Fluorescence Characteristics of Aqueous Synthesized Tin Oxide Quantum Dots for the Detection of Heavy Metal Ions in Contaminated Water

Abstract

Tin oxide quantum dots were synthesized in aqueous solution via a simple hydrolysis and oxidation process. The morphology observation showed that the quantum dots had an average grain size of 2.23 nm. The rutile phase SnO₂ was confirmed by the structural and compositional characterization. The fluorescence spectroscopy of quantum dots was used to detect the heavy metal ions of Cd²⁺, Fe³⁺, Ni²⁺ and Pb²⁺, which caused the quenching effect of photoluminescence. The quantum dots showed the response of 2.48 to 100 ppm Ni²⁺. The prepared SnO₂ quantum dots exhibited prospective in the detection of heavy metal ions in contaminated water, including deionized water, deionized water with Fe³⁺, reclaimed water and sea water. The limit of detection was as low as 0.01 ppm for Ni²⁺ detection. The first principle calculation based on the density function theory demonstrated the dependence of fluorescence response on the adsorption energy of heavy metal ions as well as ion radius. The mechanism of fluorescence response was discussed based on the interaction between Sn vacancies and Ni²⁺ ions. A linear correlation of fluorescence emission intensity against Ni²⁺ concentration was obtained in the logarithmic coordinates. The density of active Sn vacancies was the crucial factor that determined fluorescence response of SnO₂ QDs to heavy metal ions.

1. Introduction

Water pollution has become a grave concern throughout the world. Industrial wastewater discharge heavy metals, which are produced from factories fabricating metals, papers and chemicals [1,2,3]. These heavy metal ions bring severe risks to living creatures because most of them are non-biodegradable and toxic even at trace levels [4,5,6]. Most heavy metals are non-biodegradable and may accumulate in the aquatic and plant organisms [7]. The danger caused by heavy metals are biomagnified in the food web [8]. Fe³⁺ ions are one of the most fundamental elements in body and the excess of Fe³⁺ from the permissible limit could result in several severe diseases [9]. Pb²⁺ of extremely low concentration increases the risks of cardiovascular disease and cancer, especially in children [10]. It is toxic to cells after the interaction with calcium and zinc proteins, which are important in the process of cell signal transmission and gene expression [11,12,13]. Cd²⁺ has a high transferability from environment to plants by the absorption through roots, causing withered or dead plants [14,15]. High concentration intake of Ni²⁺ causes skin dermatitis, nausea, chronic asthma, coughing and cancer [16].

Therefore, it is urgent to develop a technique that is of high response, low limit of detection, simplicity in operation and capability of in situ detection. There are a few of techniques to detect heavy metal ions, such as atomic absorption spectroscopy (AAS) [17], inductively coupled plasma mass spectrometry (ICP-MS) [18] and fluorescence spectroscopy (FS) [19,20]. The quantum dot (QD) method, with grain size less than 5 nm, has fluorescence effects, which could be used in the detection of drugs [21], anions [22] and organic pollutants [23]. It also has prospects in the detection of heavy metal ions by using its characteristics of fluorescence.

The effect of fluorescence is a process where a QD emits light after it has absorbed electromagnetic radiation from a excitation source. The electrons in valence band are stimulated to reach conduction band by the excitation light. Then, when the electrons transit from conduction band to valence band, the fluorescence emission takes place as a kind of energy release [24]. It has been found that the fluorescence emission could be influenced by many factors, and one of them is the presence of heavy metal ions, which caus the quenching of fluorescence [25]. The ions of heavy metals can adsorb the released energy of the electron transition, interfering with the fluorescence emission. Therefore, the fluorescence nature of semiconductor QDs has been put into practice of heavy metal ion detection, even though the mechanism of fluorescence quenching is still of high complexity.

Several kinds of QDs have been synthesized, such as CdS [23], CdTe [26], ZnS [27] and their composites [28,29]. However, some of them contain toxic elements in themselves. The tin oxide (SnO₂) QD is an environment-friendly semiconductor. It has the advantages of non-toxicity, chemical stability and low cost. Based on the optical characteristics, SnO₂ photoluminescence sensors were developed for xanthene dyes [30], DNA [31] and 1,4 Bis ((2-Methyl) thio) Phenylamino methyl benzene Schiff [32]. However, there have been few reports of heavy metal ion detection by SnO₂ sensors. There are some techniques to prepare SnO₂ QDs. However, the organic reagents of oleic acid, toluene, oleylamine and hydrazine need to be used in the fabrication [33,34,35]. The organic compounds are harmful to human beings and the environment. They also increase the risk of operator poisoning and the cost of environmental remediation in factories. Therefore, it is expected to find a route to prepare SnO₂ QDs with simple, cheap and environment-friendly fabrication. Furthermore, these SnO₂ QDs are potentially applicable to the detection of heavy metal ions in contaminated water.

In the present work, SnO₂ QDs were synthesized in the aqueous solution for the detection of heavy metal ions. Several characterizations were used to confirm the structure and composition of the prepared QDs. The detection of heavy metal ions was completed by using the fluorescence effect of QDs, which is quenched by the ions of Cd²⁺, Fe³⁺, Ni²⁺ and Pb²⁺. The mechanism of fluorescence quenching by the heavy metal ions is discussed in combination with the first principle calculation based on the density function theory.

2. Materials and Methods

SnO₂ QDs were synthesized in the aqueous solution by a facial method [36]. Analytical reagents of SnCl₂·2H₂O (≥98.0%, Sinopharm Chemical Reagent Co., Ltd., Shanghai, China) and thiourea (CH₄N₂S, ≥99.0%, Sinopharm Chemical Reagent Co., Ltd., Shanghai, China) were used as raw materials. 2.257 g SnCl₂·2H₂O and 0.077 g CH₄N₂S were dissolved into deionized water of 50 mL. The stannous chloride transformed to stannous hydroxide during hydrolysis process and the suspension was stirred in a magnet stirring apparatus for 24 h at room temperature. In this process, the thiourea, as an accelerator, promoted the forward reaction by consuming HCl in the solution, as shown in Equation (1). Meanwhile, stannous hydroxide was oxidized by aerial oxygen with SnO₂ QDs obtained, as shown in Equation (2):

$${\mathrm{SnCl}}_2+2{\mathrm{H}}_2\mathrm{O}\leftrightarrow {\mathrm{Sn}\left(\mathrm{OH}\right)}_2+2\mathrm{HCl}$$

(1)

$${2\mathrm{Sn}\left(\mathrm{OH}\right)}_2+{\mathrm{O}}_2\to {2\mathrm{SnO}}_2+2{\mathrm{H}}_2\mathrm{O}$$

(2)

Thus, the aqueous SnO₂ QD solution was acquired after the completion of hydrolysis and oxidation. The grain size and Zeta potential of the SnO₂ QDs were analyzed by dynamic light scattering (DLS, Malvern Zetasizer Nano ZS 90, Malvern panalytical Ltd., Malvern, UK). The morphology was observed by high resolution transmission electron microscopy (HRTEM, JEM-3200FS, JEOL, Tokyo, Japan). The solution was dried to powder for X-ray diffraction (XRD, Rigaku D/MAX-Ultima, Rigaku, Tokyo, Japan) and X-ray photoelectron spectroscopy (XPS, Thermo Scientific ESCALAB 250 XI, ThermoFisher Scientific, Waltham, MA, USA). A fluorescence spectrometer (FLS-980, Edinburgh Instruments, Edinburgh, UK) was used to characterize the fluorescence performances of the SnO₂ QDs. The wavelength of excitation in fluorescence characterization was 280 nm. The SnO₂ QD solution was diluted to 0.002 mol/L of Sn atoms and it was incorporated with heavy metal ions of Cd²⁺, Fe³⁺, Ni²⁺ as well as Pb²⁺. The fluorescence response (S) was defined as the ratio of the maximum intensity of SnO₂ QDs (F₀) to the one of SnO₂ QDs with heavy metal ion incorporation (F), as S = F₀/F. The characterization of fluorescence was carried out immediately after the incorporation. In order to evaluate the applicability of SnO₂ QDs in the practical detection of heavy metal ions, several types of background water were employed, namely, deionized water, reclaimed water and sea water. The sea water was collected from Xinghai Bay of Yellow Sea, Dalian, China. There were no Ni²⁺ ions in the deionized water and reclaimed water. The reclaimed water contained cations of Fe³⁺ (<0.3 mg/L) and Mn²⁺ (<0.1 mg/L) as well as several anions (<1.0 mg/L). The main composition of sea water included cations of Na⁺ (11.04 mg/L), K⁺ (0.40 mg/L), Ca²⁺ (0.42 mg/L) and Mg²⁺ (1.33 mg/L) as well as anions of Cl⁻ (19.86 mg/L) and SO₄²⁻ (2.77 mg/L). Ni²⁺ was not taken into account because it was insignificant compared to other major solutes.

3. Results and Discussion

3.1. Structure and Morphology

The grain size distribution of the SnO₂ QDs from DLS is shown in Figure 1. The grain size was from 2 to 10 nm. The peak appeared at 5.3 nm and approximate 90% of the grains were of the size within 4–6 nm. The morphology of the SnO₂ QDs was observed by HRTEM, as shown in Figure 2. The prepared QDs have a uniform dispersion in the aqueous solution. The Zeta potential of the as-prepared sample was 17.3 mV and it was measured to be 17.1 mV after 3 months of storage at room temperature. Thus, the SnO₂ QDs were stable in the aqueous solution for several months. The average grain size was measured to be 2.23 nm. The grain sizes of QDs were from 1.4 nm to 3.4 nm, and over 50% of them were between 2.0 to 2.5 nm. The characteristic spacing of 0.33 nm was observed, corresponding to the (110) planes of the rutile phase of SnO₂.

Figure 3a shows the XRD pattern of the SnO₂ powder, which was obtained from the dried aqueous solution with SnO₂ QDs. Four main peaks of (110), (101), (211) and (112) were observed, in agreement with the rutile phase of SnO₂. The lattice constants of SnO₂ unit cells were evaluated to be a = b = 4.74677 Å and c = 3.18196 Å. The crystallite size of the QDs was calculated to be 2.3 nm according to the Scherrer’s formula. The size coincided with the grain size observed from HRTEM, but was smaller than the result of DLS size distribution in Figure 1. The deviation may be ascribed to the aggregation of QDs, which affected the light scattering during the DLS measurement. The XPS spectrum of the SnO₂ QDs is shown in Figure 3b, which shows the presence of C 1s, O 1s and Sn 3d. The high solution pattern of Sn 3d shows two peaks of 487.3 eV and 495.6 eV, corresponding to the Sn 3d_3/2 and Sn3d_5/2, respectively. The spectrum is in good agreement with the standard pattern from the rutile SnO₂ sample [37,38].

3.2. Fluorescence Response to Heavy Metal Ions

The fluorescence spectra of SnO₂ QDs with various concentrations are shown in Figure 4, where the peak appears at the emission wavelength of 300 nm. Considering the excitation wavelength of 280 nm, the present SnO₂ QDs show a low Stocks shift. The self-quenching property of QDs was observed when the Sn concentration increased. The heavy metal ion solutions of 100 ppm were incorporated with the SnO₂ QDs and the incorporations result in the quenching of fluorescence, as shown in Figure 5. It was observed that Ni²⁺ and Fe³⁺ perform stronger attenuations to the fluorescence emission than other heavy metals. Figure 6a illustrates the fluorescence responses of SnO₂ QDs to the various heavy metal ions. The QDs show responses to all the heavy metals, which may interact with QDs by interfering the electronic transition from conduction band to valence band. The Ni²⁺ incorporation stimulates the highest response of 2.48.

The detection of heavy metal ions is completed by the quenching of fluorescence. The quenching mechanism has been proven to be complex [39,40], in which the heavy metal ions interfere with the fluorescence emission by adsorbing the energy of electron transition from conduction band to valence band. The prepared SnO₂ QDs have an emission peak at 300 nm, in agreement with the previous report [41]. The position of the emission peak remained the same after the incorporation of heavy metals, revealing that the band gap had not shifted. Thus, the fluorescence quenching may result from the variation of surface states of the QDs. The radius of Sn⁴⁺ ion was found to be 69 pm, while the heavy metals of Cd²⁺, Fe³⁺, Ni²⁺ and Pb²⁺ have the ion radii of 78, 64.5, 69 and 119 pm [42], as shown in Figure 6a,b. It was found that the radius difference between heavy metal ions with Sn⁴⁺ had the same relationship with the response of fluorescence quenching. The Ni²⁺ ion had the same radius as the Sn⁴⁺ ion and this could promote its interaction with the QD surface, where the crystal lattice is lacking in integrity. Therefore, Ni²⁺ ions perform as surface states on QDs and cause a strong fluorescence quenching. For the other heavy metal ions, their radii differed from Sn⁴⁺ and the radius difference would bring mismatches in crystal lattice when they interact with QD surface. Hence, the density of surface states would be limited, leaving the little fluorescence responses.

Figure 7 shows the fluorescence response of SnO₂ QDs to Ni²⁺ with concentration of 0.01–500 ppm in the background solutions of deionized water, deionized water with 10 ppm Fe³⁺, reclaimed water and sea water. In the deionized water, the QDs reveal positive dependence of fluorescence response with Ni²⁺ concentration. The concentration linear range is from 10⁻² to 500 ppm in the logarithmic coordinates. If the sensitivity is defined as the slope of fluorescence response against target pollutant concentration in the logarithmic coordinates, it is evaluated to be 0.073 for SnO₂ QDs in deionized water for Ni²⁺ detection. However, the response appears to be degraded in the presence of 10 ppm Fe³⁺, which is competitive to Ni²⁺ in the deionized water. A similar dependence was also observed for the fluorescence response of QDs in reclaimed water, because it contains impurities of Fe³⁺ and Mn²⁺. They were also responsible for the non-linear correlation at the high Ni²⁺ concentration over 100 ppm. The limit of detection is the least concentration of target pollutant, which can stimulate detectable fluorescence response of SnO₂ QDs. As shown in Figure 7, the limits of detection are 0.01 ppm with the responses of 1.26 and 1.01 in deionized water and reclaimed water, respectively. The fluorescence illustrated a different performance in case of the sea water background. The response is between 2.06 and 2.42 within the Ni²⁺ concentration range of 0.01–500 ppm, being less sensitive to the target ion. It would be ascribed to the cations of Na⁺, K+, Ca²⁺ and Mg²⁺ as well as anions of Cl⁻ and SO₄²⁻, which may interfere with the detection of Ni²⁺ by their competitive interaction with SnO₂ QDs.

Apart from the present SnO₂ QDs, the Ni²⁺ detection has to be completed by other QDs in a variety of circumstances. Hydrophobic core/shell CdSe/ZnS QDs were used for Ni²⁺ sensing in organic solvent. A similar non-linear dependence of fluorescence response on Ni²⁺ concentration was observed [43]. In CdS QD sensors, the correlation was found to be linear at low concentration and it became non-linear when a high Ni²⁺ concentration was introduced [44]. Furthermore, the sensing performance was found to be dependent on pH condition [45]. Thioglycolic acid capped CdTe semiconductor in aqueous solution was applied as the fluorescence sensor, which could determine Ni²⁺ without any tangible influence of a few interfering ions [46]. Imidazole modified carbon dots were also employed for photoluminescence sensors with limit of detection of 0.93 × 10⁻³ mol/L [47]. Compared to those sensors, the present SnO₂ QDs show promising properties to develop photoluminescence sensors, which take advantages of the chemical stability, non-toxicity and low cost. On the other hand, highly sensitive spectroscopic techniques, such as inductively coupled plasma mass spectrometry (ICP-MS), inductively coupled plasma optic emission spectrometry (ICP-OES) and square wave anodic stripping voltammetric (SWASV), provide precise results with low limit of detection [48,49,50]. For example, the limits of detection of ICP-OES are 1.2, 1.1, 1.0 and 6.3 µg/L for Cu²⁺, Zn²⁺, Cd²⁺ and Ni²⁺, respectively [48]. However, these techniques are usually of high cost and need complex operations by experienced staffs. The present photoluminescence sensor of SnO₂ QDs would be beneficial to the design of in situ devices for heavy metal ions in contaminated water.

It is noted that selectivity is an essential characteristics in the detection of heavy metal ions, because they usually coexist in the contaminated water. However, the present SnO₂ QDs show a fluorescence response to all of them. It is necessary to develop the ability to discriminate among heavy metal ions for a practical sensor. The technique using a neural network is one of the candidates for the potential device, which contains a sensor array with various sensing properties, e.g., sensors with various Sn concentrations. Each sensor in the array would be trained by a series of fluorescence responses to an individual type of heavy metal ion or a mixture of them. Then, the device would acquire the ability of discrimination to a specific type of heavy metal ion after a group of fluorescence responses is collected. In addition, the heavy metal ions of Cd²⁺, Fe³⁺, Ni²⁺ and Pb²⁺ were investigated in the present work because they are typical pollutants in the environment. These heavy metal ions are representative pollutants, which were used to develop SnO₂ QD photoluminescence sensors. Other heavy metal ions, such as Cu²⁺, Zn²⁺, Fe²⁺, Mn²⁺ and Hg²⁺, will need to be investigated as target pollutants in further researches. There were four different background solutions in the present work, including deionized water, deionized water with 10 ppm Fe³⁺, reclaimed water and sea water. All of them were used to check the validity of SnO₂ QDs in the detection of Ni²⁺. Although the prepared QDs were able to detect Ni²⁺ ions as a photoluminescence sensor, the sensor performances are different in those background solutions. Therefore, it was necessary to study the SnO₂ QD properties in a diversity of background solutions so that it can be put into practical use.

It is known that the Stern-Volmer relationship describes the dependence of fluorescence response to the concentration of quencher, as S = F₀/F= 1+k_qτ₀ [Q]. Here, k_q is the quencher rate coefficient and τ₀ is the lifetime of the emissive excited state without a quencher present. [Q] is the concentration of the quencher Q. Therefore, S is of linear dependence with [Q] provided that k_q and τ₀ are constants. The Stern-Volmer relationship is established based on a model involving double molecules. However, the intermolecular deactivation differs from the present detection, where several individual heavy metal ions interact with a QD assembled by a matrix of super cells. Therefore, the results in Figure 7 deviate from the linear correlation and the sensing mechanism needs further discussions.

3.3. First Principle Calculation

A first principle calculation has been employed for further discussion of the interaction between SnO₂ QDs and heavy metal ions. The calculation was implemented based on the density function theory (DFT) in the Cambridge sequential total energy package (CASTEP) [51]. The Perdew-Burke-Ernzerhof (PBE) function was used to describe the exchange-correlation interaction in the generalized-gradient approximation (GGA). The structural model was established based on rutile SnO₂ tetragonal unit cells with lattice constants of a = b = 4.7373 Å and c = 3.1864 Å [52]. The (110) plane with the lowest energy [53,54,55] was chosen as the surface interacted with heavy metal ions. The crystal plane was cleaved from the optimized system of SnO₂, which contained 2 × 2 × 2 matrix of unit cells. A vacuum region of 10 Å was also employed to prevent the interaction between adjacent layers. The Brillouin zone was sampled using a 2 × 2 × 1 k-point Monkhorst-Pack mesh. In order to calculate the adsorption energy of heavy metal ions on SnO₂ surface, one Sn atom was removed from the (110) crystal surface for a point defect as the adsorption site, as shown in Figure 8a. The system energy was indicated by E_def. Then, the heavy metal ions were introduced and one of them was adsorbed on the site of defect, as shown in Figure 8b. The system energy after interaction was denoted by E_metal. Thus, the adsorption energy (E_ads) of the specific heavy metal ion on the SnO₂ QD surface could be calculated according to Equation (3):

$$E_{ads}=E_{metal}-E_{def}$$

(3)

The calculation results of adsorption energy are listed in

Table 1. Adsorption energies of heavy metal ions from first principle calculation based on the density function theory.

Heavy Metal Ion	Adsorption Energy (eV)	Ion Radius (Å)	Fluorescence Response
Cd2+	4.21	78	1.14
Fe3+	13.46	64.5	2.13
Ni2+	7.65	69	2.48
Pb2+	5.39	119	1.03

. Fe³⁺ and Ni²⁺ show large E_ads values of 13.46 and 7.65 eV, while the adsorption energies for Cd²⁺ and Pb²⁺ are quite low. Therefore, the Fe³⁺ and Ni²⁺ ions are much easier to be interacted with SnO₂ QDs and the conclusion is in agreement with the correlation between fluorescence response and ion radius. It was concluded that the fluorescence performance is dependent on the adsorption energy of heavy metal ions. However, an inverse correlation was observed between adsorption energy and fluorescence response for Fe³⁺ and Ni²⁺. It is known that the fluorescence response is the consequence of the quenching of energy emission during the transition of electrons from the conduction band to the valence band. There are several ways to release the energy, such as self-quenching, resonance energy transfer (RET), exciton coupling and photoinduced electron transfer (PET) [25]. Among these, PET involves the transfer of electrons between an excited fluorescence agent and a ground state species creating a charge separation [56]. When adsorbed on the site of Sn vacancy, divalent Ni²⁺ ions may have a stronger interference to PET than trivalent Fe³⁺ ions. Therefore, the SnO₂ QDs show a more significant fluorescence to Ni²⁺ even though Fe³⁺ has greater adsorption energy.

3.4. Mechanism of Fluorescence Response

As shown in the structural model of the SnO₂ system in Figure 8, the interaction between Ni²⁺ and SnO₂ QDs is described by a Ni²⁺ ion entering a Sn vacancy on the QD surface. It is known that a Sn vacancy acts as an acceptor in SnO₂ system and its ionization can be expressed by the Kroger-Vink notation, as shown in Equation (4):

$$V_{Sn}+4e^{\prime }\leftrightarrow V_{Sn}{}^{⁗}$$

(4)

where V_Sn and V_Sn⁗ are the Sn vacancy before and after ionization and e′ represents a free electron in the SnO₂ grain. After being adsorbed on the SnO₂ QD, the Ni²⁺ interacts with the Sn vacancy, as expressed in Equation (5):

$$V_{Sn}{}^{⁗}+N{i}^{••}\underset{}{\overset{}{\leftrightarrow }}N{i}_{Sn}{}^{″}$$

(5)

where Ni^•• denotes a bivalence nickel ion and Ni_Sn″ indicates a Ni ion occupying the Sn site with two electrons. A presumption was made that there are m Sn vacancies on the surface of a single SnO₂ QD, which adsorbs t ions of Ni²⁺. Thus, the interaction between the SnO₂ QD and Ni²⁺ ion is described by combining Equations (4) and (5), as shown in Equation (6):

$$m{V}_{Sn}+tN{i}^{••}+4m{e}^{\prime }\underset{k_{-1}}{\overset{k_1}{\leftrightarrow }}(m-t)V_{Sn}{}^{⁗}+tN{i}_{Sn}{}^{″}$$

(6)

where k₁ and k₋₁ are the rate constants of the reversible reaction. Hence, Equation (7) is obtained at the equivalence state:

$$k_1{[V_{Sn}]}^m{[N{i}^{••}]}^t{[e^{\prime }]}^{4m}=k_{-1}{[V_{Sn}{}^{⁗}]}^{m-t}{[N{i}_{Sn}{}^{″}]}^t$$

(7)

where [X] denotes the density of X for each reactant. Therefore, the density of electrons [e′] can be formulated as in Equation (8):

$$[e^{\prime }]={(\frac{k_{-1}{[V_{Sn}{}^{⁗}]}^{m-t}{[N{i}_{Sn}{}^{″}]}^t}{k_1{[V_{Sn}]}^m})}^{1/4m}{[N{i}^{••}]}^{-t/4m}$$

(8)

Considering the rate constants of k₁ and k₋₁ follow the Arrhenius equation, they are correlated to E_ads, the adsorption energy of Ni²⁺ on SnO₂ QDs, as shown in Equations (9) and (10):

$$k_1=A\exp (\frac{E_{ads}}{kT})$$

(9)

$$k_{-1}=A\exp (-\frac{E_{ads}}{kT})$$

(10)

where A is pre-exponential constant and k and T are the Boltzmann constant and temperature. Thus, Equation (8) can be rewritten as in Equation (11):

$$[e^{\prime }]={(\frac{{[V_{Sn}{}^{⁗}]}^{m-t}{[N{i}_{Sn}{}^{″}]}^t}{{[V_{Sn}]}^m})}^{1/4m}{[N{i}^{••}]}^{-t/4m}\exp (-\frac{E_{ads}}{2mkT})$$

(11)

It is noted that the fluorescence emission results from the recombination of electrons and holes, as expressed in Equation (12):

$$h^{•}+e^{\prime }\underset{k_{-2}}{\overset{k_2}{\leftrightarrow }}h\nu$$

(12)

where k₂ and k₋₂ are the rate constants and hν represents an emitted photon. Therefore, the fluorescence emission intensity (F) is proportional to the reaction rate of Equation (12). If α is the coefficient of the proportional correlation, Equation (13) can be obtained:

$$F=\alpha k_2[h^{•}][e^{\prime }]$$

(13)

Therefore, the expression of F is obtained as Equation (14) and its logarithmic form is shown in Equation (15):

$$F=\alpha k_2[h^{•}]{(\frac{{[V_{Sn}{}^{⁗}]}^{m-t}{[N{i}_{Sn}{}^{″}]}^t}{{[V_{Sn}]}^m})}^{1/4m}{[N{i}^{••}]}^{-t/4m}\exp (-\frac{E_{ads}}{2mkT})$$

(14)

$$\ln F=-\frac{t}{4m}\ln [N{i}^{••}]+\ln \alpha k_2[h^{•}]+\frac{1}{4m}\ln {[V_{Sn}{}^{⁗}]}^{m-t}{[N{i}_{Sn}{}^{″}]}^t{[V_{Sn}]}^{-m}-\frac{E_{ads}}{2mkT}$$

(15)

It is obvious that lnF is of linear dependence with logarithmic Ni²⁺ concentration provided that other parameters are constants. The slope of the linear correlation (n) could be found according to Equation (16). It infers that the slope is determined by the number of Sn vacancies and adsorbed Ni²⁺ ions on the SnO₂ QD surface.

$$n=\frac{d\ln F}{d\ln [N{i}^{••}]}=-\frac{t}{4m}$$

(16)

Figure 9 shows the correlation of fluorescence emission intensity against Ni²⁺ concentration in the logarithmic coordinates. The slope (n) is evaluated to be −0.073 from the linear fitting. Thus, t/m is equal to 0.29. It means that 71% of Sn vacancies on the surface are left vacant, while 29% of them are active to Ni²⁺ ions. Therefore, the fluorescence response of SnO₂ QDs to heavy metal ions is controlled by the density of active Sn vacancies. Furthermore, it is likely to be correlated to several factors, such as adsorption energy and concentration of heavy metal ions as well as total density of surface Sn defects. It is known that n is proportional to t/m, where t and m are the number of Ni²⁺ ions and Sn vacancies on the surface. If Ni²⁺ is replaced by another metal ion, Equation (16) is still valid. In this case, however, F will be influenced, because its E_ads value changes in Equation (15). Thus, the present mechanism of fluorescence response could be general for the detection of a series of heavy metal ions.

4. Conclusions

The SnO₂ QDs were prepared in the aqueous solution by the hydrolysis and oxidation of SnCl₂ source material. The average grain size of the QDs was 2.23 nm from HRTEM observation. The rutile phase SnO₂ of the prepared QDs was confirmed from the XRD pattern, HRTEM observation and XPS spectrum. The fluorescence spectra of the SnO₂ QDs show intensity peaked at an emission wavelength of 300 nm. The SnO₂ QDs showed a fluorescence response to various heavy metal ions and the response of 2.48 was observed to be 100 ppm Ni²⁺. The fluorescence performance to Ni²⁺ were evaluated in the background solutions of deionized water, deionized water with Fe³⁺ ions, reclaimed water and sea water. The limit of detection was as low as 0.01 ppm for Ni²⁺. The prepared QDs showed a great potential in the sensor development for the detection of heavy metal ions in contaminated water. The first principle calculation demonstrated that Ni²⁺ and Fe³⁺ had an adsorption energy of 7.65 and 13.46 eV, respectively. The fluorescence response was found to be dependent on the adsorption energy as well as ion radius of heavy metal ions. The mechanism of fluorescence response was discussed based on the interaction between Sn vacancies and Ni²⁺ ions. The fluorescence emission intensity was formulated as a function of Ni²⁺ concentration. 71% of Sn vacancies on the surface were left vacant, while 29% of them are active to Ni²⁺ ions. The density of active Sn vacancies was the crucial factor that determined the fluorescence response of SnO₂ QDs to heavy metal ions.