Solid-phase extraction of iron(III) with an ion-imprinted functionalized silica gel sorbent prepared by a surface imprinting technique

Solid-phase extraction of iron(III) with an ion-imprinted functionalized silica gel sorbent prepared by a surface imprinting technique

Talanta 71 (2007) 38–43 Solid-phase extraction of iron(III) with an ion-imprinted functionalized silica gel sorbent prepared by a surface imprinting ...

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Talanta 71 (2007) 38–43

Solid-phase extraction of iron(III) with an ion-imprinted functionalized silica gel sorbent prepared by a surface imprinting technique Xijun Chang a,∗ , Na Jiang a , Hong Zheng a,b , Qun He a , Zheng Hu a , Yunhui Zhai a , Yuemei Cui a a

School of Chemistry and Chemical Engineering, Lanzhou University, Lanzhou 730000, PR China b Qinghai Normal University, Xining 810008, PR China Received 19 October 2005; received in revised form 25 February 2006; accepted 3 March 2006 Available online 18 April 2006

Abstract A new Fe(III)-imprinted amino-functionalized silica gel sorbent was prepared by a surface imprinting technique for selective solid-phase extraction (SPE) of Fe(III) prior to its determination by inductively coupled plasma atomic emission spectrometry (ICP-AES). Compared with non-imprinted polymer particles, the ion-imprinted polymers (IIPs) had higher selectivity and adsorption capacity for Fe(III). The maximum static adsorption capacity of the ion-imprinted and non-imprinted sorbent for Fe(III) was 25.21 and 5.10 mg g−1 , respectively. The largest selectivity coefficient of the Fe(III)-imprinted sorbent for Fe(III) in the presence of Cr(III) was over 450. The relatively selective factor (αr ) values of Fe(III)/Cr(III) were 49.9 and 42.4, which were greater than 1. The distribution ratio (D) values of Fe(III)-imprinted polymers for Fe(III) were greatly larger than that for Cr(III). The detection limit (3σ) was 0.34 ␮g L−1 . The relative standard deviation of the method was 1.50% for eight replicate determinations. The method was validated by analyzing two certified reference materials (GBW 08301 and GBW 08303), the results obtained is in good agreement with standard values. The developed method was also successfully applied to the determination of trace iron in plants and water samples with satisfactory results. © 2006 Elsevier B.V. All rights reserved. Keywords: Fe(III)-imprinted amino-functionalized silica gel sorbent; Preparation; Surface imprinting technique; Solid-phase extraction (SPE); ICP-AES

1. Introduction The traditional preconcentration and separation methods for metal ions are liquid–liquid extraction, coprecipitation, and ionexchange, etc. These methods often require large amounts of high purity organic solvents, some of which are harmful to health and cause environmental problems [1]. Nowadays, the solid-phase extraction (SPE) is being widely utilized for preconcentration or separation of metals due to the following advantages. These include [2–5]: (1) higher enrichment factors; (2) absence of emulsion; (3) safety with respect to hazardous samples; (4) minimal costs due to low consumption of reagents; (5) flexibility; (6) easy of automation. An efficient adsorbing material should possess a stable and insoluble porous matrix having suitable active groups (typically organic groups) that interact with metal ions. Silica gel is an ideal support for organic groups



Corresponding author. Tel.: +86 931 8912582; fax: +86 931 8912582. E-mail address: [email protected] (X. Chang).

0039-9140/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.talanta.2006.03.012

because it is a stable under acidic conditions and non-swelling inorganic material, and has high mass exchange characteristics and very high thermal resistance [6]. Immobilization and crosslinking of organic compounds with certain functional groups on the surface of silica gel has gained important application in different research and industrial fields [7–11]. The effectiveness of such materials in binding metal ions has been attributed to the complexation chemistry between the ligand and the metal. However, the basic disadvantage of these solid sorbents is the lack of metal selectivity, which leads to other species interfering with the target metal ion(s) [12]. But molecular imprinting technique can exactly change this problem. Molecular imprinting is a technique for preparing polymeric materials that are capable of high molecular recognition. In molecular imprinting, a molecular “memory” is imprinted on the polymer. Molecular imprinting polymers (MIPs) are capable of recognizing and binding the desired molecular target with a high affinity and selectivity [13]. Because of the highly crosslinked polymeric nature of MIP materials, they are intrinsically stable and robust. Moreover, MIP materials are low cost

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to produce and can be stored in a dry state at room temperature for long periods of time [14]. Ion-imprinted polymers (IIPs) are similar to MIPs, but they can recognize metal ions after imprinting and retain all the virtues of MIPs [15–18]. IIPs have outstanding advantages such as predetermined selectivity in addition to being simple and convenient to prepare. A particularly promising application of IIPs is the solid-phase extractive preconcentration of analytes present in low concentration or the separation from other coexisting ions or complex matrix. Thus, ion-imprinted polymers for solid-phase extraction is a fast developing area for the application of ion imprinting technology [19]. One of the first ionic template effects in the synthesis of chelating polymers was reported by Nishide and Tsuchida [20] in the mid-1970s. Recently, Takagi and co-workers [21] introduced a novel imprinting technique called surface template polymerization. Surface molecular imprinting is one of the important types of molecular imprinting. Surface molecularly imprinted polymer not only possesses high selectivity but also avoids problems with mass transfer [22]. For metal ions, molecular imprinting can be interpreted as ionic imprinting exactly. So far there are a lot of metal ions imprinted polymers have been prepared, including Pb(II) [23], Ni(II) [24,25], Pd(II) [26], Dy(III) [27], UO2 (II) [28], Cd(II) [1,29], Th(IV) [30], Ca(II) [31] and Mg(II) [32] imprinted polymers. However, few people developed procedure to research Fe(III). In this study, a new Fe(III)-imprinted aminofunctionalized silica gel sorbent was synthesized by combining a surface molecular imprinting technique for selective extraction or preconcentration of Fe(III). A new method using Fe(III)-imprinted sorbent for preconcentrating trace iron in real solution samples prior to its determination by ICP-AES was established. The proposed method presented high selectivity and adsorption capacity for Fe(III), and possessed simple, convenient and accurate characteristics. 2. Experimental 2.1. Instruments and apparatus An IRIS advantage ER/S inductively coupled plasma spectrometer (TJA, USA) was used for the determinations of all metal ions. The operation conditions and the wavelengths were summarized in Table 1. A pHS-10C digital pH meter (Xiaoshan Instrument Factory, China) was used for the pH adjustments. Infrared spectra were recorded on a Nicolet NEXUS 670 FT-IR apparatus (USA). An YL-110 peristaltic pump (General Research Institute for Nonferrous Metals, Beijing, China) was used in the preconcentration process. A self-made glass microcolumn (45 mm × 2.5 mm i.d.) was used in this study. 2.2. Chemicals and reagents Reagents of analytical and spectral purity were used for all experiments and doubly distilled deionized water was used throughout. Standard stock solutions of Fe(III) and Cr(III) (1 mg mL−1 ) were prepared by dissolving spectral pure-grade

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Table 1 Instrumental and operating conditions for ICP-AES measurements Parameter

Type or amount

R.F. Power (kW) Carrier gas (Ar) flow rate (L min−1 ) Auxiliary gas (Ar) flow rate (L min−1 ) Coolant gas (Ar) flow rate (L min−1 ) Nebulizer flow (psi) Pump rate (rpm) Observation height (mm) Integration time (s) On-axis Off-axis Wavelength (nm) Fe Cr

1.15 0.6 1.0 14 30 100 15 20 5 259.940 267.716

FeCl3 ·6H2 O (Tianjin Yaohua Chemical Factory, Tianjin, China) and CrCl3 ·6H2 O (Shanghai First Reagent Factory, Shanghai, China). Silica gel (60–100 mesh, Mouping Kangbinuo Chemical Factory, Yantai, China) and 3-aminopropyltrimethoxysilane (APS, Qingdao Ocean University Chemical Company, Qingdao, China) were used to prepare the ion-imprinted and nonimprinted functionalized silica gel sorbent. 2.3. Sample preparation The reference materials (GBW 08301, river sediment and GBW 08303, polluted farming soil) were obtained from the National Research Center for Certified Reference Materials (Beijing, China). Qinghai Lake water was collected from Qinghai Lake, Qinghai, China. Yellow River water was collected from Yellow River, Lanzhou, China. To oxidize organic matter such as humic acid, the sample was digested by oxidizing UV-photolysis in the presence of 1% H2 O2 using a low pressure Hg-lamp which was integrated in a closed quartz vessel [33]. The digested samples were immediately filtered through a Millipore cellulose nitrate membrane, pore size 0.45 mm, acidified to pH 3 with hydrochloric acid and stored in precleaned polyethylene bottles. Tap water samples taken from our research laboratory were analyzed without pretreatment. The pH value was adjusted to 3 with 0.1 mol L−1 HCl or 0.1 mol L−1 NH3 ·H2 O prior to use. Balsam pear leaves was obtained from Anning village, Lanzhou, China. The plant samples were dried in an oven at 80 ◦ C to constant weight. A 1.000 g balsam pear leaves samples were weighted and transferred to a digestion tube before adding 5 mL of concentrated HNO3 . Following the directions found in the literature [34], the tube was left at room temperature for one night. Then it was placed in a digester block and heated slowly until the temperature was up to 165 ◦ C. This temperature was maintained until no more brown fumes evolved. After the tube had cooled down, 1.3 mL perchloric acid was added into it. Then the temperature was raised to 210 ◦ C until white fumes begin to form. The volume was adjusted to 100 mL with doubly distilled deionized water after the tube had cooled off.

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2.4. Preparation of the Fe(III)-imprinted amino-functionalized silica gel sorbent The silica gel surfaces were activated by refluxing 8 g of silica gel (60–100 mesh) with 60 mL of 6 mol L−1 hydrochloric acid under stirring for 8 h, then the activated silica gel was filtered and washed with doubly distilled water to neutral and dried under vacuum at 70 ◦ C for 8 h. To prepare the Fe(III)-imprinted amino-functionalized silica gel sorbent, 2.271 g of FeCl3 ·6H2 O was dissolved in 80 mL of methanol under stirring and heating, then 4 mL of APS was added into the mixture. The solution was stirred and refluxed for 1 h, to which 6 g of activated silica gel was added. After 20 h of stirring and refluxing the mixture, the product was recovered by filtration, washed with ethanol to remove the remnant APS, and stirred in 50 mL of 6 mol L−1 hydrochloric acid for 2 h to remove metal ions from the polymer. The final product was filtered, washed with doubly distilled water to neutral and dried under vacuum at 80 ◦ C for 12 h. The non-imprinted functionalized silica gel sorbent was also prepared using an identical procedure without adding FeCl3 ·6H2 O. 2.5. General procedure for preconcentration/separation of Fe(III) 2.5.1. Static adsorption test A portion of standard or sample solution containing Fe(III) was transferred into a 10 mL beaker, and the pH value was adjusted to the desired value with 0.1 mol L−1 HNO3 or 0.1 mol L−1 NH3 ·H2 O. Then the volume was adjusted to 10 mL with doubly distilled deionized water. And 50 mg of Fe(III)imprinted amino-functionalized silica gel sorbent was added, and the mixture was shaken vigorously for 30 min to facilitate adsorption of the metal ions onto the ion-imprinted sorbent. After the solution was centrifuged, the concentrations of the metal ions in the solution were directly determined by ICP-AES. 2.5.2. Dynamic adsorption test Firstly, the glass column (45 mm in length and 2.5 mm in diameter) was packed with 50 mg of the imprinted functionalized silica gel sorbent. A small amount of glass wool was placed at both ends to prevent loss of the polymer particles during sample loading. Before use, pH 3 of HNO3 solution and doubly distilled deionized water were successively passed through the microcolumn in order to equilibrate, clean and neutralize it. Each solution was passed through the column at a flow rate of 1.0 mL min−1 (controlled by a peristaltic pump) after adjusting pH 3. The metal ions adsorbed on the column were eluted with 0.5 mol L−1 HCl. The analytes in the elution were determined by ICPAES. 2.5.3. Constants The adsorption capacity, the extraction percentage, the distribution ratio, the selectivity coefficient and the relative selectivity

coefficient were calculated as the following equations: Q=

(C0 − Ce )V , W

αFe/Cr =

DFe , DCr

E= αr =

(C0 − Ce ) , Ce

D=

Q , Ce

αi αn

Where Q represents the adsorption capacity (mg g−1 ), C0 and Ce represent the initial and equilibrium concentration of Fe(III) (␮g mL−1 ), W is the mass of Fe(III)-imprinted aminofunctionalized silica gel polymer (g) and V is the volume of metal ion solution (L), E (%) is the extraction percentage, D is the distribution ratio (mL g−1 ), αFe/Cr is the selectivity coefficient, αr is the relative selectivity coefficient, αi and αn represent the selectivity factor of imprinted sorbent and non-imprinted sorbent, respectively. 3. Results and discussion 3.1. Preparation of the Fe(III)-imprinted amino-functionalized silica gel sorbent Silica gel is an amorphous inorganic polymer having siloxane groups (Si–O–Si) in the bulk and silanol groups (Si–OH) on its surface. The latter are responsible for chemical modification that may occur on the silica surface. Because commercial silica gel contains a low concentration of surface silanol groups suitable for modification, the activation of silica gel surface is necessary. In this work hydrochloric acid was used for the activation of silica gel. The complex was formed between Fe(III) and APS, then cohydrolyzed and co-condensed with the activated silica gel. Thus, the activated silica gel surface was grafted with the complex of Fe(III) and APS rather than just the free APS. After the remnant APS and Fe(III) were removed by ethanol and 6 mol L−1 HCl, respectively, the imprinted functionalized silica gel sorbent which contained a tailor-made cavity for Fe(III) was formed. 3.2. Characteristic of the FT-IR spectra To ascertain the presence of APS in the functionalized silica gel sorbents, FT-IR spectra were obtained from activated silica gel, Fe(III)-imprinted and non-imprinted aminofunctionalized silica gel sorbents. The observed features around 1101.5 and 964.6 cm−1 indicated Si–O–Si and Si–O–H stretching vibrations, respectively. The presence of adsorption water was reflected by νOH vibration at 3439.9 and 1635.1 cm−1 . The bands around 802.6 and 468.4 cm−1 resulted from Si–O vibrations. The νNH2 band present in silica gel modified amine derivatives was absent in the IR spectra owing to the participation of the amino group in the Schiff base formation [35]. Imprinted and non-imprinted sorbent showed a very similar location and appearance of the major bands. It indicated that N–H was recovered after removal of Fe(III) in the imprinted sorbent.

X. Chang et al. / Talanta 71 (2007) 38–43

Fig. 1. Effect of pH on sorption of Fe(III) on Fe(III)-imprinted aminofunctionalized silica gel sorbent. Other conditions: 50 mg of the sorbent; 1.0 ␮g mL−1 of Fe(III); shaking time 30 min; temperature 25 ◦ C.

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Fig. 2. The effect of Fe(III) initial concentration on the adsorption quantity of Fe(III)-imprinted amino-functionalized silica gel sorbent. Other conditions: 20 mg of ion-imprinted sorbent; pH 3; shaking time 30 min; temperature 25 ◦ C.

3.5. Adsorption capacity of Fe(III)-imprinted sorbent for Fe(III)

3.3. Effect of pH According to the recommended procedure (static method), the effect of pH on the adsorption of Fe(III) was tested by equilibrating 50 mg of Fe(III)-imprinted amino-functionalized silica gel sorbent with 10 mL of the buffer solutions containing 1.0 ␮g mL−1 of Fe(III) under different pH conditions. It can be seen in Fig. 1, the sorption quantity of Fe(III) was very low when the pH was lower than pH 3 because of the protonation, but it increased dramatically with the pH. After pH 3, the sorption quantity remained relatively constant. In order to avoid hydrolyzing at higher pH values, pH 3 was selected as the enrichment acidity for subsequent experiments. 3.4. Effect of elution condition on recovery Elution of Fe(III) from the column containing the Fe(III)imprinted amino-functionalized silica gel sorbent was investigated by using 2 mL of various concentrations of HCl as eluent following the general procedure (dynamic method). When HCl is used as a desorption agent, the coordination spheres of chelated Fe(III) ions is disrupted and subsequently Fe(III) ions are released from the iron templates into the desorption medium. The quantitative recoveries (>95%) of Fe(III) can be obtained using 2 mL of 0.5 mol L−1 HCl as eluent. Therefore, 2 mL of 0.5 mol L−1 HCl was used as eluent in subsequent experiments.

The adsorption capacity is an important factor because it determines how much adsorbent is required to quantitatively concentrate the analytes from a given solution. The adsorption capacity was tested following the general procedure. To measure the static adsorption capacity, 20 mg of Fe(III)-imprinted or non-imprinted sorbent was equilibrated with 50 mL of various concentrations of Fe(III) solutions buffered with 0.1 mol L−1 of HNO3 or NH3 ·H2 O at pH 3. As can be seen in Fig. 2, the amount of Fe(III) adsorbed per unit mass of IIPs increased with the initial concentrations of Fe(III). The initial Fe(III) concentrations were increased till the plateau values (adsorption capacity values) were obtained. The static adsorption capacity of the ion-imprinted and non-imprinted sorbent for Fe(III) was calculated as 25.21 and 5.10 mg g−1 , respectively. The static adsorption capacity of the ion-imprinted was about five times of non-imprinted one. The results showed that the ion-imprinted polymers had a high adsorption capacity for Fe(III). 3.6. Selectivity of the imprinted sorbent The Cr(III) ion was chosen as the competitive species with Fe(III) because these two ions have the same charge and similar ionic radius. As can be seen in Table 2, the D values of Fe(III)-imprinted amino-functionalized silica gel sorbent for Fe(III) were large, while D decreased significantly

Table 2 Competitive loading of Fe(III) and Cr(III) by the Fe(III)-imprinted and non-imprinted silica gel sorbent Sorbent

Fe(III)-imprinted

Non-imprinted

Initial solution (␮g mL−1 )

Uptake (%)

Capacity (mg g−1 )

D (mL g−1 )

Fe(III)

Cr(III)

Fe(III)

Cr(III)

Fe(III)

Cr(III)

Fe(III)

1 1 1

0 1 2

99.75 99.66 99.41

39.4 53.2

1.995 1.994 1.986

0.788 2.128

798112.0 586352.9 279684.5

1300 2273.1

1 1 1

0 1 2

98.2 97.3 97.2

86.38 84

1.964 1.946 1.944

1.727 1.680

109106.7 114470.6 15185.6

12683.1 5250.4

α

αr

451.0 123.0

49.9 42.4

Cr(III)

9.03 2.9

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X. Chang et al. / Talanta 71 (2007) 38–43

for Cr(III). The αr values were 49.9 and 42.4, which were greater than 1 for Fe(III)-imprinted amino-functionalized silica gel sorbent of Fe(III)/Cr(III). The results indicated that the Fe(III)-imprinted amino-functionalized silica gel sorbent had higher selectivity for Fe(III). And these results demonstrated that Fe(III) could be determined even in the presence of Cr(III) interference.

solutions containing 1.0 ␮g of Fe(III) were passed through the column at the optimum flow rate. The maximum sample volume can be up to 150 mL with the recovery >95%. Therefore, 150 mL of sample solution was adopted for the preconcentration of analytes from sample solutions. And a high enrichment factor of 75 was obtained because 2 mL of 0.5 mol L−1 HCl was used as eluent in these experiments.

3.7. Effect of flow rate

3.9. Effect of coexisting ions

The flow rate of the Fe(III) solution through the packed volume is a very important parameter because the retention of elements on adsorbent depends upon the flow rate of the sample solution. Its effect was examined under the optimum conditions (pH, eluent, etc.) by passing 50 mL of sample solution through the column with a peristaltic pump. Faster flow rates could not be investigated due to the back-pressure generated by the column. So the flow rates were adjusted in the range of 0.5–3.0 mL min−1 . The adsorption in this system is a rapid kinetic process and at higher flow rates the contact time of iron ions with the column material is shorter. In the test, the quantitative recoveries of the metal ions will decrease with the further increasing of the flow rate that is over 1.5 mL min−1 . Thus, a flow rate of 1.0 mL min−1 was selected in this work.

Different foreign ions were added to equal quantities of the diluted mixed standard solutions and enriched and determined according to the general procedure. The results showed that up to 4000 ␮g mL−1 of K(I), 4000 ␮g mL−1 of Na(I), 200 ␮g mL−1 of Ca(II), 200 ␮g mL−1 of Mg(II), 200 ␮g mL−1 of Ni(II), 200 ␮g mL−1 of Mn(II), 200 ␮g mL−1 of Zn(II), 100 ␮g mL−1 of Co(II), 50 ␮g mL−1 of Cd(II), 50 ␮g mL−1 of Cu(II), 50 ␮g mL−1 of Pb(II), 50 ␮g mL−1 of Hg(II) had no significant interferences with the determination of 1 ␮g mL−1 of Fe(III). There are three possible factors for this reason [29]. One is the amino-functionalized group inherent selectivity. The amino group is a soft base and it would not interact with alkali metal and alkali earth metal ions that are classified as hard acids. The second is the hole-size selectivity. The size of Fe(III) exactly fits the cavity of the Fe(III)-imprinted sorbent. The third is the coordination-geometry selectivity because the Fe(III)imprinted silica gel sorbent can provide the ligand groups arranged in a suitable way required for coordination of Fe(III) ion. Although some ions have similar size with Fe(III) ion, and some ions have high affinity with the amino ligand, the Fe(III)imprinted amino-functionalized silica gel sorbent still exhibits high selectivity for extraction of Fe(III) in the presence of other metal ions. These results suggest that the coordination-

3.8. Maximum sample volume and enrichment factor The enrichment factor was studied by recommended column procedure by increasing volume of Fe(III) solution and keeping the total amount of loaded Fe(III) constant to 1.0 ␮g. For this purpose, 10, 50, 100, 150, 200, 250 and 300 mL of sample

Table 3 Analytical results for the determination of trace ferric in standard reference materials, plant sample and natural water samples Samples

Fe(III) added (␮g mL−1 )

Standard materials (mg g−1 ) 36 ± 1.4 27 ± 2.2

GBW 08301 GBW 08303 Balsam pear leaves

Certified (mg g−1 )

Measured Plant sample (mg g−1 )

Water samples (␮g mL−1 ) 39.4 ± 0.12 29.7 ± 0.20

3.48 ± 0.09

Founded with ICP-AES (mg g−1 )

Recovery (%)

3.59 ± 0.12

Qinghai Lake water

0.00 0.50 1.00 5.00

0.17 0.66 1.55 5.13

± ± ± ±

0.02 0.03 0.05 0.02

– 98.0 98.0 99.2

Yellow River water

0.00 0.50 1.00 5.00

6.65 7.14 7.67 11.58

± ± ± ±

0.03 0.02 0.06 0.07

– 98.0 102 98.6

Tap water

0.00 0.50 1.00 5.00

0.05 0.53 1.03 5.10

± ± ± ±

0.02 0.03 0.05 0.08

– 96.0 98.0 101

The value following “±” is the standard deviation.

X. Chang et al. / Talanta 71 (2007) 38–43

geometry selectivity may dominate in the selectivity enhancement. 3.10. Analytical precision and detection limits Under the selected conditions, eight portions of standard solutions were enriched and analyzed simultaneously following the general procedure. The relative standard deviations (R.S.D.) of the method was lower than 2.0%, which indicated that the method had good precision for the analysis of trace Fe(III) in solution samples. In accordance with the definition of IUPAC [36,37], the detection limit of the method was calculated based on three times of the standard deviation of 11 runs of the blank solution. The detection limit (3σ) of the proposed method was 0.34 ␮g L−1 . 3.11. Application of the method

References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17]

The proposed method was applied to the analysis of iron in two certified reference materials (GBW 08301, river sediment and GBW 08303, polluted farming soil), plants, tap water and river water samples. The results were listed in Table 3. The analytical results for the standard material were in good agreement with the certified values. The analytical results for plant sample were in agreement with the ICP-AES method. For the analytical of natural water samples, the standard addition method was used, the recoveries of iron were in the range of 96–105%. These results indicated the suitability of Fe(III)imprinted amino-functionalized silica gel sorbent for selective solid-phase extraction and determination of trace Fe(III) in environmental samples. 4. Conclusions In this paper, a selective and sensitive method for the determination of trace levels of iron was developed using Fe(III)imprinted amino-functionalized silica gel (prepared by a surface imprinting technique) as a solid-phase extractant. The preparation of Fe(III)-imprinted amino-functionalized silica gel sorbent was relatively simple and rapid. The ion-imprinted sorbent had higher adsorption capacity and selectivity for Fe(III), and the method was successfully applied to the analysis of trace iron in plants and water sample solutions. The precision and accuracy of the method are satisfactory.

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