Synthesis of Ag₂S colloidal solutions in D₂O heavy water

Abstract

For the first time, colloidal solutions of silver sulfide are synthesized by chemical deposition from solutions of silver nitrate and sodium sulfide in heavy water D₂O. In the synthesis, sodium citrate was used as a stabilizer. The sizes of Ag₂S quantum dots in colloidal solutions were estimated by dynamic light scattering and transmission electron microscopy. The size of silver sulfide quantum dots in colloidal solutions in heavy water that were prepared from reaction mixtures with different concentrations of reagents is from 3 to 19–20 nm. An increase in the concentration of silver nitrate and a decrease in the concentration of sodium citrate in the initial reaction mixtures lead to a small increase in the size of Ag₂S quantum dots in the synthesized colloidal solutions. Colloidal silver sulfide solutions synthesized using D₂O heavy water retain the stability and constant size of the nanoparticles after storage for more than 100 days. The calculated exciton diameter for Ag₂S is about 3 nm, and is consistent with experimental observations.

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1. Introduction

Ag₂S QDs can be used in infrared detectors,^1–3 in resistance-switches and nonvolatile memory devices.^4–6 Ag₂S QDs can be used in the manufacture of nanocomposite photocatalysts and materials for conversion of solar energy into electrical energy.^7,8 Stable Ag₂S QDs possess high fluorescence emission from the UV to NIR region.

Nanostructured silver sulfide including quantum dots has been produced by different methods such as hydrochemical deposition, template method, sol–gel method, synthesis in microemulsions, as well as by sonochemical, hydrothermal, solvothermal, electrochemical, microwave and other techniques. Detailed description of various methods for the synthesis of nanostructured silver sulfide is given in review.⁹ However, many of these methods are not universal and allow synthesis of nanostructured silver sulfide only in one form: either nanopowders, or films, or heteronanostructures. Bad control of the size and non-uniform broad size distribution of nanoparticles, use of multistage (3–4 stages) sequential processes, complicated technique and special defenders, the raised temperatures, rare and expensive reagents are the main disadvantages of many preparation methods of nanostructured Ag₂S.

Different synthetic methods of Ag₂S QDs have been summarized in review.¹⁰ Recently a group of Prof. J. G. Tang, using a reverse microemulsion approach, synthesized uniform 3–8 nm Ag₂S nanoparticles.^11,12

The chemical deposition from aqueous solutions is the most simple and widespread method used for the synthesis of nanocrystalline sulfide powders and colloidal solutions of sulfide quantum dots including Ag₂S QDs.

Usually colloidal solutions of silver sulfide synthesize by hydrochemical deposition from aqueous solutions of silver nitrate AgNO₃ and sodium sulfide Na₂S. Solution of trisodium citrate dihydrate (sodium citrate) Na₃C₆H₅O₇·2H₂O≡Na₃Cit uses as an electrostatic stabilizer, disodium salt of ethylenediaminetetraacetic acid (Trilon B) is used as the complexing agent. Chemical deposition with using sodium citrate Na₃Cit is a well-known, simple and reliable universal green method which allows preparing colloidal solutions of Ag₂S QDs.

Not only homogeneous size distribution, but also the exact control of the real form (sphere, ellipsoid etc.) of Ag₂S QDs is required for their application in electronic and optoelectronic devices.

Modern diagnostics of nanosystems uses various types of radiation to obtain information about the structure of nano-objects in volume and on surfaces. The special properties of low-energy neutrons with a wavelength of about 0.15 nm (1.5 Å), which include thermal and cold neutrons, make it possible to effectively use their scattering in studies of solids, liquids, and colloidal systems. Neutron diffraction methods, in particular small-angle neutron scattering (SANS),^13–15 are sensitive to structural organization features at a level of 1–100 nm.

Small angle scattering of X-rays (SAXS) and neutrons (SANS) is one of the most effective methods for studying structures with sizes from one to several hundred nanometers. The diffraction pattern is the result of interference of rays scattered elastically and coherently on the sample, that is, without changing the wavelength and phase. The main advantage of small-angle scattering is the possibility of using it to study disordered objects and in the absence of the need for special sample preparation. The basic formulas that relate the scattering intensity to the structure of an object are determined only by the scattering power of the inhomogeneities and the contrast of their electron density with respect to the main matrix.^13,14,16 Thus, small-angle scattering allows one to study objects of various physical nature and state of aggregation, including nanoparticles in an amorphous matrix (glass) or colloidal particles (quantum dots) in solution.^17,18 Small-angle neutron scattering is generally applicable for studying the structure, shape (ball, ellipsoid, prism, cylinder, etc.), the ratio of the length and width of nanoparticles smaller than 100 nm in size.

When studying colloidal solutions by the small-angle neutron scattering, it should be taken into account that the irradiating neutrons from the reactor practically does not scattered on the nucleus of a hydrogen atom, but is absorbed by the hydrogen. Therefore, when using ordinary water as a solvent, the diffraction pattern is practically impossible to obtain. In addition to the proton, a neutron is present in the nucleus of a deuterium atom; therefore, neutrons from a reactor are scattered elastically on the deuterium nucleus. For this reason, to study the structure of colloidal solutions by small angle neutron scattering, heavy water D₂O should be used as a solvent instead of ordinary H₂O water. Indeed, coherent scattering amplitudes of hydrogen and deuterium atoms differ in magnitude and sign. This leads to the fact that the densities of coherent scattering amplitudes of light and heavy water also differ in magnitude and sign (−0.56 × 10¹⁰ cm⁻² and +6.39 × 10¹⁰ cm⁻², respectively).^19,20

In small-angle neutron scattering, contrast variation plays an important role in studying the fine structure of nano-objects. The use of heavy water or a mixture of light and heavy water changes the scattering contrast between particles and solvent and allows us to study the heterogeneity of nano-objects.^19,21 Measurements in heavy water can significantly reduce the concentration of the studied colloidal solutions compared to the concentration of colloidal solutions obtained using ordinary (light) water. Small-angle neutron scattering covers the wavelength range from 0.1 to 2.0 nm (1–20 Å), which corresponds to scattering vectors from 1 to 10⁻⁶ Å⁻¹.¹⁹ Such a wide range of scattering vectors allows the study of colloidal solutions with a very low concentration of nanoparticles.

To study colloidal solutions using small angle neutron scattering, it is most effective to use colloidal solutions obtained using heavy water.

It is known that the solvent has a significant effect on the rate of chemical reactions, which is associated, in particular, with the dielectric constant of the solvent. The dielectric constant of ordinary H₂O water and heavy D₂O water at room temperature is ∼81.0 and 78.2, respectively. Reactions involving D₂O usually proceed at a slower rate than with H₂O, and the solubility of salts in heavy water is slightly less (5–10%) than in ordinary H₂O.²² Recently, the difference between the standard reduction potentials of H₂O and D₂O during hydrothermal synthesis of iron-containing solids has been established.²³ However, the effect of heavy water on the dissolution of salts has been studied very poorly, and the formation of sulfide colloidal solutions in heavy water has not been studied at all.

Nobody has obtained colloidal solutions of silver sulfide in heavy water, suitable for studying by small-angle neutron scattering. An essential property of these colloidal solutions should be their stability. In the literature there is no information about such colloidal solutions. From private reports it is known that attempts to synthesize stable colloidal solutions of silver sulfide in heavy water were failed. For example, stable colloidal solutions of Ag₂S in ordinary water can be synthesized in solutions of silver nitrate AgNO₃, sodium sulfide Na₂S using 3-mercaptopropyl-trimethoxysilane (MPS) HSC₃H₆Si(OCH₃)₃ (C₆H₁₆O₃SSi) as a stabilizer.²⁴ However, with the same synthesis in D₂O heavy water using MPS, colloidal silver sulfide solutions are unstable: Ag₂S nanoparticles precipitate 3–4 days after the synthesis of solutions.

Present work is devoted to study of the synthesis of stable colloidal solutions of silver sulfide in D₂O heavy water as a solvent. Such research is carried out for the first time in the world. The main characteristics of Ag₂S quantum dots synthesized in colloidal solutions of silver sulfide in heavy water are determined. Potentially synthesized colloidal solutions are intended for the subsequent study of the real fine structure of Ag₂S quantum dots using small-angle neutron scattering. The study of fine structure is not available for other methods. Direct measurements of synthesized colloidal solutions by small-angle neutron scattering will be the subject of independent research.

2. Experimental

For the synthesis of colloidal solutions of Ag₂S based on D₂O, the same procedure was used as for the synthesis of colloidal solutions based on H₂O described in study.²⁵ Colloidal solutions of Ag₂S were synthesized by chemical deposition from aqueous solutions of silver nitrate AgNO₃, sodium sulfide Na₂S and sodium citrate Na₃C₆H₅O₇≡Na₃Cit in high-purity deionized heavy water D₂O. The D₂O content in the used heavy water was not less than 99.9 mol%, the admixture of light water H₂O was less than 0.1 mol%. The electrical conductivity of heavy water did not exceed 5 μS cm⁻¹ = 0.0005 S m⁻¹.

A transparent stable colloidal solution with a solid dispersed phase of Ag₂S (nano-Ag₂S) was obtained by chemical deposition in D₂O heavy water. Solutions of sodium sulfide Na₂S and silver nitrate Ag(NO₃)₂ in heavy water with the same concentrations of 50 mmol L⁻¹ were used as initial solutions. It was shown earlier²² that reaction mixtures with such concentrations are supersaturated by silver and sulfur ions; therefore, the synthesis of Ag₂S was carried out for a very short time.

The synthesis was carried out at a temperature of 298 K in the dark. Sodium citrate in the synthesis of Ag₂S in heavy water D₂O plays the role of a stabilizing agent to prevent nanoparticle growth. The stabilizing role of sodium citrate in the hydrochemical synthesis of nanostructured silver sulfide in ordinary (light) water was described earlier in study.^9,25–28 In colloidal solutions of Ag₂S QDs in heavy water, citrate ions are attached on the surface of the Ag₂S nanoparticles and form a negatively charged citrate layer, which prevents sulfide nanoparticles from coming together.

In aqueous solutions with low S²⁻ ion concentration, sodium citrate can reduce Ag⁺ ions to form silver metal nanoparticles^9,26–28 and form a citrate shell on Ag₂S particles.^9,29–33 Therefore, to obtain colloidal solutions of silver sulfide without Ag impurities and without a citrate shell, reaction mixtures with a small relative excess of sodium sulfide Na₂S and a minimum concentration of Na₃Cit were used. The synthesis was carried out in the dark in a neutral medium at pH ≈ 7 by the following reaction scheme

where 0.01 ≥ δ ≥ 0.5 is a small excess of Na₂S, needed for synthesizing Ag₂S colloidal solutions without admixture of Ag.

For the synthesis, solutions of AgNO₃, Na₂S, and Na₃Cit previously prepared in heavy water D₂O were used. The synthesis was performed in the following order: to 5 mL of a silver nitrate solution was poured in 5 mL of a sodium citrate (stabilizer) solution, and the resulting solution was mixed with 10 mL of a Na₂S solution for 1–2 seconds.

The stable colloidal solutions with Ag₂S quantum dots with an average size less than 20 nm were prepared from reaction mixtures 1–8 with silver nitrate concentrations C_AgNO3 from 0.3125 to 2.5 mmol L⁻¹ (Table 1). Earlier, reaction mixtures of the same compositions were used for the synthesis of Ag₂S colloidal solutions in ordinary H₂O water.²⁵ The identical reaction mixtures were used to compare the sizes of Ag₂S nanoparticles synthesized in aqueous colloidal solutions on heavy D₂O and ordinary H₂O water.

Table 1 Composition of reaction mixtures and average size D of silver sulfide quantum dots in colloidal solutions

No.	Reagent concentration in the reaction mixtures (mmol L^−1)			D (nm), (synthesis in D2O)			D (nm),^25 (synthesis in H2O)
	AgNO3	Na2S	Na3Cit	DDLS ± 0.5^a	DDLS ± 0.5^b	DTEM	DDLS ± 0.5^a	DTEM
a Quantum dot size corresponding to the maximum of DDLS size distribution.b The average quantum dot size according to DLS data.
1	0.3125	0.165	5	3.1	3.5	2–3	2.3	2–3
2	0.3125	0.168	2.5	4.2	5.1	3–5	2.7	2–3
3	0.3125	0.170	1	6.5	7.9	6–7	3.1	2–4
4	0.625	0.313	5	8.7	10.1	8–9	4.2	3–4
5	0.625	0.325	3.75	10.1	10.7	8–10	5.6	5–6
6	2.5	1.30	1	11.7	14.2	10–12	8.0	8–10
7	0.625	0.330	2.5	15.7	17.3	15–16	9.2	8–10
8	0.625	0.335	1.25	18.7	20.0	18–20	10.0	9–11

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The size (hydrodynamic diameter D_DLS) of Ag₂S quantum dots and the zeta potential ζ were determined directly in the colloidal solutions by non-invasive Dynamic Light Scattering (DLS) method on a Zetasizer Nano ZS facility (Malvern Instruments Ltd.) at a temperature of 298 K. The He–Ne laser with radiation wavelength 633 nm was used as a radiation source, and the detection angle of backscattered light was 173°. To provide the reproducibility of results, the scattering of light and the size of particles was measured in each solution no less than three times. The conductivity of synthesized colloidal solutions was also determined on a Zetasizer Nano ZS instrument.

The synthesized colloidal solutions were dried by sublimation methods in an Alpha 1–2 LD plus freeze dryer (Martin Christ) at an ice condenser temperature of −55 °C (218 K). Dried powders of nanostructured silver sulfide stored in a Vacuum Desiccator Sanplatec MB, evacuated to a residual pressure of 13.3 Pa (0.1 mm Hg).

Dried silver sulfide powders were examined by X-ray diffraction (XRD) method on a Shimadzu XRD-7000 diffractometer in Cu Kα_1,2 radiation. X-ray measurements were performed in the angle interval 2θ = 20–95° with a step of Δ(2θ) = 0.02° and scanning time 20 s in each point. The determination of the crystal lattice parameters and final refinement of the structure of the synthesized sulfide powders were carried out with the use of the X'Pert Plus software suite.³⁴

The JEOL JEM-2010 transmission electron microscope with 0.14 nm (1.4 Å) lattice resolution was also used to determine the size of Ag₂S quantum dots. The elemental chemical composition of Ag₂S quantum dots was studied on the same microscope with the use of an Phoenix (EDAX) Energy Dispersive Spectrometer with a Si(Li) detector having energy resolution of 130 eV. Colloidal solutions of Ag₂S quantum dots were placed on a copper grid for examination. A copper grid with an aperture diameter of 50 μm was used for TEM observing of nanoparticles. Additionally, one or two layers of hydrocarbon-glue were applied to copper grid.

In addition, the average particle size D (to be more precise, the average size of coherent scattering regions (CSR)) in synthesized dried silver sulfide nanopowders was estimated by XRD method from the diffraction reflection broadening using the dependence of reduced reflection broadening β*(2θ) = [β(2θ)cos θ]/λ on the scattering vector s = (2 sin θ)/λ.³⁵

UV-vis absorption spectra of colloidal solutions of Ag₂S QDs were recorded on a Shimadzu UV-2401 PC spectrophotometer at room temperature.

The photoluminescence (PL) emission spectra of quantum dots were measured under an excitation of 658 nm on a spectrometer FLS920 (Edinburgh Instrument).

3. Discussion

The XRD pattern of silver sulfide nanopowder obtained by sublimation drying of colloidal solution 6 in heavy water D₂O (Table 1) is shown in Fig. 1a. The diffraction reflections of the nanopowder are strongly broadened and therefore the reflections located close to each other overlap. For comparison, the XRD pattern³⁶ of larger Ag₂S nanopowder with particle size ∼45 nm deposited from reaction mixture of AgNO₃, Na₂S and Na₃Cit with concentrations 50.0, 25.4 and 25.0 mmol L⁻¹, respectively, is shown in Fig. 1b. A quantitative refinement of the structure of the nanopowder obtained from colloidal solution 6 was carried out using the X'Pert HighScore Plus software package.³⁴ Structure refinement and its comparison with the data of studies^36,37 has shown that the observed set of diffraction reflections corresponds to monoclinic (space group P2₁/c) silver sulfide with α-Ag₂S acanthite-type structure. The composition of this nanopowder corresponds to nonstoichiometric silver sulfide Ag_1.93±0.02S_1.00±0.01. The average size D of CSR estimated from the broadening of non-overlapping diffraction reflections is 12 ± 4 nm. The size of Ag₂S QDs according to DLS and TEM is about 12 nm.

Fig. 1 XRD pattern (a) of nanocrystalline silver sulfide with a monoclinic (space group P2₁/c) structure of α-Ag₂S acanthite obtained from colloidal solution 6 in D₂O heavy water (Table 1). For comparison, an XRD pattern³³ (b) of a larger nanopowder of monoclinic silver sulfide with a particle size of ∼40–45 nm is shown.

The size distributions of Ag₂S quantum dots in synthesized colloidal solutions, measured by the DLS method, are shown in Fig. 2.

Fig. 2 Size distributions of silver sulfide QDS in colloidal solutions 1–8, measured by the DLS method. The numbering of DLS curves corresponds to the colloidal solutions 1–8 in Table 1. Size D is presented in logarithmic coordinates.

According to DLS data, the average size of Ag₂S quantum dots in colloidal solutions no. 1–8 does not exceed 20 nm (Fig. 2). The quantum dot size corresponding to the maxima of the size distributions D_DLS is from 2 to 10 nm (Table 1), and the average quantum dot size D_aver in the obtained colloidal solutions varies from ∼3 to ∼11 nm. With an increase in the concentration of silver nitrate in the initial reaction mixtures, the size of Ag₂S quantum dots in the synthesized colloidal solutions increases slightly. A decrease in the concentration of sodium citrate, all other things being equal, leads to a decrease in the stabilizing effect of Na₃Cit and is also accompanied by some increase in the size of Ag₂S quantum dots (Table 1).

The size of Ag₂S quantum dots in colloidal solutions synthesized in D₂O heavy water is slightly larger than in colloidal solutions in ordinary H₂O water (see Table 1). This may be the result of a slightly lower solubility of sodium citrate in heavy water compared to ordinary water²¹ and, as a result, a slight weakening of the stabilizing effect of sodium citrate. However, the qualitative effect of reagent concentrations on the size of silver sulfide quantum dots in colloidal solutions synthesized using heavy water is the same as in colloidal solutions in ordinary H₂O water.²⁵

It is known that the zeta potential ζ of quantum dots or nanoparticles in a solution is an indicator of the system stability.^38,39 The absolute values ±(35 ± 15) mV of zeta potential are indicative of electrostatic stability of colloidal solutions. The particles with highly negative or positive surface electric charge are considered as stable particles. The DLS measurements revealed that three days after synthesis of solutions 1–8 their zeta potential ζ was −28 to −18 mV, and the quantum dot size was equal to 3–19 nm. The zeta potential ζ and the size of Ag₂S quantum dots measured 100 days after synthesis of colloidal solutions remained almost unchanged. Small variation of the zeta potential during long-term storage of colloidal solutions and a large negative value of the zeta potential of solutions 1–8 confirm their stability. The conductivity of the synthesized colloidal solutions ranged from 0.067 to 0.108 S m⁻¹. An increase in the conductivity of colloidal solutions in comparison with the heavy D₂O water used confirms the presence of quantum dots with electric charges in solutions. Thus, silver sulfide colloidal solutions synthesized using D₂O heavy water retained the stability and unchanged QDs size after storage for more than 100 days, i.e., they have the same high stability as colloidal solutions synthesized in ordinary water.

Transmission electron microscopy (TEM) confirmed the small size of the Ag₂S quantum dots in the synthesized colloidal solutions.

A TEM image of quantum dots contained in a colloidal solution obtained from reaction mixture 3 with a minimum concentration of sodium citrate is shown in Fig. 3. The size of most quantum dots is from 6 to 7 nm. This is consistent with measurements of the size distribution of Ag₂S quantum dots in this solution by dynamic light scattering (see Fig. 2). As an example, HRTEM image of a quantum dot about 6 nm in size is shown in Fig. 3a. The selected area of electron diffraction (Fig. 3b) was calculated using the Fast Fourier Transform (FFT)⁴⁰ of HRTEM image of this quantum dot. A detailed description of the Fast Fourier Transform using the Gatan Microscopy Suite program³⁷ is given on the site.⁴¹ The observed electron diffraction spots (011) and (1−02) correspond to the [21−1] plane of the reciprocal lattice of monoclinic (space group P2₁/c) silver sulfide with α-Ag₂S acanthite structure. To reliably identify the observed diffraction reflections and their indices, it is necessary to calculate the angle φ_refl between the reflections with the expected indices (h_ik_il_i) on the selected area of electron diffraction, i.e., the angle between the lines passing through each reflection and the central spot (000). The coincidence of the estimated and experimental φ_refl angles unequivocally proves that the indices (h_ik_il_i) are determined correctly.

Fig. 3 TEM image of colloidal solution 3 (Table 1). (a) HRTEM image of a quantum dot about 6 nm in size; (b) the selected area of electron diffraction calculated by fast Fourier transform of HRTEM image of this quantum dot.

According to study,⁴² the formula for determining the φ_refl angle between the reflections (h₁k₁l₁)_mon and (h₂k₂l₂)_mon in the reciprocal lattice of the monoclinic structure has the form

where with i = 1 or 2.

In Fig. 3b, the angle between the supposed reflections (011) and (−102) is ∼76°. The calculated angle between reflections with such indices for monoclinic silver sulfide should be 76.4° and coincides with the observed angle. Consequently, the reflection indices are defined correctly. The analysis has shown that these reflections are observed along the [2−11] zone axis.

Analysis of the HRTEM image (Fig. 3) confirmed that, as a result of synthesis in colloidal solutions in heavy water, monoclinic (space group P2₁/c) silver sulfide with α-Ag₂S acanthite structure is actually formed.

Fig. 4 show TEM images of colloidal solutions 4 and 5. It is seen that the size of silver sulfide quantum dots in colloidal solution 4 is from 8 to 9 nm (Fig. 4a). According to TEM, the size of silver sulfide quantum dots in colloidal solution 8–10 nm (Fig. 4b).

Fig. 4 TEM images (a) and (b) of colloidal solutions 4 and 5, respectively. The numbering corresponds to the Table 1.

Larger silver sulfide quantum dots are observed in colloidal solution 6: the Ag₂S quantum dot from this solution has a size of ∼12 nm (Fig. 5). Fig. 5 clearly shows the interplanar distance 0.187 nm, which coincides with the distance between the atomic planes (014) of silver sulfide with monoclinic (space group P2₁/c) structure of the α-Ag₂S acanthite type.^37,43,44 The inset shows the EDX spectrum of Ag₂S nanoparticles from colloidal solution 6.

Fig. 5 HRTEM image of a silver sulfide quantum dot from colloidal solution 6 (Table 1). The inset shows the EDX spectrum of Ag₂S nanoparticles.

TEM images of colloidal solutions, as well as the sizes of quantum dots according to TEM which given in Table 1, confirm the results of DLS measurements of quantum dot size.

In the EDX spectra obtained using a JEOL JEM-2100 transmission electron microscope, in addition to silver and sulfur, Kα lines of copper Cu from the copper grid are observed, on which the quantum dots under study and a weak Kα line of carbon C from the glue were applied (see Fig. 5, inset). A source of carbon C in colloidal solutions of silver sulfide is also an admixture of the initial reagent – sodium citrate Na₃Cit. The sodium citrate solution is adsorbed on the surface of Ag₂S quantum dots. According to EDX data, impurity oxygen is also present in silver sulfide quantum dots, which is distributed over the surface of the particles, which is reflected in the presence of a weak Kα line of oxygen at 0.525 keV.

According to the EDX results (Fig. 5, inset), minus the impurity elements, the silver and sulfur contents in the synthesized silver sulfide are 83.4 ± 0.5 and 12.8 ± 0.2 wt%, which corresponds to silver sulfide Ag_1.96±0.02S_1.00±0.01.

The UV-vis absorption spectra of colloidal solutions 1–8 are displayed in Fig. 6. According to the DLS data, the size of Ag₂S QDs in these solutions changes from to 3.1 to 18.7 nm. The UV-vis absorption spectra of the investigated colloidal solutions reveal wide bands (Fig. 6) characteristic of semiconductor QDs in the region from 280 to 800 nm (4.40–1.55 eV) associated with the ground state exciton absorption.

Fig. 6 The UV-vis absorption spectra of colloidal solutions of Ag₂S QDs 60 days after synthesis. The weak absorption peak observed in the spectra of solutions with a quantum dots of size 3.1, 4.2, 6.5, and 8.7 nm at wavelength λ about 280–310 nm corresponds to Ag₂S QDs. The positions of ground state exciton absorption are marked by arrows.

The weak absorption peak observed at ∼280–310 nm corresponds to Ag₂S nanoparticles.^45,46 This weak absorption peak is absent in the absorption spectra of Ag₂S QDs with a size more than 8.7 nm. Considering a large experimental data array,^47–49 the absorption spectra of colloidal Ag₂S QDs do not contain a peak corresponding to the ground state exciton absorption. It can be assumed that the considerable contribution to the absorption band of colloidal QDs is associated with the nonstoichiometry of silver sulfide,³⁶ which is always accompanied by impurity absorption and leads to the absence of features in the absorption spectrum.

The position of the ground state exciton absorption band in the UV-vis absorption spectra of colloidal solutions 1–5 was found from the minimum of the second derivative for the optical absorption spectra with respect to the photon energy. These positions are marked by arrows in Fig. 6.

Fig. 7 presents the size-dependent photoluminescence (PL) emission spectra of Ag₂S colloidal solutions 1–5 in which the fluorescence of Ag₂S quantum dots is tunable from ∼1090 to ∼1182 nm by increasing the nanoparticle size D_DLS from 3.1 to 10.1 nm. PL emission spectra of colloidal solutions 5, 6, 7, and 8 with Ag₂S quantum dots larger 8 nm practically coincide; therefore, only the spectrum of colloidal solution 5 is shown in Fig. 7.

Fig. 7 The size-dependent PL emission spectra of Ag₂S colloidal solutions 1–5 with quantum dots of size D_DLS from 3.1 to 10.1 nm under an excitation of 658 nm. For comparison, dashed line show the position of PL emission peak for Ag₂S quantum dots with a size ∼1.5 nm.⁵⁰ The wavelengths corresponding to the maxima of the PL peaks are indicated.

According to,⁵⁰ the PL peak for Ag₂S quantum dot with a size about 1.5 nm is observed at a wavelength of ∼640 nm (see Fig. 7); the PL emission spectrum of Ag₂S QD with a size about 1.5 nm was measured under an excitation of 785 nm. Perhaps, there was a misprint in study⁵⁰ because generally the PL emission wavelength of the sample is longer than it's the excitation wavelength. In study⁵⁰ water-soluble Ag₂S quantum dots have been synthesized at heating of mixed solution of mercaptopropionic acid, ethylene glycol, and silver nitrate AgNO₃. The PL emission peaks shift from ∼1090 to ∼1182 nm with the size of Ag₂S quantum dots increasing from ∼3.1 to 10.1 nm and keep constant at 1182–1190 nm with increase of the quantum dot size from ∼10.1 to 16 nm and further. The continuous blue shift of the PL emission of Ag₂S quantum dots from ∼1182 to ∼640 nm may be attributed to the strengthened quantum confinement effect and increasing the band gap E_g which resulted from the decreasing Ag₂S quantum dots size (band gap of bulk monoclinic Ag₂S crystals is about 1.0 eV).^25,51 Almost constant position of the PL emission peaks at ∼1140–1180 nm for the Ag₂S quantum dots with a boundary value of size 4.2 nm and larger is evidence for transition from the strong quantum confinement regime to the weak quantum confinement regime. The absence of quantum confinement for semiconductor Ag₂S nanocrystals larger 4 nm is in good agreement with the data.^51–53 Thus, we experimentally estimated Ag₂S exciton radius R_ex as less than half of boundary value of size 4.2 nm, i.e. ≤2.1 nm.

According to,⁵⁴ the characteristic size of the Wannier–Mott exciton (or the Bohr radius of the of the first exciton state) in the macroscopic semiconductor is determined by the equation

where h = 1.055 × 10⁻²⁷ cm² g s⁻¹ is the reduced Planck constant, e = 4.803 × 10⁻¹⁰ cm^3/2 g^1/2 s⁻¹ is the charge on the electron, μ_ex = m_em_h/(m_e + m_h) is the reduced exciton mass, and m_e and m_h are the electron and hole effective masses. For Ag₂S, dielectric constant ε is about 6, m_e = 0.286m₀ and m_h = 1.096m₀ (m₀ = 9.1095 × 10⁻²⁸ g is the free electron mass),⁵⁵ respectively. Taking this into account, the reduced exciton mass μ_ex for acanthite α-Ag₂S is equal ∼0.23m₀. At such values of ε, m_e and m_h, the Ag₂S exciton radius R_ex which is calculated by the formula (3) is equal to ∼1.4 ± 0.1 nm, and the exciton diameter is about 2.8 nm. However in study⁵⁵ there are no data on the Brillouin zones estimation or measurement of effective masses by cyclotron resonance. Other effective masses of carriers are given in study:⁵¹ m_e = 0.42m₀ and m_h = 0.81m₀. These effective masses of electron and hole have been calculated for the lowest conduction band and the highest valence band centered at Г point of the Brillouin zone of Ag₂S, respectively. Apparently, results of study⁵¹ on the electron and hole effective masses are more correct. According to,⁵⁶ real part of dielectric constant ε of silver sulfide is equal to 8.36. For these values m_e, m_h and ε exciton mass μ_ex is ∼0.28m₀, exciton radius R_ex is equal to ∼1.6 ± 0.1 nm, and the exciton diameter is ∼3.2 nm.

Found exciton diameter ∼3 ± 0.2 nm of silver sulfide is in satisfactory agreement with experimentally estimated Ag₂S exciton diameter ∼4.2 nm which follows from the size-dependent PL emission spectra (see Fig. 7).

Photoluminescence bands of Ag₂S colloidal solutions 1–5 (Fig. 7) are distinguished by the significant Stokes shift of luminescence peaks relative to the position of ground state exciton absorption (see Fig. 6), which increases slightly with decreasing the QD size. The Stokes shift values lie at 0.93–0.99 eV. Fig. 8 shows the change in energies corresponding to the luminescence peaks of colloidal solutions 1–8, depending on the size (diameter) of the Ag₂S QDs. It is clearly illustrated that there is no obvious blue shift of either excitonic energy until the size of QDs is below ∼5 nm. As the QD size D → ∞ increases, the deviation of the excitonic ground state energy from the band gap value of bulk Ag₂S allows one to estimate the exciton binding energy. According to the estimate, it is about 0.05 eV. This is quite close to the exciton binding energy value found in study⁵¹ and equal to 0.096 eV.

Fig. 8 Exciton energy change with the decreasing of Ag₂S QDs size. Black points are the experimental PL energies, corresponding Fig. 7. Band gap of bulk Ag₂S is shown by dashed line.

4. Conclusion

For the first time, colloidal solutions of silver sulfide quantum dots were synthesized in heavy water D₂O. The synthesized colloidal solutions retain stability and small size of the quantum dots during long-term storage for more than 100 days. The high stability of colloidal solutions synthesized in heavy water is confirmed also by the large negative value of their zeta potential.

Sodium citrate in the synthesis of Ag₂S in heavy water D₂O plays the role of a stabilizing agent. In colloidal solutions of Ag₂S QDs in heavy water, citrate ions are attached on the surface of the Ag₂S QDs and form a negatively charged citrate layer, which prevents sulfide quantum dots from coming together.

The study of colloidal solutions of silver sulfide synthesized in D₂O heavy water by dynamic light scattering, transmission electron microscopy, and X-ray energy dispersive analysis has shown that under these synthesis conditions it was possible to obtain colloidal solutions with silver sulfide QDs from 3 to 19 nm in size with monoclinic (space group P2₁/c) α-Ag₂S acanthite structure. Changing the concentration of reagents in the reaction mixtures allows us to control the size of silver sulfide QDs in the resulting colloidal solutions in the range from 2–3 to 20 nm.

An increase in the concentration of silver nitrate and a decrease in the concentration of sodium citrate in the initial reaction mixtures lead to a small increase in the size of Ag₂S QDs in the synthesized colloidal solutions no. 1–5. The size of Ag₂S quantum dots in colloidal solutions synthesized in D₂O heavy water is slightly (by 1–2 nm) larger than in colloidal solutions in ordinary H₂O water. This is evidence of the specific of synthesis and stabilization of colloidal particles of silver sulfide in heavy water compared to ordinary water. It can be assumed that the difference in the size of the quantum dots is associated with different properties of the dispersed medium (heavy and ordinary water), in particular, with a lower solubility of sodium citrate in heavy water compared to ordinary water that leads to a slight weakening of the stabilizing effect of sodium citrate.

The prepared colloidal solutions are suitable for studying the structure of silver sulfide quantum dots by the method of small-angle neutron scattering.

Author contributions

Stanislav I. Sadovnikov: ideas and formulation of research aims, methodology, synthesis and investigations, validation, writing – review and editing, supervision. Aleksandr I. Gusev: analysis of the data, writing – original draft, project administration.

Conflicts of interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

The authors thank Dr Y. Kuznetsova for her help in the DLS measurement. This study was supported by the Russian Science Foundation (grant no. 19-73-20012) through the Institute of Solid State Chemistry of the Ural Branch of the RAS.

Notes and references

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