Thermodynamic Factors in Partitioning and Rejection of Organic

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Environ. Sci. Technol. 2006, 40, 7023-7028

Thermodynamic Factors in Partitioning and Rejection of Organic Compounds by Polyamide Composite Membranes ADI BEN-DAVID, YORAM OREN, AND VIATCHESLAV FREGER* Zuckerberg Institute for Water Research and Department of Biotechnology and Environmental Engineering, Ben-Gurion University of the Negev, POB 635, Beer-Sheva 84105, Israel

The paper analyzes the mechanism of partitioning and rejection of organic solutes by polyamide membranes for reverse osmosis and nanofiltration. The partitioning of homologous series of alcohols and polyols, in which polarity changes with size in opposite ways, was measured using attenuated total reflection IR spectroscopy. The results show that the partitioning of polyols monotonously decreases with size, whereas for alcohols it is not monotonous and slightly decreases for small C1-C3 alcohols followed by a sharp increase for larger alcohols. These results may be explained by assuming a heterogeneous structure of polyamide comprising a hydrophobic polyamide matrix and a polar internal aqueous phase. The partitioning data could consistently explain the results of rejection in standard filtration experiments. They clearly demonstrate that high/low partitioning may play a significant role in achieving a low/high rejection of organics. In particular, this points to the need to account for the partitioning effect while using molecular probes such as polyols or sugars for estimating the effective “pore” size or molecular weight cutoff of a membrane and for choosing/developing organicrejecting membranes.

1. Introduction Many natural water sources and industrial and municipal waste streams contain low-molecular-weight organic substances that need to be removed for subsequent use, reuse, discharge, or recharge of water to the environment (1, 2). Trace contaminants present a particular challenge, since the treatment often must combine efficient removal and low cost. Membrane filtration by reverse osmosis (RO) and nanofiltration (NF) can be a simple and technologically attractive option, as it combines intense continuous processing without the need for regeneration, reduced use of chemicals, and small plant footprints (3). These membranes, mostly thin-film polyamide composites, usually show excellent rejection of salts. However, their rejection to small organics is often insufficient (4-14). Membrane manufacturers today offer a variety of thinfilm composite membranes with a wide range of selectivity to inorganic salts and ions (15). Unfortunately, with few exceptions, the choice of material for the selective layer is limited nearly exclusively to cross-linked polyamides pro* Corresponding author phone: +972 8 6479316; fax: +972 8 6472960; e-mail: [email protected]. 10.1021/es0609912 CCC: $33.50 Published on Web 10/19/2006

 2006 American Chemical Society

duced by interfacial polymerization. Their superior desalting characteristics are due largely to the favorable combination of properties (high cross-linking, moderate hydrophobicity, and sufficient water permeability), of which the hydrophobicity might not necessarily be optimal for removal of organics (16). Unlike ions, neutral organic solutes do not experience a strong charge exclusion (17-20), hence, they may relatively easily enter (partition) and pass through the active layer. The effect of partitioning is superimposed on the size exclusion, so that rejection is ultimately determined by the combined effect of thermodynamic affinity and size (16). This may explain why it has been difficult to observe correlation of rejection with molecular size for a wide range of small organic solutes (7, 10-12). Splitting the overall selectivity into sorption and diffusion selectivities has become routine for some membrane processes, such as gas separation or pervaporation (21, 22). However, in RO and NF the role of thermodynamic factors has not received proper attention until recently. In our previous papers, we introduced a novel IR spectroscopybased technique for measuring partitioning in films of submicrometer thickness in solution, which was applied to some solutes in the polyamide selective layer of composite membranes (16, 23). In this article, this analysis is extended to another group of solutes, polyols of general formula CnH2n+2On, which (together with chemically similar sugars) have been popular as molecular probes for testing RO/NF membranes. These data offer a more systematic insight into the relations between size, partitioning (affinity), and rejection of organics.

2. Theoretical Relations The steady-state transport of a solute in a pressure-driven membrane separation process is described by the KedemSpiegler equation (24, 25) written here as follows

dC* dC + JvC*(1 - σˆ ) ) -DK + JvCK(1 - σˆ ) (1) dx dx

Js ) -D

Here, Js and Jν are the solute and total volume fluxes, D is the diffusivity of the solute in polyamide, K is the partition coefficient, σˆ is the modified reflection coefficient related to the regular reflection coefficient σ by means of 1- σ ) K(1σˆ ), and C is the virtual solute concentration at distance x from the feed side related to the local solute concentration inside the membrane C* by C* ) CK. For constant coefficients, the solute rejection R will be given by the well-known solution of eq 1

1-R)

1-σ ) 1 - σ exp( -Pe) (1 - σˆ )K (2) 1 - [1 - (1 - σˆ )K] exp( -Pe)

where Pe ) Jνδ(1 - σˆ )/D and δ is the active layer thickness. K is not lumped into 1 - σˆ (unlike 1 - σ), thereby σˆ primarily reflects the difference in friction between different fluid components and the polymer matrix inside the membrane. This is most clearly seen by relating the parameter 1- σˆ to the coefficients of the friction model as follows (25)

1 - σˆ )

fsw

(3)

(fsw + fsm)φw

where fsw and fsm are friction coefficients (defined as the average frictional force per mole of solute between the solute VOL. 40, NO. 22, 2006 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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and water inside the membrane and between the solute and the membrane, respectively), and φw is the volume fraction of water in the membrane. As follows from eq 3, 1 - σˆ depends on the relative magnitude of the hydrodynamic friction between the solute and water compared to that between the solute and membrane. Since the membrane is a rigid medium with a characteristic “mesh” size of the polymer network (“pore size”), fsm is more sensitive to the molecular size of the solute than fsw and should steeply increase as the solute size approaches the pore size. This is believed to be the primary origin of the size exclusion. However, size exclusion is embedded not only in the friction coefficients and ultimately in D and 1- σ but also in the partitioning coefficient K, since accommodation of larger solutes in a rigid pore requires extra free energy. One may write a rigorous thermodynamic relation (see ref 26, chapter 15)

K≡

C * γw ) ) exp( - ∆G/kBT) C γm

(5)

The term ∆Gi reflects the differences in the intermolecular interactions of the solute in the two phases, and it will be present irrespective of whether the phases are liquid or solid. The second term will only be present if the phase, to which the solute partitions, possesses some rigidity, that is, is solidlike. It contains the molecular volume v and the pressure Π exerted by the rigid polymeric medium on the solute molecules, which may be of elastic or entropic nature. For ideally rigid solid pores, the pressure Π will steadily increase as the solute size approaches the pore size and the volume accessible to the solute or the number of allowed configurations (i.e., the entropy) decreases. Obviously, Π will become infinite and hence K will become zero once the solute size exceeds the pore size. In a more realistic picture, the decrease in accessible space may reflect the pore size distribution, so that K will be finite even for relatively large solutes because of the presence of a small fraction of large pores. For an elastic (expandable) pore, there will be no total exclusion as well. The elastic pressure Π could be a constant or increase with solute size, yet vΠ will always increase with solute size, which will exponentially reduce K, as with rigid pores. In RO/NF experiments, this thermodynamic size exclusion embedded in K will be superimposed on the frictional size exclusion embedded in D and 1 - σ and, if only the rejection is measured, the two exclusion mechanisms will be indistinguishable. However, availability of partitioning data may allow a more detailed analysis, which was one of the objectives of this study.

Experimental Section 2.1. Membranes and Materials. The solutes used in this study were n-alcohols (CnH2n+1OH, 1e n e 5), benzyl alcohol (BzOH), and polyols (CnH2(OH)n, 1e n e 4). Their main characteristics are shown in Table 1. The membrane studied was high-flux ESPA1 (Hydranautics) with nominal NaCl rejection of 99.3% and a hydraulic permeability (Lp) of 4.9 L/m2/h/bar (www.membranes.com), comprised of a fully aromatic polyamide active layer supported by a porous polysulfone layer reinforced with a nonwoven polyester 7024

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organic compounds methanol ethanol 1-propanol 1-butanol 1-pentanol benzyl alcohol ethylene glycol glycerol meso-erythritol dextrane

supplier

molecular weight

Frutarom 32.04 Frutarom 46.07 Frutarom 60.1 Frutarom 74.12 Fluka 88.15 Aldrich 108.14 Fluka 62.07 Frutarom 92.09 Alfa Aesar 122.12 Aldrich ∼30 000

Stokes wavenumber,b radiusa, Å cm-1 1.58c 1.88c 2.19c 2.39c 2.61c 2.87c 1.98c 2.17c 2.47d

1014 1014 961 1026 1050 1000 1084e 1110e 1084e 1080e

a Calculated from the diffusion coefficients in water at 25 °C using the Einstein-Stokes equation. b The IR band used for quantifying partitioning. c On the basis of diffusion coefficients from refs 26, 28, and 29. d The value obtained by interpolation between C1-C3 and C6 polyols. e The strongest peak of a multiplet band.

(4)

where γw and γm are the activity coefficients of the solute in the external solution and membrane. The last equality is essentially the Boltzmann distribution (27), in which ∆G is the free-energy change associated with transfer of a solute molecule from water to polyamide. For polymer-solvent systems, ∆G may be split into two terms (27)

∆G ) ∆Gi + vΠ

TABLE 1. Organic Compounds Used in this Work and Their Characteristics

ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 40, NO. 22, 2006

fabric. The membranes were kindly supplied by Dr. Mark Wilf (Hydranautics, United States) as flat sheets. 2.2. Filtration Experiment. The setup for RO filtration experiments is described in detail elsewhere (16). Briefly, the feed solution from a 1.5-L tank pressurized with nitrogen was fed by means of a gear pump (Ismatec BVP-Z) through a thermostat to two filtration cells mounted in series (16 cm2 membrane area each) at 0.6 m/s and 20 bar and then back to the tank. Flux and rejection were measured after running the system for about 30 min to reach steady state, which was verified in separate experiments by measuring permeate concentration over a period of a few hours. The flux was determined by collecting and weighing the permeate; the solute rejection was determined by measuring the total organic carbon content in the feed, the retentate, and the permeate. The integrity of the membrane was tested by adding 1500 ppm NaCl and verifying 95% or higher NaCl rejection (by conductivity) in all experiments. The rejection R of the organic solute was determined using the formula

(

R) 1-

)

CP × 100% CF

(6)

where CF (equal to 100 ppm for all organic solutes) and CP are the concentrations of the organic solute in the feed and permeate, respectively. As all organic solutes tested were uncharged, no interference from the added salt was assumed. 2.3. Sample Preparation and Characterizations. The preparation of free polyamide films and their characterization are described in detail elsewhere (16, 30). Briefly, a polyamide film 184 ( 22 nm thick (16) was separated from a commercial membrane and was attached to a ZnSe attenuated total reflection (ATR) element (incident angle 45° and 6 nominal reflections) by careful dissolution of polysulfone in organic solvents. The ATR crystal formed the bottom of a trough cell of a Gateway ATR assembly (Specac, United Kingdom), which was then mounted in the spectrometer and was filled with the appropriate solutions. The refractive index of the wet film was calculated from the indices of dry polyamide and water (see eq A4 in Supporting Information). The refractive index of the dry film (n ) 1.70) was estimated using appropriate structure-property correlations (31). It was initially assumed that the swelling of the film, as determined by atomic force microscopy (AFM) (φw ≈ 0.06 ( 0.011) (30), may estimate its water content. However, the actual water content in ESPA1 films was reassessed in the course of this study, as described below. 2.4. FTIR Experiments and Quantitative Analysis. The spectra (64 scans at 4 cm-1 resolution) were recorded on an Impact 410 FTIR spectrometer (Nicolet) using a nonpolarized

beam at room temperature. The IR spectra of all solutes used in this study have a strong band around 1000-1100 cm-1 assigned to C-O stretching (Table 1). Benzyl alcohol and n-alcohols show a single band, while polyols show several overlapping bands (multiplet) in that region. For that reason, the band intensity A was measured as the total integrated area of the multiplet band. The specific absorptivity for each solute was first determined from the slope of the band intensity versus the concentration measured for a bare crystal using three to six different concentrations ranging from about 0.5 to 50 g/L. To determine partitioning of the solutes in polyamide, the intensity was measured for the same set of solutions using a crystal covered with a polyamide film. Spectra were recorded in the order of increasing concentration, setting the first spectrum of neat water as a background. The measurements for each sample were averaged for three to four similarly prepared samples. The partitioning coefficient K was then calculated from the intensity of the band using the following formula (23)

A ) aC(1 - b + dK),

(7)

where a, b, and d are coefficients. The coefficients b and d were calculated assuming no polarization (eqs A1-A3 in Supporting Information). They are proportional to the thickness of the wet film h and also depend on the angle of incidence, wavelength, and the indices of refraction of the crystal (n1 ) 2.4), the solution (n3 ) 1.29 at 1000 cm-1), and the wet film. The coefficient a was calibrated in experiments with a bare crystal, in which case b ) d ) 0. The values of K reported in this work were obtained by extrapolation of the results for all measured concentrations to C ) 0 using a Langmuir isotherm, as described in refs 16 and 23. 2.5. Assessment of Water Content in the ESPA1 Film. For larger polyols (glycerol and meso-erythritol), the measured A was smaller than aC(1- b), yielding negative K values (cf. eq 7). Since the amount of polyamide was known with reasonable precision, the most likely explanation was that the water fraction in the membrane was underestimated. This means that the polyamide may contain more water than was presumed based on its swelling (about 6% (30)). Indeed, the polyamide film of ESPA1 is known to contain voids and asperities in both its surfaces (30, 32) that could affect the average optical properties of the film, thus possibly explaining the inconsistencies found for large polyols. The water fraction was then reassessed using solutions of dextrane (Mw ) 30 kDa), assuming that dextrane is completely excluded from the membrane (K ) 0) because of its size and hydrophilicity. The measured dependence of A on the dextrane concentration in the presence of film was then fitted to eq 2 with K ) 0 and water content φtotal as a fitting parameter (Figure 1). The best fit, φtotal ) 0.32, primarily reflects the average optical properties rather than the actual water content of the film, since it lumps together all possible uncertainties of the other parameters and nonideal film geometry. This value of φtotal was subsequently used in calculations, which also slightly corrected the previously reported results for alcohols (16).

3. Results and Discussion 3.1. Partitioning of n-Alcohols and Polyols. The two homologous series of solutes tested in this study are characterized by opposite trends in polarity (hydrophilicity). This is seen in Figure 2a, which shows the values of log P, the logarithm of octanol-water partitioning coefficients, plotted versus molecular weight. The value of log P linearly increases with the length of the molecule for n-alcohols, indicating increasing hydrophobicity, while for polyols it linearly decreases. As follows from eq 4, the slopes indicate the incremental change of the free-energy difference ∆G )

FIGURE 1. ATR-FTIR absorbance of dextrane solutions (integrated area of the multiplet band at 1080 cm-1) vs dextrane concentration for the bare and film-covered crystal. Assuming K ) 0, the slopes fit best eq 7 with optical parameters corresponding to a water content in the ESPA1 film Ototal ) 0.32.

FIGURE 2. Values of (a) log P and (b) the activity coefficients in water at infinite dilution for n-alcohols, BzOH, and polyols vs molecular weight. Data based on refs 33-36. ∆Gi ) ∆Go/w upon addition of one more group in the series (CH2 for alcohols and CHOH for polyols). For instance, a positive slope for alcohols indicates that addition of a hydrophobic CH2 group to an alcohol raises its energy of interaction with water more than with octanol, which results in a linear decrease in ∆Go/w and an increase in log P. The observed linear trends are characteristic of homologous series of solutes in homogeneous phases (37) and are analogous to the well-known Traube rule for homologous series of surfactants (38). A more direct way to examine the hydrophilicity of the solutes is to look at the values of γw, activity coefficient in water at infinite dilution, shown in Figure 2b. A smaller γw means a higher affinity toward water and Figure 2b confirms that n-alcohols become more hydrophobic with molecular weight, while polyols grow more hydrophilic. Obviously, the aromatic benzyl alcohol, not an n-alcohol, deviates from the trends shown in Figure 2. These trends may be compared with the measured values of the partitioning coefficient log K ) log Km/w between the polyamide and water, shown in Figure 3. For polyols, only the results for methanol, ethylene glycol, and glycerol (C1C3) are included, since K for meso-erythritol (C4) was too small and virtually indistinguishable from zero within experimental error. As for log P, linear trends could be expected for log K, but with smaller slopes, since the polarity of polyamide is intermediate between water and octanol, as indicated by the values of the solubility parameter (respectively, 23, 40, and 21 MPa0.5 (39, 40)). Indeed, a simple linear dependence of log K on molecular weight is observed for polyols, however, n-alcohols show a non-monotonous trend (Figure 4). To clarify this behavior, the activity coefficients of the solutes in water (γw), in octanol (γo ) γw/P), and in polyamide VOL. 40, NO. 22, 2006 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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FIGURE 6. Rejection (R) and partitioning in polyamide (K) vs molecular weight for n-alcohols, BzOH (a), and polyols (b). Filtration conditions: membrane, ESPA1; pressure, 20 bar; temperature, 25 °C; solute concentration in the feed, 100 ppm.

FIGURE 3. Values of log K (partitioning coefficient between ESPA1 polyamide film and water) for n-alcohols, polyols, and benzyl alcohol vs molecular weight.

FIGURE 4. Values of the activity coefficients of (a) polyols and (b) n-alcohols and benzyl alcohol in the water, octanol, and polyamide (ESPA1) phase vs molecular weight.

FIGURE 5. Stokes radii of the solutes used in this study vs their molecular weight. Calculated from the data of refs 26, 28, and 29. (γm ) γw/K), separately representing the affinity toward each phase, are presented in Figure 4a and b. It is seen that for polyols (Figure 5a) the values of γm are, as expected, intermediate to γw and γo, all showing approximately linear dependence on the molecular weight. However, for smaller polar alcohols (C1-C3), the values of γm and the slope practically coincide with γw, while for larger alcohols the values of γm and the slope become intermediate between γw and γo. With only quantitative differences, the activity coefficients measured for aromatic BzOH follow the same sequence, despite the fact that this alcohol is not an n-alcohol. Perhaps the most reasonable explanation for the nonmonotonous behavior of alcohols is that K reflects some heterogeneity of polyamide that might contain two separated microscopic phases: the relatively hydrophobic polyamide matrix (phase 1) and an aqueous solution filling interstitial spaces or “pores” (phase 2). Alternatively, existence of two types of solute-binding sites in the swollen membrane, organophilic and hydrophilic, may be assumed. The solute should partition differently in each phase (or bind to each site type), and thus the observed value of K and the slope of 7026

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log K versus molecular weight would be characteristic of the microscopic phase that takes up most of the solute. The larger alcohols would mostly partition into the more hydrophobic microphase, whereas most of the hydrophilic alcohols and polyols could partition to the aqueous phase and the slope would be different. The aqueous microphase phase could be more organophilic than bulk water, since proximity to the hydrophobic microphase may reduce the energy required for accommodation of a partly hydrophobic solute (e.g., an alcohol), similar to adsorption of surfactants at an air-water interface (38). This may explain why for small alcohols K ≈ 1, while φw < 1. This above picture seems to almost satisfactorily explain the partitioning results without invoking any size exclusion, that is, without the need to consider the second term in eq 4. However, size exclusion could be present but indistinguishable from regular molecular interactions. If the vΠ term changes linearly with molecular size, that is, Π is constant and independent of solute size, the plot of log K will remain linear with a reduced slope and so will log γm but with an increased slope. This is not unlikely, since, for instance, the Flory-Rehner theory predicts just that type of behavior for the elastic pressure in a swollen Gaussian gel (41). For instance, inspection of Figure 4 shows that for small hydrophilic alcohols, γm changes in the same manner as γw, while for hydrophilic polyols the slope is more negative than for γw. This was explained above by assuming higher organophilicity of the aqueous phase compared to bulk water. A possible alternative explanation is that in both cases the size exclusion modifies (makes more positive) the slopes of log γ, and hence the observed trends might reflect both the heterogeneity of polyamide and size exclusion. Unfortunately, the data do not allow an unequivocal conclusion, yet irrespective of the mechanism, the observed differences in partitioning of different solutes have a clear effect on rejection of the solutes, as discussed in the next section. 3.2. Correlation between Partitioning, Size, and Rejection. As follows from eq 2, the rejection depends both on the molecular friction (through the parameters σˆ and Pe) and on the partitioning coefficient K. The molecular weight may adequately represent the size effect for the solutes in this study, since it is uniquely correlated to the Stokes radius (Figure 5), which is also known to correlate well with molecular width that is the generally recommended choice (11, 12, 42). Figure 6a shows the measured partitioning and rejection of n-alcohols for the ESPA1 membrane, plotted versus the molecular weight. Although rejection increases with molecular size, the effect of increasing partitioning may be discerned. The partitioning coefficient is very similar for the C1-C3 alcohols, and hence rejection is determined mainly by size (friction) and sharply increases for propanol, indicating that its size approaches the characteristic pore size. However, thereafter the increase in rejection is moderate, indicating that the increasing friction is nearly offset by the rapidly increasing partitioning. A similar effect was observed for the chemically similar but looser NF-200 membrane, for

which the rejection of alcohols remains low and nearly constant for all alcohols beginning with ethanol (C2) (16). For a cellulose acetate membrane, Schutte found that the rejection of n-alcohols may even decrease with size (14). Notably, the rejection of BzOH appears to be unreasonably low in Figure 6a compared to n-alcohols. Presumably, the aromaticity of BzOH and its different shape could reduce the frictional parameters inside the aromatic polyamide. This manifests the complexity of the rejection mechanism, which involves both frictional and thermodynamic effects and makes comparison of chemically different solutes problematic. However, for polyols, partitioning decreases with molecular size, hence, the size and partitioning act in the same direction. As is seen in Figure 6b, rejection indeed increases rapidly, reaching nearly 99% for meso-erythritol, the largest in size among the analyzed polyols and the one with the lowest partitioning coefficient. This result suggests that high rejection of large polyols or chemically similar sugars is not necessarily the consequence of their large size only. For instance, glucose (C6H12O6, Mw ) 180, log P ) -3.24 (33)) closely follows the log P trend for polyols in Figure 2a, and then presumably its K could be estimated roughly by extrapolating the log K dependence for polyols, which yields K ) 0.024. Taking a typical Pe ) 1, even for a fairly poor friction σˆ ) 0.75, eq 2 predicts that the glucose rejection will be about 99%. Sucrose (C12H24O12, Mw ) 342, log P ) -3.7 (33)) deviates from the polyol trend. Still, it is more hydrophilic and larger than glucose, hence, low K and high rejection (>>99%) could be expected, even for the same poor frictional parameters, for purely thermodynamic reasons. Glycerol, glucose, sucrose, and similar solutes are often used as molecular probes to assess the characteristic pore size of RO and NF membranes. This choice is justified by a widely accepted premise that they should have similar hydrophilicity, hence, their rejection may be related to pore size using an idealized hydrodynamic model (19, 43). However, the present analysis demonstrates that this approach requires greater care, since the hydrophilicity of these solutes is by no means similar, and then strong thermodynamic effects are likely to significantly increase their rejection. In conclusion, we see that thermodynamic and frictional effects are, in general, superimposed in RO/NF, which leads to complex behavior that is difficult to interpret in terms of simple concepts borrowed from porous membranes, such as the molecular weight cutoff or pore size. In particular, we see that polar solutes such as large polyols and sugars, often used as molecular probes for dense RO/NF membranes, may, to a significant extent, owe their high rejection to partitioning effects rather than size exclusion. This implies that, unlike porous membranes (ultra- and microfiltration), the very use of the effective pore size or molecular weight cutoff for RO and NF membranes requires much care and should always address the issues of thermodynamic affinity. As we have seen, this may not be straightforward even for simple and chemically similar solutes, such as polyols. Another important consequence, already raised in our previous report (16), is the fact that polyamide membranes are not necessarily optimal for removal of many organics and that new types of membranes, presently not existing as commercial products, may be necessary. Since organics largely vary in characteristics pertaining to intermolecular interactions, the need to have a range of membrane products tailored for removal of different classes of organics may be envisaged.

Acknowledgments The authors are indebted to Prof. Ora Kedem for numerous stimulating discussions and encouragement. Financial support from the Israel Ministry of Science (Project N 01-01-

01496, the Program for Scientific and Technological Development for the Quality of the Environment and Water) is gratefully acknowledged.

Supporting Information Available Formulas used for calculating the coefficients of eq 7 and the average optical properties of a film containing water. This material is available free of charge via the Internet at http:// pubs.acs.org.

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Received for review April 25, 2006. Revised manuscript received July 12, 2006. Accepted September 14, 2006. ES0609912