## 2 Materials and Methods
### Terahertz Time-Domain Spectroscopy (THz-TDS)  
THz-TDS is the main experimental approach used in the present study. Spectra were measured on a TPS Spectra 3000 spectrometer (TeraView Limited, Cambridge, UK) in a wavenumber range from 1.2 to 120 cm\({}^{-1}\) with a resolution of 4 cm\({}^{-1}\). Dynamic rangewas 40-80 dB in the specified spectral range. Each spectrum was obtained by averaging over 3600 scans. In the course of measurements, the spectrometer was purged with dried air obtained using a Parker Balston 74-5041 FT-IR Purge Gas Generator (Parker Hannifin Corporation, Haverhill, MA, USA).  
The spectra of all the solutions studied were measured in two identical cuvettes with different distances between the windows: 50.7 \(\upmu\)m and 103.7 \(\upmu\)m. Teflon gaskets were installed between the windows. After being filled with the sample, the cuvettes were hermetically closed with two screws with PTFE gaskets. The windows of the cuvettes are made of single-crystal quartz which has a high transmittance in the specified frequency range. Both cuvettes with the specified thickness were assembled before the cycle of conducted measurement and were not disassembled until the full completion of the experimental part of this work. Thus, the specified thickness can be considered standardized with an accuracy of \(\pm\) 0.1 \(\upmu\)m.  
The exact distances between the windows were determined in an interferometric manner after the cuvettes were assembled. For this purpose, the transmittance spectra were measured for empty cuvettes in the range of 4000-8000 cm\({}^{-1}\) using an IR spectrometer Nicolet 6700. The spectra contain periodic bands which result from the interference of two waves: a wave transmitted through the cuvette without reflections, and a wave twice reflected between the windows of the cuvette. The distance between two adjacent interference fringes \(\Delta\
u\) on a wavenumber scale is related to the distance between the planes of the windows (\(l\)) through an equation:  
\[l(\mu\mathrm{m})=\frac{5000}{\Delta\
u(\mathrm{cm}^{-1})} \tag{1}\]  
Prior to measuring, the temperature of the analyzed solutions was stabilized at \(30\pm 0.5\)\({}^{\circ}\)C by placing the cuvette into a temperature-controlled rack of 4000 Series High Stability Temperature Controller (Specac Ltd., Orpington, UK). After reaching the target temperature of the cuvette, a two-minute intermission was made prior to starting the measurement in order to stabilize the sample temperature and dry the optical part of the spectrometer.  
Following sequential measurement of the sample spectra in two indicated cuvettes, the single-beam spectrum obtained using the cuvette with a distance between windows of 103.7 \(\mu\)m was divided by a single-beam spectrum obtained in a cell with a distance between windows of 50.7 \(\mu\)m. Thus, a 53 \(\mu\)m thick transmittance spectrum of the solution was obtained avoiding virtually all optical artifacts. In addition, taking into account the known difference in the thickness of the sample (53 \(\mu\)m) in two cuvettes, the refractive index spectrum from the differential spectrum of the wave phase was calculated.  
In order to account for the experimental error, 6 test solutions (10% w/w) were prepared from each of the powders studied. For each of the solutions, the spectra were recorded four times.  
Such number of observations is sufficient for evaluating the experimental error and comparing various solutions with special statistical methods described in the section \"Statistical data analysis\".