A hydrofluoric acid-free method to dissolve and quantify silica nanoparticles in aqueous and solid matrices

As the commercial use of synthetic amorphous silica nanomaterials (SiO2-NPs) increases, their effects on the environment and human health have still not been explored in detail. An often-insurmountable obstacle for SiO2-NP fate and hazard research is the challenging analytics of solid particulate silica species, which involves toxic and corrosive hydrofluoric acid (HF). We therefore developed and validated a set of simple hydrofluoric acid-free sample preparation methods for the quantification of amorphous SiO2 micro- and nanoparticles. To circumvent HF, we dissolved the SiO2-NPs by base-catalyzed hydrolysis at room temperature or under microwave irradiation using potassium hydroxide, replacing the stabilizing fluoride ions with OH−, and exploiting the stability of the orthosilicic acid monomer under a strongly basic pH. Inductively coupled plasma – optical emission spectroscopy (ICP-OES) or a colorimetric assay served to quantify silicon. The lowest KOH: SiO2 molar ratio to effectively dissolve and quantify SiO2-NPs was 1.2 for colloidal Stöber SiO2-NPs at a pH >12. Fumed SiO2-NPs (Aerosil®) or food grade SiO2 (E551) containing SiO2-NPs were degradable at higher KOH: SiO2 ratios >8000. Thus, hydrofluoric acid-free SiO2-NP digestion protocols based on KOH present an effective (recoveries of >84%), less hazardous, and easy to implement alternative to current methods.


Results and Discussion
Molar ratio of KOH: SiO 2 for complete SiO 2 dissolution-mechanism. The results of the method optimization using the High_SiO 2 digestion method outlined in the method section and Table 1 are presented in Fig. 2. The dissolution of colloidal SiO 2 into Si(OH) 4 species was less dependent on the concentration of KOH, and more on the ratio of KOH to SiO 2 , which optimally is >1.2, and the pH, which should be >12. A volume of 10.0 mL of 0.1 M KOH (final concentration 82 mM) solubilized up to 50 mg of colloidal SiO 2 -NPs in suspension (Fig. 2). This corresponds to a molar ratio of 1.2 KOH: SiO 2 , in line with the results from Yang et al. 19 . The same volume of 0.05 M KOH still dissolved up to 30 mg colloidal SiO 2 -NPs (molar ratio: 1.0 KOH: SiO 2 ), but did not dissolve 50 mg SiO 2 -NPs anymore (molar ratio: 0.6 KOH: SiO 2 ), apparent from the high particle counts per second detected by DLS in that particular sample (Fig. 2). A slightly elevated DLS signal was also observed for the molar ratio of 1.0 KOH: SiO 2 . These results demonstrate that at least an equimolar concentration of KOH and optimally an excess of >20% is needed to dissolve SiO 2 . The constant ratio suggests that KOH fulfills a two-fold purpose: (a) installing a pH of >12 for the base-catalyzed hydrolytic degradation of hydrated silica 31 , and (b) neutralizing the Si(OH) 4 liberated during this reaction to maintain the high pH. The threshold pH of >12 corresponds to the 14 mM KOH that are not neutralized by Si(OH) 4 in the sample digested with 1.2 KOH: SiO 2 (82 mM KOH, 68 mM SiO 2 ), and is in agreement with the pH of 9-12 reported by Croissant et al. to dissolve SiO 2 -NPs 31 . We therefore adapted 0.1 M KOH and 1.2 KOH: SiO 2 ratio as minimum values for further digestions for colloidal SiO 2 -NPs, and slightly more for fumed SiO 2 NPs based on our observations (discussion below).
For further investigation on the dissolution mechanism, the incompletely digested sample containing 50 mg colloidal SiO 2 -NPs in suspension with the insufficient 0.6 KOH: SiO 2 ratio (Fig. 2) was dialyzed after the digestion against water for 1 d to remove KOH and dissolved Si species, and then inspected by transmission electron microscopy (TEM, Fig. 2). The structure of these partially dissolved SiO 2 -NPs revealed electron-transparent www.nature.com/scientificreports www.nature.com/scientificreports/ nanopores and more surface roughness compared to the dense, non-porous, and smooth structure of freshly synthesized SiO 2 -NPs (Fig. 2), confirming results of Li et al., who, based gas adsorption analysis results, ascribed some nanoporosity to colloidal SiO 2 -NPs due to aggregation-based NP growth 32 . An alternative explanation for the porosity is that the dissolution does not progress from the surface towards the core, but is targeted on specific silanol bonds 31 throughout the molecular structure. These observations are in line with Park et al., who showed that SiO 2 -NPs undergo a shape evolution due to Si-O bond-breaking and bond-making caused by hydroxyl ions, leading to rearrangement of high-energy bonds in the core 33,34 . No remaining NPs were observable by TEM in the samples digested using ratios >0.6 KOH: SiO 2 (Fig. 2 Fig. 3 and their fitting parameters in Supplementary Table S2. As apparent from the high R 2 (0.9987-0.9998), both Si and Y were stable in the concentration range of the calibrations under all conditions. As expected, calibrations exclusively containing acids showed the most stable Si signal (R 2 = 0.9998), and the most complex calibration was slightly more unstable (R 2 = 0.9987). A similar trend was observed for the signal of the internal standard yttrium. Only subtle signal suppression of Si or Y due to the matrix were observable: the maximal relative difference between the sensitivity of the different calibrations was 7.7% for Si and 9.5% for Y. For Si, the highest sensitivity (652 ± 9.5 counts/(µg L −1 )) was observed for the . Key steps and reagents used to hydrolytically degrade SiO 2 nanoparticles under basic conditions using potassium hydroxide, and detect dissolved Si and Si(OH) 4 , respectively, under acidic conditions. The SiO 2 concentrations stated are those used for the method development. (A) HF-free procedure for detection by inductively coupled plasma -optical emission spectrometry (ICP-OES) method suitable for complex matrices and accurate detection of low Si concentrations. (B) Procedure for detection by the colorimetric method using a UV-vis spectrophotometer. This method involves in situ HF, was used to validate method A, and is suitable for simple sample matrices.  www.nature.com/scientificreports www.nature.com/scientificreports/ matrix-matched + H 2 SO 4 + digested calibration, and the lowest for the BgS calibration (602 ± 3 counts/(µg L −1 )). The digestion and addition of 0.1 M KOH moderately stabilized free Si. However, Fig. 3 shows that neither the acids used (2.25 M H 2 SO 4 , 0.5% HCl, and 2.0% HNO 3 ), nor the 0.1 M KOH, nor the digestion in the microwave led to a change of the Si signal noticeable in the statistical scatter of the data. For Y, the trends in matrix effects were somewhat different than for Si, and the highest sensitivity (18204 ± 321 counts/(µg L −1 )) was observed for the BgS calibration, in agreement with HSAB theory (stabilizing effect of soft nitrate ligands on the soft Y metal ions which is less effective for hard Si ions) 35 . The variability of the Y intercept was somewhat increased due to an accidental systematic second addition of internal standard which had to be corrected in the data by subtraction. The Y calibrations suffered from slight sensitivity loss under the matrix-matched KOH conditions by ~2-7%. Nevertheless, the absolute sensitivity for Y was excellent throughout all experiments. We therefore used the matrix-matched + H 2 SO 4 + digested calibrations with the highest sensitivity for Si for all measurements shown in Fig. 4 and Table 2. www.nature.com/scientificreports www.nature.com/scientificreports/ Repeatability and recovery. The measured concentrations of the SiO 2 -NP suspensions (Table 1) digested via the method KOH0.1 are compared with their calculated concentrations of Si in Fig. 4. A total recovery of Si/SiO 2 of 85 ± 2% was achieved with an instrument limit of detection of 41 µg L −1 and an instrument limit of quantification of 80 µg L −1 SiO 2 ( Table 2). The method was linear in the investigated range of injected Si (373-1981 µg L −1 ) which corresponds to 1.88-8.53 mg L −1 SiO 2 during the digestion. The relative error of the Si sensitivity, which can be attributed to measurements being taken over the course of multiple days by different investigators with different calibration matrices, was 31%. Three outliers are present among the hundred-twenty repeated measurements in Fig. 4. We attribute them to human pipetting errors. In practice, such errors can be detected and eliminated by analyzing, as in the present study, at least n = 3 replicate samples. While no outliers were deleted in the present study to present the reader with a realistic dataset, performing for example a Grubbs outlier test can identify such anomalies. In potential future large-scale applications, a robotic pipetting system can prevent such outliers. Overall, the repeatability of the measurements of concentration series prepared individually, digested in different microwave runs, and measured on the same day was very high (Fig. 4). This demonstrates that there is no significant buildup of Si in the instrument within one run, and the selected rinsing time of 55 s (10% HNO 3 ) between samples was sufficient. We found, however, that it is necessary to clean the detector window in regular intervals and to thoroughly rinse the instrument with 10% HNO 3 and Milli-Q (18.2 MΩ · cm) after each run.
We expected the recovery of Si in ICP-OES to be proportional to the stability of free Si(OH) 4 , and inversely proportional to the fraction of re-polymerized Si(OH) 4 in the sample. The polymerization of silica is accelerated under several conditions such as pH >2, high temperature, and ionic strength >0.2 M 19,36 . Here, the pH was adjusted by the addition of H 2 SO 4 to a pH of <2 to minimize polymerization and push the equilibrium towards orthosilicic acid. Although this addition of H 2 SO 4 also increased the ionic strength, previous studies found that Si(OH) 4 polymerization in the presence of H 2 SO 4 is minimal 36 . The present results (Fig. 3) show a moderate stabilizing effect of H 2 SO 4 on dissolved Si, based on a 3.5% difference between the sensitivities of Si calibrations in H 2 SO 4 or BgS.
The higher the excess KOH concentrations, the lower the Si recovery was, which is in line with the abovementioned destabilization of Y and stabilization of Si in high KOH environments. The Si recovery dropped by 15% in samples containing 0.1 M KOH compared to 1.0 M KOH. Hence, it is important to add the same concentration of KOH to the calibration in case the samples require KOH concentrations >0.1 M for digestion to account for this matrix effect. Finally, the SiO 2 polymerization is accelerated by high Si(OH) 4 concentrations 36 . We found plasma instability starting from 4000 µg Si L −1 upwards, and therefore limited routine concentrations to <1000 µg Si L −1 .
Sample storage. Storing samples for extended periods showed that digestates could be analyzed after up to two weeks without a statistically significant loss of recovery. A 3.6% decrease of Si recovery from 101.1% to 97.5% was observed between day 1 and at day 14 (  www.nature.com/scientificreports www.nature.com/scientificreports/ dissolved Si in the sample (ANOVA p < 0.02), likely due to re-polymerization. We noted improved stability of (1) refrigerated, (2) diluted, (3) low ionic strength, and (4) low pH samples. All these three conditions are known to push the equilibrium of polymerized SiO 2 towards Si(OH) 4 36 .

Method applicability. Suspensions containing fumed SiO 2 -NPs (Aerosil ® ). The recoveries for fumed
SiO 2 -NP suspensions digested using the method KOH1.0 (Table 1) are summarized in Table 2. The fumed SiO 2 -NP stock suspensions mainly contained aggregates (hydrodynamic diameter 267 nm) of smaller primary NPs 13 ± 5 nm in diameter (Supplementary Fig. S1 and Supplementary Table S1). We chose a harsher KOH concentration of 1.0 M for fumed SiO 2 -NPs due to the expected poorer solubility of the non-porous and less hydroxylated fumed SiO 2 -NPs compared to the more porous and more hydroxylated colloidal SiO 2 -NPs 8,32,37 . While the specific surface area is, for the present particle sizes and fractal dimensions, expected to be higher for the fumed SiO 2 -NPs (200 m 2 g −1 ) than the colloidal SiO 2 -NPs (~23-32 m 2 g −1 based on literature for colloidal particles of smaller size) 32 , both the lower surface hydroxylation and lower porosity of fumed SiO 2 -NPs can hamper the base-catalyzed hydrolytic degradation due to the postulated mechanism of amorphous SiO 2 dissolution that first requires hydration and hydrolysis of amorphous siloxane networks into silanols before the nucleophilic attack of OH − 31 . Also, suspensions of pre-digested, oven-dried SiO 2 -NPs formed acidic suspensions, which partially neutralized the added KOH in initial attempts to use 0.1 M KOH for digestion. Using 1.0 M KOH, we obtained a recovery of 114 ± 25% for fumed SiO 2 -NPs, and the same digestion at RT without microwave 105 ± 1.4% (Table 2). This elevated recovery (not significantly higher than 100%, one sample T-test, p > 0.22) may be a result of slightly less stabilized free Si ions than Y ions in the digestates, which were slightly more acidic than the calibrations. In samples digested using KOH concentrations ≤0.5 M, recoveries remained <85% in ICP-OES measurements ( Table 2), confirming that significant matrix effects occur due to excess KOH, as discussed in section Repeatability and Recovery, only in SiO 2 samples that are digested in >0.1 M KOH.
SiO 2 in complex matrices. The performance of the method in SiO 2 -containing complex matrices tested is shown in Table 2 (cell culture medium, tomato sauce, potato seasoning). We observed low recoveries for the digestion of SiO 2 in complex samples using 0.1 M KOH in preliminary tests. By using the method KOH0.5 on the SiO 2 -NP-spiked cell culture medium samples, we obtained a recovery of 84 ± 20% of SiO 2 without pre-digestion ( Table 2). The large statistical scatter can be connected to the complex formulation of the cell culture media Dulbecco Modified Eagle Medium (DMEM). Among many amino acids and vitamins, DMEM also contains ~10 g L −1 of dissolved inorganic salts, of which 3.6 g L −1 is sodium, which is notorious for causing high variability in ICP-OES measurements 30,38 . The present results show that the KOH digestion of SiO 2 -NPs in a serum-free cell culture medium delivered, despite some variability, an acceptable accuracy and recovery.
For the food matrix samples, i.e. the tomato sauce spiked with colloidal SiO 2 -NPs and the potato seasoning, the matrix was first digested in HNO 3 to isolate the SiO 2 -NPs (i.e. pre-digestion) and then these NPs were dissolved by KOH (refer to Experimental Section). As with DMEM, we had to use higher KOH concentrations of 1.0 M to get satisfactory recoveries. We obtained a recovery of 124 ± 5% and 95 ± 13% for colloidal SiO 2 -NPs in tomato sauce and food grade SiO 2 (E551) in potato seasoning, respectively. The recoveries of both samples (tomato sauce, potato seasoning) were calculated relative to the mass of remaining solids after the first acid-mediated digestion step, as SiO 2 was the sole remainder detected by energy-dispersive X-ray spectroscopy (EDX) after the harsh HNO 3 pre-digestion (data not shown). According to the literature, the natural Si concentration in tomatoes is maximally ~61 mg kg −1 39 , corresponding to ~31 µg natural Si in the analyzed mass of tomato sauce. The high recovery of 124 ± 5% for colloidal SiO 2 -NPs spiked into the tomato sauce (Table 2) indicates that additional natural SiO 2 was detected in the tomato sauce. The recovery of 95 ± 13% SiO 2 found for the potato seasoning (Table 2) Figure 5. Stability of digestates containing hydrolytically degraded SiO 2 over time. The concentration is proportional to the recovery: the data can be read from both y-axes. Certified Si standard solutions digested according to method KOH0.1 (Table 1) and stored at room temperature were measured at different time points after digestion. The storage time significantly affected the concentration after sixty-one days, but not after fourteen days (analysis of variance, p < 0.02, Tukey's post-hoc test, p > 0.69).
www.nature.com/scientificreports www.nature.com/scientificreports/ corresponds to a total of 4.8 g SiO 2 kg −1 for the potato seasoning. Sodium residues from the pre-digestion can be the reason for the more variable results compared to the other tested matrices, in line with the results for DMEM, and as also reported by Frantz et al. 30 . The quantity of the anti-caking agent was not indicated on the potato seasoning package. However, our results are in good agreement with Si analyses of related products in the literature 40 .

SiO 2 -NP digestion at room temperature-ICP-OES (HF-free) vs. colorimetry (not HF-free).
For colloidal SiO 2 -NPs in a simple matrix, the microwave digestion is replaceable by an RT digestion overnight in 0.1 M or 1.0 M KOH, without much reduction in recoveries ( Table 2). Colloidal SiO 2 -NPs digested in 1.0 M KOH at RT yielded a recovery of 84 ± 5% compared to 85 ± 2% for 0.1 M KOH in the microwave (both measured by ICP-OES). This demonstrates that porous, almost entirely hydroxylated colloidal SiO 2 -NPs are digestible at RT without expensive instrumentation, and confirms reports by Tanakaa and co-workers, who found that silica gel dissolves in 0.1 M KOH without the aid of microwave irradiation 18 .
The efficiency of ICP-OES and colorimetry in detecting SiO 2 -NPs was directly compared for samples digested using the method RT + KOH1.0 (Tables 1 and 2). Using colorimetry, the recovery for fumed SiO 2 -NPs was lower (76 ± 9%) than for ICP-OES (105 ± 1.4%). Also, for the fumed SiO 2 -NPs, the recovery was only 67 ± 2% when digested in 0.1 M KOH at RT (Table 2), revealing a limitation of the digestion methods at RT for fumed SiO 2 -NPs and colorimetry that only detects fully dissolved orthosilicic acid or small Si oligomers 21 . Despite the larger specific surface area, the non-porous, less hydroxylated fumed SiO 2 -NPs were, in agreement with Zhang and co-workers 37 , harder to completely digest and required the harsher 1.0 M KOH conditions, in contrast to the more soluble porous, more hydroxylated colloidal SiO 2 -NPs. The ICP-OES method was more robust in detecting incompletely digested SiO 2 at RT: a high recovery was found for fumed SiO 2 -NPs of 105 ± 1.4% in 1.0 M KOH.
The trend in the recovery of the two detection methods for colloidal SiO 2 -NPs was inverse: despite milder digestion conditions (0.1 M KOH), colorimetry detected more Si (111 ± 7%) than ICP-OES (84 ± 5%, 1.0 M KOH). The simplest explanation for this seemingly contradictory result is that the harsh 1.0 M KOH conditions readily dissolved the colloidal SiO 2 -NPs, and because the easier to dissolve colloidal SiO 2 -NPs did not consume all of the 1.0 M KOH, the excess KOH negatively affected the ICP-OES recovery. This confirms the earlier finding that, for colloidal SiO 2 -NPs, KOH concentrations <0.5 M are sufficient for ICP-OES analysis and excess KOH should be avoided.
The present results show that the ICP-OES detection of Si is more widely applicable than colorimetry because, despite satisfactory recoveries, the quantification via colorimetric detection of Si has several limitations. First, as mentioned before, the colorimetric quantification of Si suffers from a wide variety of interferences 20,41 and exclusively detects fully dissolved Si(OH) 4 or small oligomers 21 . Second, the present colorimetric determination of Si employed a four-fold higher dilution factor (105) compared to ICP sample preparation (25). Based on the LODs in Table 2, this results in an estimated detectable concentration for the colorimetry of >15-32 mg SiO 2 L −1 , and for the ICP-OES of >1.7-7.4 mg SiO 2 L −1 , depending on the sample matrix. The high detection limit for the colorimetry makes it challenging to detect Si in samples with low SiO 2 concentrations of <15 mg SiO 2 L −1 without additional pre-concentration steps as used e.g. by Rimmelin-Maury and co-workers 6 . Future development of the KOH digestion method for colorimetry should, therefore, focus on reducing the LOD by reducing this dilution factor or including pre-concentration steps. Finally, the digestion protocol for colorimetry uses ammonium fluoride at a low pH, which raises concerns of in situ hydrofluoric acid formation due to its pK a of ~3.17.

Conclusion
Herein, we report a series of methods using basic KOH digestion to quantify Si in a broad variety of samples. Digested samples containing particulate amorphous SiO 2 or Si(OH) 4 could be quantified by ICP-OES or colorimetry (Fig. 6). The method was successfully applied in samples of low and high complexity including aqueous colloidal or fumed SiO 2 -NP suspensions, SiO 2 -NP-spiked cell culture media, SiO 2 -NP-spiked tomato sauce, and potato seasoning containing food grade SiO 2 (E551). SiO 2 dissolved at a minimum KOH: SiO 2 ratio of 1.2 at pH values >12. The complexity of the sample matrix and the manufacturing process of the SiO 2 under investigation www.nature.com/scientificreports www.nature.com/scientificreports/ both affect the Si recovery. Recovery can be improved by controlling the excess of KOH. The different optimal KOH concentrations reflect trade-offs between high excess KOH and harsh pH conditions that favor the rapid dissolution of less porous and less hydroxylated fumed SiO 2 -NPs and Si in more complex matrices; and low excess KOH concentrations, where less matrix effects occur. In case KOH concentrations >0.1 M are used, the calibration has to be prepared in the same concentration of KOH to account for these matrix effects (matrix-matched calibration). Some limitations of the method to be addressed in follow-up studies are the efficiency for larger SiO 2 particles ≥397 ± 22 nm, long term sample storage, the applicability of the method in sera (e.g. 10% fetal calf or bovine serum), and the differentiation of dissolved and particulate SiO 2 species that can be addressed by size fractionation steps prior to further analysis.
Both detection by ICP-OES or colorimetry yielded satisfactory recoveries of up to 100% for SiO 2 -NPs ≤397 ± 22 nm. This shows that our approach without HF can lead to recoveries and detection limits comparable to the state-of-the-art colorimetry method involving HF that was tested here to validate our method 42 . While colorimetry is easy and fast for simple matrices and colloidal SiO 2 -NPs and also feasible with a preceding HF-free KOH digestion, the ICP-OES method presented here is completely hydrofluoric acid-free, independent from color interferences due to matrix components such as Fe, nitrates, and sugars, and more accurate than colorimetry for incompletely digested nanoparticles (e.g. from fumed SiO 2 ). Thus, the hydrofluoric acid-free SiO 2 dissolution and quantification methods presented here are simple to implement alternatives to current standard procedures and applicable in fields such as biomedical sciences and environmental chemistry where SiO 2 -NP quantification in complex matrices is important.

Method Section
Materials, chemicals, and matrices. Commercially available fumed (pyrolytic) SiO 2 -NPs (Aerosil ® 200, 98% SiO 2 , specific surface area of 200 m 2 g −1 ) were purchased from Evonik (former Degussa). Fumed SiO 2 -NPs are produced by continuous flame hydrolysis, are reported to be non-porous by the manufacturer and Mebert and co-workers 8 , and are less hydroxylated than colloidal SiO 2 -NPs 37 . All chemicals used were per analysis grade unless it is stated otherwise. Water was pre-purified by a Milli-Q system (18.2 MΩ.cm arium 611DI, Sartorius Stedim Biotech, Germany). Dialysis membranes were purchased from Roth (Membra-Cel ™ , 14 kDa cut-off).
Both cell culture medium and food matrices are relevant chemically complex matrices that reportedly pose significant analytical challenges for NP analytics 43,44 . We selected three representative complex matrices according to the following criteria: (1) the cell culture media DMEM is widely used in in vitro NP-cell interaction studies 45 ; (2) tomato sauce is a typical food matrix containing with <61 mg kg −1 comparatively little SiO 2 39 ; and (3) potato seasoning is a foodstuff where E551, i.e. food grade SiO 2 , was listed on the packaging as an anti-caking ingredient. The potato seasoning (Qualité & Prix Country Potato Seasoning Blend, Germany) and the tomato sauce (Cirio Rustic Tomato Purée, Italy) were purchased from a local supermarket.
Colloidal SiO 2 -NP synthesis. Colloidal SiO 2 -NPs were synthesized via a co-condensation reaction adapted from Stöber et al. 46 . Briefly, ethanol (522 mL, absolute, Honeywell), ammonia (122.7 mL, 1.65 mol, 25% aqueous solution, Merck), and water (40.5 mL, MilliQ) were mixed and heated to 60 °C. The mixture was stirred at that temperature for 1 h to equilibrate. Tetraethyl orthosilicate (67.5 mL, 302 mmol, Sigma-Aldrich) was added, and the mixture was stirred at 60 °C overnight. The mixture was allowed to cool to RT, and the NPs were washed three times by centrifugation (Thermo Scientific, F15-8 × 50cy fixed-angle rotor, 5000 × g, 10 min) and redispersed in water. The final opaque SiO 2 -NP suspension (500 mL) contained 23.1 g SiO 2 kg −1 , as determined gravimetrically by drying aliquot volumes of the suspension. Due to the sol-gel manufacturing process, colloidal Stöber SiO 2 -NPs are more porous and almost fully hydroxylated compared to the fumed SiO 2 -NPs 8,32,37 . Nanoparticle characterization. The SiO 2 -NPs were characterized by TEM (primary particle diameter), and dynamic light scattering (DLS, hydrodynamic particle diameter, surface charge). The results are summarized in Supplementary Fig. S1 and Supplementary Table S1. For TEM analysis, samples were prepared by diluting NP suspension (1 μL) with ethanol (5 μL, absolute, Honeywell) for SiO 2 -NPs and water for fumed SiO 2 -NPs directly on the TEM grids (carbon film, 300 mesh on Cu, Electron Microscopy Sciences) and wicking remaining liquid using a precision wipe tissue (Kimtech Science). The TEM images were recorded in 2048 × 2048 pixel resolution (Veleta CCD camera, Olympus) on a FEI Tecnai Spirit TEM, operating at an acceleration voltage of 120 kV. The DLS samples were diluted with water (1% v/v) and measured on a Brookhaven Particle Size Analyzer Plus90 (USA) (scattering angle 90°, 1 min acquisition, 10 repetitions). The size distribution of the particles was analyzed by computer-assisted particle size analysis software (imageJ, plugin: psa-r12) 47 , applied to the TEM micrographs.
Digestion pretests to find the KOH concentration for complete SiO 2 dissolution. A series of digestion methods (throughout the text referred to as High_SiO 2 ) was tested to find the highest SiO 2 mass and lowest KOH concentration that allowed for complete solubilization of all SiO 2 nanoparticles in the sample. Colloidal SiO 2 -NP suspensions (433-2165 µL of a 23.1 g SiO 2 kg −1 suspension, equivalent to 10, 20, 30, and 50 mg of SiO 2 ) were weighed into the PTFE microwave vessels, and KOH (10 mL, 0.05, 0.1, 0.5, or 1.0 M) was added ( Table 1). The mixtures were sealed and digested in the microwave (details below). The digestates were measured by DLS (particle counts per second) and visualized using TEM to detect undigested SiO 2 -NPs. Figure 1 shows the key steps, and Table 1 the reagents and concentrations used in the different digestion protocols investigated. All microwave digestions were conducted using an Anton Paar Multiwave PRO, equipped with a 24HVT50 rotor holding 25 mL PTFE microwave vessels with pressure-activated-venting caps (PTFE-TFM, max. pressure 40 bar). All microwave runs consisted of a temperature ramp to 200 °C for 7 min followed by a temperature hold for 7 min and concluded by a cooling (2019) 9:7938 | https://doi.org/10.1038/s41598-019-44128-z www.nature.com/scientificreports www.nature.com/scientificreports/ segment until the internal temperature in all containers reached 70 °C (Supplementary Fig. S2) resulting in a total duration of the microwave digestion of ~28 min. The power limit for all runs was set to 1500 W. If not stated otherwise, digested samples and calibrations were stored at RT and analyzed by ICP-OES within 24 h. Digestates spiked with internal Y standard and stabilized in acidic BgS and were stored in the fridge. The background equivalent concentrations (BEC), the limits of the detection (LOD) and limits of quantification (LOQ) were calculated by adding three times the BEC standard deviation to the BEC (LOD), and ten times the BEC standard deviation to the BEC (LOQ).

Digestion methods investigated for ICP-OES.
KOH0.1-KOH1.0. These methods served to assess the Si recovery for (a) 120 colloidal SiO 2 -NP suspensions in the range of 1.88 to 8.53 mg L −1 SiO 2 in the course of ten experiments (method KOH0.1); (b) a different SiO 2 source (fumed SiO 2 -NPs, method KOH0.1 and KOH1.0); (c) more complex matrices spiked with colloidal SiO 2 -NPs in the concentration range of 0.4-1.7 mg L −1 SiO 2 (0.5 g of tomato sauce and 0.5 mL of cell culture medium, pre-digestion except for cell culture medium as explained below, then methods KOH0.1-KOH1.0); and (d) the pre-digested commercial potato seasoning (0.5 g) with an unknown Si concentration treated equally to the complex matrices in (c). For all methods, SiO 2 -NP stock suspensions (25 mg SiO 2 kg −1 ) were weighed into the PTFE microwave vessels and diluted with water to ~2 g. Aqueous KOH (3 mL, 0.1, 0.5, or 1.0 M, respectively, Table 1) was added, and the mixtures were prepared for the microwave run. The digestates were transferred to conical tubes (polypropylene, Falcon ® ) and acidified by H 2 SO 4 (2.25 M) to pH 1-2. Internal standard (yttrium, 50 mg L −1 solution in 2% HNO 3 /0.5% HCl, 100 μL) was spiked, and the samples were topped off with water to 10 mL for the ICP-OES analysis.
RT + KOH0.1, RT + KOH1.0. Here, the SiO 2 digestion at RT was tested, and the Si detection of ICP-OES was compared with colorimetry. For the ICP measurements, stock suspensions (25 mg SiO 2 kg −1 in water) of either colloidal or fumed SiO 2 -NPs were mixed with KOH (3.0 mL, 1.0 M) and stirred overnight at RT (Table 1). Then, H 2 SO 4 (2.25 M) was added until pH 1-2 was reached. Internal standard (yttrium, 50 mg L −1 solution in 2% HNO 3 /0.5% HCl, 100 μL) was spiked, and the resulting digestates were topped off with water to 10 mL for the ICP-OES analysis.
Pre-digestion of samples containing food matrix. The colloidal SiO 2 -NP-spiked tomato sauce samples and the food grade SiO 2 -NP containing potato seasoning were pre-digested according to a procedure for food analysis established in our laboratory. In pretests, we found that for these food matrices, the method KOH0.1 to KOH1.0 was not suitable due to the high solid content. We therefore used a two-step digestion for these samples, consisting of an acidic pre-digestion of the food matrix followed by KOH digestion of the oven-dried SiO 2 -containing residue. Briefly, for the pre-digestion, the sample (~0.5 g) was added to the PTFE microwave vessels and nitric acid (63%, 3 mL) was added. The closed vessels were heated in the microwave (700 W, 10 min at 60 °C) without previously running a ramp. After this run, the vessels were opened to release nitric oxide gases, closed again, and heated in the microwave (800 W) according to the following program: ramp (90 °C, 5 min), hold (2 min), ramp (180 °C, 6 min), hold (15 min) and cool to 70 °C. The cooled digestates were transferred into 15 mL conical tubes (polypropylene, Falcon ® ) and diluted with water to 5 mL. The digested samples were cleaned by centrifugation at 8000 × g for 10 min at 4 °C and redispersed in 1 mL of water. The centrifugation-redispersion cycle was repeated until the pH of the suspensions reached 5-6. The water was evaporated in an oven and the resulting Si-containing solids were operationally defined to consist of 100% SiO 2 , as an energy dispersive X-ray spectrometric (EDX) elemental analysis found no impurities. These solids were used to prepare stock suspensions in water for quantification experiments using the basic digestion methods KOH1.0-KOH0.1 and subsequent ICP-OES analysis.
Four types of Si calibrations with increasing complexity were prepared using the same volumes and concentrations as in the digestion method KOH0.1 to assess the effects on the Si sensitivity of the ICP-OES for samples in different acids, in KOH matrix, and digested in the microwave. The four Si calibrations were Si in water and H 2 SO 4 (short: water + H 2 SO 4 ); Si in BgS; Si in water and KOH (3 mL, 0.1 M), acidified by H 2 SO 4 (short: matrix-matched + H 2 SO 4 ); and Si in water and KOH (3 mL, 0.1 M) digested in the microwave, and acidified by H 2 SO 4 (short: matrix-matched + H 2 SO 4 + digested). The background was accounted for by subtraction of the blank concentration.

Sample preparation for colorimetric SiO 2 analysis.
To test the suitability of the KOH digestion method for colorimetry, and to cross-validate the ICP-OES results using a conventional approach involving hydrofluoric acid, we quantified the dissolved silicon dioxide according to a modified version of the colorimetric method based on the blue molybdosilicic acid complex (Fig. 1) 19 . For the digestion, lyophilized colloidal SiO 2 -NPs (2.0 mg, 33.0 µmol SiO 2 ) or fumed SiO 2 -NPs (1.7 mg, 28.3 µmol SiO 2 ) were suspended in 0.1 M KOH (20 mL) for the colloidal SiO 2 -NPs or 1.0 M KOH (20 mL) for the fumed SiO 2 -NPs and stirred overnight at RT. All the resulting digestates were then diluted to a final concentration of 0.1 M KOH. From here, we followed the colorimetric SiO 2 analysis protocol reported by Yang et al. 19 using 5 mL of the colloidal SiO 2 -NP digestate and 9 mL of the fumed SiO 2 -NP digestate (concentration: 9.2-92 colloidal SiO 2 L −1 , and 9.2-14.4 mg fumed SiO 2 L −1 , respectively). Water (5 mL), HCl (1 M, 5 mL) and NH 4 F (1 M, 1 mL) were added, and the mixtures were stirred at 25 °C in a water bath for 45 min. Mixing a 5-fold excess of HCl with NH 4 F produces HF in situ due to the pK a of HF of