## 2 Experimental
### Physicochemical Techniques  
IR transmission and multiple attenuated total internal reflection spectra were recorded using a Perkin Elmer-580 spectrophotometer (Stockholm, Sweden). Multiple attenuated total internal reflection spectra were recorded using a KRS-5 crystal with an incidence angle of 45\({}^{\circ}\) and a film scanning depth of \(\sim\)5 \(\upmu\)m.  
Differential scanning calorimetry (DSC) was used to record thermal effects accompanying the melting (crystallization) and glass transition of the graft copolymer under the conditions of programmed temperature changes. The heating rate varied from 4 to 50 deg/min. Measurements were performed on a DSC 204 F1 Phoenix (Netzsch, Selb, Germany) in the temperature range from 25 to 150 \({}^{\circ}\)C in an Ar atmosphere with a flow rate of 60 mL/min. All experiments were performed using samples weighing at least 2 mg. For automatic processing of measurement results, we used the Proteus Analysis software (Version 6.1.0) in which the glass-transition temperature value \(T_{g}\) was defined as an inflection point of the \(\Delta C_{p}\)(\(T\)) curve, and the melting point value \(T_{m}\) was defined as a maximum (peak) point. The surface area of the peak bounded by the DSC curve and zero baseline was assumed to be equal to a change in the melting enthalpy (\(\Delta H_{m}\)). To determine the glass transition temperature, we also used the tangent method [14], which was applied to the left, right, and middle parts of the heat capacity step \(\Delta C_{p}\)(\(T\)). The degree of crystallinity of the studied sample was determined using the following equation:  
\[\alpha=\frac{\Delta H}{\Delta H_{100\%}} \tag{2}\]  
where \(\Delta H\) is the melting enthalpy of the studied sample; \(\Delta H_{100\%}\) is the melting enthalpy for the completely crystalline polymer; and \(\Delta H_{100\%}\) = 293 \(\mathrm{J/g}\)[15]. The structural and morphological characteristics of the graft copolymers were studied using transmission electron microscopy, scanning electron microscopy, and X-ray micro-analysis. In the first case, the outer surface of the graft films was used as the object of the study, which was subjected to etching in high-frequency oxygen plasma in order to reveal the supramolecular structure. The oxygen pressure in the etching zone was 0.03 mm Hg, the electron energy was 2-3 eV, the etching time was 15-20 min, the generator power was 100 W, and the frequency was 10 MHz. The morphology of the etched surfaces was examined via the method of one-step carbon-platinum replicas using a TEM-301 transmission electron microscope (Amsterdam, The Netherlands) at an accelerating voltage of 80 keV. In the cases of scanning microscopy and X-ray microanalysis, studies were carried out on cross-sections of the sulfated graft PE film obtained on an LKB cryo ultramicrotome. Surface analysis was performed using a JSM-U3 scanning electron microscope (JEOL, Tokyo, Japan) at an accelerating voltage of 5-7 keV equipped with an EDAX energy dispersive spectrometer (Hamburg, Germany). The \(o\)-xylene absorption (\(\Delta m\), %) was determined according to Equation (3):  
\[\Delta m=\frac{m_{s}-m_{d}}{m_{d}}\cdot 100 \tag{3}\]  
where \(m_{s}\) and \(m_{d}\) are the film weights (in g) of the swollen and dry films, respectively. The degree of swelling on the surface area (\(\Delta S\), %) in \(o\)-xylene was calculated from the surface area values of the film in the swollen state (\(A_{s}\)) and in the dried state (\(A_{d}\)) using Equation (4):  
\[\Delta S=\frac{A_{s}-A_{d}}{A_{d}}\cdot 100 \tag{4}\]The self-diffusion coefficients of water in the membranes with different DVB contents were measured for \({}^{1}\)H with the pulsed field gradient technique at frequencies of 400.22 MHz. The measurements were carried out on a Bruker AVANCE-III-400 NMR spectrometer equipped with a diff60 gradient unit. A pulsed field gradient-stimulated echo sequence was used.