Environ. Sci. Technol. 2009, 43, 2400–2406
Influence of Solute-Membrane Affinity on Rejection of Uncharged Organic Solutes by Nanofiltration Membranes A R N E R . D . V E R L I E F D E , * ,†,‡ EMILE R. CORNELISSEN,‡ S E B A S T I A A N G . J . H E I J M A N , †,‡ ERIC M. V. HOEK,§ GARY L. AMY,| BART VAN DER BRUGGEN,⊥ AND JOHANNIS C. VAN DIJK† Department of Sanitary Engineering, Faculty of Civil Engineering and Geosciences, Delft University of Technology, P.O. Box 5048, 2600 GA Delft, The Netherlands, Kiwa Water Research (KWR), P.O. Box 1072, 3430 BB Nieuwegein, The Netherlands, Civil & Environmental Engineering Department and Water Technology Research Center, University of California, Los Angeles, California 90095, UNESCO-IHE, P.O. Box 3015, 2601 DA Delft, The Netherlands, and Laboratory for Applied Physical Chemistry and Environmental Technology, Department of Chemical Engineering, University of Leuven, W. de Croylaan 46, B-3001 Leuven, Belgium
Received November 10, 2008. Revised manuscript received January 27, 2009. Accepted January 28, 2009.
A simple, analytical method for predicting transport of uncharged organic solutes through nanofiltration (NF) and reverse osmosis (RO) membranes is presented in this paper. The method requires characterization of key solute and membrane parameterssnamely, solute size, membrane pore size, and solute-membrane affinity. All three parameters can be experimentally determined from relatively simple permeation tests and contact angle analyses. The parameters are fed into an analytical model of solute transport, which accounts for hindered convection and diffusion of solutes in the membrane pores, as well as the combined effects of steric exclusion and solute-membrane affinity on solute partitioning from the feed solution into the membrane pores. Overall model predictions for organic solute rejection agreed well with experimental data for three different solutes and two different polymeric NF membranes. Further, the model demonstrates the dramatic influence of solute-membrane affinity on organic rejection by NF and RO membranes. Solute transport predictions made assuming only steric exclusion significantly overestimated rejections for solutes with strong affinity for membrane polymers and similarly underestimated rejections for solutes that were strongly repelled by membrane polymers.
Introduction During the last few decades, concerns about the occurrence of organic micropollutants (e.g., pharmaceutically active * Corresponding author phone: +31 (0)15 27 83347; fax: +31 (0)15 27 84918; e-mail:
[email protected]. † Delft University of Technology. ‡ Kiwa Water Research. § University of California. | UNESCO-IHE. ⊥ University of Leuven. 2400
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compounds, personal care products, pesticides, flame retardants, etc.) in source waters for drinking water supply have rapidly increased, as a result of more accurate analytical methods that have revealed significant levels of these pollutants in aquatic environments (1, 2). Endocrine disrupting compounds received special attention (e.g., 17Rethinylestradiol) because of their potential to adversely affect the hormonal systems of humans and aquatic organisms at extremely low concentrations (3). Since health risks related to consumption of drinking water containing traces of organic pollutants are yet unknown, or difficult to predict, removal of these pollutants during drinking water (and/or wastewater treatment) is essential. However, removal of low molecular weight, polar organics (e.g., N-nitrosodimethylamine) is often problematic in both drinking water production and wastewater treatment processessthe latter application ultimately having implications for both aquatic organisms and drinking water sources (4, 5). Pressure-driven membrane processes such as nanofiltration (NF) and reverse osmosis (RO) are effective at removing some, but not all, organic micropollutants (6, 7); relatively high rejections are observed for most organic micropollutants, but traces of some pollutants can still be found in NF/RO permeate. As analytical methods and NF/ RO membrane materials continuously improve, and new maximum contaminant levels for drinking water are set, there will be an ongoing need to assess (and reassess) the removal of emerging micropollutants by NF/RO. At present, however, there is no accepted method of predicting organic solute rejection by polymeric membranes. Rejection of organic solutes by NF and RO processes depends on feedwater quality, operating conditions, module and system design, and solute-membrane physicochemical interactions. The diversity of known and emerging organic pollutants and membrane polymers make experimental determination of rejection for every possible combination of pollutant, membrane module, system, and water type impracticalsakin to conducting toxicity tests for every possible combination of chemical pollutant and aquatic organism. Therefore, it is highly desirable to develop methods for predicting the probable rejection of organic pollutants based on quantifiable physicochemical properties of solutes and membranes. Some work has already been carried out on the rejection of emerging organic micropollutants by NF/RO membranes (8-10) and a comprehensive understanding of rejection mechanisms is beginning to emerge. In general, three major solute-membrane interactions are distinguished: steric exclusion (sieving), Donnan (charge) interactions, and solute-membrane affinity (i.e., hydrophobic attraction, hydrogen bonding, dielectric effects, etc.). Solute-membrane interactions are mainly determined by solute and membrane physicochemical parameters. Although it is generally accepted that the solute-membrane interactions contribute to organic solute rejection, relatively few models have been proposed that predict these governing interactions (and thus solute rejection) through deterministic interaction parameters, described by quantifiable physicochemical properties. In this paper, a new method for elucidating the fundamental mechanisms governing rejection of uncharged organic solutes by polymeric NF/RO membranes is presented. The method relies on experimental measurements of solute-membrane intermolecular free energies (i.e., “affinities”) via contact angle analyses, and of membrane pore size by permeation experiments. Measured interaction parameters are used to predict a solute-membrane partition 10.1021/es803146r CCC: $40.75
2009 American Chemical Society
Published on Web 03/03/2009
coefficient, which is then combined with models of external mass-transfer and membrane transport, to predict solute transport through the membrane (and thus rejection). Model predictions are compared to observed rejections of three organic solutes by two commercial NF membranes.
• at x ) 0 (within the membrane at the feed side): c(x ) 0) ) cf ) φCm ) φβCf
(4)
• at x ) ∆x (within the membrane at the permeate side): c(x ) ∆x) ) cp ) φCp
Theory For uncharged organic solutes, two solute-membrane interactions govern solute rejection: steric hindrance and solute-membrane affinity (9-11). Steric hindrance is mainly determined by the size of the solute and the membranes pores. Solutes larger than the pores are well rejected; solutes smaller than the pores can permeate through the membrane more easily. This typically leads to an S-shaped curve when rejection is plotted as a function of the solute molar mass or the solute size (9). In addition to steric hindrance, solutemembrane affinity also influences rejection. Experiments have shown that the use of a rejection model, purely based on size exclusion effects, leads to overestimation of solutes which show affinity for the membrane (9). Solutes with high affinity for the membrane material partition into the membrane matrix more easily (e.g., by van der Waals forces, the formation of H-bonds, or hydrophobic attraction), and diffuse through the membrane, leading to lower rejection values. This is often observed for hydrophobic solutes since most commercial membranes are also comprised of relatively hydrophobic polymers and affinity between hydrophobic solutes and hydrophobic polymers is high (11). Here, we describe membrane transport and partitioning models that account for solute-membrane affinity. Membrane Transport Model. Solute transport through nanofiltration and reverse osmosis membranes can be described as a combination of diffusive and convective transport, as expressed by the well-known Spiegler-Kedem equation for steady-state transport in pressure-driven membrane processes (12, 13), Js ) 〈V〉Cp ) -Dp
Jv dc + Kcc dx ε
(1)
where Js and Jv are respectively the solute and solvent flux, 〈V〉 is the average fluid velocity in the pores (〈V〉 ) Jv/ε), Cp is the solute bulk permeate concentration, ε is the membrane porosity, Dp() KdD∞) is the solute diffusion coefficient in the membrane, D∞ is the solute diffusion coefficient in water, c and x are respectively the solute concentration and axial position within the membrane, and Kc and Kd are the hindrance factors against convective and diffusive transport. If a fully developed parabolic (Hagen-Poisseuille) flow velocity profile is assumed for the flow within the membrane pores, the hindrance factors for convection and diffusion can be calculated as follows (14), Kc ) (2 - (1 - λ)2)(1 + 0.054λ - 0.988λ2 + 0.441λ3) (2) Kd ) 1 - 2.3λ + 1.154λ2 + 0.224λ3
(3)
with λ ) rs/rp being the ratio of the solute radius to the hypothetic “pore radius”. In this study, it will be assumed that NF/RO membranes contain “voids”, which can be regarded as actual cylindrical pores and can be represented by a mean average pore size rp (in practice, there will probably be a pore size distribution, which may contribute to small deviations between model predictions and experimental rejection values). The hindrance factors for convection and diffusion are thus determined only by steric hindrance between the solute and the membrane matrix. Equation 1 can be integrated with the following boundary conditions (9, 14),
(5)
where ∆x is the membrane thickness, β is the hydrodynamic concentration polarization, cf and cp are the solute concentrations in the membrane matrix at the feed and permeate sides, respectively, Cf, Cp, and Cm are respectively the solute feed and permeate concentrations in the bulk and the solute feed concentration at the membrane surface, and φ is the solute partition coefficient in the membrane polymeric matrix. It is assumed here that Cf is constant throughout the membrane element (which is reasonable at low recoveries, but may cause slight deviations at high water fluxes). Integration of eq 1 with the boundary conditions gives Cp βφKc ) Cf 1 - ((1 - φKc)exp(-Pe))
(6)
where Pe ) (JvKc∆x)/(KdεD∞) is the Peclet number. If the rejection of a solute is determined as R ) 1 - (Cp/Cf), eq 6 can be rewritten as R)1-
βφKc
(
(
1 - (1 - φKc)exp -
JvKc∆x KdεD∞
))
(7)
Equation 7 describes the rejection of a solute as a function of the solvent flux and contains four unknown model parameters: the partition coefficient φ, the steric hindrance factors Kc and Kd, and the ratio of membrane thickness to membrane porosity ∆x/ε. Detailed equations to calculate the hydrodynamic concentration polarization are given in the Supporting Information. The diffusion coefficients D∞ of different organic solutes are generally known from the literature, or can be determined experimentally or estimated using known correlations. It is important to notice that eq 7 is also the basis of traditional size exclusion based convection-diffusion models (9, 14). The main difference between those models and the model developed in this paper lies in the determination of the partition coefficient φ. If the solute size and the partition coefficient φ are known, eq 7 for the solute rejection becomes solely dependent on the unknown parameters λ and ∆x/ε. When the experimentally obtained rejection data as a function of permeate flux for a single solute are fitted to eq 7, the values of ∆x/ε and λ (and thus rp) can be determined. This characterizes the membrane completely and turns eq 7 into a predictive rejection model for other solutes, if their solute size and partition coefficient φ are known. Solute Partitioning Model. The partition coefficient φ relates the solute concentration outside the membrane pores to the solute concentration inside the membrane pores. φ can be written as (15), φ)2
∫
1-λ
0
g(F)F dF
(8)
where F is the dimensionless position in the pore (F ) r/rp) (with r the radial position in the pore) and g(F) the radial distribution function. In the traditional size exclusion approach for organic solute rejection, g(F) ) 1 and the partition coefficient φ is equal to (1 - λ)2. In the traditional size exclusion approach, φ is thus independent of solute-membrane interactions, which leads to an overestimation of rejection for solutes which demonstrate membrane affinity (9). VOL. 43, NO. 7, 2009 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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LW LW LW γL - √γSLWγM ∆Gi ) A∆GSLM ) 2A[√γSLWγLLW + √γM
+ - √γL-) + √γL-(√γS+ + √γM - √γL+) γLLW + √γL+(√γS- + √γM
√γS+γM- - √γS-γM+ ]
(11)
where γiLW is the apolar (Lifshitz-van der Waals) component and γi+ and γi- describe the polar (electron-acceptor and electron-donor) components of the surface tension. A is the contactable surface area between the solute and the membrane.
Materials and Methods
FIGURE 1. Conceptual illustration of partition coefficient, O ()cm/cb), plotted against the ratio of solute-to-pore size for different solute-membrane free energy values. In the transport model formulated here, φ will be determined from equilibrium thermodynamics and will thus be dependent on solute-membrane affinity. It may be assumed that the radial concentration profile of the solute in the membrane pore is governed by the Boltzmann equation (15),
(
g(F) ) exp -
∆Gi(F) kT
)
(9)
where k is the Boltzmann constant, T is the absolute temperature (in K), and ∆Gi(F) is the free-energy difference associated with the differences in interactions of the solute in the water phase and the membrane phase (the interaction energy between solute and membrane in the water phase). After substitution of eq 9 and integration, eq 8 then becomes (since ∆Gi(F) is constant for small pores)
( )
∆Gi φ ) (1 - λ) exp kT 2
9
D∞ )
13.26 × 10-5 η1.4 × Va0.589
(10)
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(12)
where Va is the Le Bas molecular volume (18). The contact area A between a solute molecule and the membrane is determined from the solute radius as (15) A)
Thus, the partitioning of a solute from the water phase to the membrane phase (membrane pores) is dependent on both size exclusion effects (expressed by the factor (1 - λ)2) and on solute-membrane affinity (expressed by ∆Gi, the free energy of interaction between solute and membrane in the water phase). ∆Gi can be considered as the quantification of attractive or repulsive solute-membrane affinity interactions: if ∆Gi is negative (e.g., for a hydrophobic solute), transfer of the solute to the membrane will be facilitated. This will result in a lower rejection than was expected, based solely on size exclusion effects. However, if ∆Gi is positive (e.g., for a hydrophilic solute), there will be resistance against partitioning of the solute into the membrane phase, resulting in a higher rejection than expected based on size exclusion effects. Traditional size exclusion models will only be valid for solutes for which ∆Gi ) 0. Figures 1 and 2 give a conceptual illustration of the partition coefficient and of the contributions of different mechanisms to organic solute transport, respectively. The intermolecular free energy of interaction, per unit area, between the solute (S) and the membrane (M) in a liquid (L), ∆GSLM, can be related to ∆Gi and the surface tensions of the solute, membrane, and liquid (see Supporting Information for the full derivation) (16): 2402
Solutes. The solutes used for the rejection experiments were mainly selected based on their different physicochemical properties. Four different model solutes with different size and hydrophobicity (expressed as log Kow, the logarithm of the octanol-water partitioning coefficient) were chosen. All the solutes were liquids, to be able to determine the surface tension parameters used in the model. The solutes and their physicochemical parameters are summarized in Table 1. The solute radii were determined using the definition of the Stokes radius: rs ) (kT)/(6πηD∞) where η is the solvent viscosity (in Pa · s). The Stokes radius is a simple descriptor for solute size and assumes all molecules to be spherical. Hence, the model presented here does not account for molecular shape and orientation (which may cause small deviations between model predictions and experimental rejection values, especially for long-chain, linear molecules). The solute diffusion coefficients were determined using the equation developed by Hayduk and Laurie (17),
πrS2 2
(13)
All solutes were spiked separately in Milli-Q water and measured by analyzing the nonpurgeable organic carbon (NPOC ∼ total organic carbon (TOC)) - content of feed and permeate. The limit of detection for the NPOC analysis is 0.2 mg/L. Therefore, all solutes were spiked in concentrations
FIGURE 2. Conceptual mechanistic illustration of the combined effects of external and internal mass transfer, and solute-membrane size and affinity-based interactions. Note that rp and rs represent average pore and solute radius. (Does not account for orientation of molecules or nonspherical shape of pores.)
TABLE 1. Physico-chemical Characteristics for Selected Organic Solutes for Rejection Experiments
2-ethoxyethanol glycerol diethylphthalate (DEP) dibutylphthalate (DBP)
MW (g/mol)
log Kow
solute radius (nm)
diffusion coefficient (m/s)
90 92 222 278
-0.77 -1.76 2.42 4.5
0.23 0.19 0.32 0.35
9.3 × 10-10 1.1 × 10-9 6.1 × 10-10 5.1 × 10-10
of 10 mg of carbon/L, to be able to measure at least 98% rejection (i.e., a permeate concentration of 0.2 mg/L). Polymeric Membranes. The membranes used in this study were commercially available nanofiltration membranes: Trisep TS80 TSF (Trisep Corp., Goleta CA, USA) and Desal HL (GE Osmonics, Fairfield CT, USA). Both membranes are polyamide thin film composite membranes. Before use, membranes were rinsed with tap water for two hours to remove preservation liquids. Afterward, membranes were characterized for pure water permeability with Milli-Q water and for MgSO4 rejection with a 500 ppm MgSO4 solution in Milli-Q water. The membrane properties are summarized in Table 1 in the SI. The molecular weight cutoff (MWCO) values were provided by the membrane manufacturers. Membranes with different properties were chosen in order to assess the influence of membrane properties on rejection. For the rejection experiments, single elements (4040membrane modules) were used. Solute and Membrane Surface Tensions. Equation 11 for the solute-membrane affinity contains 10 variables, including the three surface tension parameters for the solute, membrane, and liquid, and the contactable surface area between solute and membrane. The surface tensions for water are known from the literature. The surface tension parameters for the membrane can be determined through contact angle measurements via the Young-Dupre´ equation (16), LW LW + - + (1 + cos θ)γL ) 2(√γM γL + √γM γL + √γM γL )
(14)
where θ is the contact angle formed between a droplet of liquid L and the membrane surface. With contact angle measurements performed on the membrane surface, three times with three different liquids L of known surface tensions, the membrane surface tension parameters can be determined by solving eq 14 three times. If the organic solute (S) is a solid in pure form, its surface tensions can be determined similarly. If the organic solute (S) is a liquid in pure form, its surface tension parameters can be determined using an analogous approach. Measured contact angles of the liquid of unknown surface tension on three solid probe surfaces with known (and different) surface tensions allows one to determine the liquid surface tension parameters. For many liquids, the surface tensions are already available from the literature (19). LW , γ+ The surface tension components γM M, and γM of the membranes were determined by performing contact angle measurements on the membrane surfaces and solving the set of three equations (eq 14) using the following three liquids: Milli-Q water, diiodomethane, and glycerol. The surface + tension parameters γLW L , γL , and γL of Milli-Q, diiodemethane, and glycerol are given in Table 2 in the Supporting Information (20). After the surface tension components of the two different membranes were determined, the surface tension components of a clean piece of glass were also determined in a similar way. The surface tension components γSLW, γS+, and γS- for the liquid solutes used for the validation of the advanced
TABLE 2. Calculated Values of Solute-Membrane Interaction Energies ∆Gi (in J) for the Different Solutes on the Different Membranes ∆Gi ( × 10-21 J) Trisep TS-80 glycerol 2-ethoxyethanol diethylphthalate (DEP) dibutylphthalate (DBP)
1.6 -3.6 -6.8 -24.7
Desal HL glycerol 2-ethoxyethanol diethylphthalate (DEP) dibutylphthalate (DBP)
1.4 -2.7 -5.2 -19.0
transport model were determined by performing contact angle measurements on three different solid surfaces: the two membranes and the glass. Afterward, the set of three equations was solved for each solute. All contact angles were measured using commercial contact angle equipment (Kru ¨ ss DSA10 goniometer, Kru ¨ ss GmbH, Hamburg, Germany) equipped with commercial contact angle calculation software (Drop Shape Analysis, Kru ¨ ss GmbH). For the determination of all contact angles, the average was taken of at least 20 different measurements on different locations of the clean membrane and glass samples. Equipment and Filtration Protocol. A schematic diagram of the bench-scale membrane system used in the membrane filtration experiments can be found in a previous publication (21). The feed solution is delivered to a pressure vessel, accommodating a single 4040-membrane element, by a multi-impellor centrifugal pump (Grundfos CRE-3). The feed water is fed from a 600 L stainless steel vessel, maintained at constant feed water temperature using a cooling system (Tamson TLC 10B). Membrane filtration experiments were carried out in recycle mode with a single batch of water, at a constant crossflow velocity of 0.2 m/s, corresponding to a feed flow of 1500 L/h (representative for full-scale installations). Feed pressure was varied, and rejection was measured as a function of permeate flux. Feed water temperature was set to 20 ( 1 °C. Since adsorption of solutes onto the membrane surface, and sorption into the inner membrane structure, may influence measured rejection values (it may lead to a temporary overestimation of rejection), an accurate evaluation of the rejection of a given solute is not possible until saturation of the membrane with the solute of interest is accomplished (10). Therefore, all rejection experiments were carried out for 4 days, which was shown in a previous publication (21) to be adequate to accomplish saturation and ensure that steady state rejection values are obtained at the concentration levels used in the experiments.
Results and Discussion Solute-Membrane Affinity. The different surface tension parameters of the membranes and the solutes, determined from contact angle measurements, are shown in Table 2 in the Supporting Information. The same table also shows the surface tension parameters of the clean glass plate used. The Trisep TS80 membrane has the highest contribution of LW of the surface tension, whereas the polar the apolar part γM surface tension components appear to be comparable for both membranes. With the values for all surface tension components, the solute-membrane affinities ∆Gi in aqueous solution were determined using eq 11. The different calculated values of ∆Gi are summarized in Table 2. A positive value of ∆Gi VOL. 43, NO. 7, 2009 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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FIGURE 3. Experimental and fitted rejection values for glycerol as a function of flux on Trisep TS80 (left) and Desal HL (right) membranes. indicates repulsive forces between solute and membrane (and thus no spontaneous transfer of the solute from the water phase to the membrane phase). A negative value of ∆Gi indicates solute-membrane affinity (attractive forces) and easier transfer of the solute from the water phase to the membrane phase. As can be seen from Table 2, ∆Gi is more negative for the Trisep TS80 membrane, indicating more affinity of the organic solutes for the Trisep TS80 than for the Desal HL membrane, probably due to its more hydrophobic character (higher contact angle with water). For the organic solute glycerol, ∆Gi > 0 for both membranes, indicating that no spontaneous partitioning of glycerol due to solute-membrane affinity will occur. In contrast, 2-ethoxyethanol shows significant affinity for both membranes, as can be seen from the negative values of ∆Gi in Table 2. This presence of solute-membrane affinity for 2-ethoxyethanol is not predicted from its log Kow, which suggests that it is a hydrophilic solute, like glycerol (log Kow 2-ethoxyethanol: -0.77; log Kow glycerol: -1.76). This indicates that log Kow is not always the best parameter to quantitatively describe solute-membrane affinity, even though in some cases it appears to correlate well with rejection (11). Determining Membrane Pore Size. Experimentally obtained rejection values for glycerol are plotted as a function of solvent flux for the Trisep TS80 and Desal HL membranes in Figure 3 (squares). To determine the pore size of the membrane, the advanced transport and partition coefficient model are used to fit these experimentally obtained data. The rejection curves (full lines) in Figure 3 were fitted to the experimental data using eq 7 and the solute-membrane affinity dependent partition coefficient (eq 10), by changing the parameters rp (the average membrane pore size) and the ratio of membrane thickness to membrane porosity ∆x/ε, using an optimization procedure (Solver, Excel). ∆Gi is known from Table 2. Correlation coefficients were added to the figures to show the quality of the fit. The values of the average pore radii rp obtained for the Trisep TS80 and the Desal HL membrane are 0.36 and 0.43 nm, respectively. The steric definition for the partition coefficient (φ ) (1 - λ)2) can also be used with the transport model to fit the experimental rejection data (dashed lines in Figure 3). The pore radii obtained with the steric model, using the solute glycerol, are 0.33 and 0.39 nm for the Trisep TS80 and Desal HL membranes, respectively. The pore sizes obtained with both models demonstrate that the Trisep TS80 has a smaller pore size than the Desal HL. This could already be expected based on the lower pure water permeability of the Trisep TS80 (see Table 1 in Supporting Information) and indicates that steric hindrance between solutes and membrane will be larger for the Trisep TS80. 2404
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Predicting Rejection. With the pore radii known, the transport models can now be used to predict the rejection of other organic solutes by the Trisep TS80 and Desal HL membranes. Experimentally determined rejection values of the solutes 2-ethoxyethanol, diethylphthalate, and dibutylphthalate as a function of permeate flux are shown in Figure 4 (squares). For all three solutes, rejection was modeled using the purely steric and the solute-membrane affinity dependent models (eq 10). For each model, the respective pore radii, as determined by fitting the rejection data for glycerol with the different models in the previous paragraph, were used. In addition, the steric model was also used with the pore radius determined from the solute-membrane affinity model. The purely steric model significantly overpredicts the rejection values for all solutes. The model based on solute-membrane affinity, however, quite reasonably predicts the experimental rejections (Figure 4). This shows the dramatic effect of incorporating solute-membrane affinity on the accuracy of rejection predictions. The membrane pore size was underestimated by the steric model since it was determined with the solute glycerol, which experiences repulsive interactions (∆Gi > 0) with the membrane surface, and these repulsive interactions are not taken into account in the steric model. Using this underestimated pore size to predict rejection values with the steric model then results in an overprediction of rejection for solutes which show affinity for the membrane surface (∆Gi < 0) because (i) the fitted pore size underestimates the real pore size and (ii) the solute-membrane affinity, which facilitates solute partitioning into the membrane matrix, is not taken into account. The effects of the underestimated pore size and of including solute-membrane affinity become clear when the purely steric models is compared to the steric model using the correct pore size (determined with the solute-membrane affinity model). When the correct pore size is used for the steric model, the rejection of 2-ethoxyethanol, diethylphthalate, and dibutylphthalate is still overpredicted since solute-membrane affinity is not accounted for, but the overprediction is smaller than the overprediction by the purely steric model. Incorporating solute-membrane affinity into the partition coefficient overcomes problems with pore size determination and solute-membrane affinity and significantly improves rejection predictions. Determining Membrane Pore Size with 2-Ethoxyethanol. The pore sizes of both membranes have also been estimated by fitting with the solute 2-ethoxyethanol (Figure 1 in Supporting Information). The pore radii obtained with the solute-membrane affinity model correspond exactly to the pore radii determined with glycerol, and thus, rejection predictions will still be accurate for all solutes. This dem-
FIGURE 4. Experimental and predicted rejection values for 2-ethoxyethanol ((a),(b)), diethylphthalate (DEP) ((c),(d)) and dibutylphthalate (DBP) ((e),(f)) as a function of flux on Trisep TS80 (left) and Desal HL (right) membranes (pore size determined with glycerol). onstrates that using only one model solute to determine membrane pore size is sufficient if the affinity-based partition coefficient is used. The estimated pore radii obtained from fitting with 2-ethoxyethanol using the purely steric model are 0.43 and 0.52 nm, respectively, much larger than the pore radii obtained with glycerol. The rejection of glycerol (Figure 2 in Supporting Information) is therefore significantly underpredicted by the steric model, also because the solutemembrane repulsive interactions for glycerol are not taken
into account. For the other solutes, the steric model rejection predictions are not very accurate either. Since 2-ethoxyethanol shows affinity for the membrane surface, the membrane pore size is overestimated when it is fitted with the steric model. Since dibutylphthalate and diethylphthalate also show affinity for the membrane surface, using this overestimated pore size slightly improves rejection predictions by the steric model, compared with the steric model predictions using the correct pore size. Glycerol, however, shows repulsive interactions with the membrane VOL. 43, NO. 7, 2009 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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surface. Therefore, using the overestimated pore size with the steric model results in larger underpredictions of its rejection than when using the correct pore size (Figure 2 in the Supporting Information). To accurately determine the real pore radius and correctly predict rejection, incorporation of solute-membrane affinity is thus a necessity. The solute-membrane affinity based model can be used as a quantitatively predictive model for the rejection of organic solutes, in contrast to the steric model. The disadvantage of the affinity-based transport model is, for the moment, that calculation of solute-membrane affinity is relatively easy for liquid solutes, but may be difficult for nonliquid organic solutes. The results presented here represent only a limited set of solute and membrane physicochemical properties. The model validation relies on relatively simple and wellcontrolled laboratory experiments. However, the model offers a rational framework for assessing rejection of any organic solute by any polymeric membrane, given that the requisite physico-chemical interaction parameters are known.
Acknowledgments This work was cofunded by Delft Cluster. The authors thank Gil Hurwitz and Guillaume Roussillon for their help with the contact angle measurements.
Supporting Information Available Theoretical derivation of concentration polarization and free energy of interaction, information on membranes, and additional rejection results. This material is available free of charge via the Internet at http://pubs.acs.org.
Literature Cited (1) Barnes, K. K.; Kolpin, D. W.; Focazio, M. J.; Furlong, E. T.; Meyer, M. T.; Zaugg, S. D.; Haack, S. K.; Barber, L. B.; Thurman, E. M. Water-Quality Data for Pharmaceuticals and Other Organic Wastewater Contaminants in Ground Water and in Untreated Drinking Water Sources in the United States, 2000-01; U.S. Geological Survey, Denver, 2008. (2) Global Water Research Coalition. Pharmaceuticals and Personal Care Products in the Water Cycle; Global Water Research Coalition: London, 2004. (3) Barlow, S.; Kavlock, R. J.; Moore, J. A.; Schantz, S. L.; Sheehan, D. M.; Shuey, D. L.; Lary, J. M. Teratology society public affairs committee position paper: Developmental toxicity of endocrine disruptors to humans. Teratology 1999, 60, 365–375. (4) Plumlee, M. H.; Lo´pez-Mesas, M.; Heidlberger, A.; Ishida, K. P.; Reinhard, M. N-Nitrosodimethylamine (NDMA) Removal by Reverse Osmosis and UV Treatment and Analysis via LC-MS/ MS. Water Res. 2008, 42 (1-2), 347–355.
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