Article pubs.acs.org/IECR
Kinetic and Equilibrium Profiles of Adsorptive Recovery of Thorium(IV) from Aqueous Solutions Using Poly(methacrylic acid) Grafted Cellulose/Bentonite Superabsorbent Composite T. S. Anirudhan,*,† P. S. Suchithra,†,‡ P. Senan,† and A. R. Tharun† †
Department of Chemistry, University of Kerala, Kariavattom, Trivandrum 695 581, India Materials Science and Technology Division, National Institute for Interdisciplinary Science and Technology (CSIR), Trivandrum 695 019, India
‡
ABSTRACT: The removal and recovery of thorium(IV) [Th(IV)] ions from aqueous solutions were investigated using poly(methacrylic acid)-grafted-cellulose/bentonite (PMAA-g-Cell/Bent) superabsorbent composite through batch adsorption experiments. Surface characterizations of the adsorbent were investigated. The adsorbent showed significant Th(IV) removal (>99.7%) at pH 5.0. The influence of coexisting ions on the adsorption of Th(IV) was studied. Mass transfer aspects of Th(IV) adsorption onto PMAA-g-Cell/Bent were evaluated. The Sips adsorption isotherm described the adsorption data very well, with a maximum adsorption capacity of 188.1 mg/g. Thermodynamic parameters such as standard enthalpy (ΔH°), standard entropy (ΔS°), standard free energy (ΔG°), activation energy (Ea), isosteric enthalpy (ΔHx), and entropy (ΔSx) were calculated. Tests with a seawater sample revealed the effectiveness of PMAA-g-Cell/Bent for adsorptive removal of Th(IV) from aqueous solutions. Desorption experiments showed that 0.1 M HNO3 can effectively desorb adsorbed thorium ions with a contact time of 3 h. A single stage batch reactor is designed for commercial applicability of the adsorbent. impregnated silica gel, silk fibroin,4 fly ash,5 tannin-immobilized collagen fibres,6 zeolites, erionite,7 sodium alginate films,8 muscovite,9 Th(IV) ion-imprinting microbeads10 perlite,11 and N-trimethoxylsilylpropyl-N,N,N-trimethylammonium anionic resin.12 Inorganic−organic superabsorbent composites display more properties of the effective adsorbents than the inorganic and organic components individually. The presence of twodimensional platelike silicate layers in the matrix of a polymer leads to improved comprehensive properties such as tensile strength, modulus, and increased heat resistance, when compared to weak and fragile polymers with randomly crosslinked network structure.13 Minimal additions of clays enhance mechanical, thermal, and barrier performance properties significantly because of the large contact area between polymer and clay on a nanoscale. Therefore, inorganic−organic superabsorbent composites have gained importance due to their flexibility, reversible deformation, pH responsiveness, large surface area, nontoxicity, biocompatiblility, easy processability, reusability, and biodegradability.14 Our group developed a novel poly(methacrylic acid)-grafted-cellulose/bentonite (PMAA-g-Cell/Bent) superabsorbent composite by graft copolymerization of methacrylic acid (MAA) on to the active hydroxyl methyl group of cellulose (Cell) using N,N′methylenebisacrylamide (MBA) as cross-linker and potassium peroxydisulphate (KPS) as an initiator in presence of commonly used clay bentonite (Bent), resulting in an intercalation polymerization of Cell-PMAA into the interlayer
1. INTRODUCTION Effluents from industries such as thorium mining, optics, radio, gas mantle, aeronautics, aerospace, metallurgy, chemical industry, milling, phosphate fertilizer plants, and nuclear energy power plants are expected to be sources of thorium contamination in water. The evaluation of adverse health effects of thorium(IV) (Th(IV)) requires a slightly different approach than that with chemicals because radioactive elements, once entered in living bodies, start emitting electromagnetic radiations that can cause progressive and irreversible damage to cells, lymph nodes, lungs, liver, pancreas, and bone and finally leading to cancer.1 At the same time, recovery of Th(IV) ions from resources such as seawater and industrial wastewater is of great concern of scientific community, because of the increasing need for this metal for the production of electricity, as well as the expected shortage of this metal in the near future. In view of its extensive application, toxicity, and hazard, it is very important to develop new techniques for the removal and recovery of Th(IV), particularly from seawater and nuclear industry waste streams. Technologies employed for the removal and recovery of Th(IV) ions from aqueous solutions include liquid−liquid extraction, solidphase extraction, chromatography, ion exchange, functionalized resins, coprecipitation, electrode deposition, and adsorption.2 Among these, adsorption with different adsorbents is a promising technique with many advantages, such as higher enrichment factors, lower consumption of reagents, flexibility, and, more importantly, environmental friendliness. So far, many different types of adsorbents for Th(IV) have been reported in literature: activated carbon, 1 tannin-modified poly(glycidylmethacrylate)-grafted zirconium oxide-densified cellulose,3 manganese-impregnated fibers, hydrous oxides, goethite, silica gel coated with Amberlite, trioctylphosphine oxide© 2012 American Chemical Society
Received: Revised: Accepted: Published: 4825
November 5, 2011 February 4, 2012 March 6, 2012 March 6, 2012 dx.doi.org/10.1021/ie202538q | Ind. Eng. Chem. Res. 2012, 51, 4825−4836
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w/v) as a chromogenic agent in 3.0 M HNO3 medium at a wavelength of 660 nm. The effect of solution pH was studied in the pH range 1.0−7.0 with an initial concentration of 25 and 50 mg/L. Initial pH values were adjusted using 0.1 M NaOH or 0.1 M HNO3 solution. To account for the change of pH during adsorption, the pH of the solution was tested every 10 min and readjusted to initial value. To optimize the solid/liquid ratio (g/ L) in terms of cost effect, batch experiments were conducted using different amounts of adsorbent ranging between 50 and 500 mg in 50 mL of 100 mg/L Th(IV) ions at 30 °C. Ten different concentrations of Th(IV) ions between 10 and 600 mg/L were used for isotherm studies. For kinetic experiments, four different Th(IV) concentrations ranging from 25.0 to 100.0 mg/L were used. The adsorbed amount of metal ions was calculated from the difference between the initial and final concentrations, as determined by UV−visible spectrophotometry. Batch experiments were carried out to determine the effect of ionic competition on the adsorption of Th(IV) by making 0.05 M solutions of Fe(III), Ce(III), Sr(II), Al(III), Co(II), Ni(II), Mn(II), Zn(II), Cu(II), Cd(II), Pb(II), Li, Na, K, Mg, Ca, and Ba and anions such as bicarbonate, chloride, sulfate, and nitrate ions, present individually with 0.5 M Th(IV) solution. Since other ions such as Ca, Cd, and Zn could form the complexes with Arsenazo as well, the atomic absorption spectrophotometer is used to analyze the concentration of competitive ions. Reusability of the adsorbent is tested by conducting desorption experiments with an aqueous solution of HNO3 (0.1 M). The desorption ratio was calculated from the amount of Th(IV) adsorbed in the adsorbent and the final metal concentration in the desorption medium. For each adsorption experiment, the average of three replicates was reported, with standard deviation of 2.0%. When the relative error exceeded 2.0%, the data were discarded and a new experiment was conducted until the relative error falls within an acceptable range. The values of the kinetic and isotherm parameters were determined by a nonlinear regression analysis using ORIGIN program (version 7.5). The nonlinear chi-square test statistic (χ2), which is basically the sum of the squares of the difference between the experimental data and calculated data, with each squared difference divided by the corresponding data obtained by calculating from models, was used to analyze the data set to confirm the best fit kinetics and isotherm model for the adsorption. χ2, which is actually the degree of deviation of the experimental data with that of predicted from standard model, will be a small number for a best fitted model; otherwise, it will be a large number.
of Bent. Then, we investigated its adsorption behavior for bovine serum albumin from aqueous solution.15 As a continuation, for the present study, we decided to further explore the adsorption efficiency of PMAA-g-Cell/Bent for Th(IV) from aqueous solutions in batch process under the influence of various experimental parameters to determine the optimum conditions for the maximum removal for designing a single stage batch reactor for practical recovery of Th(IV) from aqueous solutions.
2. EXPERIMENTAL SECTION 2.1. Materials. The starting materials, Bent and Cell to prepare PMAA-g-Cell/Bent were obtained from Fluka, Switzerland. MAA, MBA, KPS, and sodium bicarbonate were supplied by E. Merk India, Ltd. Th(NO3)45H2O and Arzanazo(II1) were also obtained from E. Merk India, Ltd. All chemicals were of analytical grade and were used without further purification. All solutions were prepared with deionized water of specific conductivity less than 1 μ/(ohm cm). 2.2. Preparation of PMAA-g-Cell/Bent. Detailed schematic route for the preparation of PMAA-g-Cell/Bent were reported in our earlier publication.15 Very briefly, the adsorbent was prepared as follows: 6.0 g MAA monomer was dissolved in 20 mL of distilled water, and to this 1.0 g each Cell and Bent were added simultaneously with continuous stirring to prevent aggregation or precipitation of Bent. 0.15 g of MBA (crosslinker) and 0.1 g of KPS were then added to this mixture and refluxed at 70 °C and under N2 atmosphere for 4 h to ensure complete consumption of monomer. After 4 h, 1.5 g NaHCO3 (porogen) was added to prevent hardening of the product. On completion of polymerization, the product was washed with methanol several times for complete removal of the homopolymer. The product (PMAA-g-Cell/Bent) was filtered and washed several times with ethanol to remove any unreacted reagents and surface water, dried in an air oven at 50 °C for 4 h, ground and sieved to obtain 80 +230 mesh size of particles, with an average diameter of 0.096 mm. 2.3. Measurements. The bulk surface area was determined by the Brunauer−Emmet−Teller (BET) technique using a Micromeritics Gemini 2370 instrument that uses an N2/77 K adsorption−desorption method. Fourier transform infrared (FTIR) analysis of the samples was performed on a Schimadzn FTIR Model 1801 instrument. A Philips Model-XL-30 CP scanning electron microscope (SEM) was used to take microscopy images of the adsorbent samples. A Systronic microprocessor pH meter (Model μ-362) was used for pH measurements. A Jasco UV−visible (Model V-530) spectrophotometer was used for determining the concentration of Th(IV) ions in solution. GBC Avanta (A5450) atomic absorption sphectrophotometer (AAS) was used to determine the concentration of Fe(III), Ce(III), Sr(II), Al(III), Co(II), Ni(II), Mn(II), Zn(II), Cu(II), Cd(II), Pb(II), Li, Na, K, Mg, Ca, and Ba. 2.4. Adsorption Experiments. The adsorption studies were conducted by batch equilibrium method. The batch procedure used for the study is a commonly practiced one. Briefly, 50 mL of Th(IV) solution containing 100 mg of the adsorbent in a 100 mL Erlenmeyer flask was agitated at 200 rpm in a temperature controlled water bath shaker for 3 h to achieve an equilibrium adsorption state. At the end of 3 h, the samples were centrifuged (3000 rpm, 5 min), and then, the concentrations of thorium ions in the centrifugate were determined by spectrophotometry using Arsenazo-III (0.05%,
3. RESULTS AND DISCUSSION 3.1. Synthesis and Characterization of Adsorbent (PMAA-g-Cell/Bent). Detailed discussion of mechanism underlying graft copolymerization of the MAA onto the Cell backbone leading to the final product PMAA-g-Cell/Bent and characterizations at each stage of adsorbent preparation were reported in our previous publication.15 The degree of MAA grafting on the composite was found to be 61.0%, which is much greater than that of the reported values. It was proposed to utilize the cation exchange capacity of the carboxyl groups from the adsorbent surface to adsorb Th(IV) from aqueous solutions. The amount of carboxylic acid groups in PMAA-gCell/Bent was found to be 1.91 meq/g. The surface area was calculated from the BET adsorption data and the values were found to be 25.2, 05.9, and 132.6 m2/g, respectively, for Bent, Cell, and PMAA-g-Cell/Bent. The enhanced surface area of 4826
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and 1360 cm−1, respectively, confirm the grafting of MAA onto cellulose. A sharp peak at 1710 cm−1 is observed in the spectrum of PMAA-g-Cell/Bent, confirming the presence of −COOH moiety. The peaks appeared at 1420 cm−1 in the spectrum of Th(IV) loaded PMAA-g-Cell/Bent, indicating that the −COOH moiety gets converted into its salt, carboxylate,16 and the peak at 420 cm−1 indicates Th−O stretching vibrations.10 Moreover, the presence of the characteristic peak of Th(IV) at 624.3 cm−1, in the spectrum of Th(IV)-loaded PMAA-g-Cell/Bent, further confirmed the adsorption of Th(IV) to PMAA-g-Cell/Bent.17 The surface morphology of PMAA-g-Cell/Bent and Th(IV)loaded PMAA-g-Cell/Bent was studied by SEM analysis (Figure 2). The samples were sonicated for 30 min in acetone and drop casted to a SEM pin stub specimen mount. It can be seen that the surface of the Bent was very smooth, with a fluffy appearance. The SEM image of PMAA-g-Cell/Bent showed a corn flake-like structure with many small grooves. The heterogeneous and macroporous nature of the PMAA-g-Cell/ Bent is also revealed in the SEM image. The high surface area of PMAA-g-Cell/Bent is attributed to its macroporous nature. The SEM image of Th(IV)-loaded PMAA-g-Cell/Bent showed a polished plane surface, which can be attributed to a high uptake of thorium ions onto the surface of PMAA-g-Cell/Bent. 3.2. Effect of pH on Th(IV) Adsorption. The pH of the solution is the most significant factor in adsorption of metal ions, as it has a major effect on the protonation and deprotonation of the adsorbent and adsorbate functional groups and influence the metal speciation and surface metal binding sites. Thorium uptake was significantly affected by change in pH and maximum Th(IV) uptake by the PMAA-gCell/Bent was observed at pH 5.0 (Figure 3). The uptake was 99.7 and 95.4% corresponding to initial 10 and 25 mg/L Th(IV). Increasing or decreasing the pH on either side of the peak resulted in decline of Th uptake. Zero point charge of PMAA-g-Cell/Bent at pH 4.0 implies that, at pH < 4.0, the surface is positive and, at pH > 4.0, it is negative. At pH < 4.0, both the adsorbent and adsorbate is positively charged and the net interaction is that of electrostatic repulsion. Above pH 4.0, the surface of the adsorbent is negative and the positive hydrolysis species of thorium are adsorbed through a favorable electrostatic attraction. Often, determination of uptake as a function of pH becomes difficult because of the increasing
PMAA-g-Cell/Bent from its inorganic (Bent) and organic component (Cell) and the presence of carboxylic acid groups justifies superabsorbent composite formation with elevated adsorption capabilities. Zero point charge (pHzpc) values of Bent, Cell, and PMAA-g-Cell/Bent were found to be 3.0, 3.2 and 4.0, respectively. The FTIR spectra of PMAA-g-Cell/Bent and Th(IV)-loaded PMAA-g-Cell/Bent are shown in Figure 1. As shown, the FTIR
Figure 1. FTIR spectra of PMAA-g-Cell/Bent and Th(IV)-loaded PMAA-g-Cell/Bent.
spectra of PMAA-g-Cell/Bent and Th(IV)−loaded PMAA-gCell/Bent showed most of the characteristic peaks of Bent and Cell illustrating the presence of Bent and Cell in the polymer network.15 The broad peak centered at 3362 cm−1 corresponds to the O−H stretching vibrations from carboxyl group and the N−H stretching vibration from the amide groups. A peak at 1650 cm−1 is due to the carbonyl stretching from the amide group of MBA. The characteristic CO stretching and C−OH in plane bending frequencies of the carboxyl groups are 1270
Figure 2. SEM images of PMAA-g-Cell/Bent and Th(IV)-loaded PMAA-g-Cell/Bent. 4827
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Figure 3. (a) Adsorption of Th(IV) ions onto PMAA-g-Cell/Bent as a function of pH. (b) Distribution of the Th(IV) hydrolysis species as a function of pH.
more negative binding sites, so that adsorption process is more effective. 3.3. Effect of Solid/Liquid Ratio on Th(IV) Adsorption. Figure 4 shows the effect of solid/liquid ratio (0.5−5.0 g/L) on
tendency of the metal ion undergoing hydrolysis with decreasing hydrogen ion concentration. In the case of thorium, it becomes even more complicated as a result of a significant decrease in its solubility with increasing pH of the solution.18 A detailed literature survey had been conducted to have an insight to the thorium species in aqueous solution of different pH and thereby understanding the effect of pH of the solution in the adsorption process.19,20 Figure 3(b) shows the pH dominance diagram of thorium hydrolysis species. The following equations describe the adsorption of these species onto PMAA-g-Cell/ Bent: (PMAA‐g‐Cell/Bent) − COOH + Th4 + ↔ (PMAA‐g‐Cell/Bent) − COO−......Th4 + + H+
(1)
(PMAA‐g‐Cell/Bent) − COOH + Th4 + + H2O ↔ (PMAA‐g‐Cell/Bent) − COO−......[Th(OH)]3 + + 2H+
Figure 4. Effect of solid/liquid ratio on the adsorption of Th(IV) ions onto PMAA-g-Cell/Bent.
(2)
(PMAA‐g‐Cell/Bent) − COOH + Th4 + + 2H2O −
Th(IV) (50 mg/g) adsorption at 30 °C and at initial pH 5.0. At the beginning, the removal ratio increases with increase in solid/liquid ratio, which can be attributed to an increasing surface area at higher solid/liquid ratios, since small quantity of adsorbent is more quickly saturated than a larger one. The maximum removal is more than 99.0% when solid/liquid ratio is 2.0 g/L. The increase in removal is only a little (8.0%), on an economical ground, 30 °C, which is the normal temperature in India, is selected as the working temperature for all adsorption studies for better practicability. With increase in concentration from 25 to 100 mg/L, the amount of thorium adsorbed increased from 12.34 to 45.75 mg/g while the percentage removal decreased from 98.7 to 91.5%, and when temperature increased from 20 to 50 °C, the amount of thorium adsorbed increased from 42.75 to 49.95 mg/g and the percentage removal also increased from 85.5 to 99.9%, thereby indicating the Th(IV) removal by adsorption on PMAA-g-Cell/Bent is concentration dependent and endothermic. The increased adsorption capacity at high concentration is due to the increase in the driving force, which is the Th(IV) concentration difference between the liquid and the solid phases. The enhanced adsorption with temperature may be attributed to either increase in the number of active binding sites available for adsorption on the adsorbent surface or the
Figure 5. Kinetic plots for the adsorption of Th(IV) ions onto PMAAg-Cell/Bent at different concentrations and temperatures.
decrease in the boundary layer thickness surrounding the adsorbent, and thereby decreased boundary layer mass transfer resistance owing to the decrease in the viscosity of the solution. 3.5.1. Kinetic Models. The kinetics study is essential to determine the optimum operating conditions for the full-scale batch reactor. The kinetic parameters, which are useful for the prediction of adsorption rate, give important information for designing and modeling the batch process. Due to the fast decrease in concentration of Th(IV) ions in solution at a short time of contact, it is implied that the strong electrostatic interaction existed between the negatively charged PMAA-gCell/Bent surface and Th(IV) cations. For verification, pseudofirst-order model of Lagergren and the pseudo-second-order rate expression given by Ho and McKay are used to fit the kinetics of Th(IV) on PMAA-g-Cell/Bent.22,23 qt = qe(1 − exp(−k1t ))
qt =
(6)
k2qe2t 1 + k2qet
(7)
In the above equations, qe and qt are the amounts of metal ions adsorbed at equilibrium and at a time t, respectively, and k1 (min) and k2 (g/(mg min)) are the pseudo-first-order and pseudo-second-order rate constant. The kinetic parameters were calculated by nonlinear regression analysis. The calculated values of k1 and k2 and their corresponding regression coefficients (R2) and chi-square (χ2) values are presented in Table 1, and the results suggest that Th(IV) ions adsorption by PMAA-g-Cell/Bent can be best described by pseudo-second4829
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Table 1. Kinetic Parameters for the Adsorption of Th(IV) onto PMAA-g-Cell/Bent k1 (min−1)
qe, exp (mg/g) Concn. (mg/L) 25 12.34 50 23.93 75 35.15 100 45.75 Temp. (°C) 20 42.72 30 45.75 40 47.76 50 49.91
qe, cal (mg/g)
R2
χ2
k2 (mg/g/min)
qe, cal (mg/g)
h
R2
χ2
2.25 8.51 5.23 4.02
× × × ×
10−1 10−2 10−2 10−2
12.12 22.56 34.01 44.13
0.986 0.982 0.970 0.983
1.81 2.81 1.22 1.78
1.33 6.48 4.24 3.05
× × × ×
10−2 10−3 10−3 10−3
12.77 24.83 36.54 47.12
2.17 3.99 5.66 6.77
0.998 0.998 0.999 0.997
0.02 0.10 0.22 0.85
2.18 4.02 9.21 1.13
× × × ×
10−2 10−2 10−2 10−2
40.95 44.13 46.15 47.88
0.976 0.983 0.912 0.985
1.99 1.78 2.53 2.31
1.98 3.05 7.09 8.30
× × × ×
10−3 10−3 10−3 10−3
43.39 47.12 47.92 50.91
4.13 6.77 16.08 20.58
0.999 0.997 0.998 0.999
0.55 0.85 0.60 0.47
Table 2. Mass Transfer Parameters for the Adsorption of Th(IV) onto PMAA-g-Cell/Bent Di (cm2/s) Concn. (mg/L) 25 1.39 50 1.38 75 1.37 100 1.35 Temp. (°C) 20 1.31 30 1.35 40 1.41 50 1.45
R2
BL (cm/s)
α
kb
R2
× × × ×
10−11 10−11 10−11 10−11
0.993 0.981 0.986 0.991
3.12 2.97 2.87 2.49
× × × ×
10−6 10−6 10−6 10−6
0.763 0.746 0.699 0.772
0.057 0.048 0.045 0.044
25.52 28.20 29.59 30.49
0.974 0.949 0.992 0.986
× × × ×
10−11 10−11 10−11 10−11
0.985 0.991 0.992 0.975
1.91 2.49 3.62 3.80
× × × ×
10−6 10−6 10−6 10−6
0.783 0.772 0.659 0.781
0.056 0.044 0.022 0.020
29.41 30.49 31.95 32.19
0.939 0.978 0.984 0.952
order rate expressions. Experimental qe values were compared with both pseudo-first-order and pseudo-second-order kinetic models at different concentrations and temperatures, and Figure 5 shows excellent fit between experimental data and calculated pseudo-second-order model. This suggests that adsorption systems studied belong to pseudo-second-order kinetic model on the basis of the assumption that the rate determining step may be chemisorption, involving valence forces through sharing or exchange of electrons between adsorbent and adsorbate. The initial adsorption rate,24 h, expressed as h = k2qe2, obtained for the present study increased from 2.17 to 6.77 mg/g min and 4.13 to 20.58 mg/g min when initial concentration increased from 25 to 100 mg/L and reaction temperature increased from 20 to 50 °C, respectively. With an increase of concentration, the values of k2 decreased and that of qe increased, whereas with increase of temperature both the values of k2 and qe increased; therefore, it can be assumed that the adsorption of Th(IV) ions onto PMAA-gCell/Bent is controlled by diffusion kinetics. The apparent activation energy gives an idea about the influence of temperature on diffusivity. The activation energy, Ea, was obtained from the Arrhenius equation, which is given as follows: ln kad = ln A −
R2
Ea RT
revealed that both physisorption and chemisorption take place. This is in excellent agreement with pseudo-second-order kinetics obtained for the present study; a pseudo-secondorder suggests that this adsorption depends on the adsorbate as well as the adsorbent and involves a chemisorption process in addition to physisorption. The chemisorption might be the rate limiting step where valency forces are involved via electron sharing or exchange between the adsorbent and the adsorbate.25 The positive values of Ea suggest that increase in temperature favors the adsorption. Consequently, the adsorption process is endothermic in nature. Moreover, the calculated values of Ea are in the range of pore diffusion (20−40 kJ/mol), suggesting that Th(IV) adsorption onto PMAA-g-Cell/Bent is of pore diffusion-controlled adsorption as the rate-limiting processes.26 3.5.2. Mass Transfer Aspects of Th(IV) Adsorption onto PMAA-g-Cell/Bent. Both the external mass transfer model and the intraparticle mass transfer diffusion model (eqs 10 and 11, respectively) are used for the dynamic analysis of Th(IV) adsorption onto PMAA-g-Cell/Bent:27 ⎡ d(C /C0) ⎤ = − BL S ⎢ ⎥ ⎣ dt ⎦t → 0
f (qt /qe) = −[log(1 − (qt /qe)2 )] = 4π 2Dit /2.3d2
(8)
(9) (10)
where BL is the external mass transfer coefficient (cm/s) and S is the specific surface area for mass transfer. C and C0 is the concentration of solute in the solution and the initial concentration (mg/L), respectively. Di is the diffusion coefficient in the solid (cm2/s), and d the particle diameter. The values of BL and Di for different temperatures were determined from the plots of C/C0 versus t and log[1 − (qt/ qe)2] versus t, respectively (figures not shown), and the results are presented in Table 2. As shown in Table 2, the BL values decreased from 3.12 × 10−6 to 2.49 × 10−6 cm/s and increased
where Ea is the activation energy (kJ/mol), kad is the sorption rate constant, A is the Arrhenius constant, R is the gas constant (8.314 J/(mol K)), T is the solution temperature (K), and kad is the pseudo-second-order rate constant. The plots of ln kad vs 1/ T were found to be straight lines, and the values of Ea for Th(IV) ions uptake onto PMAA-g-Cell/Bent calculated from the slope of linear plots were found to be 40.5 kJ/mol . This value existing at the interface between the physisorption (5−40 kJ/mol) and the chemisorption (40−800 kJ/mol) ranges, 4830
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from 1.91 × 10−6 to 3.80 × 10−6 cm/s when the initial concentration increased from 25 to 100 mg/L and reaction temperature increased from 20 to 50 °C, respectively. Since increasing the metal concentration in the solution reduced the diffusion of metal ions in the boundary layer, the values of BL decreased with increasing concentration, and this has been the reason for the decreasing trend of percentage of Th(IV) adsorption by PMAA-g-Cell/Bent at higher concentration. The BL values suggest that the velocity of metal transport from the bulk solution to the solid phase is quite rapid, and this substantiates the favorable physical and chemical characteristics anticipated for PMAA-g-Cell/Bent for use as an adsorbent for the treatment of radioactive Th(IV) ions bearing nuclear wastewaters. The Di values are also decreased from 1.39 × 10−11 to 1.35 × 10−11 cm2/s and increased from 1.31 × 10−11 to 1.45 × 10−11 cm2/s when the initial concentration increased from 25 to 100 mg/L and reaction temperature increased from 20 to 50 °C. The increase in mass transfer coefficients with increasing temperature is due to enhanced diffusion of metal ions in the boundary layer and a decrease in retarding forces acting on the diffusing ions as a consequence of a higher thermal agitation at elevated temperatures. According to earlier works, the values of Di in the range 10−11−10−13 cm2/s reflect pore diffusion as the rate-limiting step.28 It appeared that the rate-limiting step was the pore diffusion process because the magnitudes of the coefficient for all metals are in the order of 10−11 cm2/s. Kinetic data were further tested using Bangham’s equation29 to confirm whether pore diffusion is the only the rate-limiting step. ⎛ C ⎞ ⎛ k m ⎞ 0 ⎟⎟ = log⎜ b ⎟ + α log t log log⎜⎜ ⎝ 2.303V ⎠ ⎝ C0 − qtm ⎠
In general, fitting the experimental data to Langmuir adsorption isotherms is a strong indication of monolayer formation, equivalent surface sites, and no interaction between the adsorbed molecules. The Langmuir constants Q0 (mg/g) and b represent the amount of solute adsorbed per unit weight of adsorbent required for monolayer coverage of the surface and the heat of adsorption, respectively. The Freundlich equation is an empirical expression based on adsorption onto a heterogeneous surface. KF and 1/n are the Freundlich constants, indicating adsorption capacity and adsorption intensity, respectively. This isotherm usually fits the experimental data over a wide range of concentrations. The Sips isotherm is a hybrid form of the Langmuir and Freundlich models and explains the physical and chemical characterization of adsorptions. At low adsorbate concentrations, it effectively reduces to a Freundlich isotherm, while at high adsorbate concentrations it predicts a monolayer adsorption capacity characteristic of the Langmuir isotherm. Sips constants Qs, Ks, and ns indicate adsorption capacity, equilibrium constant, and model exponent, respectively. The adsorption constants of Th(IV) ions onto PMAA-g-Cell/Bent were calculated according to these models using nonlinear regression analysis, and the results are listed in Table 3. Based on R2 values (>0.99) and χ2 Table 3. Isotherm Parameters for the Adsorption of Th(IV) onto PMAA-g-Cell/Bent model
(11)
Langmuir:
Freundlich:
qe =
Q 0bCe (1 + bCe)
Langmuir−Freundlich (Sips):
20
30
40
50
Langmuir
Q0 (mg/g) b (L/mg) R2 χ2 KF 1/n R2 χ2 Qs Ks ns R2 χ2
138.7 0.034 0.995 14.47 17.84 0.257 0.976 68.24 161.6 0.054 0.755 0.999 0.458
149.2 0.045 0.990 34.93 22.07 0.289 0.981 64.14 188.1 0.075 0.669 0.999 0.281
152.2 0.077 0.970 12.67 30.61 0.299 0.992 31.08 253.5 0.114 0.478 0.999 0.601
157.4 0.158 0.951 23.24 41.52 0.362 0.994 28.04 302.4 0.148 0.391 0.999 0.873
Sips
values (
