pubs.acs.org/Langmuir © 2010 American Chemical Society
Study on Transmembrane Electrical Potential of Nanofiltration Membranes in KCl and MgCl2 Solutions Cong-Hui Tu, Hong-Li Wang, and Xiao-Lin Wang* State Key Laboratory of Chemical Engineering, Department of Chemical Engineering, Tsinghua University, Beijing 100084, P. R. China Received June 10, 2010. Revised Manuscript Received September 20, 2010 The transmembrane electrical potential (TMEP) across two commercial nanofiltration membranes (ESNA1-K and Filmtec NF) was investigated in KCl and MgCl2 solutions. TMEP was measured in a wide range of salt concentrations (1-60 mol 3 m-3) and pH values (3-10) at the feed side, with pressure differences in the range of 0.1-0.6 MPa. A twolayer model based on the Nernst-Planck equation was proposed to describe the relation between TMEP and permeation flux. From the pattern of these curves, the information of membrane structure could be deduced. In the concentration range investigated, TMEP in KCl solutions was always positive and decreased as the salt concentration increased. The contribution of the membrane potential to the TMEP decreased. TMEP was greatly affected by the feed pH. When the feed pH increased, the mobility of cations increased, which indicated that the charges of NF membranes were more negative. The zero point of TMEP and the minimum of rejection in KCl solution were consistent and occurred at the isoelectric point of NF membranes, while in MgCl2 solution the zero point of TMEP located at a higher pH value. The TMEP in MgCl2 solutions changed its sign at a given concentration, and by calculating the transport number the location of the minimum rejection could be determined.
1. Introduction Nanofiltration (NF) membranes are well-known to have unique features: they have nanoscale pores of ∼1 nm, and they are normally negatively charged at neutral pH. Therefore, they are well-suited for the separation of small charged and uncharged molecules, with a molecular size of around 1 nm or, in the case of charged solutes, smaller. For this reason, NF membranes find many uses in the fractionation or removal of specific (charged or uncharged) solutes such as in water softening, partial desalination, concentration of juices, or effluent treatment.1-4 However, these two features also yield difficulties in the determination of the transport mechanism of solutes through NF membranes. In the nanoscale pores, the hindrance-steric effect is important,5-7 and the overlap of the double-electric layer makes the Helmholtz-Smoluchowski equation invalid.8,9 Therefore, an unpredictable change in the character of the solvent may occur: for example, the decrease of the dielectric constant of water *To whom correspondence should be addressed. E-mail: xl-wang@ tsinghua.edu.cn. Telephone: þ86-10-62794741. Fax: þ86-10-62794742. (1) Van der Bruggen, B.; Vandecasteele, C. Environ. Pollut. 2003, 122(3), 435– 445. (2) Chakraborty, S.; Purkait, M. K.; DasGupta, S.; De, S.; Basu, J. K. Sep. Purif. Technol. 2003, 31(2), 141–151. (3) Van der Bruggen, B.; Everaert, K.; Wilms, D.; Vandecasteele, C. J. Membr. Sci. 2001, 193(2), 239–248. (4) Warczok, J.; Ferrando, M.; Lopez, F.; Guell, C. J. Food Eng. 2004, 63(1), 63–70. (5) Nakao, S. I.; Kimura, S. J. Chem. Eng. Jpn. 1982, 15(3), 200–205. (6) Bowen, W. R.; Mohammad, A. W.; Hilal, N. J. Membr. Sci. 1997, 126(1), 91–105. (7) Wang, X. L.; Tsuru, T.; Togoh, M.; Nakao, S.; Kimura, S. J. Chem. Eng. Jpn. 1995, 28(2), 186–192. (8) Christoforou, C. C.; Westermannclark, G. B.; Anderson, J. L. J. Colloid Interface Sci. 1985, 106(1), 1–11. (9) Szymczyk, A.; Aoubiza, B.; Fievet, P.; Pagetti, J. J. Colloid Interface Sci. 1999, 216(2), 285–296. (10) Yaroshchuk, A. E. Adv. Colloid Interface Sci. 2000, 85(2-3), 193–230. (11) Senapati, S.; Chandra, A. J. Phys. Chem. B 2001, 105(22), 5106–5109. (12) Bowen, W. R.; Welfoot, J. S. Chem. Eng. Sci. 2002, 57(7), 1121–1137. (13) Bandini, S.; Vezzani, D. Chem. Eng. Sci. 2003, 58(15), 3303–3326. (14) Szymczyk, A.; Fievet, P. J. Membr. Sci. 2005, 252(1-2), 77–88.
17656 DOI: 10.1021/la102363y
can “push” the ions out of the membranes.10-15 This essentially comes down to the fact that, on the nanoscale of the membrane pores, bulk properties are not valid anymore. The formation of charge on NF membranes involves many mechanisms, such as dissociation equilibrium or adsorption equilibrium.16-20 Therefore, the unpredictable character of the solvent in nanopores and the charge density of NF membranes make the transport mechanism ambiguous, as it determines both the rejection and the permeation flux. Therefore, the separation performance should be combined with electrokinetic characters in order to promote study of transport mechanism of NF membranes.21,22 As an important electrokinetic phenomenon of NF, the transmembrane electrical potential (TMEP) plays an important role in theoretical studies.21-25 The TMEP is the potential resulting from the convection of electrolyte solutions, diffusion of cations and anions, and difference between bulk and membrane phases, when a pressure gradient is applied through charged selective membranes. Compared with other methods, such as measurement of the tangential streaming potential and the membrane potential,26-29 the TMEP has its own advantage. The TMEP can be measured (15) Deon, S.; Dutournie, P.; Limousy, L.; Bourseau, P. Sep. Purif. Technol. 2009, 69(3), 225–233. (16) Ariza, M. J.; Benavente, J. J. Membr. Sci. 2001, 190(1), 119–132. (17) Takagi, R.; Nakagaki, M. J. Membr. Sci. 1990, 53(1-2), 19–35. (18) Takagi, R.; Nakagaki, M. Sep. Purif. Technol. 2001, 25(1-3), 369–377. (19) Bandini, S.; Drei, J.; Vezzani, D. J. Membr. Sci. 2005, 264(1-2), 65–74. (20) Bandini, S. J. Membr. Sci. 2005, 264(1-2), 75–86. (21) Szymczyk, A.; Sbai, M.; Fievet, P. Langmuir 2005, 21(5), 1818–1826. (22) Fievet, P.; Sbai, M.; Szymczyk, A. J. Membr. Sci. 2005, 264(1-2), 1–12. (23) Benavente, J.; Jonsson, G. Colloids Surf., A 1999, 159(2-3), 431–437. (24) Benavente, J.; Jonsson, G. J. Membr. Sci. 2000, 172(1-2), 189–197. (25) Yaroshchuk, A. E.; Boiko, Y. P.; Makovetskiy, A. L. Langmuir 2002, 18 (13), 5154–5162. (26) Elimelech, M.; Chen, W. H.; Waypa, J. J. Desalination 1994, 95(3), 269–286. (27) Mullet, M.; Fievet, P.; Szymczyk, A.; Foissy, A.; Reggiani, J. C.; Pagetti, J. Desalination 1999, 121(1), 41–48. (28) Shang, W. J.; Wang, X. L.; Wang, H. L. Desalination 2008, 233(1-3), 342– 350. (29) Fievet, P.; Aoubiza, B.; Szymczyk, A.; Pagetti, J. J. Membr. Sci. 1999, 160 (2), 267–275.
Published on Web 10/13/2010
Langmuir 2010, 26(22), 17656–17664
Tu et al.
Article
Figure 1. Sketch map of the model.
simultaneously with the rejection in NF process under the same conditions. Therefore, it can realistically reflect the relationship between the separation performance and electrokinetic phenomena. Combining the results of rejection and TMEP, the actual volume charge density of NF membranes in the filtration process and the character of the solvent in pores of NF membranes can be conveniently calculated. However, tangential streaming potential, the charge density of the outer membrane surface, can be obtained, but possible differences in the chemistry of the outer membrane surface and the inner membrane structure can exist, according to Lettmann et al.30 And the measurement of the membrane potential is carried out under conditions with zero pressure drop, that is, without contribution of convection, and the concentration profiles in membranes are necessarily different from the ones during the filtration process. Therefore, the simultaneous measurement of TMEP and rejection in NF process makes it possible to apply online monitoring and prediction of membrane fouling. The composition of the TMEP was determined in the literature.21-25,31,32 Commonly, the TMEP is composed of three contributions, that is, the convection potential Δjc, the diffusion potential Δjd, and the Donnan potential ΔjD, accompanied by the instantaneous pressure drop and concentration difference between feed and permeate side. The convection potential is caused by the flux of electrolytes in the charged pores under the pressure gradient. Owing to the concentration difference in NF membranes, electrolytes will diffuse from the high-concentration side to the low-concentration side, and the different mobility between anion and cation leads to the accumulation of highmobility ions on the low-concentration side. As a result, the diffusion potential is built up by the imbalance of anion and cation concentrations. The Donnan potential is the electrical potential at the interfaces (feed-membrane and membranepermeate), which is usually combined with the diffusion potential as membrane potential to be discussed. Some researchers assumed that these three potentials only exist in the active layer.24 However, according to other researchers,21,22,25 the potentials in the support layer could not be neglected given the pressure drop and low conductance of the support layer. (30) Lettmann, C.; Mockel, D.; Staude, E. J. Membr. Sci. 1999, 159(1-2), 243–251. (31) Lefebvre, X.; Palmeri, J.; David, P. J. Phys. Chem. B 2004, 108(43), 16811– 16824. (32) Lefebvre, X.; Palmeri, J. J. Phys. Chem. B 2005, 109(12), 5525–5540.
Langmuir 2010, 26(22), 17656–17664
Therefore, the contribution of each potential in each layer is still somewhat unclear. Furthermore, when the surface of the NF membrane is covered by foulants forming a gel layer or cake layer, the TMEP may be different; this has not yet been investigated in detail. Because of its complex composition, the investigation of the effect of the outer solution and membrane characteristics on the TMEP has proven to be not sufficient, and its combination with rejection was quite unclear. However, it is important to study the TMEP in view of its significance and its potential to clarify how ions migrate. Moreover, the establishment of a universal model to describe the TMEP is necessary by taking every layer into account. In this paper, the TMEP in two commercial NF membranes has been investigated experimentally in KCl and MgCl2 solutions with different conditions, and a model has been proposed to describe the relationship of TMEP and permeation flux with respect to the fact that NF membranes have two layers. According to experimental data and the model, the transport number and contribution of each potential will be predicted, and the effects of membrane structure and external conditions on TMEP will be discussed.
2. Model Commercial thin film composite NF membranes usually consist of three layers: a polypropylene or polyester nonwoven backing, a microporous polysulfone or polyethersulfone support, and a proprietary thin active layer. Without considering the influence of the nonwoven backing, NF membranes are considered to be composed of two layers in the two-layer model. The two layers are the active layer and the support layer. The active layer is thought to dominate the separation performance. Because of the comparable pore size with ions, the ion flux inside the charged capillaries of the active layer obeys the extended Nernst-Planck equation by considering the steric-hindrance effects. It is considered that the support layer cannot separate the ions, and so there is almost zero concentration gradient in this layer. Thus, the concentration in the support layer equals that at the permeate side. The steric-hindrance effect is considered to be absent in the support layer. As a result, the ion flux in the support layer can be described by the Nernst-Planck equation. A Boltzmann distribution of ions is assumed at the two interfaces: the interface of feed solution and active layer and the interface of active layer and support layer. And the concentration and the potential are continuous at the interface DOI: 10.1021/la102363y
17657
Article
Tu et al.
Combining eqs 2-4 and 6, the electrical potential gradient equation can be obtained, integrating from feed side to permeate side, and the TMEP is then expressed as
Table 1. Collection of Governing Equations in the Model Boltzmann distribution at the interfaces ki, f ¼ ci, act ð0 þ Þ=ci, f ¼ exp - Δμi, f =Rg T ki, p ¼ ci, act ðΔxact - Þ=ci, p ¼ exp - Δμi, p =Rg T
(1)
Zero electric current condition (steady state) F
zi Ji ¼ 0
ð2Þ
i¼1
Transport equations Ji ðAk Þact
2 X
ΔjT ¼ ΔjD, f - ΔjD, p þ ΔjT, act þ ΔjT, sup 0 ! 2 P 2 ci, sup P z D c ln B i ip i, act Jv ðzi Kic ci, act Þ B ci , f Rg T Bi ¼ 1 Δx i¼1 B ¼ þ 2 2 P P F B Ak act @ zi 2 Dip ci, act zi 2 Dip ci, act i¼1
i¼1
dci, act zi F dj Jv þ Kic ci, act Dip ci, act ¼ - Dip ðactive layerÞ Rg T dx dx ðAk Þact
2 P
ð3Þ Ji zi F dj Jv þ ci, sup Di ci, sup ¼ Rg T dx ðAk Þsup ðAk Þsup
HDi ¼ 1 ,
,
i¼1
SDi ¼ ð1 - ηi Þ2 h i, ¼ ð1 - ηi Þ2 2 - ð1 - ηi Þ2
16 2 η SFi 9 i ηi ¼ rsi =rp , Dip ¼ Kid Di
Kic ¼ SFi HFi HFi ¼ 1 þ
ð5Þ
of the support layer and permeate side, which means ci,sup = ci,p and jT,sup = jT,p at this interface. The sketch map of the model is shown in Figure 1 (subscripts act and sup refer to the active layer and the support layer, respectively; f is the feed and p is the permeate; i refers to ion i). The governing equations of this model are given in Table 1. As already mentioned, the distribution of ions at the interfaces is described by a Boltzmann distribution (eq 1). The Boltzmann distribution depends on the change of molecular free energy at the interfaces. The change of free energy is caused by electrostatic interaction of ions and charged membranes (Donnan effect, ΔμiD,f(p) =ziFΔjD,f(p)), the steric-hindrance effect in membranes (ΔμiS,f(p) =-RgT ln(SDi)), the electrostatic interaction of ions in solution (activity, ΔμiA,f(p) = RghT ln(γi,act/γi,f(p))), the interaction of ions and solvent (Born energy33), and the interaction between ions and polymer membranes (image forces10). The activity coefficient of solution was considered as a unit in the concentration investigated, and the Born energy was considered as the primary contribution on dielectric repulse effect.12 As a result, only the change of Donnan effect is different at the interfaces of the feed solution/active layer and active layer/support layer, and all other energy changes are the same. Therefore, the difference of Donnan potential at these two interfaces can be expressed as follows: k1, f Rg T ln ΔjD, f - ΔjD, p ¼ z1 F k1, p
! ð6Þ
The solute transport through the active layer and the support layer of NF membranes is described by the extended NernstPlanck equation. The relevant equations and parameters have been described in detail in the electrostatic and steric-hindrance model and the Teorell-Meyer-Sievers model.34,35 (33) Rashin, A. A.; Honig, B. J. Phys. Chem. 1985, 89(26), 5588–5593. (34) Wang, X. L.; Tsuru, T.; Nakao, S.; Kimura, S. J. Membr. Sci. 1997, 135(1), 19–32. (35) Wang, X. L.; Tsuru, T.; Nakao, S.; Kimura, S. J. Membr. Sci. 1995, 103 (1-2), 117–133.
17658 DOI: 10.1021/la102363y
i¼1 2 P
zi ci, sup Jv
zi 2 Di ci, sup
C C Δx C Ak sup C A
ð7Þ
ðsupport layerÞ ð4Þ
with Kid ¼ SDi HDi
þ
1
Then, z1c1,supþ z2c2,sup should be equal to the volume charge density -Xw,sup in the support layer, and ci,sup approximates ci,p. In order to simplify the expression of TMEP, membrane parameters including the electric transport number ti as proposed in irreversible thermodynamics36 are introduced. Electric transport numbers are considered as the average transport numbers and are treated as constant in membranes. Equation 7 can then be rewritten as follows: 0 2 BX
Rg T B B F @i ¼ 1
ΔjT ¼
1 X 2 C ti, act ti, act Kic cp Δx Jv B C þ ln Jv þ 2 C A P zi cf z D A i ip k act i¼1 2 z i Di c i , p i¼1
B ¼ - ðXw Þsup ti, act ¼
Δx Ak
zi 2 Dip ci, act , 2 P zi 2 Dip ci, act
ð8Þ sup
i ¼ 1, 2
ð9Þ
i¼1
The first term on the right side of eq 8 is the membrane potential in the active layer, the second term is the convection potential in the active layer, and the third term is the convection potential in the support layer. If the support layer has no contribution on TMEP, the third term should be zero. Therefore, if the third term is ignored, the model is a one-layer model. The model can also be extended to describe the TMEP in NF membranes with multiple layers, such as the gel or cake layer, following the same process mentioned above. However, in this paper, only clean NF membranes are considered, and there are no other layers apart from the active layer and the support layer. With the experimental data of ΔjT and Jv, the average values of transport number of ions in the active layer can be obtained by multivariate linear regression according to eq 8.
3. Experimental Section 3.1. Membranes and Chemicals. The membranes used in this work are Filmtec NF (Dow) and ESNA1-K (Nitto Denko). Both of the membranes are made of aromatic polyamide and are negatively charged in the pH range of 5-10. Experiments have been carried out with potassium chloride and magnesium chloride of reagent-grade (Beijing Modern Eastern Fine Chemical (36) Hijnen, H. J. M.; Vandaalen, J.; Smit, J. A. M. J. Colloid Interface Sci. 1985, 107(2), 525–539.
Langmuir 2010, 26(22), 17656–17664
Tu et al.
Article
Figure 2. Schematic view of the experimental set ((1) thermostated liquid container; (2) turbine pump; (3) manometer; (4) membrane module; (5) membrane; (6) valve; (7) potential difference meter). Corporation). The Stokes radii of potassium, chloride, and magnesium ion are 0.124, 0.12, and 0.365 nm, respectively. Millimolar solutions at different concentration have been prepared from deionized water. The salt concentrations ranged from 1.0 to 60.0 mol 3 m-3.
3.2. Rejection, Permeation Flux, and TMEP Measurements. The rejection, the permeation flux, TMEP, and the
pressure difference were measured synchronously in a laboratory setup. The experimental setup is shown in Figure 2. The experimental unit used in this work allowed measuring rejection rate, permeation flux, and TMEP simultaneously, which was done for transmembrane pressures ranging from 0.1 to 0.6 MPa. The crossflow is fixed at 6.0 L 3 min-1. According to the theory, the influence of concentration polarization on rejection and TMEP can be ignored at this condition. A pump allowed circulating the solution to the membrane module. Both feed and permeate streams were recycled in the feed tank. After every experiment, the pure water permeability was measured to make sure the characters of membranes did not change. A heat exchanger was used to keep the temperature at 20 ( 0.2 °C. The permeate volume flux Jv was determined by weighting the permeate amount flowing through the membrane. The rejection was obtained from solution concentration, which was determined by conductivity measurements carried out in both feed and permeate compartments. The electrical potential difference was measured by two Ag/ AgCl electrodes. The electrical potential measurements include the Nernst (electrode) potential for Cl- reversible electrodes. The electrode potential is given by the following expression.
Figure 3. Relationship of rejection and permeation flux in ESNA1-K (a) and Filmtec NF (b) membranes for neutral solutes (ethanol, isopropyl alcohol, and t-butyl alcohol) with 10 mol 3 m-3. The points are experimental data. The solid lines are the fitting results by the steric-hindrance pore model. Table 2. Reflection Coefficient and Pore Size Calculated by Steric-Hindrance Pore Model membranes
solutes
σ (-)
rp
ESNA1-K
ethanol alcohol isopropyl alcohol t-butyl alcohol
0.6276 0.8972 0.9305
0.60 0.43 0.46 0.49
ethanol alcohol isopropyl alcohol t-butyl alcohol
0.337 0.4997 0.6082
1.2 1.0 0.9 1.0
average Filmtec NF average
4. Results and Discussion
be determined. Then the rejection, permeation, and TMEP were introduced into eq 8 to obtain the value of ti and B with multilinearity fitting method. If the membranes are considered as one layer, only the value of ti would be fitted. The pore size of NF membranes was used to calculate the steric-hindrance factors Kic and Kid. In this paper, the pore size of two NF membranes was determined by the separation experiments of neutral solutes (ethanol, isopropyl alcohol, and t-butyl alcohol) based on the steric-hindrance pore model.37 By providing the solutes parameters (rs, Di) which are constant and the rejection and flux obtained in the experiments, the effective pore size and the ratio of thickness over porosity can be determined. Figure 3 shows the rejections of three solutes as a function of permeation flux. And the resulting structural membrane parameters are given in Table 2. The mean pore radii of ESNA1-K and Filmtec NF are 0.49 and 1 nm, respectively.
4.1. Pore Size and Ratio of Effective Thickness over Porosity of NF Membranes. Before the fitting of TMEP, the pore size and ratio of effective thickness over porosity should
(37) Labbez, C.; Fievet, P.; Thomas, F.; Szymczyk, A.; Vidonne, A.; Foissy, A.; Pagetti, P. J. Colloid Interface Sci. 2003, 262(1), 200–211.
Δjelectrode ¼
Rg T af ln , afðpÞ ¼ γfðpÞ cfðpÞ ap F
ð10Þ
The pressure effects on electrodes immersed into solutions was neglected, thus the TMEP was obtained by subtracting the electrode potential from the potential directly read on potential difference meter.
Langmuir 2010, 26(22), 17656–17664
DOI: 10.1021/la102363y
17659
Article
Tu et al.
Figure 4. Relationship of permeation flux and effective pressure in ESNA1-K and Filmtec NF membranes for KCl solutions with different concentrations. The points are the experimental data. The solid lines are the linear fitting results by eq 10.
The values of Δx/Ak vary with the fitting methods (water permeability, rejection experiments of neutral solutes, and rejection experiments of ions). Δx/Ak calculated by the water permeability is based on eq 11. The solution permeability is shown in Figure 4. The permeability seems independent of concentration. Although the pore size of ESNA1-K is smaller, the permeability is larger than that of Filmtec NF. It may be caused by the difference of materials of the active layer, or the characteristic of the support layer. For the thickness of the support layer, the pressure drop in it may not be ignored. And it is difficult to measure this pressure drop. Therefore, in this paper, to avoid the measurement of the pressure drop in the support layer, the relationship of permeation flux and TMEP mainly was investigated. Δx/Ak calculated by the neutral solutes used the steric-hindrance pore model.37 And Δx/Ak was calculated by the ions based on the Speigler-Kedem (SK) equation and the relationship of σ and P.34 The relationship of rejection and permeation flux is displayed in Figure 5. These results are listed in Table 3. However, the values of Δx/Ak are very different, which has also been published by other researchers.6,37 In this paper, Δx/Ak from the rejection experiments of ions was used to fit TMEP for the reason that only rejection of ion and creation of TMEP caused at the same conditions, in which the ions transport in the same path. Jv ¼
r p 2 Ak ðΔP - ΔπÞ, 8μΔx
Δπ ¼ Rg T
X
Δci
ð11Þ
i
4.2. Influence of Structures of NF Membranes. Figure 6 shows the relationship between TMEP and permeation flux in Filmtec NF membranes for KCl solutions. The broken lines are the curve-fitting results without regard to the influence of the support layer (one-layer model), and the solid lines are the curvefitting results for the two-layer model (eq 8). As can be seen, the one-layer model failed to describe the real experimental phenomena, especially in the low concentration range, while the two-layer model agrees well with the experimental data. Table 4 presents the transport number and the value of B of Kþ calculated by these two models. The transport numbers predicted by the one-layer model are larger than the two-layer model. Moreover, when the feed concentration is 2 mol 3 m-3, the transport number predicted by one-layer is above 1, which is unreasonable. Therefore, it can be concluded that the one-layer model is not suitable to describe the TMEP of NF membranes, which means that the potential in the support layer of NF membranes cannot be ignored. This potential may be caused by the pressure drop and low conductance in the thick support layer.21,22,25 17660 DOI: 10.1021/la102363y
Figure 5. Relationship of rejection and permeation flux in in ESNA1-K (a) and Filmtec NF (b) membranes for KCl solutions with different concentrations. The points are the experimental data. The solid lines are the fitting results by the SK equation.
Figure 6. Relationship of TMEP and permeation flux in Filmtec NF membrane for KCl solution with 2, 10, 21, and 52 mol 3 m-3. The points are the experimental data. The solid lines are the fitting results by the two-layer model, and the broken lines are the fitting results by the one-layer model. Table 3. Values of Δx/Ak by Different Methods (10-5m) Δx/Ak by rejection Δx/Ak by solution Δx/Ak by rejection of neutral solutes permeability of KCl ESNA1-K NF
3.9 22.5
0.2 1.2
69.7 8.9
Nevertheless, the separation performance of the support layer can still be ignored. The thickness of the support layer of Filmtec NF is about 100 μm by Dow. If the influences of tortuosity and porosity are taken into account, the effective thickness over porosity might be on a magnitude of 10-3m. From the fitting results of B in table 4, it was calculated that the volume charge density of support layer is about 0.5-5 mol 3 m-3 (which means Xw/c = 0.1-0.2). This value range coincides with the results Langmuir 2010, 26(22), 17656–17664
Tu et al.
Article Table 5. Transport Number of Kþ and Contribution of Every Potential in Filmtec NF and ESNA1-K Membranes Calculated by the Two-Layer Model
Figure 7. Relationship of TMEP and permeation flux in Filmtec NF and ESN1-K membranes for KCl solution with 2.22 mol 3 m-3. The points are experimental data, and the solid lines are the fitting results by the two-layer model. Table 4. Transport Number of Kþ and B in Filmtec NF Membrane Calculated by One-Layer Model and Two-Layer Models 2
10
22
52
t1
one-layer two-layer
1.16 0.87
0.96 0.80
0.86 0.76
0.84 0.73
B (10-3 mol 3 m/m3)
one-layer two-layer
0 0.62
0 1.36
0 1.89
0 4.72
obtained in ultrafiltration membranes.38-40 Therefore, the volume charge density of the support layer calculated would be reasonable. The reflection coefficient is almost zero without consideration of the steric hindrance effect by the TMS model.35 Therefore, the potential in support layer is only the convection potential. From the results of TMEP, the structure of NF membranes can be deduced. Figure 7 shows the relationship between TMEP and the permeation flux in Filmtec NF and ESNA-1K membranes. The TMEP in ESNA1-K membranes is larger than that in Filmtec NF membranes for KCl solution with the same concentration. There are three reasons to explain this: (1) ESNA1-K membranes have the smaller pores, (2) they have the larger thickness, and (3) they have the higher charge density. However, from Table 5, it can be seen that transport numbers of Kþ in ESNA1-K membranes are smaller than those in Filmtec NF membranes. Because Kþ and Cl- have almost the same diffusion coefficient and steric hindrance effect, according to eq 9, transport numbers are primarily dependent on the difference of concentration of Kþ and Cl-, which is decided by the charge density of membranes. Therefore, the charge density of ESNA1-K might be smaller, which would cause the decrease of TMEP. However, higher TMEP in ESNA1-K means the smaller pore size and larger thickness. This phenomenon can also be confirmed by the results of rejection. From the permeation experiments of neutral solutes, it was calculated that the pore radius of ESNA1-K membranes is 0.49 nm and that of Filmtec NF membranes is 1 nm. Moreover, the rejection becomes steady in lower permeation flux in ESNA1K membranes from Figure 5, which means that ESNA1-K membranes have a thicker and denser active layer (Table 2). It is seen that the curves of two membranes are typically nonlinear. The pattern of nonlinearity (sub- or superlinearity) depends on the relative contribution of constituent potentials. The existence (38) Martinez, F.; Martin, A.; Malfeito, J.; Palacio, L.; Pradanos, P.; Tejerina, F.; Hernandez, A. J. Membr. Sci. 2002, 206(1-2), 431–441. (39) Huisman, I. H.; Pradanos, P.; Hernandez, A. J. Membr. Sci. 2000, 178, 55–64. (40) Pastor, R.; I., C. J.; Pradanos, P.; Hernandez, A. J. Membr. Sci. 1997, 137, 109–119.
Langmuir 2010, 26(22), 17656–17664
membrane
cKCl (mol 3 m-3)
t1
ESNA1-K
2 22
0.76 0.70
45% 55%
55% 45%
95% 87%
5% 13%
Filmtec NF
2 22
0.87 0.76
23% 33%
77% 67%
61% 73%
39% 27%
Δjc,act Δjm,act Δjact Δjsup
of convection potential in the support layer causes the superlinearity of the curves, while membrane potential causes the sublinearity. It can be deduced from Figure 7 that the contribution of the convection potential in the support layer of Filmtec NF membranes is larger. According to the analysis results shown in Table 5, the contribution of the convection potential in the support layer of Filmtec NF membranes is about 30%, while it is only 10% in ESNA1-K membranes. Figure 8 displays SEM pictures of a cross section of these two membranes. The nonwoven layer was peeled off before taking the SEM pictures. The lines on the pictures would be the approximated boundaries of active layers and support layers. This proves that the Filmtec NF membranes have a thicker and denser support layer. Whatever the pattern of nonlinearity, all the curves sooner or later tend to become linear. Since both the membrane potential of the active layer and the convection potential of the support layer generally control the nonlinearity, not much useful information can be obtained from the slope, unless the permeation flux is large enough to omit the change of rejection. However, it is hard to judge when the permeation flux is large enough. 4.3. Influence of Concentrations of Feed Solution. As can be seen in Figure 6 and Table 6, with the increase of concentration in the feed solution, the TMEP decreases and the transport number of Kþ decreases. The screening effect caused by the increase of concentration of feed solution decreases the electrostatic effect of membranes and ions. The smaller repulsion between Cl- and membranes increases the concentration of Cl- in membranes, resulting in the decrease of TMEP and the transport number of Kþ. The linearity of the curves increases with the growth of concentration of feed solution and permeation flux. It is indicated in Figure 9 that the contribution of the membrane potential on the TMEP of the active layer decreases with the increase of the concentration in the feed solution and the permeation flux. Since it is the membrane potential that causes the nonlinearity, the smaller contribution surely increases the linearity. 4.4. Influence of pH Values of Feed Solution. The results of the measurements of rejection and TMEP of KCl and MgCl2 with concentration of 10 mol 3 m-3 and pH values ranging from 3 to 10 in Filmtec NF membranes are given in Figure 10. The concentration of feed solution is chosen for two reasons. The first one is the compromise between values of TMEP that are either too high or too low. If the value is too high (low concentration), the signal is not steady, and if the value is too low, the change of TMEP is too small. The other reason is when the pH was 3 or 10, the ratios of concentration of Hþ to Kþ or OH- to Cl- are above 10, and the influence of rejection of Hþ and OH- can be ignored. In this case, it is assumed that the change of pH values only took effect on the charge density of membranes. The relationship of TMEP and permeation flux at different pH is also measured to obtain transport number. To avoid the damage of membranes by extreme conditions, only three mild pH values of 4, 6.5, and 8 have been chosen. From Table 6, it can be seen that the transport number of Kþ increases as pH increases. When pH increases, the charge density of membranes is more negative, and the interactions DOI: 10.1021/la102363y
17661
Article
Tu et al.
Figure 9. Relationship of contribution of convection potential and membrane potential on TMEP and permeation flux in the active layer of Filmtec NF membrane for KCl solution calculated by the two-model layer. ((a) 2 mol 3 m-3; (b) 10 mol 3 m-3; (c) 21 mol 3 m-3; (d) 52 mol 3 m-3).
Figure 8. SEM pictures of ESNA1-K (a) and Filmtec NF (b) membranes. Table 6. Transport Number of Cations in Filmtec NF Membrane with Different Condition Calculated by the Two-Layer Model solute
c (mol 3 m-3)
pH
t1/z1
2 10 22 52 10 10 10
6.5 6.5 6.5 6.5 4.9 6.5 8.0
0.87 0.80 0.76 0.73 0.77 0.80 0.92
2 6 20 46
6.5 6.5 6.5 6.5
0.38 0.3 0.15 0.13
KCl
MgCl2
of ions and membranes are stronger. Therefore, the transport number of Kþ increases, and so does TMEP. However, with the increase of pH in KCl solution, rejection decreases first and then increases. It is worth mentioning that the zero point of TMEP and the minimum of rejection occur at the same pH value, which is about 4.3. Based on irreversible thermodynamics,36 the relationship of the reflection coefficient (the maximum rejection) σ of transport numbered can be expressed as follows: 1-σ ¼
K1c c1, act t2, act K2c c2, act t1, act þ c1, f c2, f
17662 DOI: 10.1021/la102363y
ð12Þ
Figure 10. Relationship of TMEP and pH, rejection and pH in Filmtec NF membrane for KCl (a) and MgCl2 (b) solutions with 10 mol 3 m-3; the pressure is fixed at 0.52 MPa, and the average permeation flux is 6.3 10-6 m3 3 m-2 3 s-1.
Then the partial derivative of reflection coefficient was calculated to find out when reflection coefficient (rejection) achieved its minimum. eq 13 is the expression of the partial derivative of the reflection coefficient: 2 !3 v c Dσ t t 2 1 , act 1m 2m z1 K2c t1m - z1 ¼ 4 þ K1c t2m 5 Dðc2, act =c2, f Þ z1 z2 v1 c2, act ð13Þ Therefore, when t1m/z1 þ t2m/z2 = 0, eq 13 equals zero, and the reflection coefficient reaches its minimum. At the same time, the membrane potential is also equal to zero according to eq 8. For KCl, only when membranes are neutral, both of the transport numbers of Kþ and Cl- are 0.5. At this condition, the membrane Langmuir 2010, 26(22), 17656–17664
Tu et al.
Article
5. Conclusions
Figure 11. Relationship of TMEP and permeation flux in Filmtec NF membrane for MgCl2 solutions with 2, 6, 20, and 46 mol 3 m-3. The points are the experimental data, and the solid lines are the fitting results by two-layer model.
potential and convection potential of membranes are also zero. Therefore, 4.3 is the isoelectric point of Filmtec NF membranes. For KCl, when membranes are neutral, the rejection will be minimum and TMEP will be zero. Different from the case of KCl, when the membranes are neutral, the ratio of transport number over valence of Mg2þ is below 0.333 for the large size and low diffusion coefficient of Mg2þ. And it means that the rejection of MgCl2 is not the minimum and TMEP is negative at the condition with neutral membranes (pH = 4.3), as can be seen in Figure 10b. These experimental results confirm the theory. The zero point of TMEP and minimum of rejection in MgCl2 occur at the condition when membranes are charged negatively. In our case, the zero point of TMEP in MgCl2 is at the condition with pH 6, and the minimum rejection is located at pH 7. When the pH is 7, the ratio of transport number over valence of Mg2þ is equal to 0.333, and membrane potential is zero. However, the convection potential is positive for the low diffusion of Mg2þ according to the expression of convection potential (Dip/Kic of Mg2þ is larger than that of Cl-). 4.5. Influence of Mg2þ. The relationship of TMEP and permeation flux in MgCl2 solution is presented in Figure 11. When concentration increases, TMEP decreases. Different from the case of KCl, TMEP becomes negative when concentration of MgCl2 solution is above 10 mol 3 m-3. In bulk, the transport number of Mg2þ is smaller than that of Cl-, while in membranes, especially in the low concentration range, the excess concentration of Mg2þ makes it possible that the transport number of Mg2þ is larger than that of for Cl-, and in this situation, the sign of TMEP is opposite to that in the bulk. When the feed concentration increases, the mobility of Mg2þ will be slowly weakened, and the sign of the membrane potential changes. Because of the equivalent mobility of Kþ and Cl- in bulk, Kþ in membranes always transports faster than Cl-, and the sign of TMEP will not change. As mentioned in section 4.3, the minimum rejection occurs at t1/z1 = 0.333 for MgCl2 solutions. From Table 6, the transport number of Mg2þ can be obtained; it decreases with the increase of concentration. When the range of concentrations is 2-6 mol 3 m-3, the values of t1/z1 are between 0.38 and 0.3. Therefore, it can be deduced that the minimum of rejection of MgCl2 is located at concentrations above 2 mol 3 m-3 and below 6 mol 3 m-3. This deduction is proven by experiments. From Figure 11, it can be seen that the reflection coefficient of MgCl2 decreases first and then increases with the increase of concentration, and the minimum of rejection is indeed located in the range of 2-6 mol 3 m-3. Langmuir 2010, 26(22), 17656–17664
The TMEP for two commercial NF membranes was investigated in KCl and MgCl2 solutions. A two-layer model was proposed to describe the relationship of TMEP and permeation flux. The curve-fitting results proved that the convection potential in the support layer could not be ignored, and the two-layer model was suitable to analyze the experimental data of TMEP. Based on this model, the effects of membrane structure and solution characteristics on TMEP in two commercial NF membranes (Filmtec NF and ESNA1-K) were investigated. From the pattern of the curves of TMEP and permeation flux, the contribution of convection potential in the overall potential could be deduced. With the increase of concentration solution, the screening effect made the transport number of Kþ decrease. The zero point of TMEP and the minimum of rejection for KCl solution were located at the same pH of 4.3, which was the isoelectric point of Filmtec NF membranes, while they were located at a higher pH of 6-7 for MgCl2 solution. Based on the results of the transport number of Mg2þ, the rejection of MgCl2 could be predicted to have a minimum point in the concentration range of 2-6 mol 3 m-3, which was confirmed by experimental observations. Acknowledgment. This work was supported by the National High Technology Research and Development Program of China (2009AA062901), the National Basic Research Program of China (2009CB623404), and Beijing Natural Science Foundation (2100001). Thank for the project of bilateral scientific cooperation between Tsinghua University and University of Leuven. And thank Professor Bart Van der Bruggen’s valuable comments on our paper.
Nomenclature a ci Di Dip F HDi HFi Ji Jv K ki Kic Kid rsi rp R Rg SDi SFi
Activity (mol 3 m-3) Concentration of ion i (mol 3 m-3) Diffusion coefficient of ions i (m2 3 s-1) Effective diffusion coefficient of ions i (m2 3 s-1) Faraday constant (=96 487) (C 3 mol-1) Steric-hindrance parameters related to the wall correction factors of ions i under diffusion condition Steric-hindrance parameters related to the wall correction factors of ions i under convection condition Flux of ion i over the membrane surface (mol 3 m-2 3 s-1) Solution volume flux over the membrane surface (m 3 s-1) Boltzmann constant (=1.38 10-23) (J/K) Local distribution coefficient of ion Convection hindrance factor of ions i Diffusion hindrance factor of ions i Stokes radius of ions i (m) Membrane pore radius (m) Rejection Gas constant (=8.314) (J mol-1 K-1) Contribution to the averaged distribution coefficients caused by the steric-hindrance effects of ions under diffusion condition Contribution to the averaged distribution coefficients caused by the steric-hindrance effects of ions under convection condition DOI: 10.1021/la102363y
17663
Article
T ti Xw Δx/Ak zi
Tu et al.
Temperature (K) Transport number of ions i Effective volume charge density (mol 3 m-3) The ratio of effective membrane thickness over porosity (m) Electrochemical valence of ion
Greek Letters Δμi ΔμiA ΔμiD ΔμiS
Difference of free energy between phases (J 3 mol-1) Difference of free energy caused by electrostatic interaction of ions in solution between phases (J 3 mol-1) Difference of free energy caused by steric-hindrance effect in membranes between phases (J 3 mol-1) Difference of free energy caused by electrostatic interaction of ions and charged membranes between
17664 DOI: 10.1021/la102363y
Δjc Δjd ΔjD Δjm ΔjT ηi σ γi
phases (J 3 mol-1) Convection potential (V) Diffusion potential (V) Donnan potential (V) Membrane potential (V) Transmembrane electrical potential (V) Ratio of Stokes radius of ions to pore radius Reflection coefficient Activity coefficient
Subscript act sup F P i
Active layer Support layer Feed side Permeate side ith ion (= 1 cation; =2 anions)
Langmuir 2010, 26(22), 17656–17664
