Size control mechanism of ZnO nanoparticles obtained in microwave solvothermal synthesis

Zinc acetate dihydrate (Zn(CH₃COO)₂ · 2H₂O, analytically pure, SKU: 112654906-1KG, Chempur); zinc acetate dihydrate (Zn(CH₃COO)₂ · 2H₂O, analytically pure, SKU: 265490116-1KG, Avantor Performance Materials Poland S.A.); dehydrated zinc acetate (Zn(CH₃COO)₂, analytically pure, SKU: 112654907-250G, Chempur); ethylene glycol (EG, ethane-1,2-diol, C₂H₄(OH)₂, pure, SKU: 114466303-5L, Chempur); diethylene glycol (DEG, 2-(2-hydroxyethoxy)ethanol, (C₂H₄OH)₂O, pure, Chempur); triethylene glycol (TEG, 2-[2-(2-hydroxyethoxy)ethoxy]ethanol, HOCH₂(C₂H₄O)₂CH₂OH, analytically pure, SKU: T59455-1L Sigma-Aldrich); tetraethylene glycol (TTEG, 2-[2-[2-(2-hydroxyethoxy)ethoxy]ethoxy]ethanol, HOCH₂(C₂H₄O)₃CH₂OH, analytically pure, SKU: 110175-1KG Sigma-Aldrich) and deuterium oxide (D₂O, 99.9 atom% D, SKU: 151882-100G, Sigma-Aldrich), were used. All the reagents were used without additional purification. Deionised water with specific conductance below 0.1 μS cm⁻¹ was obtained using a deioniser (HLP 20UV, Hydrolab).

ZnO NPs syntheses were carried out in accordance with the procedure included in our earlier publications [12, 38, 39]. The reaction precursor, 1500 ml of solution of zinc acetate hydrate in EG (0.3037 mol dm⁻³), was prepared using a hot-plate magnetic stirrer (SLR, SI Analytics, Germany) at the constant temperature of 70 °C, stirring speed of 450 rpm. After complete dissolution of zinc acetate, the solution was poured to two 1000 ml PP bottles and closed tightly. After cooling down to the room temperature (RT), an analysis of water content in the precursor was carried out (1.05 ± 0.03 wt% of H₂O). An appropriate calculated amount of D₂O was added to the precursor to obtain the water content being 1.5 wt% and 4 wt%, and subsequently the solution was stirred again and an analysis of water content in the prepared precursor was carried out. Then 75 ml of the solution was poured into a 110 ml Teflon^® reaction container and closed tightly.

The reaction, initiated with microwave radiation, was carried out in a Magnum 02-02 reactor (600 W, 2.45 GHz, ERTEC). The durations of individual synthesis reactions were 5, 6, 7.5, 10, 15, 20 and 25 min; temperature 190 °C; capacity 100%, and after that the reaction container was cooled down for 20 min. After the synthesis, the obtained powder was sedimented, rinsed three times with deionized water, centrifuged (MPW-350, MPW Med Instruments) and dried in a freeze dryer (Lyovac GT-2, SRK Systemtechnik GmbH).

Diffraction patterns of the x-ray powder diffraction (XRD) were gathered at the RT within the range of 2 theta angle from 10° to 100° with the step of 0.02°, using the x-ray powder diffractometer (CuK_α1) (X'Pert PRO, Panalytical) [41]. The full width at half maximum was determined by the Pearson VII function implemented in Fityk software, version 0.9.8. Based on the diffraction patterns, the size of crystallites was determined in the direction of the crystallographic axes a and c using Scherrer's formula [12, 39].

The analysis of XRD peak profile was performed using the analytical formula for polydispersive powders [42]. This technique provides four parameters: average crystallite size, deviation of the average crystallite size, dispersion of size and deviation of dispersion of sizes. Hence, a full crystallite size distribution curve and an estimation of 'thickness' of this curve (deviation bars) are obtained.

For calculating the crystallite diameter and size distribution, the Nanopowder XRD Processor Demo web application employs equations dedicated to spherical crystallites. The website http://science24.com/xrd provides an on-line tool where diffraction files can be directly dropped [43]. The files are processed on a server to extract particle size distribution for XRD peaks [44]. Unlike the standard fitting, the tool does not act in the reciprocal space but solves all sets of equations in a few auxiliary spaces simultaneously. This allows an analysis of XRD data with heavily convoluted reciprocal space peaks.

Skeleton density (pycnometric density) measurements were carried out using the helium pycnometer [45] (AccuPyc II 1340, FoamPyc V1.06, Micromeritics), the measurements were carried out in accordance with ISO 12154:2014 at the temperature of 25 ± 2 °C. The SSA of NPs was determined using the surface analyser (Gemini 2360, V 2.01, Micromeritics) by the nitrogen adsorption–desorption method based on the linear form of the Brunauer–Emmett–Teller isotherm equation, in accordance with ISO 9277:2010. Prior to performing measurements of density and SSA, the ZnO samples were subjected to 2 h desorption (VacPrep 061, Micromeritics), under vacuum (0.05 mbar) at the temperature of 150 °C. The samples with the intermediate were subjected to 8 h desorption under vacuum (0.05 mbar) at the temperature of 60 °C. Based on the determined SSA and skeleton density, the average size of particles defining their diameter was determined, with the assumption that all particles are spherical and identical. The equation used for calculating the average particle size can be found in our earlier publications [12, 38, 39].

The morphology of NPs was determined using the SEM (ZEISS, ULTRA PLUS). Powder samples were coated with a thin carbon layer using the sputter coater (SCD 005/CEA 035, BAL-TEC). An internal laboratory measurement procedure was applied (P5.10, edition 6 of 26.08.2015).

The morphology of the nanopowder samples was examined using transmission electron microscopy (TEM—Talos F200X). The TEM tests using the dark field (DF) and selected area electron diffraction were conducted at 200 kV. High-resolution (HRTEM) tests were conducted at 300 kV. The specimens for the TEM observations were prepared by dropping the ethanol particle dispersion, created by an ultrasonic technique, on a carbon film supported on a 300 mesh copper grid. TEM tests were used to determine the nanoparticle size distribution. The grain size histograms were obtained by considering a region of a sample having about 200 nanocrystals and approximating the shape of each nanocrystal by a sphere. The obtained histograms were fitted to log-normal distributions [12].

The quantitative analysis of water in the precursor was carried out in accordance with the assumptions of the Karl Fischer method using the coulometric titration technique with the titrator (Cou-Lo AquaMAX KF, GR Scientific) [12]. The following reagents were used for the analysis: Aquagent^®Coulometric OIL, cat. no. AQ00250100, Scharlau and Aquagent^®Coulometric CG, cat. no. AQ00230050, Scharlau. An internal laboratory measurement procedure was applied. Liquid samples were introduced to the titration vessel using a glass syringe (1 ml) with a Luer type needle. An analytical scales was used for weight measurement (WAA 100/C/1, RADWAG).

Reaction products were identified using GC-MS (Agilent 7890 B). Before the GC, injection samples (100 μl) were dissolved in trichloromethane (1 ml). An HP-5 capillary column (5% diphenyl and 95% dimethylpolysiloxane, 30 m × 0.25 mm × 0.25 μm) was applied. The injector was operated in splitless mode. The carrier gas was He and column flow rate was 1.2 ml min⁻¹. The following temperature programme was used for the analysis: initial temperature of 50 °C for 3 min, temperature rate of 10 °C min⁻¹ until 240 °C and final temperature of 240 °C for 20 min.

Before the GC-MS analysis, the samples of ZnO NPs suspended matter in EG were centrifuged with the centrifugal force of 24.270 g (MPW-251, MPW Med. Instruments) for 60 min.

A Bruker Tensor 27 infrared spectrometer, equipped with an attenuated total reflectance (ATR, model: Platinium ATR-Einheit A 255), was used for the FT-IR spectroscopy analysis. For each ATR-FT-IR spectrum, 100 scans within the range of 350–4000 cm⁻¹ with the resolution of 4 cm⁻¹ at RT were collected.

Before the FT-IR analysis, the samples of ZnO NPs suspended matter in EG were centrifuged with the centrifugal force of 24.270 g (MPW-251, MPW Med. Instruments) for 60 min at RT.

The TGA was carried out using the thermal analyzer (STA 449 F1 Jupiter^® Netzsch) from RT to 970 °C, with a heating rate of 5 °C min⁻¹ in an alumina crucible under synthetic air (40 ml min⁻¹). TGA's equipment error is 0.01 mg.

The elemental analysis of C and H was carried out using the Vario EL III device by Elementar in accordance with the manufacturer's recommendations.

Figures 1 and 2 present representative SEM images of the ZnO NPs synthesis products. SEM images 1(a)–(c), 2(a) show the lamellar structure of the obtained intermediate. We did not observe an impact of the synthesis duration on the thickness of the lamellar structures, which was 50 ± 6 nm. When comparing synthesis products with differing contents of H₂O in the precursors, differences in the obtained product types are noticeable for the same synthesis durations. For the H₂O content of 1.5 wt%, lamellar structures were obtained for synthesis durations of 5, 6 and 7.5 min. For the H₂O content of 4 wt%, in turn, lamellar structures were observed only in the sample with the synthesis duration of 6 min. It should be emphasised that for the synthesis duration of 5 min no solid product was obtained from the precursor with the 4% H₂O content, which probably results from the impact of the 4% H₂O content on the kinetics of the reaction of intermediate formation.

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Figures from 1(d)–(g) and from 2(c)–(f) present homogeneous ZnO NPs with the spherical shape. Figure 1(d) shows conglomerates of ZnO NPs with the shape resembling the structure of a cauliflower. The average size of particles obtained from the 1.5%H₂O precursor increases from ≈20 ± 3 nm (10 min, figure 1(d)) to ≈25 ± 5 nm (25 min, figure 1(g)). For the 4%H₂O precursor, the average size of ZnO NPs increases from ≈21 ± 5 nm (7.5 min, figure 1(b)) to ≈47 ± 7 nm (25 min, figure 2(f)). When viewing SEM photos for the synthesis products from the 4%H₂O precursor, we noticed growth of medium-size ZnO NPs by circa 20 nm, while for the 1.5% H₂O content in the precursor—by merely circa 3–5 nm.

XRD tests indicated the presence of only hexagonal phase ZnO (JCPDS card No. 36-1451) in the samples with synthesis durations of 10, 15, 20, 25 min obtained from 1.5%H₂O precursor (figure 2) and with synthesis durations of 7.5, 10, 15, 20, 25 min obtained from 4%H₂O precursor (figure 3). Figures 3 and 4 show differences between the widths of diffraction peaks of the ZnO phase. Namely, the observed decrease of the diffraction peaks width in line with the increase in the ZnO NPs synthesis duration means at the same time an increase in the crystallite size. The phase analysis of samples with the synthesis durations of 5, 6, 7.5 min (1.5%H₂O, figure 3) and with synthesis durations of 6 min (4%H₂O, figure 4) indicated the existence of only the phase of the intermediate, probably of Zn₅(OH)₈(CH₃COO)₂ · 2H₂O.

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The literature review revealed [46–48] that the hexagonal phase of Zn₅(OH)₈(CH₃COO)₂ · 2H₂O contains also peaks below 10°. In order to confirm the correctness of the phase analysis, extended XRD tests of the samples were carried out within the range of 2 theta angle from 5° to 65° at RT (figure 5). All diffraction peaks in figure 5 were attributed to the hexagonal phase of hydroxy-zinc acetate—Zn₅(OH)₈(CH₃COO)₂ · 2H₂O [46–48]. Zn₅(OH)₈(CH₃COO)₂ · 2H₂O is a monomer of lamellar sheet compounds and therefore it is also called lamellar hydroxy-zinc acetate (LHZA) [20]. The observable shifts of the position and the changes in the peak shapes in the diffraction patterns of LHZA compounds in figure 5 result from:

• -  
  the different quantity of OH⁻, CH₃COO⁻ function groups,
• -  
  the quantity of crystallisation water 'x', which may range from 1.5 to 4, depending on the synthesis method employed [20, 47–51],
• -  
  obtaining a hybrid material, e.g. Zn₅(OH)₈(CH₃COO)₂(C₂H₄(OH)₂)₂ · 2H₂O, through the process of EG intercalation between the layers of LHZA [52].

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In addition, possible changes in the lattice parameters in LHZA caused by the exchange of OH⁻ or CH₃COO⁻ groups by EG should be taken into account. Such cases are known where EG created a covalent bond with a metal in metal hydroxide layers, e.g. in brucite, boehmite and layered double hydroxides [53–58].

The interlamellar distances of intermediates that we calculated and presented in table 1 increase in line with the increase in the synthesis duration and with the increase in the H₂O content in the precursor. The interlamellar distance (001) of all the obtained samples are lower than 14.72 Å, i.e. for the interlamellar distance (001) of the reference sample of LHZA (JCPDS card No. 56-0569). Kasai et al [52] report that the decrease of the interlamellar distance (001) value below 14.72 Å in LHZA, which they observed, can be caused by a reduction of the quantity of CH₃COO⁻ groups and of crystallisation H₂O. The increase in the interlamellar distance (001) above 14.72 Å, in turn, is explained with EG intercalation [52]. We believe that, based on the results of interlamellar distance (001), intercalation of EG between the layers of LHZA cannot be excluded even if the interlamellar distance (001) value is below 14.72 Å without verifying the lack of presence of EG in the obtained LHZA samples. XRD results indicate that the LHZA compounds obtained by us were characterised by differing stoichiometry (different quantity of CH₃COO⁻, OH⁻, H₂O groups). The interlamellar distance (001), and at the same time stoichiometry, that was most similar to the reference sample of LHZA (JCPDS card No. 56-0569) was exhibited by ZnO-4%H₂O-6 min sample (table 1).

The empirical formulas of compounds were determined based on the obtained mass contents of C, H, Zn, O. The elemental analysis of C and H was carried out by the combustion method. Zn contents were calculated based on the results of mass loss of LHZA samples after their thermal decomposition to ZnO at 950 °C (figure 6). Contents of O, in turn, were calculated based on the following formula: O% = 100% − C% − H% − Zn% (table 2). We assumed that C% content in LHZA corresponds only to the carbon content in CH₃COO⁻ groups.

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In order to verify the determined empirical formulas of LHZA samples, theoretical calculations of C, H, Zn, O contents and of mass loss after their decomposition to ZnO were performed (table 2). Calculated percentages in table 2 are based on the ideal formulas. The obtained results of total %C content in the samples are consistent with the calculations that verified them (table 2). However, in the case of samples with C content exceeding 7.78%, i.e. for ZnO-1.5%H₂O-6 min and ZnO-1.5%H₂O-7.5 min, we presumed that the excess %C content was caused by the presence of EG in these samples. This was confirmed by TGA results (figure 6), where a shift of thermal stability towards higher temperatures was observed for ZnO-1.5%H₂O-6 min and ZnO-1.5%H₂O-7.5 min samples, which results from a high boiling point of EG (197.3 °C) [52]. EG in these samples may have been physically adsorbed on LHZA surface or intercalated between the layers of LHZA [46, 58]. The total thermal decomposition of the stoichiometric LHZA compound leads to a theoretical mass loss equal to 34.05% (table 2). Total mass losses observed in our samples ranged from 35.59% to 38.52% (table 2). Results of works by different research groups [20, 46–49, 51, 59], in turn, concerning the value of total LHZA mass loss were as follows: 32.15%, 37.4%, 38.4%, 39.7% and 43.9%. This means that the majority of the reported syntheses led to obtaining non-stoichiometric LHZA. Hosono et al [20] report that stoichiometry of LHZA depends on synthesis conditions. Kasai et al [52] note, in turn, that stoichiometry of LHZA changes depending on the time of its storage in EG at RT. Moreover, Moezii et al [49] observed partial decomposition of LHZA to ZnO during its storage in ethanol. The presented results prove that the stoichiometry of LHZA compounds depends not only on synthesis parameters but also on the duration of sample storage directly after the synthesis in the form of suspended matter in alcohols and polyols.

The results of the elemental analysis of our samples are consistent with the results of the phase analysis, where the shifts of LHZA phase peaks were explained with obtaining different stoichiometry (figure 5). The change in stoichiometry can be explained with a different share of the nucleation stage and the growth stage on the moment of synthesis finish for individual LHZA samples.

FT-IR spectra and spectral assignments of the samples are presented in figures 7, 8 and in table 3, respectively. The characteristic band coming from the stretching vibrations of –OH is observed primarily within the range between 2900 and 3600 cm⁻¹. Depending on the quantity of –OH groups, the process of intermolecular hydrogen bond formation intensifies, which can be an explanation of the shift of a broad band of -OH group from 3380 to 3450 cm⁻¹ in the obtained results (figure 7). Two bands with the maximums at 2930 and 2867 cm⁻¹ coming from symmetric and asymmetric stretching vibrations of C–H prove the presence of C₂H₄(OH)₂ or CH₃COO^- groups. Bands coming from the stretching vibrations of C–H were visible only in two LZHA samples with the carbon content exceeding 7.78%, which proved the presence of C₂H₄(OH)₂ in these samples. The spectra of ZnO-1.5%H₂O-6 min, ZnO-1.5%H₂O-7.5 min and ZnO-4%H₂O-6 min in figure 7 show a band at 2360 cm⁻¹, which comes from asymmetric stretching vibrations in CO₂, which means that a change in CO₂ content in atmospheric air occurred during the measurements of the samples (measurement background). Strong absorption bands with wavenumbers of 1573 and 1404 cm⁻¹ come from asymmetric and symmetric stretching vibrations of C=O group in CH₃COO⁻. Bands with frequencies of 1324 cm⁻¹ were attributed to symmetrically bending vibrations of –CH₃ groups in CH₃COO⁻. The band within the range of 1083–1030 cm⁻¹ observed in the spectra of samples with LHZA phase comes from asymmetrical stretching vibrations of C–O groups in C₂H₄(OH)₂. Presence of C₂H₄(OH)₂ in the samples is confirmed also by changes of band intensity within the range of 1083–1030 cm⁻¹, which are in proportion to the changes in carbon content (table 2, figure 7). FT-IR spectra of LHZA compounds obtained by us are consistent with the results of other authors [20, 46, 51–58] and confirmed the presence of CH₃COO⁻, OH⁻ groups and EG.

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The results of FT-IR, TGA tests and of the elemental analysis proved unambiguously that EG was present in two obtained LHZA samples. Nevertheless, it is possible that trace quantities of EG are present in the remaining samples. The empirical formulas of LHZA compounds that we determined can be flawed due to the failure to take into account EG content in their composition (table 2). EG in the samples could have been physically adsorbed on LHZA surface or intercalated between the layers of LHZA. All four LHZA samples were subjected to the same preparation process of both rinsing and drying, and therefore we believe that there was a greater likelihood that the EG present in two LHZA samples could be present within the interlamellar distance (001) rather than on LHZA surface.

The lack of absorption bands coming from vibrations of D₂O in dry LHZA samples (figure 7) turned out to be a breakthrough result of FT-IR analyses. We do not observe absorption bands coming from D₂O vibrations even for a sample obtained from a precursor in which the total H₂O content was 4%H₂O, where D₂O accounted for 3% of that content. This may mean that water added (D₂O) to the precursor solution did not participate in the chemical reaction of LHZA synthesis. Therefore, –OH groups (figure 7) present in LHZA may come exclusively from the reaction of Zn(CH₃COO)₂ · 2H₂O with EG. In FT-IR spectra, in turn, we do not observe absorption bands coming from the bending vibrations of crystallisation H₂O or D₂O within the range between 1627 cm⁻¹ and 1596 cm⁻¹ or between 1220 cm⁻¹ and 1200 cm⁻¹, respectively. This may mean that absorption bands of crystallisation water (H₂O or D₂O) in LHZA are not visible in the obtained spectra. Our presumptions were confirmed during the tests of a sample of the 1.5%H₂O precursor with 0.45% D₂O content (figure 8), where absorption bands coming from D₂O vibrations were virtually unnoticeable. Therefore, we presume that the quantity of crystallisation water (D₂O or H₂O) in the tested powder samples was too low for the detection threshold of FT-IR spectroscopy.

Figures 8 and 9 show FT-IR spectra of solutions of ZnO NPs precursor (0 min) and of solutions obtained by centrifuging the post-reaction suspended matter (25 min). When comparing both spectra, it is evident that such a product is formed in the ZnO NPs synthesis that had the absorption band with the wavenumber of 1724 cm⁻¹. Three groups of chemical compounds can be the potential source of absorption characterised by such vibration frequencies. One of the most probable by-products of ZnO NPs synthesis is an ester, where the range of the absorption band of the stretching vibrations of the double bond of carbon with oxygen (C=O) from saturated esters is 1715–1750 cm⁻¹. Another possible by-product of the synthesis is acetic acid, with the range of the absorption band of the stretching vibrations of C=O being 1680–1750 cm⁻¹. The least probable reaction product is an aldehyde, where carbonyl groups of aliphatic aldehydes indicate absorption at about 1720–1740 cm⁻¹.

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In order to determine the by-product of the ZnO NPs synthesis, solution samples were subject to GC-MS analysis. Figure 10(a) presents a chromatogram of the ZnO-1.5%H₂O-25 min sample (solution), where two peaks with retention times of 4.8 and 7.5 min are visible. Figure 10(b) contains mass spectra. Two peaks with different retention times in the obtained chromatogram mean obtaining two liquid products in the solvothermal synthesis of ZnO. The first peak with retention time of 4.8 min was identified as an ester, ethanediol monoacetate (HOC₂H₄OOCH₃), while the second one with retention time of 7.5 min is another ester, ethanediol diacetate (C₂H₄(OOCH₃)₂). Analogous results were obtained for the ZnO-4%H₂O-25 min sample (solution). The GC-MS analysis indicated unequivocally that esters are formed during the ZnO NPs synthesis. The presence of esters as a by-product in the solvothermal reaction of zinc acetate in various alcohols was also detected by Tonto et al [16].

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The skeleton density of LHZA samples obtained from the 1.5%H₂O precursor ranged from 2.43 to 2.57 g cm⁻³ for synthesis durations from 5 to 7.5 min (table 4). The density of the LHZA sample obtained from the 4%H₂O precursor for the synthesis duration of 6 min was 2.87 g cm⁻³. The SSA value of LHZA samples from the 1.5%H₂O precursor ranged from ≈59 to ≈40 m² g⁻¹ for synthesis durations from 5 to 7.5 min. For the sample obtained from the 4%H₂O precursor, the SSA value was ≈48 m² g⁻¹. Reinoso et al [61], in turn, obtained LZHA with the SSA of 25 m² g⁻¹ by the titration method, which once again reveals a considerable impact of the synthesis method on the properties of the obtained LZHA. LZHA structures were lamellar shaped (x, y, z), which made it difficult to calculate average sizes from SSA and from methods based on XRD results, where the spherical shape of the obtained NPs is required. The differences in the results of density and SSA between the obtained LZHA samples result probably from several factors:

• -  
  different stoichiometry (table 2);
• -  
  possible presence of an amorphous phase;
• -  
  different porosity;
• -  
  presence of substances that were not evaporated at the applied desorption temperature (60 °C, 8 h, vacuum);
• -  
  partial decomposition of LZHA resulting from sample desorption (60 °C, 8 h, vacuum).

The calculated theoretical density of ZnO is 5.61 g cm⁻³. The skeleton density of ZnO NPs samples obtained from the 1.5%H₂O precursor ranged from 4.98 to 5.29 g cm⁻³ for the range of NPs sizes from 13 to 22 nm (table 4). For samples of ZnO NPs synthesised from the 4%H₂O precursor, the density ranged from 5.12 to 5.42 g cm⁻³ for the range of NPs sizes from 16 to 43 nm. The visible correlation of density and size of NPs is known and was discussed in detail in our previous publications [12, 60].

The results of average size are summarised in table 4. The average size of ZnO NPs obtained from the 1.5%H₂O precursor calculated based on SSA and density results increased from 13 to 22 nm in line with the reaction duration progress from 10 to 25 min. The average crystallite size for the same samples calculated by the Scherrer method ranged from 13–15 to 21–26 nm, while using the Nanopowder XRD Processor Demo web application it ranged from 17 ± 7 nm to 23 ± 6 nm. Figure 11 presents crystallite size distributions of the obtained ZnO samples. Figure 12(a) displays the size distribution of ZnO NPs for synthesis duration of 25 min obtained based on TEM tests by the DF technique. The average size of ZnO NPs determined for that sample by TEM analysis was 20 ± 2 nm and coincided with the values obtained by other methods.

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The increase in the average size of ZnO particles/crystallites obtained from the 4%H₂O precursor for the reaction duration progress from 7.5 to 25 min was as follows:

• -  
  from 16 to 43 nm, calculation from SSA and density results;
• -  
  from 16–20 to 35–53 nm, Scherrer method;
• -  
  from 18 ± 5 to 41 ± 14 nm, Nanopowder XRD Processor Demo web application;
• -  
  40 ± 1 nm for synthesis duration of 25 min, DF technique (TEM).

The average sizes calculated from SSA and density results are most representative in terms of the quantity of the tested sample. When comparing two methods of XRD result conversion, Scherrer's formula and Nanopowder XRD Processor Demo, the obtained results fit in the standard deviation of those methods. The results of average NPs sizes obtained by converting the SSA and density are consistent with the accuracy of several nanometres with the results of the methods based on the XRD analysis. Average particle size and size distributions obtained by the TEM method for ZnO-1.5%H₂O-25 min and ZnO-4%H₂O-25 min samples fit in the standard deviations of all the used methods (table 4, figures 11 and 12). A conclusion may be drawn from the obtained results that crystallite sizes were similar to particle sizes, which means that the obtained ZnO NPs are single crystals.

The following products of zinc acetate reaction with EG were identified: the primary product—ZnO NPs, esters (HOC₂H₄OOCH₃ and C₂H₄(OOCH₃)₂) being by-products, and the intermediate—Zn(OH)₈(CH₃COO)₂ · xH₂O. Another expected by-product of the synthesis was H₂O. It is one of the products of the esterification reaction, i.e. the reaction of an acid with an alcohol or a polyol. The formation of H₂O as a by-product of ZnO synthesis was confirmed by an analysis in the Karl Fischer titrator. Table 5 contains the results of quantitative analyses of the products (H₂O, ZnO) created as a result of the synthesis. After 25 min of the synthesis reaction, the obtained ratio of the formed moles n_H2O/n_ZnO in the samples was ≈2. In accordance with the internal laboratory measurement procedure, all obtained results of H₂O content determination require a correctness confirmation. For this purpose, we verified the possible side reactions of the formed synthesis products with the applied reagents of coulometric titration. It turned out that for an ester sample (ethyl acetate, analytically pure, Chempur) and for (CH₃COO)₂Zn · 2H₂O sample the quantity of the determined H₂O was consistent with the quantity declared by the producers (table 6). However, for desorbed dry samples of ZnO NPs, where the actual values was ≈0% of H₂O, the result of the H₂O content analysis revealed between 22.6% and 22.9%. The obtained result is consistent with the value of molar mass ratio of M_H2O/M_ZnO·100%, being 22.1%. This meant that during the measurements of H₂O content in post-reaction suspended matter, also ZnO participated in the chemical reaction with the reagents apart from H₂O. The titrator converted the ZnO quantity which was present in the tested samples as an additional H₂O content. After allowing for the chemical reaction of ZnO with the titrator's reagents, the actual ratio of the mole quantities being formed n_H2O/n_ZnO was 1. In summary: in the synthesis reaction, 1 mole of zinc acetate in the synthesis reaction gives 1 mole of ZnO, 1 mole of H₂O and circa 2 moles of esters, when assuming the formation of HOC₂H₄OOCH₃ and small quantities of C₂H₄(OOCH₃)₂. The general equation (2) of the microwave solvothermal synthesis reaction of ZnO NPs in EG is as follows:

$$\begin{eqnarray}&&{({{\rm{CH}}}_{3}{\rm{COO}})}_{2}{\rm{Zn}}+2{{\rm{C}}}_{2}{{\rm{H}}}_{4}{({\rm{OH}})}_{2}\mathop{\longrightarrow }\limits^{{{\rm{C}}}_{2}{{\rm{H}}}_{4}{({\rm{OH}})}_{2},{{\rm{H}}}_{2}{\rm{O}},\,{\rm{T}},\,{\rm{P}}\,}{{\rm{ZnO}}}_{\downarrow }\\ &&\,+\,{{\rm{H}}}_{2}{\rm{O}}\,+\,(2-{m}){{\rm{CH}}}_{3}{{\rm{COOC}}}_{2}{{\rm{H}}}_{4}{\rm{OH}}\\ &&\,+\,{m}{({{\rm{CH}}}_{3}{\rm{OO}})}_{2}{{\rm{C}}}_{2}{{\rm{H}}}_{4}.\end{eqnarray} \tag{ 2 }$$

It needs to be emphasised that EG fulfilled a double function in the synthesis: the zinc acetate solvent and the substrate, and its quantity was 58 times as much as that of zinc acetate. The efficiency range of ZnO NPs synthesis is 94%–98% (table 5). The observed differences in the efficiency of ZnO NPs synthesis reaction for different H₂O contents in the precursor may be caused by several factors:

• -  
  complex preparation process of samples;
• -  
  different H₂O contents in ZnO NPs samples during their weighing.

The mechanism of size control of ZnO NPs obtained by the microwave solvothermal synthesis may be divided into four stages:

• (1)  
  dissolution of zinc acetate in EG (3), (4), preparation of the precursor with a specified H₂O content (5)–(7):

  $$\begin{eqnarray}&&{({{\rm{CH}}}_{3}{\rm{COO}})}_{2}{\rm{Zn}}\cdot 2{{\rm{H}}}_{2}{{\rm{O}}}_{({\rm{solid}})}\mathop{\longrightarrow }\limits^{70\,^\circ {\rm{C}},\,\mathrm{EG}\,}{({{\rm{CH}}}_{3}{\rm{COO}})}_{2}{\rm{Zn}}\\ &&\,\cdot \,2{{\rm{H}}}_{2}{{\rm{O}}}_{({\rm{dissolved}})},\end{eqnarray} \tag{ 3 }$$

  $$\begin{eqnarray}&&{({{\rm{CH}}}_{3}{\rm{COO}})}_{2}{\rm{Zn}}\cdot 2{{\rm{H}}}_{2}{{\rm{O}}}_{({\rm{solid}})}+\,2{{\rm{C}}}_{2}{{\rm{H}}}_{4}{({\rm{OH}})}_{2}\,\mathop{\longrightarrow }\limits^{70\,^\circ {\rm{C}},\mathrm{EG}\,}\\ &&\,{({{\rm{CH}}}_{3}{\rm{COO}})}_{2}{\rm{Zn}}\cdot 2{{\rm{C}}}_{2}{{\rm{H}}}_{4}{({\rm{OH}})}_{2({\rm{dissolved}})}+2{{\rm{H}}}_{2}{\rm{O}},\end{eqnarray} \tag{ 4 }$$

  $$\begin{eqnarray}&&{({{\rm{CH}}}_{3}{\rm{COO}})}_{2}{\rm{Zn}}\,\mathop{\longleftrightarrow }\limits^{{{\rm{H}}}_{2}{\rm{O}},{\rm{EG}}}\,({{\rm{CH}}}_{3}{\rm{COO}}){{\rm{Zn}}}^{+}\\ &&\,+\,{{\rm{CH}}}_{3}{{\rm{COO}}}^{-},\end{eqnarray} \tag{ 5 }$$

  $$\begin{eqnarray}&&{{\rm{CH}}}_{3}{{\rm{COO}}}^{-}+{{\rm{H}}}_{2}{\rm{O}}\,\mathop{\longleftrightarrow }\limits^{{{\rm{H}}}_{2}{\rm{O}},{\rm{EG}}}\,{{\rm{CH}}}_{3}{\rm{COOH}}+{{\rm{OH}}}^{-},\end{eqnarray} \tag{ 6 }$$

  $$\begin{eqnarray}&&({{\rm{CH}}}_{3}{\rm{COO}}){{\rm{Zn}}}^{+}+{{\rm{OH}}}^{-}\,\mathop{\longleftrightarrow }\limits^{{{\rm{H}}}_{2}{\rm{O}},\,\mathrm{EG}}\,({{\rm{CH}}}_{3}{\rm{COO}})({\rm{OH}}){\rm{Zn}},\end{eqnarray} \tag{ 7 }$$
• (2)  
  formation (8)–(11) and growth of the intermediate (12):

  $$\begin{eqnarray}&&5{({{\rm{CH}}}_{3}{\rm{COO}})}_{2}{\rm{Zn}}+8{{\rm{C}}}_{2}{{\rm{H}}}_{4}{({\rm{OH}})}_{2}+{{x}{\rm{H}}}_{2}{\rm{O}}\mathop{\longrightarrow }\limits^{{\rm{T}},\,{\rm{P}}\,}{\mathrm{Zn}}_{5}\\ &&\,\times \,{({\rm{OH}})}_{8}{({{\rm{CH}}}_{3}{\rm{COO}})}_{2}\,\cdot \,{{x}{\rm{H}}}_{2}{{\rm{O}}}_{({\rm{precipitation}})}\\ &&\,+\,8{\rm{C}}{{\rm{H}}}_{{\rm{3}}}{\rm{C}}{\rm{O}}{\rm{O}}{{\rm{C}}}_{{\rm{2}}}{{\rm{H}}}_{{\rm{4}}}{\rm{O}}{\rm{H}},\end{eqnarray} \tag{ 8 }$$

  or possibly e.g.

  $$\begin{eqnarray}&&5{({{\rm{CH}}}_{3}{\rm{COO}})}_{2}{\rm{Zn}}\cdot 2{{\rm{C}}}_{2}{{\rm{H}}}_{4}{({\rm{OH}})}_{2}+{{x}{\rm{H}}}_{2}{\rm{O}}\mathop{\longrightarrow }\limits^{{\rm{T}},\,{\rm{P}}\,}{{\rm{Zn}}}_{5}\\ &&\,\times \,{({\rm{OH}})}_{8}{({{\rm{CH}}}_{3}{\rm{COO}})}_{2}\cdot {{x}{\rm{H}}}_{2}{{\rm{O}}}_{({\rm{precipitation}})}\\ &&\,+\,8{\rm{C}}{{\rm{H}}}_{{\rm{3}}}{\rm{C}}{\rm{O}}{\rm{O}}{{\rm{C}}}_{{\rm{2}}}{{\rm{H}}}_{{\rm{4}}}{\rm{O}}{\rm{H}}+2{{\rm{C}}}_{2}{{\rm{H}}}_{4}{({\rm{OH}})}_{2},\end{eqnarray} \tag{ 9 }$$

  $$\begin{eqnarray}&&5({{\rm{CH}}}_{3}{\rm{COO}})({\rm{OH}}){\rm{Zn}}+3{{\rm{C}}}_{2}{{\rm{H}}}_{4}{({\rm{OH}})}_{2}+{{x}{\rm{H}}}_{2}{\rm{O}}\,\mathop{\longrightarrow }\limits^{{\rm{T}},\,{\rm{P}}\,}{{\rm{Zn}}}_{5}\\ &&\,\times {({\rm{OH}})}_{8}{({{\rm{CH}}}_{3}{\rm{COO}})}_{2}\cdot {{x}{\rm{H}}}_{2}{{\rm{O}}}_{({\rm{precipitation}})}\\ &&\,+{\rm{3}}{\rm{C}}{{\rm{H}}}_{{\rm{3}}}{\rm{C}}{\rm{O}}{\rm{O}}{{\rm{C}}}_{{\rm{2}}}{{\rm{H}}}_{{\rm{4}}}{\rm{O}}{\rm{H}},\end{eqnarray} \tag{ 10 }$$

  $$\begin{eqnarray}&&2({{\rm{CH}}}_{3}{\rm{COO}})({\rm{OH}})\mathrm{Zn}\,+\,3{({{\rm{CH}}}_{3}{\rm{COO}})}_{2}{\rm{Zn}}\\ &&\,+\,{{x}{\rm{H}}}_{2}{\rm{O}}\mathop{\longrightarrow }\limits^{{\rm{T}},\,{\rm{P}}\,}{{\rm{Zn}}}_{5}{({\rm{OH}})}_{8}{({{\rm{CH}}}_{3}{\rm{COO}})}_{2}\\ &&\,\cdot \,{{x}{\rm{H}}}_{2}{{\rm{O}}}_{({\rm{precipitation}})}+6{\rm{C}}{{\rm{H}}}_{{\rm{3}}}{\rm{C}}{\rm{O}}{\rm{O}}{{\rm{C}}}_{{\rm{2}}}{{\rm{H}}}_{{\rm{4}}}{\rm{O}}{\rm{H}},\end{eqnarray} \tag{ 11 }$$

  $$\begin{eqnarray}&&{{\rm{Zn}}}_{5}{({\rm{OH}})}_{8}{({{\rm{CH}}}_{3}{\rm{COO}})}_{2}\cdot {{x}{\rm{H}}}_{2}{\rm{O}}+\,5{({{\rm{CH}}}_{3}{\rm{COO}})}_{2}\mathrm{Zn}\,\\ &&\,+\,8{{\rm{C}}}_{2}{{\rm{H}}}_{4}{({\rm{OH}})}_{2}+{{x}{\rm{H}}}_{2}{\rm{O}}\mathop{\longrightarrow }\limits^{{\rm{T}},\,{\rm{P}}\,}(1\,\mathrm{+}\,1){{\rm{Zn}}}_{5}{({\rm{OH}})}_{8}\\ &&\,\times {({\rm{CH}}3{\rm{COO}})}_{2}\cdot {{x}{\rm{H}}}_{2}{{\rm{O}}}_{({\rm{growth}})}+8{\rm{C}}{{\rm{H}}}_{{\rm{3}}}{\rm{C}}{\rm{O}}{\rm{O}}{{\rm{C}}}_{{\rm{2}}}{{\rm{H}}}_{{\rm{4}}}{\rm{O}}{\rm{H}},\end{eqnarray} \tag{ 12 }$$

  nH₂O comes from the simultaneous esterification reaction (13) or (14)

  $$\begin{eqnarray}&&{{\rm{C}}}_{2}{{\rm{H}}}_{4}{({\rm{OH}})}_{2}+{{\rm{CH}}}_{3}{\rm{COOH}}\\ &&\,\leftrightarrow \,{\rm{C}}{{\rm{H}}}_{{\rm{3}}}{\rm{C}}{\rm{O}}{\rm{O}}{{\rm{C}}}_{{\rm{2}}}{{\rm{H}}}_{{\rm{4}}}{\rm{O}}{\rm{H}}+{{\rm{H}}}_{2}{\rm{O}},\end{eqnarray} \tag{ 13 }$$

  $$\begin{eqnarray}&&{({{\rm{CH}}}_{3}{\rm{COO}})}_{2}{\rm{Zn}}\cdot 2{{\rm{C}}}_{2}{{\rm{H}}}_{4}{({\rm{OH}})}_{2}+{{\rm{CH}}}_{3}{\rm{COOH}}\\ &&\,\leftrightarrow \,{({{\rm{CH}}}_{3}{\rm{COO}})}_{2}{\rm{Zn}}\cdot {{\rm{C}}}_{2}{{\rm{H}}}_{4}{({\rm{OH}})}_{2}\cdot {{\rm{H}}}_{2}{\rm{O}}\\ &&\,+\,{\rm{C}}{{\rm{H}}}_{{\rm{3}}}{\rm{C}}{\rm{O}}{\rm{O}}{{\rm{C}}}_{{\rm{2}}}{{\rm{H}}}_{{\rm{4}}}{\rm{O}}{\rm{H}},\end{eqnarray} \tag{ 14 }$$
• (3)  
  achievement of equilibrium constant of the ester hydrolysis reaction for equation (15) and at the same time of equilibrium constant of the esterification reaction (13) and decomposition of the intermediate caused by temperature (16)

  $$\begin{eqnarray}&&{{\rm{HOC}}}_{2}{{\rm{H}}}_{4}{{\rm{OOCH}}}_{3}+{{\rm{H}}}_{2}{\rm{O}}\leftrightarrow {{\rm{C}}}_{2}{{\rm{H}}}_{4}{({\rm{OH}})}_{2}\\ &&\,+\,{{\rm{CH}}}_{3}\mathrm{COOH},\end{eqnarray} \tag{ 15 }$$

  $$\begin{eqnarray}&&{{\rm{Zn}}}_{5}{({\rm{OH}})}_{8}{({{\rm{CH}}}_{3}{\rm{COO}})}_{2}\cdot {{x}{\rm{H}}}_{2}{\rm{O}}+2{{\rm{C}}}_{2}{{\rm{H}}}_{4}{({\rm{OH}})}_{2}\,\mathop{\longrightarrow }\limits^{{\rm{T}},\,{\rm{P}}\,}\,5{\rm{ZnO}}\\ &&\,+\,2{\rm{C}}{{\rm{H}}}_{{\rm{3}}}{\rm{C}}{\rm{O}}{\rm{O}}{{\rm{C}}}_{{\rm{2}}}{{\rm{H}}}_{{\rm{4}}}{\rm{O}}{\rm{H}}+5{{\rm{H}}}_{2}{\rm{O}}+{{x}{\rm{H}}}_{2}{\rm{O}},\end{eqnarray} \tag{ 16 }$$
• (4)  
  growth of existing ZnO NPs (17), (18)

  $$\begin{eqnarray}&&{\rm{ZnO}}+{({{\rm{CH}}}_{3}{\rm{COO}})}_{2}{\rm{Zn}}+2{{\rm{C}}}_{2}{{\rm{H}}}_{4}{({\rm{OH}})}_{2}\,\mathop{\longrightarrow }\limits^{{\rm{T}},\,{\rm{P}}\,}\\ &&\,\times \,(1\,\mathrm{+}\,1){{\rm{ZnO}}}_{(\mathrm{particle}\mathrm{growth})}+{{\rm{H}}}_{2}{\rm{O}}\\ &&\,+\,2{{\rm{CH}}}_{3}{{\rm{COOC}}}_{2}{{\rm{H}}}_{4}{\rm{OH}},\end{eqnarray} \tag{ 17 }$$

  $$\begin{eqnarray}&&{\rm{ZnO}}+({{\rm{CH}}}_{3}{\rm{COO}})({\rm{OH}}){\rm{Zn}}+{{\rm{C}}}_{2}{{\rm{H}}}_{4}{({\rm{OH}})}_{2}\,\mathop{\longrightarrow }\limits^{{\rm{T}},\,{\rm{P}}\,}\\ &&\,\times \,(1\,\mathrm{+}\,1){{\rm{ZnO}}}_{(\mathrm{particle}\mathrm{growth})}+{{\rm{H}}}_{2}{\rm{O}}\\ &&\,+\,{{\rm{CH}}}_{3}{{\rm{COOC}}}_{2}{{\rm{H}}}_{4}{\rm{OH}}.\end{eqnarray} \tag{ 18 }$$

  The general equation of the microwave solvothermal synthesis reaction of ZnO NPs in EG that takes into account obtaining only HOC₂H₄OOCH₃ ester, is as follows:

  $$\begin{eqnarray}&&{({{\rm{CH}}}_{3}{\rm{COO}})}_{2}{\rm{Zn}}+2{{\rm{C}}}_{2}{{\rm{H}}}_{4}{({\rm{OH}})}_{2}\mathop{\longrightarrow }\limits^{{{\rm{C}}}_{{\rm{2}}}{{\rm{H}}}_{{\rm{4}}}{({\rm{OH}})}_{{\rm{2}}},{{\rm{H}}}_{2}{\rm{O}},\,{\rm{T}},\,{\rm{P}}\,}{\rm{ZnO}}\\ &&\,+\,{{\rm{H}}}_{{\rm{2}}}{\rm{O}}+{\rm{2}}{\rm{C}}{{\rm{H}}}_{{\rm{3}}}{\rm{C}}{\rm{O}}{\rm{O}}{{\rm{C}}}_{{\rm{2}}}{{\rm{H}}}_{{\rm{4}}}{\rm{O}}{\rm{H}}.\end{eqnarray} \tag{ 19 }$$

  The above mechanism of ZnO NPs synthesis, which is illustrated in figure 13, can be explained as follows:

  • 1.  
    The reaction precursor is a solution obtained by dissolving (CH₃COO)₂Zn · 2H₂O in EG at an increased temperature. The dissolution of (CH₃COO)₂Zn · 2H₂O in EG may not be treated solely as a physical process since during the dissolution of (CH₃COO)₂Zn · 2H₂O in EG probably (CH₃COO)₂Zn · 2C₂H₄(OH)₂ is formed [63, 64] as a result of the reaction of (CH₃COO)₂Zn · 2H₂O with EG, during which EG replaces H₂O without disturbing the zinc-acetate bond [63, 64]. H₂O present in the precursor, in turn, causes dissociation (5) of (CH₃COO)₂Zn, as a result of which CH₃COOH and (CH₃COO)(OH)Zn are formed in the subsequent hydrolysis reactions (6), (7).
  • 2.  
    The intermediate, Zn₅(OH)₈(CH₃COO)₂ · xH₂O, is formed as a result of the course of simultaneous reactions (8)–(11) and (13), (14), where an ester, (HOC₂H₄OOCH₃), is one of the by-products of all these reactions. FT-IR tests did not reveal the presence of OD group in the intermediate, which makes us conclude that the water present in the precursor did not participate in the reaction of formation of OH⁻ groups in Zn₅(OH)₈(CH₃COO)₂ · xH₂O. The 'Zn₅(OH)₈(CH₃COO)₂' part in Zn₅(OH)₈(CH₃COO)₂ · xH₂O is formed, thus, as a result of the reactions (8, 9, 10, 11) of zinc acetate or its derivatives with EG. 'Crystallisation H₂O' in Zn₅(OH)₈(CH₃COO)₂ · xH₂O, in turn, is formed as a result of the simultaneous reaction (13), (14) of acetic acid with EG or acetic acid with (CH₃COO)₂Zn·2C₂H₄(OH)₂. Zn₅(OH)₈(CH₃COO)₂ · xH₂O compound is a heterogeneous catalyst of the esterification reactions [61, 62]. It should be stressed that H₂O formed from the esterification reaction (13), (14), which took place on the surface of Zn₅(OH)₈(CH₃COO)₂ · xH₂O, was at the same time the substrate of reactions (8)–(11) of formation of Zn₅(OH)₈(CH₃COO)₂ · xH₂O compound. Equation (12) presents an example course of growth of the intermediate, where the formation and subsequent growth of Zn₅(OH)₈(CH₃COO)₂ · xH₂O occurred thanks to the course of the esterification reaction.
  • 3.  
    Concentrations of the reagents HOC₂H₄OOCH₃, CH₃COOH, H₂O and EG are correlated by means of the equilibrium constant. The equilibrium constant describes only equilibrium states of reversible chemical reactions. The equation of the equilibrium constant of the hydrolysis reaction (15) of the formed esters is as follows: K_eqH =$\tfrac{[{{\rm{C}}}_{2}{{\rm{H}}}_{4}{({\rm{OH}})}_{2}]\cdot [{{\rm{CH}}}_{3}{\rm{COOH}}]}{[{{\rm{HOC}}}_{2}{{\rm{H}}}_{4}{{\rm{OOCH}}}_{3}]\cdot [{{\rm{H}}}_{2}{\rm{O}}]}.$ The equation of the equilibrium constant of the esterification reaction (13) is defined as follows: K_eqE =$\tfrac{[{{\rm{HOC}}}_{2}{{\rm{H}}}_{4}{{\rm{OOCH}}}_{3}]\cdot [{{\rm{H}}}_{2}{\rm{O}}]}{[{{\rm{C}}}_{2}{{\rm{H}}}_{4}{({\rm{OH}})}_{2}]\cdot [{{\rm{CH}}}_{3}{\rm{COOH}}]}.$ The presented equilibrium constants are closely correlated, K_eqE = $\tfrac{1}{{{\rm{K}}}_{{\rm{eqH}}}}.$ Only chemically unbound H₂O takes part in the reaction of ester hydrolysis. Therefore, we can introduce water concentration to the derived equations of the equilibrium constants of the reactions, which concentration decreases in line with the progress of the intermediate formation/growth reaction. The quantity of the unreacted H₂O in the precursor determines the moment when the equilibrium value K_eqH and K_eqE is achieved. The reactions (8)–(11) of creation or growth (12) of Zn₅(OH)₈(CH₃COO)₂ · xH₂O occurring simultaneously with the esterification reaction are not equilibrium reactions, so they were still occurring on the moment of achievement of K_eqE equilibrium value. The further progress of the reactions (8)–(11) of formation and growth (12) of Zn₅(OH)₈(CH₃COO)₂ · xH₂O without the formation of H₂O in the esterification reactions (10), (11) led to rapid decomposition of Zn₅(OH)₈(CH₃COO)₂ · xH₂O (16) to nuclei of ZnO crystals (NPs), H₂O and esters.
  • 4.  
    The formed homogeneous spherical nuclei of ZnO crystals (NPs) sized 16 ± 2 nm grew until the unreacted substrates (zinc acetate or its derivatives) were exhausted, which is shown in equations (17), (18) and figure 14. By-products of the growth of ZnO (NPs) crystals are H₂O and esters. The formed ZnO is an autocatalyst of the esterification reaction and at the same time of the growth of ZnO NPs in the described mechanism [65], which explains such a high efficiency of (94%–98%) microwave solvothermal synthesis.

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The decomposition of Zn₅(OH)₈(CH₃COO)₂ · xH₂O to nuclei of ZnO (NPs) crystals sized 16 ± 2 nm was confirmed by numerous experiments. However, the mechanism of formation of so homogeneous nuclei of ZnO (NPs) crystals with repeatable sizes through decomposition of Zn₅(OH)₈(CH₃COO)₂ · xH₂O is unknown to us. This requires further research.

The ZnO NPs size control in MSS arising from the change of H₂O content in the precursor is a result from the shift of the quantitative equilibrium of esterification reaction products (K_eqE). The change of the water quantity in the precursor is inversely proportional to the quantity of the obtained Zn₅(OH)₈(CH₃COO)₂ · xH₂O (figure 14). The following conclusion emerges: the least the H₂O content in the precursor, the greater quantity of the intermediate is obtained on the moment of achievement of the equilibrium state K_eqE (figure 14). At the same time the quantity of unreacted zinc acetate, which causes the growth of ZnO NPs formed as a result of decomposition of the intermediate, is lower.

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Water in the reaction of (CH₃COO)₂Zn with EG acts as a homogeneous catalyst. Its action consists in a reaction with the substrates, as a consequence of which a temporary intermediate, Zn₅(OH)₈(CH₃COO)₂ · xH₂O, is formed, which is unstable, thanks to which it reacts further with the formation of ZnO and reconstruction of H₂O (catalyst).

The quantity of the necessary catalyst ${n}_{{\rm{REH}}2{\rm{O}}}$ to obtain Zn₅(OH)₈(CH₃COO)₂ · 2H₂O_, assuming 100% reaction efficiency, can be calculated based on equation (8), i.e. ${n}_{{\rm{REH}}2{\rm{O}}}=\tfrac{{{n}}_{({\rm{CH}}3{\rm{COO}})2{\rm{Zn}}}}{5}\cdot 2.$ However, theoretically the possibility should be considered when the H₂O quantity in the precursor is lower than the necessary quantity of ${n}_{{\rm{REH}}2{\rm{O}}}.$ This is possible only when dehydrated zinc acetate and dehydrated EG are used for the synthesis. If such a case takes place, then the change of H₂O quantity in the precursor will be proportional to the change of the quantity of the obtained Zn₅(OH)₈(CH₃COO)₂ · xH₂O (figure 14). This results from the H₂O loss caused by the zinc acetate hydrolysis.

The verification of the mechanism concerned the following aspects:

(1) According to the mechanism we propose, with minimum H₂O quantities in the precursor we observe a negligible increase in ZnO NPs size. It should be remembered, though, that the ZnO synthesis reaction cannot occur in the precursor without trace quantities of H₂O due to the fact that H₂O is the catalyst of the ZnO synthesis. The mechanism was verified experimentally by obtaining a precursor with the H₂O content of 0.065%. This precursor was prepared by dissolving dehydrated zinc acetate in EG in a tightly closed conical flask. The ZnO NPs synthesis lasted 25 min at the temperature of 190 °C. The expected average size of ZnO NPs from the completed synthesis was 17 ± 7 nm, and the value of the SSA of NPs—circa 95 m² g⁻¹. ZnO NPs formed on the moment of decomposition of the intermediate (table 7) are characterised by such properties. The average size of the obtained particle determined by four methods for the ZnO NPs sample in the experiment was 17 ± 5 nm and was consistent with our presumptions arising from the presented mechanism. Figures 15(a) and (b) show a narrow ZnO NPs size distribution, which ranges from 5 to 40 nm. However, the SSA of the obtained ZnO NPs was 74 m² g⁻¹ and was lower by 21 m² g⁻¹ than the expected surface area (table 7). This meant that the particle size increased during the synthesis, probably caused by the too small H₂O quantity in comparison to the theoretical quantity necessary for obtaining stoichiometric LHZA with the efficiency of 100% (table 8). Table 8 contains quantities of moles of (CH₃COO)₂Zn and H₂O which were present in the precursor, and quantities that were theoretically required for obtaining only Zn₅(OH)₈(CH₃COO)₂ · 2H₂O with 100% reacted substrates.

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(2) In accordance with the presented mechanism, the change of the zinc acetate concentration in the precursor with the constant H₂O content may not considerably contribute to a change of the average size of the obtained ZnO NPs. Based on the equilibrium constant K_eqE = $\displaystyle \frac{[{{\rm{HOC}}}_{2}{{\rm{H}}}_{4}{{\rm{OOCH}}}_{3}]\cdot [{{\rm{H}}}_{2}{\rm{O}}]}{[{{\rm{C}}}_{2}{{\rm{H}}}_{4}{({\rm{OH}})}_{2}]\cdot [{{\rm{CH}}}_{3}{\rm{COOH}}]}$ it may be stated that an increase in the quantity of zinc acetate with the constant H₂O content will cause only a shift of the equilibrium towards a greater quantity of products. This results from the 58 times greater quantity of EG relative to zinc acetate. This means that an increase in the zinc acetate concentration will cause a proportional decrease of H₂O and EG quantity in the precursor, with a proportional increase in the quantity of CH₃COOH and HOC₂H₄OOCH_3, and at the same time the quantity of the intermediate. The following correlation should be fulfilled for the quantity of the reacted zinc acetate:

$\begin{array}{l}\displaystyle \frac{n{({\rm{C}}{{\rm{H}}}_{3}{\rm{C}}{\rm{O}}{\rm{O}})}_{2}{\rm{Z}}{{\rm{n}}}_{{\rm{KeqE}}}}{n{({\rm{C}}{{\rm{H}}}_{3}{\rm{C}}{\rm{O}}{\rm{O}})}_{2}{\rm{Z}}{{\rm{n}}}_{{\rm{t}}{\rm{o}}{\rm{t}}{\rm{a}}{\rm{l}}}}\approx {\rm{constant}},\\ \,{\rm{when}}\,n{{\rm{H}}}_{2}{\rm{O}}={\rm{constant}},\end{array}$

where:

• −  
  ${n}{({\rm{C}}{{\rm{H}}}_{{\rm{3}}}{\rm{C}}{\rm{O}}{\rm{O}})}_{{\rm{2}}}{\rm{Z}}{{\rm{n}}}_{{{K}}_{{\rm{e}}{\rm{q}}{\rm{E}}}}$ is the quantity of reacted moles of zinc acetate until the moment of decomposition of the intermediate (achievement of K_eqE);
• −  
  ${n}{({\rm{C}}{{\rm{H}}}_{{\rm{3}}}{\rm{C}}{\rm{O}}{\rm{O}})}_{{\rm{2}}}{\rm{Z}}{{\rm{n}}}_{{\rm{t}}{\rm{o}}{\rm{t}}{\rm{a}}{\rm{l}}}$ is the quantity of zinc acetate in the precursor for the duration of 0 min;
• −  
  nH₂O is the water content in the precursor for the duration of 0 min.

In other words, when increasing the zinc acetate concentration, we should observe only an increase in the quantity of the obtained ZnO NPs of the same size. In order to verify this thesis, we carried out syntheses of ZnO NPs for 5 different concentrations of (CH₃COOZn)₂ · 2H₂O with the constant H₂O content in the precursor being 1.5% (table 9). The syntheses of ZnO NPs lasted for 25 min at the temperature of 190 °C. We did not observe significant changes in the average particle size, density, and SSA of ZnO NPs, even when the zinc acetate concentration in the precursor was tripled (table 9). The experimental results confirmed our assumption that an increase in the zinc acetate concentration in the precursor given the 58 times greater quantity of EG would shift the reaction equilibrium towards a greater quantity of products without changes in ZnO NPs size.

(3) The suggested synthesis mechanism explains the ZnO NPs size control through the shift of the equilibrium quantity of esterification products. The shift of the equilibrium quantity of esterification products depends on two factors: concentration of reagents (mainly H₂O, EG) and the value of the equilibrium constant of a given esterification reaction K_eqE. If the suggested ZnO synthesis mechanism is correct, then in line with the change of value of the equilibrium constant K_eqE, when reagent concentration is maintained constant, different equilibrium quantities of products will be obtained, and as a consequence different ZnO NPs sizes. In order to change the value of esterification equilibrium constant, a different by-product—an ester—should be obtained. This is possible only by changing the solvent (polyol) and at the same time the substrate of the ZnO synthesis reaction.

In order to verify this experimentally, we carried out syntheses of ZnO NPs in EG, DEG, TEG and TTEG, with the constant content of zinc acetate (Cm = 0.1215 mol dm⁻³) and H₂O (1.5%). ZnO NPs syntheses lasted for 25 min at the temperature of 190 °C. The characteristics of the obtained ZnO NPs is included in table 10. The average size of the obtained ZnO NPs in EG was 29 nm, in DEG—32 nm, in TEG—44 nm, while in TTEG—47 nm. Figures 16 and 17 show the change of size and shape of ZnO caused by the use of different polyols. Spherical ZnO NPs were obtained in EG and DEG, while the rod-like shape of ZnO NPs was obtained in TEG and TTEG. The change of shape of the obtained ZnO NPs may result from the solvent's impact on the direction of crystal growth through e.g. the spherical effect.

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The obtained results confirmed our assumptions regarding the ZnO particle size control through a change of polyol (K_eqE) with the constant H₂O content. Similar correlations between the change of ZnO NPs size were found by Chieng et al [18], but the average size of ZnO NPs in EG obtained by them was 20 nm, in DEG—39 nm, while in TTEG 69 nm. Chieng et al interpreted that the change of the particle size resulted from the influence of the change of glycol chain length. It should be pointed out that the greater differences in the average size of ZnO NPs obtained by them result from additional changes of H₂O content in precursors. Chieng et al did not control changes of H₂O quantity in precursors.

(4) In order to confirm that ZnO NPs grow until the substrate (zinc acetate or its derivatives) is exhausted, we carried out ZnO NPs syntheses with the following parameters: temperature >300 °C, pressure 35 bar, duration 41 min. Figure 18(a) presents the obtained ZnO NPs suspended matter after the sedimentation process. The black liquid visible above the white deposit is degraded EG. The change of EG colour proved the occurrence of degradation process caused by too high temperature and too long heating duration. However, despite achieving a temperature exceeding 300 °C with the synthesis duration of 41 min, the average ZnO NPs size was 22 ± 6 nm (figure 18(b), table 11). Figure 19 shows the spherical shape of those ZnO NPs. For the ZnO NPs sample obtained for the synthesis duration of 25 min and temperature of 190 °C, the average particle size was 23 ± 6 nm. The low density of ZnO NPs-41 min being only 4.92 g cm⁻³ resulted from the presence of impurities coming from EG degradation (table 11). The greater value of SSA in comparison with the sample obtained at the temperature of 190 °C confirms the modification of its surface by the degradation products (soot, tar). In the microwave solvothermal synthesis of ZnO NPs, EG fulfils the role of the solvent, substrate and the stabilising medium, which blocks the growth of ZnO NPs after the exhaustion of substrates. The results of the experiments revealed the lack of increase in ZnO NPs size arising e.g. from the Ostwald ripening process.

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The obtained results of the experimental verification of the developed mechanism model confirmed its correctness. Based on the presented synthesis mechanism of ZnO NPs obtained as a result of the reaction of zinc acetate with EG, the results of works by various research groups related to ZnO NPs size control can be explained by the change of:

• −  
  concentration of reagents, (change of H₂O content in the precursor [16, 19]);
• −  
  synthesis duration, (ZnO growth as a result of presence of unreacted substrates in the precursor [15, 63]);
• −  
  synthesis temperature (change of kinetics of the reaction of formation of intermediates and change of kinetics of ZnO NPs growth [15, 63];
• −  
  organic solvent, (different values of esterification equilibrium constants and different H₂O contents in the used solvents [16–18, 63]);
• −  
  precursor storage conditions, (changes of H₂O content in the precursor [19]).