Liang Zhang1 Song Hong2 Jing He2 Fuxing Gan2 Yuh-Shan Ho3,4 1
Institute of Geodesy and Geophysics, Chinese Academy of Sciences, Wuhan, P.R. China
2
School of Resource and Environmental Science, Wuhan University, Wuhan, P.R. China 3Water Research Centre, Asia University, Taichung, Taiwan 4
Department of Public Health, China Medical University, Taichung, Taiwan
Research Article
Isotherm Study of Phosphorus Uptake from
Aqueous Solution Using Aluminum Oxide
Aluminum oxide, which could be an alternative filter media for phosphorus uptake
from aqueous solution, was selected as an adsorbent for the isotherm study of
phos-phorus uptake from aqueous solution. Batch method was adopted to investigate the
adsorption behavior of phosphorus onto aluminum oxide. The Langmuir, Freundlich,
and Redlich–Peterson isotherms were used to analyze the experimental data by both
the linear and nonlinear regression methods. The adsorption experiment was
con-ducted at various temperatures, to choose the appropriate method and obtain the
creditable adsorption parameters for phosphorus uptake studies. The results indicated
that the nonlinear regression method might be a better way to compare the best-fitting
isotherm and obtain the parameters for the adsorption of phosphorus onto aluminum
oxide. Both the Redlich–Peterson and the Freundlich isotherms have high coefficients
of determination for the adsorption of phosphorus onto aluminum oxide at various
temperatures. In addition, a new relationship between the Redlich–Peterson and the
Freundlich isotherm parameters was presented.
Keywords: Adsorption; Aluminum oxide; Isotherm parameters; Nonlinear regression; Phosphorus Received: December 29, 2009; revised: March 5, 2010; accepted: March 21, 2010
DOI: 10.1002/clen.200900305
1 Introduction
Phosphorus is considered to be the significant nutrient causing water pollution. Phosphorus removal mechanism from aqueous solution includes adsorption, desorption, precipitation, leaching, uptake, fragmentation, mineralization, sedimentation, and burial [1, 2]. Adsorption equilibrium studies are always conducted to help researchers investigate the adsorption characteristic and capacity of phosphorus onto filter medium [3, 4]. The previous adsorption equi-librium studies are usually based on linear regression method, but it has also been presented that using this linear regression method for comparing the best-fitting isotherms is not appropriate [5]. The adsorption behaviors by using aluminum oxide (Al2O3) as adsorbents in various solvents have been earlier studied for several decades [6, 7]. In recent years, Bushey and Dzombak [8] used aluminum oxide as an adsorbent for removal of ferrocyanide from aqueous solution and found that ferrocyanide could be adsorbed by aluminum oxides significantly. A batch method was also employed to study the adsorp-tion behavior of Cr(VI) from synthetic soluadsorp-tions on aluminum oxide, and the Langmuir isotherm was found to describe the adsorption process well [9].
In this study, Al2O3, which could be an alternative filter media for phosphorus uptake from aqueous solution, was selected as an adsorbent to investigate its adsorption characteristic of phosphorus.
The Langmuir, Freundlich, and Redlich–Peterson isotherms were used by the linear and nonlinear regression methods. The aims of this study were to compare these two regression methods, choose the appropriate method, and then obtain the creditable adsorption parameters for Al2O3adsorption equilibrium studies.
2 Materials and Methods
A commercial Al2O3powder, available in Nanjing, Jiangsu Province, People’s Republic of China, was applied in this study. It was analyzed for particle size distribution by using laser diffraction particle size analyzer, Malvern ZetaSizer 3000. The X-ray fluorescence spectro-meter, Bruker AXS S4 Pioneer was used for the composition analysis. A synthetic phosphorus solution comprising distilled water and potassium dihydrogen phosphate was used. The concentrations of solutions were calculated as phosphorus subsequently and the phos-phates hereinafter collectively referred to as the ‘‘phosphorus.’’ A stock solution of 500 mg/dm3was prepared by dissolving a weighed amount of phosphorus in 1000 mL of distilled water. The experimen-tal solution was prepared by diluting the stock solution with dis-tilled water when necessary. A phosphorus solution of 50 mL with a concentration ranging from 10 to 150 mg/dm3 was placed into several 150 mL conical flasks. A weighed amount (0.1 g) of the Al2O3was added to the solution. The conical flasks were then shaken at a constant speed of 170 rpm in a shaking water bath at tempera-tures of 283, 293, 298, 303, and 308 K, respectively. After shaking the flasks for 12 h, the Al2O3powders were separated by centrifu-gation. The phosphorus solution was analyzed for the remaining phosphorus concentration with ammonium molybdate spectropho-tometric method by a spectrophotometer. The amount of Correspondence: Dr. Y.-S. Ho, Water Research Centre, Asia University,
No. 500, Lioufeng Road, Wufeng, Taichung 41354, Taiwan. E-mail: [email protected]
phosphorus adsorbed onto Al2O3was calculated by using the follow-ing expression:
qe¼
ðC0 CeÞV
m (1)
where qe was the equilibrium adsorption capacity of phosphorus adsorbed on unit mass of the Al2O3(mg/g); C0was the initial phos-phorus concentration (mg/dm3); Ce was the phosphorus concen-tration at equilibrium (mg/dm3); V was the volume of the phosphorus solution (dm3); and m was the weight of Al
2O3(g). The analysis of the isotherm data is important to develop an equation which accurately represents the results and could be used for design purposes. In order to investigate the adsorption isotherm, three equilibrium isotherms were analyzed: the Langmuir, Freundlich, and Redlich–Peterson, respectively.
The Langmuir adsorption isotherm is perhaps the best known of all isotherms describing adsorption [10]. The theoretical Langmuir isotherm is often used to describe adsorption of a solute from a liquid solution as Eq. (2) [11]:
qe¼
qmKaCe
1þ KaCe
(2)
where qeis the equilibrium adsorption capacity (mg/g); Ce is the equilibrium liquid phase concentration (mg/dm3); qmis the maxi-mum adsorption capacity (mg/g); Kais adsorption equilibrium con-stant (dm3/mg).
The Freundlich isotherm is the earliest known relationship describing the adsorption isotherm [12]. This fairly satisfactory empirical isotherm can be used in adsorption from dilute solutions. The ordinary adsorption isotherm is expressed by the following equation:
qe¼ KFC1=ne (3)
where Ceis the equilibrium concentration in the solution (mg/dm3); qe is the equilibrium adsorption capacity (mg/g); KF and 1/n are empirical constants. KFis the adsorption value, the amount adsorbed at unit concentration, that is, at 1 mg/dm3. It is characteristic for the adsorbent and the adsorbate adsorbed.
The Redlich–Peterson isotherm contains three parameters and incorporates the features of the Langmuir and the Freundlich iso-therms [13]. It can be described as follows:
qe¼
ACe
1þ BCge
(4)
where qeis the equilibrium adsorption capacity (mg/g) and Ceis the equilibrium liquid phase concentration (mg/dm3). It has three iso-therm constants, namely, A, B, and g (0 < g < 1).
The coefficient of determination, r2, between the experimental data and isotherms is used to test the best-fitting isotherm [14]. The coefficient of determination r2is defined as:
r2¼ P qm qe ð Þ2 P q m qe ð Þ2þPðqm qeÞ2 (5)
where qmis the equilibrium capacity obtained from the isotherm (mg/g); qe is the equilibrium capacity obtained from experiment (mg/g); andqeis the average of qe(mg/g).
3 Results and Discussion
3.1 Properties of Al
2O
3Powder
The particle size distribution of Al2O3was as follows: 315–405 nm (66.4%), 405–500 nm (33.6%), respectively. The average size was 395.6 nm. The result of XRF analysis is shown in Tab. 1.
3.2 Comparison of Linear and Nonlinear
Regression Methods
Linear least-squares regression method and trial-and-error nonlinear regression method using the solver add-in with Microsoft’s spread-sheet, Microsoft Excel, both used to obtain the isotherm parameters, were discussed [14]. These two methods were used to compare the best fitting of three isotherms. The Langmuir isotherm could be linearized as four different types, while the Freundlich isotherm had two different types usually (Tab. 2) and simple linear regression would result in different parameter estimates [14–16]. The more popular linear forms used are Langmuir-1 and Freundlich-1. In order to assess different isotherms and their performance to correlate with experimental results, the theoretical plots from each isotherm are shown with the experimental data for adsorption of phosphorus onto Al2O3at various temperatures. The isotherm was plotted in the form of phosphorus adsorbed per unit mass of Al2O3, qeagainst the concentration of phosphorus remaining in solution, Ce. Figure 1 compares the Langmuir isotherms obtained by using the regression method with four linear and the nonlinear isotherms for the adsorp-tion of phosphorus onto Al2O3 at a temperature of 303 K. The experimental data fitted better in case of the Langmuir-1 than other three linear results. Figure 2 shows three widely used isotherms by using the nonlinear regression method with the experimental data for the adsorption of phosphorus onto Al2O3at a temperature of 303 K. Values of the coefficient of determinations, r2, obtained by using both the linear and nonlinear regression methods, are pre-sented in Tab. 3 for the adsorption of phosphorus onto Al2O3at temperatures of 283, 293, 298, 303, and 308 K, respectively. These values of the coefficient of determinations obtained from linear Langmuir-1 were calculated to be 0.995, 0.992, 0.990, 0.993, and 0.992, respectively. The result indicated that there was strong positive evidence that the adsorption of phosphorus onto Al2O3 followed the Langmuir isotherm using the result of Langmuir-1 linear regression method. The Langmuir isotherm parameters obtained from various linear forms were significantly different (Tab. 3). It indicated that transformations of the nonlinear Langmuir isotherm to the linear forms implicitly altered the error structure and might also violate the error variance and normality assumptions of the standard least-squares method [5, 17]. Using different linear forms of the Langmuir equation for the linear analysis would significantly affect the calculations of Langmuir parameters. Two Freundlich linear forms were also analyzed, using the same set of experimental data, by plotting log qeversus log Ce Table 1. Main chemical compositions of Al2O3.
Composition Percent (%) Composition Percent (%)
Al2O3 86.3 MgO 0.389
CO2 7.93 SO3 0.359
CaO 3.19 Na2O 0.114
SiO2 0.727 Fe2O3 0.0935
and ln qe versus ln Ce, respectively. The Freundlich isotherm con-stants, KF, 1/n, and the coefficients of determination, r
2
, are shown in Tab. 4. The parameters obtained by using linear regression method with Freundlich-1 and Freundlich-2 are equal, that was due to the same error structures of the linear forms of the Freundlich isotherm. Figure 3 shows that two Freundlich isotherm curves, obtained by linear regression method with Freundlich-1 and Freundlich-2, are overlapped. If just the linear form of Langmuir-1 was used for comparison, Langmuir-1 should be more suitable for the experimen-tal data than the Freundlich isotherms because of the higher value of its coefficient of determinations (Tab. 3). In contrast, if using the linear form of other Langmuir linear forms, the Freundlich iso-therms were more suitable for the experimental data than the
Langmuir isotherms. This discrepancy was caused by the different error structures between linear forms of Langmuir and Freundlich isotherms. Such transformations of nonlinear isotherms to linear forms implicitly altered their error structures [5, 17]. It seems that using the linear regression method for comparing the best-fitting isotherms was not appropriate for the adsorption study of phos-phorus onto Al2O3.
The related isotherm parameters obtained by using the nonlinear regression method is shown in Tab. 5. In the case of the Langmuir isotherm, the results from the four linear Langmuir isotherms were the same. When using the nonlinear regression method, there was no problem with transformations of nonlinear Langmuir isotherm to linear forms, because they had the same error structures. The Table 2. Isotherms and their linear forms.
Isotherm Linear form
Langmuir qe¼ qmKaCe 1þ KaCe Langmuir-1 Ce qe ¼ 1 qm Ceþ 1 Kaqm Langmuir-2 1 qe ¼ 1 Kaqm 1 Ce þ 1 qm Langmuir-3 qe¼ qm 1 Ka q e Ce Langmuir-4 qe Ce ¼ Kaqm Kaqe
Freundlich qe¼ KFC1=ne Freundlich-1 logðqeÞ ¼ logðKFÞ þ
1 nlogðCeÞ Freundlich-2 lnðqeÞ ¼ lnðKFÞ þ 1 nlnðCeÞ Redlich–Peterson qe¼ ACe 1þ BCge ln ACe qe 1 ¼ g lnðCeÞ þ lnðBÞ
Figure 1. Langmuir isotherms obtained using linear and nonlinear regres-sion methods for the adsorption of phosphorus onto Al2O3at temperature of 303 K.
Figure 2. Isotherms obtained by using the nonlinear regression method for the adsorption of phosphorus onto Al2O3at a temperature of 298 K.
Langmuir parameters obtained from the nonlinear and linear regression methods differed even when compared with the results of Langmuir-1, which had the highest coefficient of determination for any Langmuir isotherm (Tab. 3). Both the Redlich–Peterson and the Freundlich isotherms had almost the same coefficients of deter-mination which were higher than those of Langmuir isotherms (Tab. 5). In addition the Redlich–Peterson and Freundlich isotherms seemed to be the best-fitting models for the experiment results from Fig. 2. Consequently, the Redlich–Peterson and Freundlich isotherms were found to be the suitable isotherm for the adsorption system of phosphorus onto Al2O3. Using different linear isotherm forms would significantly affect the coefficient of determination and impact the final determination of parameters, while the application of the nonlinear regression method would avoid such errors.
As shown in Eq. (4), the Redlich–Peterson isotherm has three isotherm constants, namely, A, B, and g (0 < g < 1), which charac-terize the isotherm. Its limiting behavior is summarized.
Where g¼ 1
qe¼
ACe
1þ BCe
(6)
i.e., the Langmuir form results. A¼ qmKaand B¼ Ka. where constants A and B are much greater than unity [5].
qe¼ A Ce B Cge ¼A BC 1g e (7)
i.e., the Freundlich form results. A/B¼ KFand 1 g ¼ 1/n. where g¼ 0
qe¼
ACe
1þ B (8)
i.e., the Henry’s Law form results. A/(1þ B) ¼ KH, KH is Henry’s constant.
Figure 2 shows the plots of experimental data also fitted well with the Freundlich adsorption isotherm of phosphorus onto Al2O3at the temperature of 298 K. Furthermore, compare Eq. (3) with Eq. (7), the values of parameter ‘‘KF’’ correlated well with ‘‘A/B’’ in a linear relationship as A/B¼ 0.988KFþ 0.155 with 1.000 coefficient of deter-mination, ‘‘1/n’’ correlated well with ‘‘1 g’’ (r2
¼ 0.988) in a linear relationship as (1 g) ¼ 0.951 (1/n) þ 0.00836. At the temperature of 298 K (Fig. 2), the Redlich–Peterson and Freundlich isotherms overlapped with coefficients of determination, r2¼ 0.992, which were higher than the case of Langmuir (r2
¼ 0.845). It indicated that the Redlich–Peterson isotherm was approaching the Freundlich form but not the Langmuir isotherm. Freundlich is a special case of Redlich–Peterson isotherm when constants A and B were much Table 3. Coefficients of determination obtained by using the linear and nonlinear regression methods.
Method T (K) 283 293 298 303 308 Linear Langmuir-1 0.995 0.992 0.990 0.993 0.992 Langmuir-2 0.852 0.861 0.837 0.799 0.763 Langmuir-3 0.667 0.731 0.677 0.600 0.620 Langmuir-4 0.667 0.731 0.677 0.600 0.620 Freundlich-1 0.990 0.996 0.991 0.990 0.988 Freundlich-2 0.990 0.996 0.991 0.990 0.988 Redlich–Peterson 0.999 1.000 1.000 1.000 1.000 Nonlinear Langmuir 0.890 0.888 0.845 0.845 0.817 Freundlich 0.985 0.996 0.992 0.988 0.990 Redlich–Peterson 0.986 0.996 0.992 0.988 0.990
Table 4. Freundlich isotherm parameters obtained by using the linear regression method.
Linear form T (K) 283 293 298 303 308 Freundlich-1 1/n 0.212 0.214 0.188 0.179 0.152 KF 6.92 8.58 10.6 11.0 15.4 r2 0.990 0.996 0.991 0.990 0.988 Freundlich-2 1/n 0.212 0.214 0.188 0.179 0.152 KF 6.92 8.58 10.6 11.0 15.4 r2 0.990 0.996 0.991 0.990 0.988
Figure 3. Freundlich isotherms obtained using linear and nonlinear regres-sion methods for the adsorption of phosphorus onto Al2O3at temperature of 308 K.
bigger than unity [5]. Moreover, the values of g were less than 0.839 and not close to unity. Unlike the linear analysis, different isotherm forms would affect r2significantly, and impact the final determi-nation of parameters while nonlinear regression methods would prevent such errors.
3.3 Effect of Temperature on Equilibrium Isotherm
The effect of temperature on the adsorption isotherm is shown in Fig. 4. The results showed that the capacity of the Al2O3for phos-phorus adsorption increased with the increase in temperature. It indicated that higher temperatures were suitable for phosphorus uptake from aqueous solution using Al2O3.
4 Conclusion
It is not appropriate to use the coefficient of determination of the linear regression method for comparing the best-fitting isotherms for the adsorption of phosphorus onto Al2O3. The nonlinear regression method is a better way to obtain the isotherm parameters for this system. Both the Redlich–Peterson and the Freundlich have
high coefficients of determination for the adsorption of phosphorus onto Al2O3at various temperatures. A linear relationship was found for Freundlich isotherm parameter ‘‘KF’’ and Redlich–Peterson iso-therm parameters ‘‘A/B’’ as well as ‘‘1/n’’ and ‘‘1 g’’ when these two isotherms were overlapped. The capacity of the Al2O3for phosphorus adsorption increased with the increase in temperature, higher tem-peratures were suitable for phosphorus uptake from aqueous solution using Al2O3.
Acknowledgments
Liang Zhang would like to thank the Knowledge Innovation Program of the Chinese Academy of Sciences (Grant Nos. kzcx2-yw-141 and 0909181018).
The authors have declared no conflict of interest.
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