsorbed at equilibrium and at time t, respectively (mmol/g), k1 is the rate
constant of Pseudo-first-order model (min-1 ).
The plots of log(qe − qt) against t for the pseudo-first-order equation give a linear relationship,
the values of k1 (rate constant) and qe can be determined from the slope and the intercept of this
equation, respectively. Figs. (11-1): (11-6) show the plots of the linearized form of the pseudo-firstorder
equation. Kinetic parameters along with correlation coefficients (R2 ) of the pseudo-first-order
model are shown in Table (3). As can be seen from the the figures and the table, despite the correlation
coefficients for the first-order kinetic model obtained at 298, 303, 313 and 323 o K for the six metal
ions, under study, are quite high (>0.90), yet the calculated qe values give reasonable values within the
experimental results at low temperature (298 °K) only, therefore the sorption of Eu3+ , Nd3+ , Sr2+ , Co2+ ,
Cd2+ and Zn2+ ions on poly-acrylic acid/Acrylonitrile (P-AAc/HEMA) fit this model at low
temperature.
Table (3) The kinetic parameters of Pseudo-first-order model for sorption of Zn 2+ , Cd 2+ Co 2+ ,
Sr 2+ , Nd 3+ and Eu 3+ onto P-AAc/HEMA at different temperatures.
Temp,
o K
k1 ,
min -1
qe, exp.
mmol/g
Zn Co Cd
qe, calc.,
mmol/g
R 2
k1 ,
min -1
qe, exp.
mmol/g
11
qe , calc.,
mmol/g
R 2
k1 ,
min -1
qe, exp.
mmol/g
qe , calc.,
mmol/g
298 0.005 0.01357 0.013 0.97 0.0051 0.01438 0.0115 0.92 0.0058 0.01424 0.0096 0.98
303 0.0037 0.01499 0.0091 0.94 0.0053 0.01467 0.0068 0.98 0.008 0.01482 0.0069 0.96
313 0.0028 0.01591 0.0074 0.93 0.0066 0.01522 0.0041 0.91 0.0068 0.01562 0.0054 0.99
323 0.0031 0.01659 0.0068 0.97 0.0052 0.01547 0.0026 0.96 0.0066 0.01657 0.0047 0.97
Temp,
o K
k1 ,
min -1
qe, exp.
mmol/g
Sr Nd Eu
qe, calc.,
mmol/g
R 2
k1 ,
min -1
qe, exp.
mmol/g
qe , calc.,
mmol/g
R 2
k1 ,
min -1
qe, exp.
mmol/g
qe , calc.,
mmol/g
298 0.0073 0.01592 0.0139 0.99 0.0073 0.01529 0.0139 0.99 0.0077 0.01717 0.0158 0.99
303 0.0059 0.01628 0.0094 0.97 0.0059 0.01566 0.0093 0.97 0.008 0.01753 0.0112 0.98
313 0.0068 0.01697 0.0061 0.99 0.0068 0.01627 0.0061 0.99 0.0079 0.0181 0.009 0.98
323 0.0069 0.01723 0.0044 0.99 0.0069 0.01673 0.0045 0.99 0.007 0.01867 0.0061 0.99
R 2
R 2

log ( q e - q t )
log ( q e -q t )
log ( q e - q t )
-1.8
-1.9
-2.0
-2.1
-2.2
-2.3
-2.4
-2.5
-2.6
-2.7
-2.8
-2.9
-3.0
-3.1
-1.8
-1.9
-2.0
-2.1
-2.2
-2.3
-2.4
-2.5
-2.6
-2.7
-2.8
-2.9
-3.0
-2.0
-2.1
-2.2
-2.3
-2.4
-2.5
-2.6
-2.7
-2.8
-2.9
-3.0
Arab Journal Of Nuclear Science And Applications, 46(2),(1-16) 2013
0 5 10 15 20 25 30
0 5 10 15 20 25 30
298 K
303 K
313 K
323 K
t , mint.
t , mint.
298 K
303 K
313 K
323 K
0 5 10 15 20 25 30
t , mint.
298 K
303 K
313 K
323 K
Fig. (11-1) Pseudo-first-order plots for Sr 2+
onto P-AAc/HEMA at different temperatures.
Fig. (11-3) Pseudo-first-order plots for Eu 3+
onto P-AAc/HEMA at different temperatures.
Fig. (11-5) Pseudo-first-order plots for Cd 2+
onto P-AAc/HEMA at different temperatures.
11
log ( q e -q t )
log ( q e - q t )
log ( q e - q t )
-1.8
-1.9
-2.0
-2.1
-2.2
-2.3
-2.4
-2.5
-2.6
-2.7
-2.8
-2.9
-3.0
-3.1
-1.8
-1.9
-2.0
-2.1
-2.2
-2.3
-2.4
-2.5
-2.6
-2.7
-2.8
-2.9
-3.0
-3.1
-2.0
-2.1
-2.2
-2.3
-2.4
-2.5
-2.6
-2.7
-2.8
-2.9
-3.0
0 5 10 15 20 25 30
t ,mint.
0 5 10 15 20 25 30
t , mint.
298 K
303 k
313 K
323 K
0 5 10 15 20 25 30
t , mint.
298 K
303 K
313 K
323 K
298 K
303 K
313 K
323 K
Fig. (11-2) Pseudo-first-order plots for Nd3+ onto P-AAc/HEMA at different temperatures.
Fig. (11-4) Pseudo-first-order plots for Co 2+
onto P-AAc/HEMA at different temperatures.
Fig. (11-6) Pseudo-first-order plots for Zn 2+
onto P-AAc/HEMA at different temperatures.

Arab Journal Of Nuclear Science And Applications, 46(2),(1-16) 2013
ii. Pseudo-second-order:
A pseudo-second-order rate model is used to describe the kinetics of the sorption of metal ions
onto sorbent materials (15,16,17) . The second model used to describe the kinetics of the adsorption of
Sr +3 , Co +2 , Cd +2 , Zn +2 , Nd +3 and Eu 3+ by poly-acrylic acid/2-Hydroxyethylmethacrylate (P-
AAc/HEMA) at different temperatures is pseudo second-order model, which presented in equation
(3).
t 1 1
t
(3)
q k q q
2
2 e e
Where, k2 is the pseudo second-order rate constant. The qe and k2 values of the pseudosecond-order
kinetic model can be determined from the slope and the intercept of the plots of t/q
versus t, respectively. Figs. (12-1) : (12-6) give the results of the linearized form of the pseudosecond-order
kinetic model. The calculated qe values are more closer to the experimental data than the
calculated values of pseudo-first-order model. Therefore, the sorption of the six ions can be
approximated more favorably by the pseudo-second-order model, Table (4) illustrates that the
correlation coefficients are very high, R 2 >0.99, for pseudo-second-order kinetic model this
reinforcing the applicability of this model.
Table (4) The kinetic parameters of Pseudo-second-order model for sorption of Sr 2+ , Nd 3+ , Eu 3+
,Co 2+ ,Cd 2+ and Zn 2+ onto P-AAc/HEMA at different temperatures.
Temp,
o K
k2
,g/mmol
.min
Sr Nd Eu
qe ,
calc.,
mmol/g
R 2
k2
,g/mmol
.min
12
qe ,
calc.,
mmol/g
R 2
k2
,g/mmol
.min
qe ,
calc.,
mmol/g
298 5.68 0.017065 0.999 5.96 0.016313 0.999 5.28 0.018797 0.997
303 7.22 0.018149 0.998 10.62 0.01642 0.999 7.77 0.01912 0.998
313 17.47 0.017637 0.999 16.96 0.016556 0.995 11.08 0.019231 0.999
323 28.25 0.017699 0.996 25.29 0.017241 0.999 17.49 0.019455 0.999
Temp,
o K
k2
,g/mmol
.min
Co Cd Zn
qe ,
calc.,
mmol/g
R 2
k2
,g/mmol
.min
qe ,
calc.,
mmol/g
R 2
k2
,g/mmol
.min
qe ,
calc.,
mmol/g
298 7.33 0.015576 0.999 8.05 0.01548 0.998 7.68 0.015748 0.999
303 9.81 0.015723 0.997 17.66 0.015552 0.999 14.271 0.015848 0.997
313 18.15 0.015823 0.999 19.6 0.016181 0.998 15.59 0.016807 0.998
323 42.2 0.015873 0.996 25.17 0.017153 0.999 27.81 0.016892 0.999
R 2
R 2

t/q, mint.g/mmol
t/q, mint. g/mmol
t/q, mint. g/mmol
4000
3500
3000
2500
2000
1500
1000
500
3500
3000
2500
2000
1500
1000
Arab Journal Of Nuclear Science And Applications, 46(2),(1-16) 2013
0
0 10 20 30 40 50 60
500
4500
4000
3500
3000
2500
2000
1500
1000
t, mint.
298 K
303 K
313 K
323 K
0
0 10 20 30 40 50 60
500
Fig. (12-1) Pseudo-second-order plots for Sr 2+
onto P-AAc/HEMA at different temperatures.
t, mint.
298 K
303 K
313 K
323 K
Fig. (12-3) Pseudo-second-order plots for Eu 3+
onto P-AAc/HEMA at different temperatures.
0
0 10 20 30 40 50 60
t, mint.
298 K
303 K
313 K
323 K
Fig. (12-5) Pseudo-second-order plots for Cd 2+
onto P-AAc/HEMA at different temperatures.
13
t/q, mint.g/mmol
t/q, mint. g/mmol
t/q, mint. g/mmol
4000
3500
3000
2500
2000
1500
1000
500
4500
4000
3500
3000
2500
2000
1500
1000
0
0 10 20 30 40 50 60
500
t, mint.
298 K
303 K
313 K
323 K
Fig. (12-2) Pseudo-second-order plots for Nd 3+
onto P-AAc/HEMA at different temperatures.
4500
4000
3500
3000
2500
2000
1500
1000
0
0 10 20 30 40 50 60
500
t, mint.
298 K
303 K
313 K
323 K
Fig. (12-4) Pseudo-second-order plots for Co 2+
onto P-AAc/HEMA at different temperatures.
0
0 10 20 30 40 50 60
t, mint.
298 K
303 K
313 K
323 K
Fig. (12-6) Pseudo-second-order plots for Zn 2+
onto P-AAc/HEMA at different temperatures.

Arab Journal Of Nuclear Science And Applications, 46(2),(1-16) 2013
iii. Intra-particle Diffusion:
Since rate of adsorption is usually measured by determining the change in concentration of
adsorbate with the adsorbent as a function of time, linearization of the data is obtained by plotting the
amount adsorbed per unit weight of adsorbent q versus t 1/2 as given by ref. (18) and Eq. (4): The intraparticle
diffusion model, Morris and Weber model, is presented as the following (19) .
q = kad t 1/2 + C (4)
where kad is the rate constant of intra-particle transport (mmol/g min 1/2 ).
The value C (mmol/g) in this equation is a constant which indicates that there exist a boundary layer
diffusion effects, and is proportional to the extent of boundary layer thickness (20) larger the value the
greater is the boundary effect (21) . If the plot of q versus t 1/2 gives a straight line, the adsorption process
is controlled by intra-particle diffusion only. However, if the data exhibit multi-linear plots, then two
or more steps influence the sorption process (22) .
The plots of q versus t 1/2 are given in Figs. (13-1) : (13-6) for the adsorption of Eu 3+ , Nd +3 ,
Sr +2 , Co +2 , Cd +2 , and Zn +2, ions on poly-acrylic acid/Acrylonitrile (P-AAc/AN) at different
temperatures. It can be seen from the figures that the adsorption data gives a straight lines, therefore
the intra-particle diffusion model is applicable for the adsorption process and the adsorption is
controlled by intra-particle diffusion.. The kinetic parameters are given in Table (5).
Table (5) The kinetic parameters of intra-particle diffusion model for sorption of Zn 2+ , Cd 2+
Co 2+ , Sr 2+ , Nd 3+ and Eu 3+ onto P-AAc/HEMA at different temperatures.
Temp
,
o K
Cd
Zn
Co
Sr
Nd
Eu
kad,
mmol
/g h 1/2
0.34
0.39
0.40
0.52
0.82
1.11
298 o K
C,
mmol
/g
0.000
4
0.002
9
0.000
8
0.000
1
0.000
2
0.000
1
R 2
0.99
0.99
0.98
0.97
0.98
0.98
kad ,
mm
ol/g
h 1/2
0.25
0.28
0.22
0.42
0.50
0.80
303 o K
C,
mmol/
g
0.0077
0.007
0.0054
0.0028
0.005
0.0049
R 2
0.97
0.97
0.99
0.98
0.96
0.97
14
kad,
mmol/
g h 1/2
0.20
0.24
0.13
0.24
0.28
0.57
313 o K
C,
mm
ol/g
0.00
93
0.00
9
0.00
94
0.00
91
0.00
95
0.00
86
R 2
0.98
0.99
0.99
0.96
0.98
0.98
kad,
mmol/
g h 1/2
0.16
0.17
0.07
0.17
0.25
0.44
323 o K
C,
mm
ol/g
0.01
1
0.01
1
0.01
2
0.01
1
0.01
1
0.01
2
R 2
0.9
8
0.9
8
0.9
8
0.9
6
0.9
9
0.9
7

q, mmol/g
q, mmol/g.
q, mmol/g
0.018
0.016
0.014
0.012
0.010
0.008
0.006
0.004
0.002
0.000
0.018
0.016
0.014
0.012
0.010
0.008
0.006
0.004
0.002
Arab Journal Of Nuclear Science And Applications, 46(2),(1-16) 2013
1 2 3 4 5 6 7 8
t 1/2 , mint.
298 K
303 K
313 K
323 K
Fig. (13-1) Intra-particle diffusion model for
sorption of Sr 2+ onto P-AAc/HEMA at
different temperatures.
0.016
0.014
0.012
0.010
0.008
0.006
0.004
1 2 3 4 5 6 7 8
t 1/2 , mint.
298 K
303 K
313 K
323 K
Fig. (13-3) Intra-particle diffusion model for
sorption of Eu3+ onto P-AAc/HEMA at
different temperatures.
298 K
303 K
313 K
323 K
1 2 3 4 5 6 7 8
t 1/2 Fig. (13-5) Intra-particle , mint. diffusion model for
sorption of Cd 2+ onto P-AAc/HEMA at
different temperatures.
15
q, mmol/g
q, mmol/g
q, mmol/g
0.016
0.014
0.012
0.010
0.008
0.006
0.004
0.002
0.000
0.016
0.014
0.012
0.010
0.008
0.006
0.004
0.002
0.000
0.016
0.014
0.012
0.010
0.008
0.006
0.004
1 2 3 4 5 6 7 8
t 1/2 , mint.
298 K
303 K
313 K
323 K
Fig. (13-2) Intra-particle diffusion model
for sorption of Nd 3+ onto P-AAc/HEMA at
different temperatures.
1 2 3 4 5 6 7 8
t 1/2 , mint.
298 K
303 K
313 K
323 k
Fig. (13-4) Intra-particle diffusion model
for sorption of Co2+ onto P-AAc/HEMA at
different temperatures.
1 2 3 4 5 6 7 8
t 1/2 , mint.
298 K
303 K
313 K
323 K
Fig. (13-6) Intra-particle diffusion model for
sorption of Zn2+ onto P-AAc/HEMA at
different temperatures.

Arab Journal Of Nuclear Science And Applications, 46(2),(1-16) 2013
Conclusions
Poly acrylic acid / 2-hydroxyethyle methacrylate ( p-AAc/ HEMA) was prepared using direct
gamma irradiation technique, characterized using DSC, ESR, IR, and SEM measurements and tested
as an ion exchange material for the removal of europium, neodymium, strontium, cadmium, zinc, and
cobalt ions from nitrate solutions. The uptake of these ions increases with increasing the pH value and
decreases with increasing the metal ion concentration. Sorption kinetics modeling was investigated by
studying some kinetic models, pseudo-first-order, pseudo-second-order kinetic model this reinforcing
the applicability of this model and intra-particle diffusion model is applicable for the adsorption
process and the adsorption is controlled by intra-particle diffusion,.
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