Micropores provide 10% (TiO2), 30% (TiO2-HZD-2) and 55% (TiO2-HZD-7) of the total membrane surface (S m) (see Table 1). Figure 6 Integral distribution of pore volume for TiO 2 (1), TiO 2 -HZD-2 (2) and TiO 2 -HZD-7 (3) samples. The ratio of values is 1:3.9 for TiO2-HZD-2 and TiO2-HZD-7 membranes, respectively (here, V micr and are the volume of micropores MLN4924 research buy for selleck compound pristine and modified

membranes, respectively). The ratio of (here, m and m l are the mass of matrix and modified membrane, respectively) is 1:1.9. This is evidently due to different porous structures of HZD: more compact structure is attributed to the TiO2-HZD-2 sample. The volume of the ion exchanger in mass unit of the membrane has been estimated as , and the porosity of the HZD layer was calculated using the

expression: (6) More compact HZD structure has been also found for the TiO2-HZD-2 membrane (Table 2). The surface of the ion exchanger was assumed to be proportional to the mass growth of membranes. Table 2 Parameters of globular model for the matrix and ion exchanger layer Parameter Homogeneous model Heterogeneous model Matrix Ion-exchanger Spheres Matrix Ion-exchanger TiO2-HZD-2 TiO2-HZD-7 TiO2-HZD-2 TiO2-HZD-7 ϵ, 0.23 0.29 0.46 – - – S, m2 kg−1 820 1.05 × 105 2.09 × 105 – - – - ϵ p – - – I – 0.03 0.42 II 0.02 0.26 0.04 III 0.21 Packing CFC or HXG AZD8931 CBC SC I – CBC SC II CFC or HXG III – - , , m2 kg−1 – - – I 7.77 × 105 2.27 × 105 II 8,176 3.06 × 104 3.88 × 104 III 201 – - r g , nm 859 7 4 I – 5 3 II 86 23 20 III 3,500 -

(≈400) r n a, nm 133 (204) 1 (≤1) 1 (≤1) I – 1 (≤1) 1 (≤1) II 13 (8) 5 (8) 8 (4) III 542 (204) – (190) Alectinib r c a, nm 355 (1,730) 2 (2) 2 (2) I – 2 (2) 2 (2) II 36 (39) 9 (8) 13 (6) III 1,449 (1730) – (331) aExperimental values identified according to pore size distributions are given in brackets. Differential distributions of pore volume are given in Figure 7. The r values are represented as logr; the peaks are symmetric. Thus, the plots can be resolved by Lorentz functions. Since , the peak area gives the pore volume caused by each type of particles. Calculation of porous structure according to globular models Both homogeneous and heterogeneous globular models were applied to relate the maxima either to the matrix or to ion exchanger. The models have been developed by A.P. Karnaukhov; their main principles are described in [12–14]. Parameters of the models are radii of globules (r p), pore necks (r n) and pore cavities (r c); the values of surface and porosity are also used. The magnitudes of r n and r c are calculated using special factors for each type of globule packing: r n = 0.41r p and r c = 0.73r p for simple cubic (SC), r n = 0.22r p and r c = 0.29r p for body-centred cubic (BCC), and r n = 0.15r p and r c = 0.41r p for hexagonal (HXG) or face-centred cubic packing (FCC).