Determination of Mercury (II) Ion on Aryl Amide-Type Podand-Modified Glassy Carbon Electrode

Güney, Sevgi; Yıldız, Gülcemal; Yapar, Gönül

doi:https://doi.org/10.4061/2011/529415

International Journal of Electrochemistry

On this page

Abstract Introduction Experimental Results and Discussion Conclusion Acknowledgments References Copyright Related Articles

Special Issue

Electrochemical Sensors and Biosensors

View this Special Issue

Research Article | Open Access

Volume 2011 | Article ID 529415 | https://doi.org/10.4061/2011/529415

Determination of Mercury (II) Ion on Aryl Amide-Type Podand-Modified Glassy Carbon Electrode

Sevgi Güney,¹Gülcemal Yıldız,¹and Gönül Yapar¹

Academic Editor: Farnoush Faridbod

Received30 Dec 2010

Revised07 Mar 2011

Accepted28 Mar 2011

Published29 May 2011

Abstract

A new voltammetric sensor based on an aryl amide type podand, 1,8-bis(o-amidophenoxy)-3,6-dioxaoctane, (AAP) modified glassy carbon electrode, was described for the determination of trace level of mercury (II) ion by cyclic voltammetry (CV) and differential pulse voltammetry (DPV). A well-defined anodic peak corresponding to the oxidation of mercury on proposed electrode was obtained at 0.2 V versus Ag/AgCl reference electrode. The effect of experimental parameters on differential voltammetric peak currents was investigated in acetate buffer solution of pH 7.0 containing 1 × 10⁻¹ mol L⁻¹ NaCl. Mercury (II) ion was preconcentrated at the modified electrode by forming complex with AAP under proper conditions and then reduced on the surface of the electrode. Interferences of Cu²⁺, Pb²⁺, Fe³⁺, Cd²⁺, and Zn²⁺ ions were also studied at two different concentration ratios with respect to mercury (II) ions. The modified electrode was applied to the determination of mercury (II) ions in seawater sample.

1. Introduction

Podands, which are the member of the crown-ether family, have an importance in supramolecular chemistry because of their applications in ion sensing and also have high productivity and selectivity in forming complexes with alkali, alkaline earth metal, and transition metal ions [1–3]. Podands could allow conformational changing in structure for the binding of a guest molecule because they have more flexibility than their crown-ether analogues [4]. Since podand-type ligands have ability to form of spheroidal cavities and strong binding sites, they have attracted considerable interest in recent years. Amide-type podands have an importance for producing the complexes possessing high fluorescent properties [5].

Determination of mercury is an important issue because of high toxicity, reactivity, and excessive mobility of mercury in environment. In addition, mercury has crucial risk to human health [6]. Therefore, there is a necessity of improving fast, sensitive, and selective analytical techniques for analysis of mercury. Current instrumental analysis methods, such as UV spectrophotometry [7], X-ray fluorescence [8], atomic fluorescence spectrometry (AFS) [9], cold vapor atomic fluorescence spectrometry [10], atomic absorption spectrometry (AAS) [11], cold vapor atomic absorption spectrometry [12], and inductively coupled plasma mass spectrometry [13], have been extensively employed for trace determination of mercury (II) ion in the laboratory conditions. Since they are expensive, time-consuming and complicated for in situ measuring, they are not suitable for point-of-use applications. Alternatively, electrochemical techniques could be used for the mercury determination, because these techniques are easier and cheaper than the instrumental analysis methods mentioned above.

Chemically modified electrodes (CMEs) have attracted great attention in the past decades since they improve the sensitivity and selectivity of electrochemical analysis methods [14]. Description and fabrication of CMEs have been mentioned in an IUPAC report [15]. CMEs have various advantages, such as low cost, short analysis time, high sensitivity and selectivity in electroanalytical determinations of different compounds [16]. They are also used in different applications, for example, corrosion protection, selective electroorganic synthesis, solar energy conversion and storage, molecular electronics, and electrochromic display devices [17]. Modification of the electrode surfaces with appropriate modifiers enhances the selectivity and sensitivity of electroanalytical methods. There are several ways to modify the working electrode surface, for example, electrochemical, chemical, or physical methods. Stripping electrochemical technique is an alternative method for mercury determination due to its versatility, sensitivity, and low cost [17]. A number of articles have been published for the analysis of mercury (II) ion by CMEs [18–23]. The limit of detection (LOD) was argued in the literature for the determination of mercury (II) ion by CMEs which were approximately in the range of 10⁻⁹ M as same as our current work. Furthermore, there has been no study in the literature for the determination of mercury (II) ion with AAP-modified electrode yet.

In the present study, the aryl amide type podand, AAP, was synthesized according to our previous work [24]. AAP modified glassy carbon electrode (AAP/GCE) was prepared, and differential pulse anodic stripping voltammetry was used for analytical response of mercury (II) ions. The effect of analytical parameters such as pH, deposition potential, deposition time, and the amount of AAP as modifying agent were investigated. Interference effects of other metallic ions that might also form complexes with Cl⁻ ion and the repeatability of the method were investigated, and also, detection mechanism was proposed. The accuracy of method was tested in the artificial seawater samples. AAP is a hopeful modifying agent in sensor application for determination of mercury (II) ion in mixture of aqueous solution compared with the other crown-ether molecules since it can be easily synthesized and also modified on electrode surface.

2. Experimental

2.1. Synthesis of AAP

Into a flask (50 mL) salicylamide (2.74 g, 20 mmoL), Na₂CO₃ (2.36 g, 22 mmoL), DMF (20 mL), and 1,8-dichloro-3,6-dioxaoctane (1.87 g, 10 mmoL) were added and heated at 80–85°C for 72 h. Then, the mixture of reaction was poured into water (200 mL). The filtered residue was washed with water and dried at 75°C. The crude product was dissolved in CH₂Cl₂ and chromatographed on silica gel (50 g) with CH₂Cl₂/acetone: 3/2 (v/v). 3.31 g, 85% yield, colorless leafs. Structure of synthesized AAP is shown in Scheme 1.

2.2. Reagents and Materials

All chemicals used in these experiments were of the highest purity (used without further purification) and were obtained from Merck, Fluka, and Riedel de Haen Chemical Companies. Salicylamide (Alfa Aesar), 1,8-dichloro-3,6-dioxaoctane and DMF (Fluka), silica gel 40–63 u 60 A (Fluorochem), Hg (CH₃COO)₂ (Merck). All solutions were prepared by using ultrapure water from Millipore MilliQ System (sensitivity equal to 18 MΩ). A stock solution of 1 × 10⁻² M AAP was prepared in ethyl alcohol. Buffer solutions were prepared by adjustment of pH with HCl or KOH. All electrochemical experiments were carried out in a conventional three-electrode system under the room temperature (25 ± 1°C).

2.3. Instrumentation

All electrochemical measurements were carried out on Autolab PGSTAT 30 (Eco Chemie) potentiostat/galvanostat. A classical three-electrode cell consists of Ag/AgCl (3 M KCl) reference electrode, a platinum wire counter electrode (BAS MW 1032), and a glassy carbon working electrode (the diameter of working electrode is 3 mm, BAS MF-2012). Instrumental parameters were as follows: pulse amplitude 50 mV, pulse width 50 ms, potential step 4 mV pulse period 0.2 s, and scan rate 50 mV s⁻¹. Solutions were deoxygenated for 10 minutes with high-grade nitrogen, and an inert atmosphere was obtained over the solutions during analysis. The solutions were adjusted using a pH meter (WTW Inolab pH 720). An ultrasonic bath was used for preparing the homogeneous solutions (Bandelin Sonorex RK 100H). Spin coating of the glassy carbon electrode was performed by using IKEA RW 20 rotator.

2.4. Preparation of the AAP Modified Glassy Carbon Electrode (AAP/GCE)

Before the modification, surface of the glassy carbon electrode (GCE) was polished to gain a mirror-like appearance with 1.0, 0.3, and 0.05 μm of aluminum oxide slurry, respectively. After the polishing, GCE was sonicated twice in ethyl alcohol and ultrapure water for 5 min each. After that, electrochemical pretreatment was performed by the potential step which was applied at +0.8 V for 5 minutes and −1.4 V for 1 minute in 1 × 10⁻¹ moL L⁻¹ H₂SO₄ solution, respectively. Then, modification of the surface of the electrode with AAP was performed by spin coating employing a rotator with a speed of 300 rpm. Two drops of 10 μL of 5.0 × 10⁻³ moL L⁻¹ AAP dissolved in ethyl alcohol were dropped on the spinning electrode and then dried in room temperature.

2.5. Analytical Procedure

The procedure of preconcentration and voltammetric determination of mercury (II) ion on AAP modified electrode includes the following steps: (1) modifying the GC electrode with AAP, (2) dipping of the modified electrode in aqueous solution of mercury (II) at open circuit, (3) electrochemical reduction of mercury (II) ions to metallic mercury at −0.8 V for 12 min by stirring in an acetate buffer solution of pH 7.0 containing 0.1 moL L⁻¹ NaCl, and (4) voltammetric determination of mercury (II) ions by DPV from −0.1 V to 0.4 V in the same solution. The modified electrode was reused by holding the potential +0.8 V for 3 min. to remove any previous deposits for repeated determinations. AAP-modified glassy carbon electrode was tested in a new buffer solution without mercury (II) ions, before each experiment.

3. Results and Discussion

3.1. Voltammetric Behavior of Mercury (II) on AAP-Modified GCE

The capability of AAP/GCE for preconcentration and determination of mercury (II) was investigated. Figure 1 shows the CVs at AAP-modified GCE in the absence and presence of mercury (II) after preconcentration.

As can be seen in Figure 1, a well-defined anodic peak () was obtained at 0.2 V (solid line) due to the electrochemical oxidation of mercury (0) to mercury (II), and mercury (0) was produced by the electrochemical reduction of captured mercury (II) at the deposition step under negative potentials. Furthermore, no mercury peak was observed in the absence of mercury (II) as a control experiment (dashed line).

These experimental results showed that mercury (II) ions from the solution can form strong HgCl₄²⁻ complex with Cl⁻ ions. Then HgCl₄²⁻ complex is deposited on the modified electrode surface and reduced to Hg⁰ following Hg⁰ being oxidized to Hg²⁺ ion. Therefore, the possible electrochemical reaction mechanism can be illustrated as follows.

Deposition:

Reduction:

Oxidation:

3.2. Optimization of Measurement Condition

In order to obtain optimum experimental conditions for mercury (II) determination, several parameters were investigated such as type and pH of the buffer solution, AAP concentration on electrode surface, deposition potential, and deposition time.

The effect of supporting electrolytes was investigated in acetate, phosphate, and B-R buffer solutions, respectively. The results indicated that voltammetric peaks were observed in all electrolyte solutions, but the electrochemical response of mercury (II) ion in 0.1 moL L⁻¹ HAc + 0.1 moL L⁻¹ NaCl solution gave the best shaped and largest peak current among these solutions. Therefore, this supporting electrolyte was used in following experiments. The effect of pH on the anodic stripping peak currents of mercury (II) ion on the modified electrode was studied by differential pulse voltammetry, and the graph of the peak currents against pH was plotted (data was not shown). AAP modified glassy carbon electrode showed the stable activity over the range of pH 3.0–12.0, and the best peak height and shape were obtained at pH 7.0. This pH-dependent behavior of mercury (II) ion can be explained by the fact that different protonation ability of AAP affects the formation constant of the complex between mercury (II) ions and AAP at different pH.

Deposition potential () is an important parameter that affects the sensitivity of detection. AAP-modified GCE was kept at the potentials varying between −0.5 V and −1.0 V for 10 min. in a solution of 5 × 10⁻⁷ moL L⁻¹ mercury (II), and DPV was performed. The change in DPV peak currents depending on the deposition potentials is shown in Figure 2. As can be seen in Figure 2, the peak current increases with the deposition potentials reaching a plateau at about −0.8 V, therefore, this potential was selected as optimal deposition potential.

The effect of deposition time () for mercury (II) determination is shown in Figure 3. The peak current increased with increasing deposition time. The longer the deposition time, the higher the sensitivity obtained in stripping voltammetry, but with narrow detection range results. In this detection system, deposition saturation was reached for 5 × 10⁻⁷ moL L⁻¹ Hg²⁺ by the preconcentration of 30 minutes as shown in Figure 3. Considering the detection limit and linear range, deposition time of 12 minutes was chosen in this study.

The concentration of AAP on the electrode surface affects the deposition capacity of mercury (II) ion and changes the oxidation current (Figure 4). As can be seen in Figure 4, the initial peak current increased up to 0.125 μmoL of AAP since the reactive areas involved in the complexation reaction between mercury and AAP increase with AAP concentration. At the higher concentration of 0.125 μmoL of AAP, the electron transfer between the mercury and electrode was blocked resulting in decrease of current. Therefore, the concentration of 0.125 μmoL was selected as the optimum AAP concentration.

3.3. Interference of Foreign Metal Ions

Under optimized experimental conditions mentioned above, the possible interferences of other metal ions like Cd²⁺, Pb²⁺, Fe³⁺, and Cu²⁺ for the determination of 1 μmoL L⁻¹ μHg²⁺ were examined with AAP-modified electrode (Figure 5). The effect of the inference was tested in two compositions of the solution containing 1 and 10 μmoL L⁻¹ of metal ions. The same experiment was also carried out with unmodified glassy carbon electrode (Figure 5, inset).

As can be seen in Figure 5, the peak current belonging to Cd²⁺ decreased but the peak current of mercury (II) was twofold increased and shifted to more negative potential on modified electrode. On the other hand, Fe³⁺ and Cu²⁺ exhibit very small peak currents comparing to that of mercury (II). Pb²⁺ ion does not affect the mercury (II) peak current since the peak potential of Pb²⁺ is more negative than that of the mercury (II). The interference effects of some metal ions are given in Table 1.

3.4. Calibration Plot, Limit of Detection, and Validation of Method

Under the optimum conditions described above, the reproducibility of the proposed method was evaluated with the solution of 1 × 10⁻⁷ mol L⁻¹mercury (II) for six repetitive measurements. The relative standard deviation (RSD) was 1.84% which presented the good reproducibility of the proposed modified electrode. Linearity of the calibration curve was also investigated in the mercury (II) concentration ranges from 1 × 10⁻⁹ mol L⁻¹ to 1 × 10⁻⁵ mol L⁻¹ (Figure 6, inset).

The calibration plot (Figure 6 ) shows a good linear behavior with correlation coefficient () of 0.9997, and the resulting equation is log I(A) = 2−0.5954 + 0.6556 log (mol L⁻¹). The limit of detection is 4 × 10⁻⁹ mol L⁻¹ (S/). These values verified the sensitivity of the proposed method for the determination of mercury (II). AAP/GCE can be stored about 4 weeks, and the decrease in response was 2.54%, indicating the good stability of electrode. When the proposed electrode was compared with the other macrocyclic kinds of modified electrodes for mercury (II) determination, it can be seen that the detection limits of them were in the range of 1.0 × 10⁻⁸ and 1.0 × 10⁻⁷ mol L⁻¹ [22, 25–28]. Consequently, AAP modified electrode could be a promising voltammetric sensor for trace analysis of mercury (II) ion.

3.5. Analytical Applications

The accuracy of the proposed method was tested in artificial seawater sample by spiking known concentrations of mercury (II) ion. Artificial seawater was prepared according to the literature [29]. Determination of mercury (II) concentration was performed by the calibration curve method. The experimental parameters were the same as described above, and the results are summarized in Table 2.

4. Conclusion

A new kind of chemically modified electrode has been developed for highly selective and sensitive determination of mercury (II) by forming complex with AAP. It was shown that AAP-coated glassy carbon electrode could be used for determination of mercury (II) ion from aqueous solutions since the sensitivity is greatly improved. The immersion of electrode into the solution containing Cl⁻ion increased the deposition of mercury (II) ion on the electrode surface due to formation of HgCl₄²⁻ complex. The results also show that AAP-modified electrode has a good reproducibility, wide linear range, high selectivity, and low detection limit. It can be a very good alternative to expensive analytical techniques such as atomic absorption spectrometry and ICP-MS. The preparation and application of proposed modified electrode are simpler and also cheaper than those of the other electrodes modified with more complex and more expensive modifying agents.

Acknowledgments

The authors would like to thank Istanbul Technical University Research Foundation (ITU-BAP Project no. 32646) and Scientific and Technical Research Council of Turkey (TUBITAK Project no. 104T079) for their financial support.

References

G. W. Gokel, “Comprehensive supramolecular chemistry,” in Molecular Recognition: Receptors for Cationic Guest, J. L. Atwood, Ed., vol. 1, chapter 1, Pergamon, New York, NY, USA, 1996.
View at: Google Scholar
G. Yidiz, G. Yapar, and C. Erk, “The association constants of Na with dibenzo[3n]crown-n in THF/water using ISE,” Talanta, vol. 64, no. 4, pp. 865–868, 2004.
View at: Publisher Site | Google Scholar
H. J. Kim, D. S. Park, M. H. Hyun, and Y. B. Shim, “Determination of Hg ion with a 1,11-bis(8-quinoyloxy)-3,6,9-trioxaundecane-modified glassy carbon electrode using spin-coating technique,” Electroanalysis, vol. 10, no. 5, pp. 303–306, 1998.
View at: Google Scholar
J. W. Steed and J. L. Atwood, Supramolecular Chemistry, Wiley, New York, NY, USA, 2000.
Y. Zhao, Y. Tang, W. S. Liu, N. Tang, and M. Y. Tan, “Synthesis and infrared and fluorescent properties of rare earth complexes with a new aryl amide podand,” Spectrochimica Acta—Part A, vol. 65, no. 2, pp. 372–377, 2006.
View at: Publisher Site | Google Scholar
W. F. Fitzgerald, C. H. Lamborg, and C. R. Hammerschmidt, “Marine biogeochemical cycling of mercury,” Chemical Reviews, vol. 107, no. 2, pp. 641–662, 2007.
View at: Publisher Site | Google Scholar
M. S. Jeoung and H. S. Choi, “Spectrophotometric determination of trace Hg(II) in cetyltrimethylammonium bromide media,” Bulletin of the Korean Chemical Society, vol. 25, no. 12, pp. 1877–1880, 2004.
View at: Google Scholar
E. K. Pavlos and G. K. K. Nikolaos, “Selective mercury determination after membrane complexation and total reflection X-ray fluorescence analysis,” Analytical Chemistry, vol. 76, no. 15, pp. 4315–4319, 2004.
View at: Publisher Site | Google Scholar
L. Rahman, W. T. Corns, D. W. Bryce, and P. B. Stockwell, “Determination of mercury, selenium, bismuth, arsenic and antimony in human hair by microwave digestion atomic fluorescence spectrometry,” Talanta, vol. 52, no. 5, pp. 833–843, 2000.
View at: Publisher Site | Google Scholar
M. Roulet, M. Lucotte, J. R. D. Guimarães, and I. Rheault, “Methylmercury in water, seston, and epiphyton of an Amazonian river and its floodplain, Tapajós River, Brazil,” Science of the Total Environment, vol. 261, pp. 43–59, 2000.
View at: Google Scholar
J. L. Capelo, I. Lavilla, and C. Bendicho, “Room temperature sonolysis-based advanced oxidation process for degradation of organomercurials: application to determination of inorganic and total mercury in waters by flow injection-cold vapor atomic absorption spectrometry,” Analytical Chemistry, vol. 72, no. 20, pp. 4979–4984, 2000.
View at: Publisher Site | Google Scholar
S. C. Hight and J. Cheng, “Determination of total mercury in seafood by cold vapor-atomic absorption spectroscopy (CVAAS) after microwave decomposition,” Food Chemistry, vol. 91, no. 3, pp. 557–570, 2005.
View at: Publisher Site | Google Scholar
J. C. A. Wuillouda, R. G. Wuillouda et al., “Gas chromatography/plasma spectrometry- an important analytical tool for elemental speciation studies,” Spectrochimica Acta—Part B, vol. 59, no. 6, pp. 755–792, 2004.
View at: Google Scholar
P. R. Moses and R. W. Murray, “Chemically modified electrodes. 3. SnO and TiO electrodes bearing an electroactive reagent [11],” Journal of the American Chemical Society, vol. 98, no. 23, pp. 7435–7436, 1976.
View at: Google Scholar
R. A. Durst, A. J. Bäumner, R. W. Murray, R. P. Buck, and C. P. Andrieux, “Chemically modified electrodes: recommended terminology and definitions,” Pure and Applied Chemistry, vol. 69, no. 6, pp. 1317–1323, 1997.
View at: Google Scholar
C. Hu, K. Wu, X. Dai, and S. Hu, “Simultaneous determination of lead(II) and cadmium(II) at a diacetyldioxime modified carbon paste electrode by differential pulse stripping voltammetry,” Talanta, vol. 60, no. 1, pp. 17–24, 2003.
View at: Publisher Site | Google Scholar
A. Giacomino, O. Abollino, M. Malandrino, and E. Mentasti, “Parameters affecting the determination of mercury by anodic stripping voltammetry using a gold electrode,” Talanta, vol. 75, no. 1, pp. 266–273, 2008.
View at: Publisher Site | Google Scholar
N. L. Dias Filho and D. R. do Carmo, “Stripping voltammetry of mercury(II) with a chemically modified carbon paste electrode containing silica gel functionalized with 2,5-dimercapto-1,3,4- thiadiazole,” Electroanalysis, vol. 17, no. 17, pp. 1540–1546, 2005.
View at: Publisher Site | Google Scholar
H. Zejli, P. Sharrock, J. L. H. H. De Cisneros, I. Naranjo-Rodriguez, and K. R. Temsamani, “Voltammetric determination of trace mercury at a sonogel-carbon electrode modified with poly-3-methylthiophene,” Talanta, vol. 68, no. 1, pp. 79–85, 2005.
View at: Publisher Site | Google Scholar
M. Colilla, M. A. Mendiola, J. R. Procopio, and M. T. Sevilla, “Application of a carbon paste electrode modified with a schiff base ligand to mercury speciation in water,” Electroanalysis, vol. 17, no. 11, pp. 933–940, 2005.
View at: Publisher Site | Google Scholar
A. Widmann and C. M. G. van den Berg, “Mercury detection in seawater using a mercaptoacetic acid modified gold microwire electrode,” Electroanalysis, vol. 17, no. 10, pp. 825–831, 2005.
View at: Publisher Site | Google Scholar
H. M. Dong, L. Lin, H. Zheng, G. Zhao, and B. Ye, “Electrode modified with Langmuir-Blodgett (LB) film of calixarenes for preconcentration and stripping analysis of Hg(II),” Electroanalysis, vol. 18, no. 12, pp. 1202–1207, 2006.
View at: Publisher Site | Google Scholar
N. L. D. Filho, D. R. D. Carmo, and A. H. Rosa, “An electroanalytical application of 2-aminothiazole-modified silica gel after adsorption and separation of Hg(II) from heavy metals in aqueous solution,” Electrochimica Acta, vol. 52, no. 3, pp. 965–972, 2006.
View at: Publisher Site | Google Scholar
S. Güney, G. Yapar, O. Güney, and G. Yildiz, “Elucidation of mercury ion binding property of a new aryl amide type podand by electrochemical and fluorescence measurements,” Analytical Letters, vol. 42, no. 17, pp. 2879–2892, 2009.
View at: Publisher Site | Google Scholar
J. Q. Lu, X. W. He, X. S. Zeng, Q. J. Wan, and Z. Z. Zhang, “Voltammetric determination of mercury (II) in aqueous media using glassy carbon electrodes modified with novel calix[4]arene,” Talanta, vol. 59, no. 3, pp. 553–560, 2003.
View at: Publisher Site | Google Scholar
A. A. Ensafi and M. Fouladgar, “A sensitive and selective bulk optode for determination of Hg(II) based on hexathiacyclooctadecane and chromoionophore V,” Sensors and Actuators, B, vol. 136, no. 2, pp. 326–331, 2009.
View at: Publisher Site | Google Scholar
G. Roa-Morales, M. T. Ramírez-Silva, R. L. González, L. Galicia, and M. Romero-Romo, “Electrochemical characterization and determination of mercury using carbon paste electrodes modified with cyclodextrins,” Electroanalysis, vol. 17, no. 8, pp. 694–700, 2005.
View at: Publisher Site | Google Scholar
C. Dridi, M. B. Ali, F. Vocanson et al., “Electrical and optical study on modified Thiacalix(4)arene sensing molecules: application to Hg ion detection,” Materials Science and Engineering C, vol. 28, no. 5-6, pp. 765–770, 2008.
View at: Publisher Site | Google Scholar
D. R. Kester, I. W. Duedall, D. N. Connors, and R. M. Pytkowicz, “Preparation of artificial seawater,” Limnology & Oceanography, vol. 12, pp. 176–179, 1967.
View at: Google Scholar

Copyright

Copyright © 2011 Sevgi Güney et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

PDF Download Citation

Download other formats

Order printed copies

Views

1585

Downloads

1308

Citations