2.1. Microstructure and Morphological Parameters of Alumina Membranes
Three NPAMs fabricated by the anodization process have been studied: one of them is a commercial sample (Anopore™ by Whatman International Ltd., Maidstone, UK), and the two other were synthesized in our laboratory by two-step anodization either in sulfuric (Al-Sf) or oxalic (Al-Ox) acids. Samples of the Al-Ox membranes were also coated with a thin layer of 5 nm in thickness of Al
2O
3 or SiO
2, both deposited by ALD, and the resulting samples will be hereafter referred to as Al-Ox/Al
2O
3 and Al-Ox/SiO
2, respectively. Contact angle measurements revealed substantial differences between SiO
2 coated membranes and uncoated ones, evidencing the hydrophobic character or silica [
8]. Geometrical parameters of the Anopore membrane given by supplier are: pore radii of 10 nm, thickness of 60 μm and porosity between 25% and 50%, although an estimated porosity of 30% seems to be a more accurate value according to indications given by Bluhm
et al. [
9] and from tritiated water diffusion results [
10].
Figure 1 shows the top-view scanning electron microscopy (SEM) images of Al-Sf and Al-Ox/SiO
2 samples, as well as for the commercial Anopore membrane. As it can be observed, both experimental samples exhibit a well-defined and regular porous structure, rather different to that shown by the commercial membrane (Anopore).
Figure 1d displays a cross-sectional SEM image of sample Al-Ox/SiO
2 evidencing the cylindrical and straight pore channels of the experimental membranes.
Figure 1.
Scanning electron microscopy (SEM) top view images of nanoporous alumina membranes (NPAMs): (a) Al-Sf; (b) Al-Ox/SiO2; (c) Anopore; and (d) cross-sectional SEM image of sample Al-Ox/SiO2.
Figure 1.
Scanning electron microscopy (SEM) top view images of nanoporous alumina membranes (NPAMs): (a) Al-Sf; (b) Al-Ox/SiO2; (c) Anopore; and (d) cross-sectional SEM image of sample Al-Ox/SiO2.
Morphological surface parameters for the different samples (pore radii,
rp, and interpore distance,
Dint) as well as membrane thickness (∆
x) were determined from SEM micrographs analysis and the values obtained are collected in
Table 1. Membrane porosity (%) was determined by using the following expression [
11]:
. The estimated average porosity values (<Θ>) have been obtained by considering the porosity from both, top and bottom, SEM surface images.
Table 1.
Morphological parameters characteristic of the studied NPAMs: pore radius (rp = dp/2), interpore distance (Dint), thickness (∆x) and estimated average porosity (<Θ>).
Table 1.
Morphological parameters characteristic of the studied NPAMs: pore radius (rp = dp/2), interpore distance (Dint), thickness (∆x) and estimated average porosity (<Θ>).
Sample | rp (nm) | Dint (nm) | (<Θ>) (%) |
---|
Al-Sf | 12 ± 2 | 65 ± 2 | 15 |
Al-Ox + Al2O3 | 11 ± 3 | 105 ± 3 | 5 |
Al-Ox + SiO2 | 11 ± 3 | 105 ± 3 | 5 |
2.2. Characterization of Diffusive Transport across the Nanoporous Membranes
Fixed charge on both external surfaces and pore wall (or internal surface) as well as membrane structure can significantly influence the transport of electrolyte solutions and/or charged species across membranes [
12,
13]. Effective fixed charge,
Xef, and ion transport number,
ti, or fraction of the total current transported for one ion (
ti =
Ii/
IT) are two significant parameters that can be determined from membrane potential values (∆Ф
mbr).
According to the Teorell-Meyer-Sievers (TMS) theory [
14,
15], membrane potential can be considered as the sum of two Donnan potentials (one at each membrane-solution interface), associated to the exclusion of the co-ions (or ions of the same sign as the membrane charge), plus a diffusion potential in the membrane due to the different mobility of the ions inside the membrane pores, that is: ∆Ф
mbr = ∆ø
Don(I) + ∆ø
dif + ∆ø
Don(II). In the following expressions, 1:1 electrolytes (|
z+| = |
z−| = 1) and diluted solutions (herein, concentrations are used instead of activities) will be considered.
- -
The Donnan potential for a positively charged membrane with effective fixed charge
Xef in contact with an electrolyte solution of concentration
C can be expressed as [
16]:
where R and F correspond to the gas and Faraday constants, and
T is the temperature of the system, while
Cm represents the concentration in the membrane, related with
Xef and
C by the electroneutrality condition [
16]:
Xef +
z+ =
z− .
- -
The diffusion potential is given by [
16]:
where
t+ and
t− are the cation and anion transport numbers in the membrane, respectively. According to transport number definition,
t+ +
t− = 1, and for single salts:
t− = 1 −
t+.
Taking into account Equations (1) and (2), the membrane potential can be expressed as [
16]:
where
w = +1/−1 for positively/negatively charged membranes,
yj =
Cj/
Xef and the parameter
U is related to the ions transport numbers (
ti) and diffusion coefficients (
Di) by the following expression:
U =
t+ −
t− = 2
t+ − 1 = (
D+ −
D−)/(
D+ +
D−), for 1:1 electrolytes.
Figure 2 shows membrane potentials as a function of the concentration ratio for the studied membranes. For comparison, membrane potential for an ideal anion-exchanger membrane (dashed line) and the solution diffusion potentials (dashed-dot line) are also represented in
Figure 2. These parameter values were determined by using in Equation (1) the following values:
t− = 1 for ideal anion-exchanger, and the solution transport number
t+ =
[
17] in the case of solution diffusion potentials. As it can be observed, significant differences in ∆Ф
mbr values were obtained depending on both membrane porosity and surface nature (consequently, different ions-membrane electroaffinity). Particularly, very similar membrane potentials have been obtained for Al-Sf and Al-Ox/Al
2O
3 samples, that is, for nanoporous membranes with alumina surfaces, similar pore radii and low porosity (15% and 5%, respectively); however, much lower ∆Ф
mbr values for the same concentration ratio were obtained for the alumina membrane with higher porosity (30%), and they are very similar to the solution diffusion potential, which is an indication of the small barrier effect of the Anopore membrane to the transport of ions. On the other hand, similar values were also obtained for the SiO
2 coated surface sample (Al-Ox/SiO
2 membrane), with significantly lower porosity (5%), and in this case they might be associated to a reduction in the electrolyte/membrane electrical interactions as a result of the SiO
2 coating.
Figure 2.
Membrane potential as a function of solution concentrations ratio for different membranes: Anopore (■), Al-Sf (♦), Al-Ox/Al2O3 (▲), and Al-Ox/SiO2 (*).
Figure 2.
Membrane potential as a function of solution concentrations ratio for different membranes: Anopore (■), Al-Sf (♦), Al-Ox/Al2O3 (▲), and Al-Ox/SiO2 (*).
Differences in the diffusive ionic transport across the studied membranes are attributed to membranes structure and their surface electrical nature. Although all membranes have similar pore radii, their different interpore distance or porosity as well as surface charge might affect the co-ion exclusion from the interface and the pores, which would increase the counter-ion presence in both interface and pore solutions, as depicted in
Figure 3, which schematically shows the ionic transport behavior of the different membranes.
The fit of the experimental values shown in
Figure 2, by using Equation (3), allows us the estimation of effective fixed charge,
Xef, and anion transport number,
t−, values for each membrane, which are indicated in
Table 2. For all membranes,
t− values are higher than the solution average value
= 0.615 ± 0.004 [
17]), which is an indication of the electropositive character of all the samples. Taking into account the relationship between ion transport numbers and diffusion coefficients [
17]:
ti =
Di/(
D+ +
D−), ion diffusion ratio for each membrane (
D−/
D+ =
t−/
t+) was also estimated and their values are also indicated in
Table 2. It should be pointed out that the value of cation diffusion coefficient through the Al-Sf membrane hardly differs from that previously reported for this sample and determined from radiotracer (
22Na
+) diffusion measurement (
DNa+Al-sf = 2.8 × 10
−10 m
2/s, [
18]), which confirms the reliability of the obtained results.
Figure 3.
Illustrative representation of diffusive ion transport through membranes with different porosities and positive surface fixed charge: (a) Anopore (high porosity and low co-ion exclusion); (b) Al-Sf (medium porosity and high co-ion exclusion); (c) Al-Ox/Al2O3 (low porosity and high co-ion exclusion); and (d) Al-Ox/SiO2 (low porosity and low co-ion exclusion).
Figure 3.
Illustrative representation of diffusive ion transport through membranes with different porosities and positive surface fixed charge: (a) Anopore (high porosity and low co-ion exclusion); (b) Al-Sf (medium porosity and high co-ion exclusion); (c) Al-Ox/Al2O3 (low porosity and high co-ion exclusion); and (d) Al-Ox/SiO2 (low porosity and low co-ion exclusion).
Table 2.
Effective fixed charge (Xef), anion transport number (t−), ionic diffusion coefficients ratio (D−/D+) and ions diffusion coefficient values (D− and D+).
Table 2.
Effective fixed charge (Xef), anion transport number (t−), ionic diffusion coefficients ratio (D−/D+) and ions diffusion coefficient values (D− and D+).
Sample | Xef (M) | t− | D−/D+ | D− (m2/s) | D+ (m2/s) |
---|
Anopore | 0.001 | 0.655 | 1.90 | 1.9 × 10−9 | 1.0 × 10−9 |
Al-Sf | 0.012 | 0.751 | 3.02 | 9.8 × 10−10 | 3.3 × 10−10 |
Al-Ox/Al2O3 | 0.012 | 0.724 | 2.66 | 9.0 × 10−10 | 3.4 × 10−10 |
Al-Ox + SiO2 | 0.003 | 0.668 | 2.01 | 1.4 × 10−9 | 7.0 × 10−10 |
Differences between interfacial (Donnan) and transport contributions to the total membrane potential depending on the membrane structure can be observed in
Figure 4. This figure presents a comparison between experimental and fitted values of the membrane potential, as well as the individual contribution of Donnan and diffusion potential (dashed and dot-dashed lines, respectively), calculated by using Equations (1) and (2) with the corresponding fitted parameters for Al-Sf and Anopore membranes. As it can be observed, for the Al-Sf sample both Donnan and diffusion potentials present practically similar contribution for
Cv ≤ 0.04 M, but the diffusion potential increases more significantly by increasing the concentration gradient. However, for the low charged Anopore sample, the interfacial effect associated to Donnan potential hardly contributes to the membrane potential, which almost coincides with the diffusion potential contribution.
Figure 4.
Experimental (symbols) and fitted (solid lines) membrane potentials as a function of solution concentration ratio, plus calculated values for Donnan (dashed lines) and diffusion (dashed-dot lines) contributions determined using Equations (1) and (2) and parameters in
Table 2: (
a) Al-Sf membrane; and (
b) Anopore membrane.
Figure 4.
Experimental (symbols) and fitted (solid lines) membrane potentials as a function of solution concentration ratio, plus calculated values for Donnan (dashed lines) and diffusion (dashed-dot lines) contributions determined using Equations (1) and (2) and parameters in
Table 2: (
a) Al-Sf membrane; and (
b) Anopore membrane.
Differences in the barrier behavior of the studied membranes can also be observed in
Figure 5, where a comparison between membrane potentials measured with stirred and non-stirred solutions is also presented.
Figure 5.
Membrane potential as a function of solution concentrations ratio measured with: (a) stirred solutions, Anopore (■), Al-Sf (♦), and non-stirred solutions, Anopore (□), Al-Sf (◊); and (b) stirred solutions, Al-Ox/Al2O3 (▲), Al-Ox/SiO2 (*), and non-stirred solutions, Al-Ox/Al2O3 (∆), Al-Ox/SiO2 (×).
Figure 5.
Membrane potential as a function of solution concentrations ratio measured with: (a) stirred solutions, Anopore (■), Al-Sf (♦), and non-stirred solutions, Anopore (□), Al-Sf (◊); and (b) stirred solutions, Al-Ox/Al2O3 (▲), Al-Ox/SiO2 (*), and non-stirred solutions, Al-Ox/Al2O3 (∆), Al-Ox/SiO2 (×).
According to the results shown in
Figure 5, concentration-polarization (or the concentration profile in the feed solution near the membrane surface) seems to affect the membrane potential values for Al-Sf and Al-Ox/Al
2O
3 samples. It is due to their higher effective charge and/or lower porosity by modifying the concentration at the membrane surface with respect to bulk solution, but it hardly affects to the values determined for ANP and Al-Ox/SiO
2 membranes, as it is schematically indicated in
Figure 6 for membranes with similar pore radii. Concentration-polarization, which is a common effect in all membrane separation processes due to the different transport characteristics of solutions (fluids in general) and membrane phases [
19], would affect to the ∆Ф
mbr values by considering non-correct concentration values as well as by increasing the screening effect on membranes fixed charge.
Figure 6.
Schematic representation of solution concentration profiles near membranes with similar pore size and: (a) high fixed charge and low porosity; and (b) low fixed charge and high porosity.
Figure 6.
Schematic representation of solution concentration profiles near membranes with similar pore size and: (a) high fixed charge and low porosity; and (b) low fixed charge and high porosity.
Assuming that the membrane potential only corresponds to a diffusion potential associated to the different mobility of the ions into its porous structure, which is usually an adequate approximation for low charged membranes and high solution concentration [
16], the value of the anion transport number
t− in the membrane for each pair of the measured solution concentrations (
Cc,
Cv) can be obtained by using Equation (2). Variation of t
- values with the average concentration (
Cavg = (
Cc +
Cv)/2) for the studied membranes under stirring and non-stirring solutions conditions is shown in
Figure 7, where solution anion transport number (
t−0) is also represented by a dashed-dot line.
Figure 7.
Anion transport number as a function of average solutions concentration determined by Equation (2) for stirred (dense symbols) and non-stirred (open symbols) solutions: Anopore (■, □); Al-Sf (♦, ◊); Al-Ox/Al2O3 (▲, ∆); and Al-Ox/SiO2 (*, ×).
Figure 7.
Anion transport number as a function of average solutions concentration determined by Equation (2) for stirred (dense symbols) and non-stirred (open symbols) solutions: Anopore (■, □); Al-Sf (♦, ◊); Al-Ox/Al2O3 (▲, ∆); and Al-Ox/SiO2 (*, ×).
According to these results, a reduction of around 12% in the value of the anion transport number through both alumina membranes, with low porosity/higher fixed charge, was obtained when measurements were performed without stirring the NaCl solutions, but its effect on the alumina membrane with similar pore size but higher porosity/lower fixed charge is only of 2% and practically independent of the concentration gradient. Moreover, the chemical modification of the membrane surface as a result of SiO2 coverage also decreases the concentration polarization effect, being the difference in transport number between stirred and non-stirred solution ~3%; this reduction seems to be directly related to differences in the NaCl/SiO2 electroaffinity when compared with the NaCl/Al2O3 interactions corresponding to the other membranes, even if similar pore size and porosity are considered.