Temperature Effects on the Morphology of Porous Thin Film

Even though polymeric nanofiltration (NF) and reverse osmosis (RO) ... The vast majority of pores were smaller than 2 nm for both membranes ..... Inse...
0 downloads 0 Views 381KB Size
Download PDF
Environ. Sci. Technol. 2005, 39, 5022-5030

Temperature Effects on the Morphology of Porous Thin Film Composite Nanofiltration Membranes RAMESH R. SHARMA† AND S H A N K A R A R A M A N C H E L L A M * ,†,‡ Department of Civil and Environmental Engineering, 4800 Calhoun Road, University of Houston, Houston, Texas 77204-4003, and Department of Chemical Engineering, University of Houston, Houston, Texas 77204-4004

Even though polymeric nanofiltration (NF) and reverse osmosis (RO) membranes often operate on surface waters and surficial groundwaters whose temperature varies over time and with season, very little detailed mechanistic information on temperature effects on membrane selectivity is available to date. Hence, a study was undertaken to investigate the effects of operating temperature (5-41 °C) on the morphology and structure of two commercially available thin film composite NF membranes. Application of hydrodynamic models to experimental rejection of dilute solutions of hydrophilic neutral alcohols, sugars, and poly(ethylene glycol)s revealed changes in both the sieving coefficient and permeability of solutes below the membrane glass transition temperature. The vast majority of pores were smaller than 2 nm for both membranes (network pores) even though evidence for a small fraction of larger aggregate pores (∼30 nm) was also obtained for one membrane. Increasing temperature appears to cause structural changes in network pores by increasing its pore size while simultaneously decreasing pore density. These increases in pore sizes partially explain reported reductions in contaminant (e.g. arsenic, salts, natural organic matter, hardness, etc.) removal by NF and RO membranes with increasing temperature. Even though nanofiltration (NF) membranes achieve high removals of several drinking water contaminants including natural organic matter and disinfection byproduct precursors (1, 2), endocrine disrupting compounds (3, 4), pesticides (5, 6), nitrogenous compounds (7), arsenic (8), etc. the factors governing their separation have not yet been comprehensively elucidated even at room temperature. Additionally, wide temperature variations (1-35 °C) of NF and reverse osmosis (RO) membrane feedwaters (9-11) necessitate mechanistic studies on temperature effects on membrane selectivity. Most investigators have simply reported that increases in water temperature increased passage of salts (9, 10, 12), hardness (13), natural organic matter (14), and arsenic (8) across polymeric membranes. Paradoxically, very little * Corresponding author phone: (713)743-4265; fax: (713)743-4260; e-mail: [email protected]. † Department of Civil and Environmental Engineering. ‡ Department of Chemical Engineering. 5022

9

ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 39, NO. 13, 2005

detailed mechanistic information on temperature effects on membrane selectivity is available to date. The pore size distribution (PSD), pore density, and morphology of nanofilters are essential to hindered diffusion and convection calculations that are central to understanding their intrinsic selectivity properties (4, 7, 15-17). In this manuscript we relate changes in selectivity with temperature to variations in the structure and morphology of the polymer (including PSD) constituting the active layer of the membrane. Recently, we reported that employing a single log-normal distribution for the PSD systematically over predicted experimental sieving data for neutral solutes larger than 0.6 nm for one nanofilter (18). An additional focus of this research is to improve our recent work (18) and derive a single PSD density function (potentially bimodal) to accurately describe membrane sieving over a wide range of solute sizes. The principal objective of this work is to deduce variations in skin layer morphology of polymeric thin film composite NF membranes (PSD, pore connectivity, and pore number density) with operating temperature. Rejection of several neutral solutes (that served as molecular tracers) by two commercially available nanofilters was measured in the environmentally significant range 5-41 °C. PSDs at different temperatures were derived from solute sieving data using hindered convection considerations. Also, diffusive permeabilities of solutes with different molecular dimensions were evaluated using a modified porous pathway model accounting for PSD, pore density, and solute dependent tortuosity.

Theoretical Work Transport Equations. For porous or “loose” nanofilters, in the absence of specific chemical and electrostatic interactions, the local uncharged solute flux (JS) through a membrane pore is due to contributions from diffusive and convective flows (4, 7, 15, 19)

dc JS ) -KdD∞ + KccJv dx

(1)

where c is the radially averaged solute concentration in the pore, Jv is the radially averaged solution velocity in the pore, D∞ is the bulk solution diffusivity, and Kd and Kc are the hindrance factors for diffusion and convection, respectively. To obtain the solute sieving coefficient (Si), eq 1 has been integrated over the effective membrane thickness (∆x) with appropriate boundary conditions on the feed and permeate side and correcting for concentration polarization effects using film theory on membrane feed side as (19)

Cp Si ) ) Cb

S∞exp

() Jv k

(1 - exp(-Pe))(1 - S∞) + S∞exp

() Jv k

(2)

where Cp and Cb are the permeate and bulk phase solute concentrations, and k is the feed side mass transfer coefficient. All our experiments were designed to minimize concentration polarization effects (k f ∞) allowing the membrane phase concentration to be closely approximated as the bulk concentration (see Experimental Work section and ref 18). S∞, the asymptotic sieving coefficient attained as Peclet number (Pe) f ∞ is a measure of solute transport solely due to convection and is equal to the product of equilibrium partitioning coefficient, Φ and Kc. The membrane Peclet number is defined as (19) 10.1021/es0501363 CCC: $30.25

 2005 American Chemical Society Published on Web 05/19/2005

Pe )

ΦKc

ΦKc J PM v

Jv )

Ak ΦKdD∞ ∆x

(3)

where Ak is membrane surface porosity, ∆x is the effective distance traveled by solute or solvent through the membrane pore (accounting for tortuosity), and PM is solute permeability coefficient, which is the measure of solute transport due to diffusion. Membrane phenomenological parameters (S∞ and PM) and feed side mass transfer coefficient (k) were obtained by fitting eq 2 to experimental measurements of Cp over a wide range of volumetric fluxes (Jv) at a constant feed flow rate and feed concentration (18). Further, hydrodynamic models of hindered convection in cylindrical pores (20) and slit pores (15) were used to relate S∞ and pore radius or half pore width. Membrane Pore Size and Pore Size Distribution Obtained from (Hindered) Convection Calculations. Because the log-normal distribution may be most appropriate for membranes (18, 21, 22) it was used as the basis for PSD calculations. A linear combination of a maximum of 2 lognormal distributions was used to quantify the entire range of pore sizes that were encountered: 2

f(r) )

2

hi

i)1

SPirx2π

∑h f (r) ) ∑ i i

i)1

(

(ln(r) - ln(rji))2

exp -

2 2SPi

)

S∞(r*) )

∑h ∫ i

i)1

1

∞

r*

(

(ln(r) - ln(rji))2

exp -

SPirx2π

2 2SPi

)

dr (5)

Next, we have employed a mechanistic approach (19) that accounts for the hydrodynamic lag and steric effects by normalizing the convective hindrance coefficient for each type of pore on the basis of volumetric flow rate through cylindrical and slit shape pores to calculate an average asymptotic sieving coefficient, 〈S∞〉

〈S∞〉 )

∫

∞

0

(ΦKc) f(r) rndr

∫

∞

0

f(r) rndr

N0 P M ) D∞ π ∆x

(6)

where r is used interchangeably to represent pore radius for cylindrical pores (n ) 4) and or half width for slit pores (n ) 3). Membrane pores were conceptualized to have these shapes because closed form analytical expressions for the hindrance factors are available for these pore geometries (15, 20). Because slit and cylindrical pore models are both only model conceptualizations of the complex pore network characteristic of NF membranes, one of them cannot be said to be better than the other. Thus, both approaches (semiem-

∫ ΦK ∞

0

d

f(r)r2 dr

(7)

The free diffusion coefficient of solutes employed in this work was obtained from the literature (26-28), and the pore size distribution has already been determined using eqs 5 and 6 as described in the previous section. Thus, the only unknown in eq 7 is the term N0/∆x, which was calculated by fitting the experimental permeability data to the respective equations. Membrane pores can be expected to be tortuous and potentially interconnected with some surface pores not even penetrating the entire thickness of the active layer (29, 30). Hence, the effective membrane thickness ∆x is given by the product of the tortuosity (τp) and membrane thickness (L):

(4)

The coefficients hi are non-negative and ∑ihi ) 1, fi(r) represents the ith log-normal distribution based on pore number with mean jri and standard deviation SPi and r is the pore radius. hi represents the sieving contribution of the ith distribution. First, using a semiempirical approach adopted by several authors (18, 21-24), we assume that solute rejection is purely due to geometric considerations. This approach, wherein a solute of radius r* permeates through all the pores whose radii are larger than itself (r* to ∞) provides consistent results (23) even though it explicitly ignores any additional drag the solute may experience in the confined environment of the membrane pore. The sieving coefficient according to this purely sieving model is 2

pirical eq 5 and mechanistic eq 6) were used to investigate general trends in PSD with temperature. The PSD parameters (rji, and SPi) were then calculated by fitting eqs 5 and 6 to the experimental asymptotic sieving coefficient using nonlinear least squares regression. Integration was performed using Simpson’s rule with a narrow step size and a truncation error of 0.01%. Analysis of Hindered Diffusion through Membrane Pores. We have incorporated steric hindrances to diffusion by introducing the hindrance factor to represent solute permeability (25) in cylindrical pores as

∆x ) τpL

(8)

Recently, a closed form expression for tortuosity as a function of pore and solute radius (τp(r*)) was derived for a cubical network of cylindrical pores (31). We have modified their equation to account for hydrodynamic lag in the pores by introducing an additional parameter in the form of a hindrance factor for diffusion (Kd) as

τp(r*) ) 1 +

( )∑ ( )

4 η 5 β

∞

n

n)1

3

n-1

4

∫

(

∞

r*

Kd f(r)dr)n

(9)

Due to the cubical geometry of pore network, pores can either be parallel or normal to the membrane surface. The distance between the two adjacent pores oriented parallel to the membrane surface is β and the distance between two normal pores is η, which is related to pore density as

η)

x

1 N0

(10)

β and N0 were estimated by fitting eqs 7-10 to experimental permeability data after obtaining L from scanning electron microscopy. Solute Size Calculations. In this study, the Stokes radius, molecular width, and mean molecular radius (MMR) of solutes were all used to characterize NF membranes. Experimental reports of diffusion coefficients at 25 °C for all solutes were obtained (26-28, 32) to calculate the Stokes radius. Bulk diffusivities of solutes at temperatures other than 25 °C were estimated using temperature and viscosity corrections (27). To better account for shape effects on the removal the molecular width and mean molecular radius were also calculated for the solutes employed. Giddings (33) theoretically analyzed a variety of molecule shapes and showed that purely steric partitioning is dominated by the extreme groups of the molecule, whereas internal shielded groups have no influence on it. Recognizing this result, we derive a mean molecular radius that represents the mean length of projection of the molecule along the X, Y, and Z axes using a VOL. 39, NO. 13, 2005 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

9

5023

commercially available software (Chem 3D, Cambridgesoft Corp., v. 5). Details of MMR estimation and a comparison of solute size parameters are given in the Supporting Information.

Experimental Work Membranes. Two commercially available, polyamide thin film composite membranes denoted as “DL” (Osmonics, Minnetonka, MN) and “TFCS” (Koch Fluid Systems, San Diego, CA) were employed. The manufacturers provided no information regarding possible surface chemical modifications. Operationally, sodium chloride rejection for DL and TFCS membrane (at 1 mequiv/L concentration and 345 kPa) were 52% and 77%, respectively. These low rejections indicate that the DL and TFCS membranes should be considered as porous or “loose” nanofilters. Solutes Employed. Tracers such as sugars and alcohols which have well-defined transport properties were chosen because of the need to quantify membrane morphology rather than their presence in water supplies. All experiments were conducted using reagent grade neutral organic solutes viz. methanol, ethanol, ethylene glycol, tert-butyl alcohol, dextrose, and sucrose (EM Science Gibbstown, NJ), xylose, glycerol, raffinose 5-hydrate, and R-cyclodextrin as well as poly(ethylene glycol)s (PEGs) of 20 kDa, 35 kDa, and 100 kDa (Sigma Aldrich Company, St. Louis, MO). These alcohols, sugars, and PEGs are often employed in studies of hindered transport across membranes (16, 18, 30, 32). Similar to other studies (4, 34), the target feedwater concentration for all solutes was set at 20 mg/L total organic carbon (TOC). This value facilitated easy, accurate, and precise measurements of both feed and permeate concentrations necessary to calculate rejection. The concentrations of all solutes were analyzed using a TOC analyzer (TOC5050A, Shimadzu, Columbia, MD). All results reported are an average of four or five injections with a coefficient of variation < 2%. Bench-Scale Cross-Flow Experimental Apparatus. All experiments were conducted at constant cross-flow velocity but varying flux using a pressurized cell (Sepa CF cell, Osmonics, Minnetonka, MN) that accommodates a 19 cm × 14 cm flat membrane sheet (effective filtration area 155 cm2). The retentate and permeate streams were recycled to the feed tank containing 20 L of water with a single organic solute maintaining a constant feed concentration ∼20 mg/L TOC. A positive displacement gear pump (model 74011-11, ColeParmer, Chicago, IL) minimized pressure fluctuations. The cross-flow velocity was maintained constant at 9.6 and 19.2 cm/s for DL and TFCS membrane, respectively. Inert materials such as Teflon or stainless steel were used for all tubing, connections, pump-heads, and the membrane cell. Filtration pressure and temperature were monitored using analogue transducers (PX303-200G5V and TJ120 CPSS 116G, Omega Engineering Company, Stamford, CT). For pure water permeability measurements, filtered water was continuously collected on a digital weighing balance (Ohaus Navigator N1H110, Fisher Scientific, Houston, TX). The built-in RS232 port in the balance was directly connected to a computer to obtain the digital signal corresponding to the weight. These analogue and digital signals were acquired at a rate of 1 per minute using LabVIEW (Version 5.1, National Instruments, Austin, TX). Permeate and retentate flows were also manually measured. The complete cross-flow filtration apparatus was housed in a chamber whose temperature was adjusted to 5, 15, 23, 35, and 41 °C. The entire apparatus including the water was equilibrated to the chosen temperature for a minimum of 30 h prior to the commencement of experiments. Conduct of Experiments. Fresh membrane coupons were first soaked face down in ultrapure water that was replenished 3 or 4 times over a 24 h period. This coupon was then placed 5024

9

ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 39, NO. 13, 2005

in the membrane holder, and ultrapure water was passed through the entire apparatus at ∼750-800 kPa pressure for 24 h. Following this membrane-setting period, steady-state fluxes were measured for pressures in the range 100-760 kPa. All experiments were conducted at low feedwater recovery ( 0.95) were obtained for the purely sieving model (see Supporting Information Figure S2). However, its use is limited because it explicitly ignores steric partitioning and hydrodynamic lag in the pore making it a strictly empirical model. Nevertheless, both eqs 5 and 6 can VOL. 39, NO. 13, 2005 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

9

5025

FIGURE 3. Influence of temperature on experimental sieving data using purely sieving log-normal model. Network pore sizes shift to higher values as temperature increases for both polymeric membranes employed in this study.

FIGURE 4. Dependence of asymptotic sieving coefficient on normalized solute radius (ratio of mean molecular radius and pore radius corresponding to 50% sieving, (rp,S∞ ) 0.5)) for both NF membranes. Insets show the increasing trend for pore radius corresponding to 50% sieving with temperature for both pore geometries. Experimental sieving coefficients for the TFCS membrane are depicted as empty symbols and those obtained for the DL membrane as filled symbols. The solid lines depict theoretical predictions of sieving coefficients using hindered transport models (eq 6) for both membranes at all five temperatures. be used to accurately represent pore size distributions. In the next section, we use these models to quantify temperature effects on network and aggregate pore sizes. Effect of Temperature on Pore Size Distributions. Experimental sieving coefficients of various solutes obtained at 5, 15, 23, 35, and 41 °C for both membranes are superposed on theoretical predictions neglecting hindered convection (eq 5) in Figure 3. For the DL membrane, which only posseses network pores, the entire PSD was shifted to higher values of pores sizes (Figure 3a), whereas for TFCS membranes, only the network pores were shifted to higher pore sizes (Figure 3b and its inset). In other words, temperature had a stronger influence on the network pores compared to aggregate pores. Figure 4 depicts the dependence of the asymptotic sieving coefficient on the ratio of solute size to pore size corresponding to S∞ ) 0.5 (denoted as rp,S∞)0.5 in Figure 4) at each temperature as suggested by Michaels (22). Pore radius for 5026

9

ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 39, NO. 13, 2005

50% sieving (S∞ ) 0.5) at 23 °C refers to the x-coordinate of the point on the solid curve in Figure 2 corresponding to the y-coordinate of 0.5. This exercise was repeated at all temperatures for both membranes. The insets of Figure 4 shows that the pore radius corresponding to S∞ ) 0.5 for both membranes and pore geometries increased with temperature. The appropriate value from the inset was used for normalization at each temperature, which collapsed all experimental sieving coefficients in the range 0.1 < S∞ < 1.0 to a single curve. Further, theoretical calculations using eq 6 for all five temperatures overlapped in Figure 4, appearing as a single curve. Therefore, this normalization allowed simultaneous comparison of sieving caused by network pores of both membranes in the entire temperature range investigated. In other words, monomodal and bimodal log-normal distributions are difficult to distinguish experimentally using larger values of the sieving coefficient. The choice of coordinate scaling suppresses the differences between two

have not been included in N0/∆x calculations. As seen in Figure 5, N0/∆x values are of the same order of magnitude (∼1023 pores m-3) as those reported at room temperature for cellulose acetate RO membranes (42). This is not surprising given that the RO membranes employed were calculated to have a pore size distribution similar to that depicted in Figure 2. Figure 5 also shows a monotonic decrease in N0/∆x with temperature for both membranes, which is probably caused by changes in the active layer polymeric structure and network pore sizes (Figure 4 and Table S2).

FIGURE 5. Decreasing N0/∆x with increasing temperature for both membranes. membrane structures to such an extent that only significantly different membrane structural characteristics are visible. For example, bimodal distribution of the TFCS membrane distinguishes from the monomodal structure of the DL membrane (both experimentally and theoretically) by the presence of the second mode for S∞ < 0.1 (aggregate pores), while the first mode overlaps the monomodal distribution for 0.1 < S∞ < 1.0 (network pores). This behavior is similar to the one reported by Wendt and Klein (40), where an exponential form for PSD was used. Further, assuming either cylindrical or slit pore shapes only weakly influenced sieving in Figure 4a,b supporting the current understanding that this nondimensionalization cannot distinguish pore shapes (40). Therefore, despite the differences in chemical composition and the subsequent response to temperature, the solute to membrane pore radius is the primary factor in determining membrane selectivity toward the alcohols and sugars employed in this study. Further, the quantitative agreement between theoretical predictions and experimental data shown in Figures 2 and 4 suggests that available hydrodynamic models (15, 20) can provide important insights into solute transport through the tortuous pores of NF membranes. Network pores shrank in size as temperature decreased whether convective hindrances were included or not (see Table S2 and associated text and Figure 3). Hence, deteriorations in membrane selectivity with increasing temperature can be attributed primarily to the increase in network pore sizes. Such increases in pore sizes can also partially explain the decreases in arsenic (8), salt (9, 10, 12), hardness (13), and natural organic matter (14) rejection reported in the literature as well as the nonviscous contributions to activated transport of water (12, 18, 41). Temperature Effects on Pore Density to Membrane Thickness Ratio (N0/∆x). The value of N0/∆x at each temperature was obtained by using it as an adjustable parameter to fit eq 7 to experimental permeabilities (Figure 5). The hindrance factors for diffusion are not strictly applicable for solutes that have dimensions comparable to that of the water molecule itself (15). Additionally, the passage of methanol, ethanol, and ethylene glycol across the membranes are enhanced by their polarity (37). Therefore, similar to the hindered convection analysis, the smallest solutes with MMR e 0.27 nm (viz. methanol, ethanol, and ethylene glycol)

Incorporating Tortuosity Factor in Pore Density Calculations. Membrane properties including pore density, size distribution, and tortuosity as well as the thickness of the skin layer influences solute permeability (see eqs 7 and 8). Scanning electron microscopy of cross sections of both DL and TFCS membranes revealed a very thin top layer (∼200 nm) supported by multiple layers of coarse granular porous material, which is approximately in the previously reported range for other thin film composite RO and NF membranes (21). Similar to the analysis of Koros and Woods (43), the skin layer thickness (200 nm) was assumed to remain invariant with temperature. The pore density (N0) and pore spacing (η and β) were then estimated by using them as fitting parameters to minimize the sum of squared error between experimental and theoretical solute permeability using eqs 7-10 at each temperature using the pore size distributions derived earlier in Figures 2 and 4. Using this procedure, the hindered transport model revealed pore densities O(1015-1016) pores/m2 for DL and TFCS membranes at 23 °C, which are in a similar range as the reported values for other NF and RO membranes (35, 44). Additionally, a power law decrease in pore number densities of the DL and TFCS membranes was calculated. Decreases in pore density and increasing pore sizes with increasing temperature manifests as if pores are being pushed apart. Hence, the normal (η) and lateral distances (β) between two pores calculated assuming a cubical geometry increased with temperature as depicted in Figure 6a,b. Once the membrane morphological parameters (PSD, η, β) were obtained, the solute dependent tortuosity was calculated using eq 9 at each temperature. Figure 7 depicts solute dependent tortuosity values for both membranes in the same range as nanoporous dialysis membranes at room temperature (45). Figure 7 also reveals a monotonic decrease in tortuosity with increasing solute mean molecular radius at any given temperature. These results are similar to transport across the upper layer of skin (stratum corneum), where smaller hydrophilic drugs have been shown to be capable of entering into a higher fraction of pores (31), allowing them to experience a more tortuous path while penetrating the skin. Further, for a given solute size, the tortuosity increased with temperature indicating a greater influence of pore size distribution and η on tortuosity as compared to the β value (see eq 9). Interpreting Temperature-Induced Changes in Skin Layer Morphology with Implications for Permeability. Solute transport measurements in conjunction with pore flow models have been successfully used to elucidate effects of several operational and manufacturing parameters on PSD and pore number density of polymeric RO and NF membranes (35, 38, 44, 46). Analogous to these studies, morphological changes with temperature can be interpreted as the consequence of reorientation and movement of polymer chains constituting the membrane matrix thereby changing the available void spaces or pores. The calculated trends in membrane morphological parameters with operating temperature shown in Figures 3-7 and S3 are manifestations of equivalent changes in void spaces due to polymer chain movement. To our knowledge, this is the first rigorous VOL. 39, NO. 13, 2005 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

9

5027

FIGURE 6. Modifications in the membrane skin structure due to temperature changes depicted as an increase in the normal and lateral distances between pores for both membranes.

the dependence of solute permeation on temperature. Movement of polymer chains with increasing temperature thereby fusing together several network pores consequently reducing pore density while simultaneously shifting the pore size distribution to higher values can explain these results. These structural changes influences solute permeation and corresponding activation energies of permeation as discussed next. Substituting eq 8 in eq 7 reveals that solute permeation is proportional to the hindered diffusivity within membrane pores, the pore density and inversely proportional to the tortuosity. Hence, the activation energy of solute permeation, Ep, is proportional to ED + EN0 - Eτp, where ED, EN0, and Eτp are the contributions of effective diffusion, pore number, and pore connectivity, respectively. We have recently reported increasing pore sizes resulted in 20 < ED < 200 kJ/mol for these solutes and membranes (18). Decreasing N0/∆x in Figure 5 indicates a net negative activation energy associated with pore number and connectivity. This is confirmed by decreasing N0 (EN0 < 0) and increasing τp (Eτp > 0) with temperature in Figures 6 and 7, respectively. The net negative contribution of pore density and connectivity to activated transport (EN0 - Eτp < 0) weakens the influence of temperature on permeability compared to the hindered diffusivity. Changes in the permeation pathways in the membrane skin layer with temperature will result in the activated transport of contaminants. However, the negative enthalpy associated with adsorption of natural organic matter (17) and hormones (4) will further serve to weaken the temperature dependence of their permeability.

Nomenclature

FIGURE 7. Increasing tortuosity with decreasing solute mean molecular radius and increasing temperature for both polymeric membranes. investigation of the effects of feedwater temperature on skin layer morphology of NF membranes. Trends shown in Figures 3-7 and S3 suggest that increasing temperature results in structural and morphological changes in network pores of the polymeric skin layer by increasing pore sizes while simultaneously decreasing pore density. This increase in the dimensions of the permeation pathways at higher temperatures can explain the reported reductions in contaminant rejection (8, 9, 12). Simultaneously, thermal expansion of the network pores decreases the number of permeation pathways to weaken 5028

9

ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 39, NO. 13, 2005

Ak

membrane porosity

c

solute concentration in pore (ML-3)

Cp

permeate solute concentration (ML-3)

Cm

membrane phase solute concentration (ML-3)

D∞

free solute diffusion coefficient (L2 T-1)

EP

activation energy of permeation (ML2 T-2 mol-1)

ED

activation energy of diffusion (ML2 T-2 mol-1)

EN0

activation energy of pore disappearance (ML2 T-2 mol-1)

EτP

activation energy of pore connectivity (ML2 T-2 mol-1)

hi

fraction of pores corresponding to ith pore size distribution

Jv

volumetric pure water flux (LT-1)

Js

solute flux (ML2 T-1)

Kc

convective hindrance factor

Kd

diffusive hindrance factor

L

membrane thickness (L)

Lp

pure water permeability (M-1 L2 T)

N0

total number of pores per unit area of membrane (L-2)

Pe

Peclet number

PM

solute permeability (LT-1)

∆P

transmembrane pressure (ML-1 T-2)

r

pore radius (L)

jri

geometric mean pore radius of the ith distribution (L)

r*

upper limit of solute radius in eq 5

Si

solute sieving coefficient

S∞

asymptotic sieving coefficient

SPi

geometric standard deviation of the ith distribution (L)

T

temperature (K)

Greek letters β

lateral distance between two pores (L)

∆x

effective distance traveled by solute within the membrane matrix (L)

Φ

solute equilibrium partitioning coefficient

η

normal distance between two pores (L)

τP

solute dependent tortuosity

µ

water viscosity (ML-1 T-1)

Acknowledgments David Paulson and Peter Eriksson of Osmonics Inc. and Randolph Truby and Tom Stocker of Koch Membrane Systems Inc. generously donated membrane samples. Prasad Taranekar and Rigoberto Advincula from the Department of Chemistry assisted with molecular mechanics simulations. The detailed comments generated during anonymous peer review of this manuscript are greatly appreciated. This research has been funded by a grant from the National Science Foundation CAREER program (BES-0134301). The contents do not necessarily reflect the views and policies of the sponsors nor does the mention of trade names or commercial products constitute endorsement or recommendation for use.

Supporting Information Available Estimation of molecular width and mean molecular radius, choice of appropriate solute size parameter, experimental reproducibility and quality assurance protocols, effect of temperature on PSD, and temperature effects on N0/∆x using water permeability measurements (Tables S1 and S2 and Figures S1-S3). This material is available free of charge via the Internet at http://pubs.acs.org.

Literature Cited (1) Tan, L.; Amy, G. L. Comparing Ozonation and Membrane Separation for Color Removal and Disinfection By-Product Control. J. Am. Water Works Assoc. 1991, 83, 74-79. (2) Nilson, J. A.; DiGiano, F. A. Influence of NOM Composition on Nanofiltration. J. Am. Water Works Assoc. 1996, 88, 53-66. (3) Kimura, K.; Toshima, S.; Amy, G.; Watanabe, Y. Rejection of Neutral Endocrine Disrupting Compounds (EDCs) and Pharmaceutically Active Compounds (PhACs) by RO Membranes. J. Membr. Sci. 2004, 245, 71-78. (4) Nghiem, L. D.; Schafer, A. I.; Elimelech, M. Removal of the Natural Hormones by Nanofiltration Membranes: Measurement, Modeling, and Mechanisms. Environ. Sci. Technol. 2004, 38, 18881896. (5) Kiso, Y.; Kon, T.; Kitao, T.; Nishimura, K. Rejection Properties of Alkyl Phthalates with Nanofiltration Membranes. J. Membr. Sci. 2001, 182, 205-214. (6) Devitt, E. C.; Ducellier, F.; Cote, P.; Wiesner, M. R. Effects of Natural Organic Matter and the Raw Water Matrix on the Rejection of Atrazine by Pressure-Driven Membranes. Water Res. 1998, 32, 2563-2568. (7) Lee, S.; Lueptow, R. M. Membrane Rejection of Nitrogen Compounds. Environ. Sci. Technol. 2001, 35, 3008-3018.

(8) Waypa, J. J.; Elimelech, M.; Hering, J. G. Arsenic Removal by RO and NF Membranes. J. Am. Water Works Assoc. 1997, 89, 102114. (9) Ventresque, C.; Turner, G.; Bablon, G. Nanofiltration: from Prototype to Full Scale. J. Am. Water Works Assoc. 1997, 89, 65-76. (10) Taniguchi, M.; Kimura, S. Estimation of Transport Parameters of RO Membranes for Seawater Desalination. AIChE J. 2000, 46, 1967-1973. (11) Abdel-Jawad, M.; El-Sayed, E. E. F.; Ebrahim, S.; Al-Saffar, A.; Safar, M.; Tabtaei, M.; Al-Nuwaibit, G. Fifteen Years of R and D Program in Seawater Desalination at KISR Part II. RO System Performance. Desal. 2001, 135, 155-167. (12) Mehdizadeh, H.; Dickson, J. M.; Eriksson, P. K. Temperature Effects on the Performance of Thin-Film Composite, Aromatic Polyamide Membranes. Ind. Eng. Chem. Res. 1989, 28, 814824. (13) Schaep, J.; Van der Bruggen, B.; Uytterhoven, S.; Croux, R.; Vandecasteele, C.; Wilms, D.; Van Houtte, E.; Vanlerberghe, F. Removal of Hardness from Groundwater by Nanofiltration. Desal. 1998, 119, 295-302. (14) Her, N.; Amy, G.; Jarusutthirak, C. Seasonal Variations of Nanofiltration (NF) Foulants: Identification and Control. Desal. 2000, 132, 143-160. (15) Deen, W. M. Hindered Transport of Large Molecules in LiquidFilled Pores. AIChE J. 1987, 33, 1409-1424. (16) Aimar, P.; Meireles, M.; Sanchez, V. A Contribution to the Translation of Retention Curves into Pore Size Distributions for Sieving Membranes. J. Membr. Sci. 1990, 54, 321-338. (17) Combe, C.; Molis, E.; Lucas, P.; Riley, R.; Clark, M. M. The Effect of CA Membrane Properties on Adsorptive Fouling by Humic Acid. J. Membr. Sci. 1999, 154, 73-87. (18) Sharma, R. R.; Agrawal, R.; Chellam, S. Temperature Effects on Sieving Characteristics of Thin - Film Composite Nanofiltration Membranes: Pore Size Distributions and Transport Parameters. J. Membr. Sci. 2003, 223, 69-87. (19) Mochizuki, S.; Zydney, A. L. Theoretical Analysis of Pore Size Distribution Effects on Membrane Transport. J. Membr. Sci. 1993, 82, 211-227. (20) Bungay, P. M.; Brenner, H. The Motion of a Closely Fitting Sphere in a Fluid Filled Tube. Int. J. Multiphase Flow 1973, 1, 25-56. (21) Singh, S.; Khulbe, K. C.; Matsuura, T.; Ramamurthy, P. Membrane Characterization by Solute Transport and Atomic Microscopy. J. Membr. Sci. 1998, 142, 111-127. (22) Michaels, A. S. Analysis and Prediction of Sieving Curves for Ultrafiltration Membranes: A Universal Correlation? Sep. Sci. Technol. 1980, 15, 1305-1322. (23) Kassotis, J.; Shmidt, J.; Hodgins, L. T.; Gregor, H. P. Modeling of the Pore Size Distribution of Ultrafiltration Membranes. J. Membr. Sci. 1985, 22, 61-76. (24) Van der Bruggen, B.; Schaep, J.; Dirk, W.; Vandecasteele, C. A Comparison of Models to Describe the Maximal Retention of Organic Molecules in Nanofiltration. Sep. Sci. Technol. 2000, 35, 169-182. (25) Tezel, A.; Sens, A.; Mitragotri, S. Description of Transdermal Transport of Hydrophilic Solutes during Low-Frequency Sonophoresis based on a Modified Porous Pathway Model. J. Pharm. Sci. 2003, 92, 381-393. (26) International Critical Tables of Numerical Data, Physics, Chemistry and Technology, 1st ed.; Washburn, E. W., Ed.; McGrawHill Book Company, Inc.: New York and London, 1929. (27) Hayduk, W.; Laudie, H. Prediction of Diffusion Coefficients for Non-Electrolytes in Dilute Aqueous Solutions. AIChE J. 1974, 20, 611-615. (28) Wang, X.-L.; Tsuru, T.; Togoh, M.; Nakao, S.-I.; Kimura, S. Evaluation of Pore Structure and Electrical Properties of Nanofiltration Membranes. J. Chem. Eng. Jpn. 1995, 28, 186192. (29) Nakao, S.-i. Determination of Pore Size and Pore Size Distribution 3. Filtration Membranes. J. Membr. Sci. 1994, 96, 131-165. (30) Bowen, W. R.; Mohammad, A. W.; Hilal, N. Characterization of Nanofiltration Membranes for Predictive Purposes - Use of Salts, Uncharged Solutes and Atomic Force Microscopy. J. Membr. Sci. 1997, 126, 91-105. (31) Tezel, A.; Mitragotri, S. On the Origin of Size-Dependent Tortuosity for Permeation of Hydrophilic Solutes across the Stratum Corneum. J. Controlled Release 2003, 86, 183-186. (32) Tam, C. M.; Tremblay, A. Y. Membrane Pore Characterization - Comparison Between Single and Multicomponent Solute Probe Techniques. J. Membr. Sci. 1991, 57, 271-287. VOL. 39, NO. 13, 2005 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

9

5029

(33) Giddings, J. C.; Kucera, E.; Russel, C.; Myers, M. N. Statistical Theory for the Equilibrium Distribution of Rigid Molecules in Inert Porous Networks: Exclusion Chromatography. J. Phys. Chem. 1968, 72, 4397-4408. (34) Seidel, A.; Waypa, J.; Elimelech, M. Role of Charge (Donnan) Exclusion in Removal of Arsenic from Water by a Negatively Charged Porous Nanofiltration Membrane. Environ. Eng. Sci. 2001, 18, 105-113. (35) Kosˇutic, K.; Kasˇtelan-Kunst, L.; Kunst, B. Porosity of Some Commercial Reverse Osmosis and Nanofiltration Polyamide Thin Film Composite Membranes. J. Membr. Sci. 2000, 168, 101-108. (36) Marcus, Y. Ion Solvation; John Wiley & Sons Limited: New York, 1985. (37) Van der Bruggen, B.; Schaep, J.; Wilms, D.; Vandecasteele, C. Influence of Molecular size, Polarity and Charge on the Retention of Organic Molecules by Nanofiltration. J. Membr. Sci. 1999, 156, 29-41. (38) Chan, K.; Matsuura, T.; Sourirajan, S. Effect of Evaporation Time on Pore Size and Pore Size Distribution of Aromatic Polyamidohydrazide RO/UF Membranes. Ind. Eng. Chem. Prod. Res. Dev. 1984, 23, 492-500. (39) Nguyen, T. D.; Chan, K.; Matsuura, T.; Sourirajan, S. Effect of Shrinkage on Pore Size and Pore Size Distribution of Different Cellulosic Reverse Osmosis Membranes. Ind. Eng. Chem. Prod. Res. Dev. 1984, 23, 501-508.

5030

9

ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 39, NO. 13, 2005

(40) Wendt, R. P.; Klein, E. Membrane Hetroporosity and the Probability Function Correlation. J. Membr. Sci. 1984, 17, 161171. (41) Chen, J. Y.; Nomura, H.; Pusch, W. Temperature Dependence of Membrane Transport Parameters in Hyperfiltration. Desal. 1983, 46, 437-446. (42) Chan, K.; Tinghui, L.; Matsuura, T.; Sourirajan, S. Effect of Shrinkage on Pore Size and Pore Size Distribution of Cellulose Acetate Reverse Osmosis Membranes. Ind. Eng. Chem. Prod. Res. Dev. 1984, 23, 124-133. (43) Koros, W. J.; Woods, D. G. Elevated Temperature Application of Polymer Hollow-Fiber Membranes. J. Membr. Sci. 2001, 181, 157-166. (44) Kosˇutic, K.; Kunst, B. Effect of Hydrolysis on Porosity of Cellulose Acetate Reverse Osmosis Membranes. J. Appl. Polym. Sci. 2001, 81, 1768-1775. (45) Kokubo, K.; Sakai, K. Evaluation of Dialysis Membranes Using a Tortuous Pore Model. AIChE J. 1998, 44, 2607-2619. (46) Van der Bruggen, B.; Geens, J.; Vandecasteele, C. Influence of Organic Solvents on the Performance of Polymeric Nanofiltration Membranes. Sep. Sci. Technol. 2002, 37, 783-797.

Received for review January 20, 2005. Revised manuscript received April 14, 2005. Accepted April 26, 2005. ES0501363