Nanoscale Research Letters

Table 2 Parameters of globular model for the matrix and ion exchanger layer

From: Composite inorganic membranes containing nanoparticles of hydrated zirconium dioxide for electrodialytic separation

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, $\bar{ϵ}$	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	CBC	SC	I	-	CBC	SC
				II	CFC or HXG	CBC	SC
				III	CFC or HXG	-	-
$S \frac{ϵ}{ϵ_{p}}$ , $S \frac{\bar{ϵ}}{ϵ_{p}}$ , 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)
r_c^a, nm	355 (1,730)	2 (2)	2 (2)	I	-	2 (2)	2 (2)
r_c^a, nm	355 (1,730)	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 $\frac{dV}{d (log r)} = 2.3 r \frac{dV}{dr}$ , the peak area gives the pore volume caused by each type of particles.

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