Porous glass membranes as model disperse systems

Colloids and Surfaces A: Physicochem. Eng. Aspects 282–283 (2006) 279–286

Porous glass membranes as model disperse systems L. Ermakova a , M. Sidorova a,∗ , T. Antropova b , N. Jura a , S. Lurie b a

Department of Colloid Chemistry, St. Petersburg State University, 198504 St. Petersburg – Petrodvoretz, Universitetskiy pr. 2, Russia b Institute of Silicate Chemistry of Russian Academy of Science, Russia Received 13 October 2005; received in revised form 2 December 2005; accepted 5 December 2005 Available online 23 May 2006 Dedicated to Professor Ivan B. Ivanov (LCPE, University of Sofia) on the occasion of his 70th birthday.

Abstract The structural, adsorption and electrokinetic characteristics of porous glass (PG) membranes, prepared by leaching of various alkali borosilicate glasses, were studied as a function of pH in the presence of 1:1, 2:1 and 3:1 electrolytes. The obtained experimental results were used to calculate both of surface reaction constants and ion adsorption potentials within the framework of a 2-pK model. The electrochemical parameters of membranes (counterion transport numbers, ion concentrations and mobilities in the pore space, Donnan potentials) were also calculated within the framework of a homogeneous model. The dependencies of membrane characteristics on the electrokinetic radius were analysed. © 2006 Published by Elsevier B.V. Keywords: Porous glass; Membrane; Pore radius; Electrokinetic radius; Surface charge; Counterion transport number; Membrane conductivity; Specific surface conductance; Electrokinetic potential; Donnan potential; Ion mobility

1. Introduction Porous glasses (PG) are the unique chemically stable channel nanostructures with adjustable structural parameters. The possibility of obtaining the PG membranes with practically identical chemical composition in a wide range of pore size provides the opportunity for the preparing of model systems for study of the influence of dispersity on electrochemical characteristics of oxide/electrolyte solution interface and transport properties of membranes. The investigation of PG’s colloidal-chemical characteristics is important not only in fundamental, but in practical respect too, because the PG are widely used as adsorbents, in optics—as active elements of solid-liquid lasers, as solid matrices in microoptical elements; semi permeable PG membranes are used for separation of fluid and gas mixtures, etc. [1–10]. In this work we analyse the influence of the counterion (cation) type, pH, background electrolyte concentration and pore size on the adsorption of potential-determining ions (surface

∗

Corresponding author. E-mail address: [email protected] (M. Sidorova).

0927-7757/$ – see front matter © 2006 Published by Elsevier B.V. doi:10.1016/j.colsurfa.2005.12.011

charge) and electrokinetic characteristics of PG membranes, prepared from various alkali borosilicate glasses. 2. Experimental 2.1. Materials and experimental methods Porous glass membranes with different pore radii were prepared from phase separated alkaline borosilicate glasses of various compositions by the acid leaching in the lab of physicochemical properties of glass of the Institute of Silicate Chemistry of Russian Academy of Science and in the Department of Physical Chemistry of the Herzen Russian State Pedagogical University. The leaching of sodium borosilicate glasses (S) with solutions of hydrochloric acid at a temperature of 50–100 ◦ C leads to obtaining of nanoporous glasses with the mean pore size less than 10 nm (membranes S–1.3, S–1.9, S–2.4, S–2.4* in Table 1). The additional treatment of porous glasses with alkaline solutions resulted in obtaining ultraporous glasses with the mean pore radii from 13 up to 160 nm (membranes S–13, S–26, S–42, S–66, S–160). Other nanoporous membranes were prepared from sodium borosilicate glass doped with fluorine and phosphor (S(FP)–5.9), from sodium–potassium borosili-

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Table 1 Chemical composition of porous glasses and leaching conditionsa Porous glass S–1.3b ,

Leaching conditions S–2.4*

50/100 ◦ C

Composition of porous glass (mass %)

S–1.9, S–2.4, S–13 S–26, S–42, S–66, S–160

0.1/3 M HCl, 3 M HCl, 20 ◦ C, 0.3 M KOH, 20 ◦ C 3 M HCl, 50 ◦ C, 0.5 M NaOH, 15 ◦ C

SiO2 : 95.5/96.6, Na2 O: –−0.1/0.3, B2 O3 : 3.5/4.2, Al2 O3 : <0.1

S(FP)–4.6

3 M HCl, 100 ◦ C

SiO2 : 93.3, Na2 O: 0.4, B2 O3 : 6.1, F: ≈0.1, P2 O5 : ≈0.1

SP–4.1

3 M HCl, 100 ◦ C

SiO2 : 93.5, Na2 O: 0.1, K2 O: 0.1, B2 O3 : 6.3

SP(LA)–2.6, SP(LA)–2.7 a b

3 M HCl, 20,

100 ◦ C

SiO2 : 95.1/95.6, Na2 O: 0.1/0.3, K2 O: 0.1/0.3, B2 O3 : 3.9/4.0, Al2 O3 : ≈0.2, PbO: ≈0.1

The compositions of PG were determined in The Institute of Silicate Chemistry of RAS. The PG labeled in accordance with their mean pore radii (nm).

cate glass (SР–4.3) and from sodium–potassium borosilicate glass doped with lead and aluminium oxides (SP(LA)–2.6 and SP(LA)–2.7) under standard conditions [11–13]. The leaching conditions and chemical composition of all investigated glasses are listed in Table 1. The structural, electrosurface and transport characteristics were measured for all investigated PG membranes in dependence on pH and background electrolyte (NaCl, KCl. CsCl, BaCl2 , LaCl3 ) concentration using standard experimental methods. The BET surface area, S0 was determined by N2 gas thermal desorption with chromatographic registration. The volume porosity, W (W = WP /WM , where WP is the pore volume and WM is the membrane volume) was calculated from the weight of dry (pD ) and wet (pW ) membrane using the values of glass (ρ) and water (ρH2 O ) densities: W=

(pW − pD ) [(pW − pD ) + ρH2 O pD /ρ]

(1)

the hydraulic permeability G (G = ν/PA, ν is the volume velocity of liquid, P is the applied pressure and A is the membrane area) was measured in 0.1 NaCl or HCl solutions to escape the influence of the electroviscous effect on the liquid filtration rate. The measurements were carried out in the pressure range 1 × 104 –4 × 104 Pa for ultraporous PG and in the pressure range 5 × 104 –3 × 105 Pa for nanoporous PG. The surface charge (σ 0 ) was measured using acid/base potentiometric titration method. The titration experiments were carried out in N2 gas atmosphere between pH 3.0 and 9.0 at a constant temperature of 20 ± 0.2 ◦ C. The cation transport numbers ncat in PG’s were determined by membrane potential method in the concentration cell with transport equipped with Ag/AgCl electrodes and were calculated using equation: ncat =

−E 2 )/(a1 ) (z+ + 1)/(z+ ) · (RT )/(F ) ln(a± ±

(2)

1 , a2 are the average activities of electrolyte solutions where a± ± 1 /(a2 ) ∼ 2), z is the cation on the each side of membrane (a± + ± = charge, R is the gas constant, T is the absolute temperature, F is the Faraday number and E is the measured potential value. The values of membrane conductivity, κM were measured by the Pt/Pt electrodes at alternating current at a frequency of 1 kHz and at a constant temperature of 20 ± 0.2 о C. In the con-

centrated solutions (C ≥ 0.1 M) the influence of electrical double layer (EDL) ions on the membrane transport processes is negligible. In this case the structural resistance coefficients β, which characterize the contribution of the non-conducting skeleton to the membrane conductivity, can be calculated using equation β = κV /κM , where κV is the specific conductivity of bulk solution. In the concentration range 10−2 –10−4 M we can calculate the pore solution specific conductivity κ using equation κ = κM β. The electrokinetic potentials (ζ) were determined using streaming potential (ES ) technique (the laboratory cell was equipped with Ag/AgCl electrodes, the pressure range was the same as for hydraulic permeability measurements) and calculated using equation: ζ = f (krβ , ζ)

κηES εε0 P

(3)

where f(krβ , ζ) is the coefficient taking into account the influence of EDL overlapping onto streaming potential values within the framework of Levin’s model [14], η is the fluid viscosity, ε, ε0 are the dielectric constants of liquid and vacuum, respectively. 2.2. Experimental results Table 2 summarizes the structural characteristics of PG. The mean pore radii, rS0 and rβ were calculated from the equations: 2W (1 − W)ρS0
rβ = 8ηGβdM

rS0 =

(4) (5)

where dM is the membrane thickness. Eq. (5) was derived with the use of the Poiseuille equation under the assumption that the paths of the electric current and of the liquid volume flux in a membrane are the same. The tortuosity coefficients K equal√to the ratio of the pore length to the membrane thickness (K = βW) were also calculated for all PG membranes. The upper part of Table 2 exhibits PG membranes for which their structural parameters stay practically constant during experimental measurements. The maintenance of structural parameters was secured by the fact that the characteristics of each membrane were measured during several days, passing from a more concentrated solution to a more dilute solution. It is seen that varying of the leaching conditions leads to an increase in the size of pore channels and also to volume porosity

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Table 2 Structural parameters of porous glasses β

K

rβ (nm)

Membranes with constant structural parameters S–1.3 0.21 182 1.3 S–1.9 0.20 117 1.9 S–2.4 0.22 107 2.4 S–13 0.50 62.4 14 S–26 0.58 48.9 25 S–42 0.62 32.8 43 S–66 0.52 15.6 60 S–160 0.57 10.0 115

15.6 14.4 13.1 3.4 2.8 2.7 2.6 2.3

1.8 1.7 1.7 1.3 1.3 1.3 1.2 1.2

13 26 42 66 160

Membranes with changing structural parameters S–2.4* 0.37 110 4.7 S(FP)–4.6 0.30 65.5 5.9 SP–4.1 0.46 170 4.7 SP(LA)–2.6 0.52 260 3.7 SP(LA)–2.7 0.48 225 3.7

6.8 11.2 4.7 5.8 5.7

1.6 1.8 1.5 1.7 1.6

Membranes

W

S0 (m2 /g)

rS0 (nm)

7.4 7.0

growth, which causes a decrease in the specific surface area and in the structural resistance coefficients and in the tortuosity coefficients. Note that a good agreement between the r-values found with the use of different methods was observed for ultraporous glasses. The measurements for nanoporous membranes with different chemical compositions were also performed during a long time (several months). In this case, the contact with electrolyte solutions leads to a change in the membrane structure due to the removal of secondary silica (highly dispersed silica formed in the pore channels during acid leaching of the initial glass) from the pores. The obtained data show that the removal of secondary silica results in increasing the pore size and the volume porosity and, at the same time, to decreasing the specific surface area and the structural resistance coefficients. The initial values of pore radii were used to membrane labeling. The other structural characteristics presented in the lower part of Table 2 correspond to the final values of the each parameter. Fig. 1 gives an example of the dependence of the structural resistance coefficient on the time of contact of the membranes with the KCl solution. The comparison of the membrane properties also shows that the doping of sodium borosilicate glass with fluorine and phosphor yields an increase of the pore sizes, while the doping of sodium–potassium borosilicate glasses with lead and aluminium oxides diminishes the mean pore radius. Note that, for nanoporous glasses, the mean pore radii found from the hydraulic permeability are larger than those calculated from the specific surface area. Apparently, the contribution of through pores with larger pore size determines the hydraulic permeability, whereas the rS0 -value is determined by all of the membrane pores, including the non-through (locked) pores. The surface charge measurements showed that all investigated PG’s were negatively charged within the pH range 3–9. The typical for oxide/electrolyte solution interface dependencies were observed: an increase in the absolute value of surface charge with pH and the background electrolyte concentration growth due to heightening the degree of dissociation of surface silanol groups. Also it has been found, that the |σ 0 |-values

Fig. 1. Structural resistance coefficients vs. time of contact of KCl solutions with membranes: (1) SP–4.1; (2) SP(LA)–2.7; (3) S(FP)–5.9; and (4) S–2.4.

are some larger for ultraporous nanoporous glasses in compare with nanoporous membranes of the same chemical composition (Fig. 2), but become independent of the pore size at rβ ≥ 26 nm in the range pH ≤ 6.5. For nanoporous glasses at a fixed ionic strength, interrelation of σ 0 -values corresponds to the direct lyotropic sequence of univalent cations (Fig. 3). The comparison of σ 0 -values for the nanoporous glass S–1.9 in the presence of counterions of various charge (Na+ , Ba2+ , La3+ ) has shown that the absolute values of the surface charge density |σ 0 | at pH = const increased with the counter ion charge. Such behaviour can be caused both by strengthening specific interaction of ions with the surface and by increasing the solution ionic strength. However, the experimental points get to a unique curve when plotted as σ 0 versus electrokinetic radius krβ , where k is the Debye parameter (Fig. 4). That gives evidence of the fact that the surface charge is primarily dependent on the ionic strength,

Fig. 2. Surface charge of S-PG membranes vs. pH on the background of 10−1 M NaCl solutions: (1) S–1.9; (2) S–2.4; (3) S–13; (4) S–26; (5) S–42; and (6) S–66.

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Fig. 3. Surface charge of S–2.4 vs. pH on the background of 10−1 M solutions: (1) NaCl; (2) KCl; and (3) CsCl.

Fig. 5. Cation transport numbers of nanoporous glasses vs. electrokinetic radius for: (1) S–1.9: (䊉) NaCl, (
) BaCl2 , () LaCl3 ; (x) S–2.4, NaCl; (2) S–2.4, KCl; (3) S–2.4, CsCl; and (4) S–13, NaCl.

so that counter ions Ba2+ and La3+ practically behave as indifferent in this case. Apparently, highly dispersed secondary silica contained in the pore space of the nanoporous glass impedes developing specific interaction of large ions with the pore surface. The comparison of surface charges for porous glasses of various chemical compositions shows that adding of lead oxide and fluorine to the sodium borosilicate glass leads to an increase in the absolute values of the surface charge. Note that the surface charges of S–2.4 and SP–4.1 membranes, obtained from sodium borosilicate and sodium–potassium borosilicate glasses, were practically the same at equal pore size—at the moment of surface charge measurements the mean pore radius of both PG was equal to 4.7 nm. The comparison of the sodium counterions transport numbers nNa+ measured for the membranes with the same chemical composition showed, that an increase in salt level and the pore size growth led to the monotonic decrease in the nNa+ -values. These tendencies are in accordance with decreasing contribution of the EDL ions to the membrane transport. The doping of the initial sodium–potassium borosilicate glass with lead and aluminium oxides led to an increase in nK+ at C ≤ 10−1 M in accordance with changes in the pore size and surface charge val-

ues. Including fluorine and phosphor in the sodium borosilicate glass practically does not influence on nK+ -values. In this case the influence of increasing the pore size is compensated by an increase in the surface charge. The dependence of ncat on electrokinetic radius krβ for nanoporous glasses is shown in Fig. 5. For the membranes S–1.9 and S–2.4 the ncat -values for counterions Na+ , Ba2+ , and La3+ lie in one curve (curve 1), that confirms the non-specific behaviour of multivalent ions in nanoporous glasses. An increase in cation transport numbers at passing to K+ and Cs+ ions can be related both to the higher mobility of less hydrated ions in the pore space and to increasing the surface charge. For the ultraporous glass S–13 nNa+ -values were increased in compare with the nanoporous PG, that was connected with the growth of the Na+ ions mobility in ultraporous glass. For ultraporous glasses S–26, S–42, S–60 and S–160 whose charge is independent on the pore radius in the neutral pH region, the nNa+ -values are determined by the electrokinetic radius only (Fig. 6), that means the constancy of counterion mobility in the pores at rβ ≥ 13 nm. The results of the membrane conductivity measurements were used for calculation of the efficiency coefficient α = κ/κV

Fig. 4. Surface charge of S–1.9 vs. kr␤ on the background of 10−1 M solutions: (䊉) NaCl; (
) BaCl2 ; and () LaCl3 .

Fig. 6. Cation transport numbers of ultraporous glasses vs. electrokinetic radius for: S–13 (); S–26 (䊉); S–42 ( ); S–66 (
); and S–160 ().

L. Ermakova et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 282–283 (2006) 279–286

Fig. 7. Efficiency coefficients of ultraporous glasses vs. electrokinetic radius for: NaCl–S–13 (); S–PG–26 (䊉); S–42 ( ); S–PG–66 (
); S–160 (); KCl–PG–66 (); and CsCl–S–PG–13 () solutions.

showing the ratio of the conductivities of the pore (κ) and bulk (κV ) solution. The α-values obey regularities similar to those for the counterion transport numbers. For sodium borosilicate ultraporous glasses in neutral NaCl solutions, the α-values depend on the electrokinetic radius only (Fig. 7). The essential decrease in α-values at krβ = const apparently due to lowering the ion mobility in pores was observed for nanoporous glasses. Both α and ncat -values for nanoporous glasses are determined by the krβ -value in the presence of multivalent cations. Comparison of the efficiency coefficients for glasses of different chemical compositions has shown (Fig. 8) that they are also dependent on the electrokinetic radius only. The specific surface conductance KS (KS = (α − 1)κV rβ /2) was also calculated for investigated PG. KS -values were equal to 2–3 × 10−10 Mho for ultraporous glasses in alkaline metal chloride solutions at krβ > 1,. For those systems KS -values were

Fig. 8. Efficiency coefficients of nanoporous glasses vs. electrokinetic radius in KCl solutions for: S–2.4 (); S(FP)–5.9 ( ); SP–4.1 (䊉); and SP(LA)–2.6 ().

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Fig. 9. Electrokinetic (ζ) and Donnan (ϕD ) potentials of nanoporous membranes vs. concentration of CsCl solutions: (1) ϕD : S–1.3 (x), S–2.4 (䊉) and (2) ␨: S–1.3 () S–2.4 ( ).

practically independent on the degree of EDL overlapping and on the solution concentration. The independence of KS -values of ultraporous PG on the type of univalent cation means that the specificity of counterions grows in the row Na+ → K+ → Cs+ . More large values of KS in HCl solutions, in compare with NaCl solutions, can be caused both by a larger mobility of H+ ions and by an additional mechanism of surface conductivity related to the participation in conductance of non-dissociated H+ ions of surface silanol groups. The increase in the degree of EDL overlapping for nanoporous PG leads to lowering KS as a result of lowering ion mobility’s. The non-specific behaviour of multivalent cations in the nanoporous PG leads to the independence of KS -values on the counterion charge. The analyses of electrokinetic potentials, calculated with account for surface conductivity and the EDL overlapping, showed that ζ − log C dependencies coincide with theoretical concepts—the |ζ|-values were diminished with an increase in the electrolyte concentration that due to the compressing of diffuse part of the EDL. Examples of the ζ − log C dependencies for nanoporous glasses in 1:1 electrolytes (in the neutral pH region) are given in Figs. 9 and 10. The analyses of obtained results showed that increasing in the specificity of a univalent counterion leads to a decrease in |ζ|-values for the PG with the same chemical composition. The high specificity of Cs+ ions to the glass surface causes the reversal of ζ-potential sign in a decimolar solution (Fig. 9). For the PG of various chemical compositions (Fig. 10) it is seen that |ζ|-values for the more charged membrane SP(LA) are smaller than these for the SP membrane. This can be related both to larger filling in a hydrodynamically immobile compact (Stern) layer and to a change of the position of shear plane. Doping of the initial sodium borosilicate glass with fluorine and phosphor, which caused an enlargement of pore size and surface charge, also causes an increase in the |ζ|-potential values at C = const. Fig. 11 exhibits the values of electrokinetic potentials in HCl and NaCl solutions for ultraporous glasses. It is seen that, for membranes with practically equal surface charge, the values of the electrokinetic potential coincide within experimental errors,

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L. Ermakova et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 282–283 (2006) 279–286 Table 3 Surface parameters of porous glasses in 1:1 electrolytes

Fig. 10. Electrokinetic potentials of nanoporous membranes vs. concentration of KCl solutions: for: (1) SP–4.1; (2) SP(LA)–2.6; (3) S(FP)–5.9; and (4) S–2.4.

System

pKaint2

int −pKMe +

−ΦOH− (kJ/mol)

−ΦMe+ (kJ/mol)

NaCl S–1.9, S–2.4, S–13 S–26, S–42, S–66, S–160

6.8 6.5

0.3 0.3

32 33

11 11

KCl S–2.4 S(FP)–5.9 SP–4.3 SP(LA)–2.7

6.4 5.8 6.6 6.0

0.4 0.4 0.5 0.9

34 36 33 36

12 12 13 15

CsCl S–2.4 S–13

6.4 6.2

1.6 1.0

34 35

19 15

where subscript “S” means the location of an ion in the electrical double layer. From the values of the surface reaction constants found by double extrapolation, the ion adsorption potentials were estimated as   Kaint2 ΦOH− = −RT ln (5) 55.5 · KW int Φe+ = −RT ln 55.5KMe +

Fig. 11. Electrokinetic potentials of ultraporous membranes vs. concentration of solutions: 1, 2 NaCl, 3 HCl: S–13 (), S–26 (䊉), S–42 ( ), S–66 (
), S–160 ().

which gives evidence of a permanent location of the shear plane in these systems. 3. Discussion The surface charge values measured on the background of 1:1 electrolytes were used for the calculation of surface parameters within the framework of the 2-pK model of charging an oxide surface [15–17]. In this model, the process of the silica surface charging (the content of silica in the investigated porous glasses changed from 93 up to 97%) is described by the following surface reactions: the reaction of dissociation of surface silanol groups Kint a

SOH←→SO− + H+ S 2

(6)

and the reaction of ion pairs formation (surface complexation) Kint +

+ − SO− + Me+ S ←→SO · · ·MeS Me

(7)

(6)

The resulting values (Table 3) of the surface reaction constants and the adsorption potentials of potential-determining OH− -ions are close to values typical for silica surfaces. The relation of the pKaint2 -values and of | − ΦOH− |-values are in agreement with the results of surface charge determination: increasing |σ 0 | at passing from nanoporous glasses to ultraporous glasses, as well as in the lyotropic sequence of the cations of alkali metals and at varying the glass composition, leads to some growth of the dissociation constants and | − ΦOH− |-values. The constants of surface complexation and the adsorption potentials of the alkali metal cations correspond to the direct lyotropic sequence. The experimental results were used for calculation of electrochemical characteristics of membranes within the framework of homogeneous model [18,19]. The homogeneous model implies the constancy of ion concentrations and electric potential over the cross-section of a pore channel and, therefore, can be used only at a strong EDL overlapping, i.e. at small electrokinetic radii. For the nanoporous PG membranes the concentration of fixed ions m, the concentrations of co-ions and counterions in pores C+,− and the Donnan potential ϕD (neglecting the activity coefficients) were calculated using the next equations (for MeClz+ electrolytes): m = −σ0 FS0 ρ(1 − W) W

(10)

m + C− = z+ C+

(11)

z+ +1/z+ − C+

m 1/z+ C − Cz+ +1/z+ = 0 z+ +

(12)

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Table 4 Ion concentrations and Donnan potentials of nanoporous glass membranes C (M)

m × 102 (M)

C+ × 102 (M)

C− × 102 (M)

−ϕD (mB)

S–1.9, NaCl 10−3 3.42 10−2 3.89 5.48 10−1

3.423 4.13 13.1

S–1.9, BaCl2 10−3 6.16 4.95 10−2 10−1 4.93

3.10 3.05 11.7

0.04 1.15 18.5

43 14 2

S–1.9, LaCl3 10−3 4.79 10−2 4.56 10−1 8.27

1.64 2.28 12.1

0.12 2.28 28.1

23 7.0 2

S–2.4, KCl 10−3 10−2 10−1

1.85 4.09 5.08

1.855 4.32 12.9

0.005 0.23 7.8

74 37 6

S(FP)–4.6, KCl 10−3 4.34 10−2 5.40 7.63 10−1

4.342 5.80 14.5

0.002 0.17 6.87

95 44 9.4

SP–4.1, KCl 10−3 3.26 10−2 5.57 10−1 6.63

3.263 5.74 13.85

0.003 0.17 7.22

88 43 8

SP(LA)–2.6, KCl 10−3 7.37 10−2 9.74 10−1 16.79

7.371 9.84 21.45

0.001 0.10 4.66

108 58 19

RT C+ ϕD ∼ ln =− z+ F C

0.003 0.24 7.62

89 36 7

Fig. 12. Cation mobility’s in the pore space of nanoporous glasses vs. electrokinetic radius for: 1–S–1.9 (䊉)Na+ , (
)Ba2+ , ()La3+ ; S–2.4 () Na+ ; and (2) S–2.4, K+ .

(13)

where z+ is the cation valence. The results of calculation are listed in Table 4. It is shown that, in dilute solutions, the counterion concentration in nanoporous glasses more than by one order exceeds the bulk concentration of equilibrium solution; the coion concentration becomes negligible in 10−3 M 1:1 electrolytes and increases with the electrolyte concentration growth, especially in the presence of multivalent cations. The comparison of the Donnan potential and the electrokinetic potential values shows that, for all the membranes investigated, |ϕD | > |ζ| and decrease with increasing the background electrolyte concentration (examples of obtained results are exhibited in Fig. 9 and in Table 4). Using the homogeneous model, the counterion mobility in pores U+ was also calculated from the counterion transport numbers: C+ z2 (U+ − Ueo ) ncat =  + 2 (i = +, −) i Ci zi (Ui − Ueo )

(14)

where Ueo = (ES )/(P)FκV α is the electroosmotic liquid mobility in the membrane pores, ES is the streaming potential, the coion 0 using mobility U− was calculated from bulk solution values U− 0 equation U− = U− /K.

The calculated counterion mobility’s for borosilicate nanoporous PG are represented in Fig. 12. It can be seen that for all membranes the counterion mobility in pores is considerably smaller than those in bulk solution. It is also seen that the z+ U+ -value increases with the electrokinetic radius growth as a result of decreasing the influence of electrostatic interactions on the characteristics of cations in the pore space. The proximity of the z+ U+ -values for ions Na+ , Ba2+ and La3+ at krβ = const confirms the assumption on a non-specific behaviour of multivalent cations in nanoporous glasses. The comparison of K+ ion mobility values for nanoporous glasses of different chemical composition shows that at equal surface charge and pore size (membranes S–2.4 and SP–4.1) z+ U+ -values are also equal. Both a decrease in pore size and an increase in the surface charge for S(FP) and SP(LA) membranes in compare with those parameters for S and SP membranes, lead to a decrease in counterion mobility values for krβ = const. 4. Conclusions The structural parameters, the surface charge and the electrokinetic characteristics of micro- and ultraporous glass membranes of various chemical compositions were measured in dependence on pH and salt level. The influence of pore size (electrokinetic radius) and counterion type on membrane characteristics were analyzed. It was obtained that the prolonged contact of nanoporous PG with electrolytes leads to a change in the membrane structure due to the removal of secondary silica from the pore space. The surface charge depends on the chemical composition of PG and on the pore size of nanoporous membranes—the tendency of increasing in |σ 0 |-values with diminishing EDL overlapping was observed. For ultraporous PG with the same chemical composition the surface charge become independent on pore size in the range pH ≤ 6.5. The electro-transport characteristics of membranes – counterions transport numbers and efficiency coefficients – depended only on the electrokinetic radius for ultraporous membranes of

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equal surface charge that means the constancy of ion mobility’s in pore channels for these PG. The comparison of ultraporous and nanoporous glasses also showed that the decrease in counterion mobility’s with an increase in EDL overlapping was observed. The specific surface conductance was practically independent on the degree of EDL overlapping and on the solution concentration for ultraporous PG at krβ > 1. The high specific surface conductance in the acid pH region could be due to an additional mechanism of surface conductivity related to the participation in conductance of non-dissociated H+ ions of surface silanol groups. The electrokinetic potential calculated with account for surface conductivity and the EDL overlapping for ultraporous PG was not depended on pore size, which gave an evidence of a permanent location of the shear plane. The non-specific behaviour of multivalent counterions in the pore space of nanoporous glasses, due to the presence of secondary silica in the pore channels, was observed; the behaviour of alkaline metal cations corresponds to the direct lyotropic sequence for all PG. Surface reaction constant, ion adsorption potential, ion concentration and mobility’s and Donnan potentials were calculated from experimental data using 2-pK model and homogeneous model. The analysis of obtained results also showed that the variation both of the chemical compositions of initial glass and of leaching conditions made possible to prepare the nanoporous glass membranes not only with adjustable pore size, but with adjustable electrosurface characteristics.

sandrov for the determination of the BET surface area, and Mrs. T. Kostyreva for the determination of PG chemical composition. Work was supported by the Russian President program “Leading Scientific Schools of Russian Federation”, project number NSh-789.2003.3. and by the Russian Foundation for Base Research under contract number 05-03-32603. References [1] [2] [3] [4] [5] [6] [7] [8] [9]

[10] [11] [12] [13] [14] [15]

Acknowledgements

[16]

The authors particularly thank academician A.I. Rusanov for the help in the preparing of this paper. Also thank Mr. D. Alek-

[17] [18] [19]

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