Conceptual Model for the Adsorption of Organic Compounds from the

A Conceptual Model for Predicting Gas Phase Adsorption. Coefficients. The adsorption equilibrium between the gas phase and a surface is completely ...
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Environ. Sci. Technol. 1997, 31, 3600-3605

Conceptual Model for the Adsorption of Organic Compounds from the Gas Phase to Liquid and Solid Surfaces KAI-UWE GOSS* Swiss Federal Institute for Environmental Science and Technology (EAWAG), CH-8600 Du ¨ bendorf, Switzerland

Adsorption of organic pollutants from the gas phase to ambient surfaces has a great impact on the environmental mobility of these compounds. In a recent paper, gas phase adsorption coefficients for different compounds and surfaces have successfully been predicted based on thermodynamic parameters (surface free energies) without the use of any empirical fitting. However, the surface free energies required for these calculations are only known for a limited number of adsorbates and surfaces. Here, it will be shown that, at least for the adsorbates, these parameters can be substituted by others (ln p°L, β, and R) that are tabulated for a wide range of compounds. Validation of this extended model with experimental data shows good results. At the same time, the conceptual understanding of the adsorption equilibrium in terms of van der Waals and Lewis acidbase (electron donor-acceptor) interactions, which is provided by the original model, remains unaltered. This paper is concluded by a discussion of our current knowledge of the surface parameters that are additionally required for the calculations.

Introduction Adsorption from the gas phase to surfaces is important for the transport and transformation of many organic chemicals in the environment. Compared to sorption processes from water to solid surfaces, only a limited number of studies have been conducted in which sorption coefficients of organic (mostly nonpolar) vapors have been determined. Adsorbents investigated include soils, soil minerals and soil organic matter (1-8, among others), aerosols (9-11, among others), and water and ice surfaces (12-15). In fact, for aerosols or organic matter, it is not even clear whether adsorption or absorption is the dominating process. The focus of this paper is on the adsorption process only. The existing experimental data reveal that adsorption coefficients depend on properties of the surface and the adsorbate, temperature, concentration (i.e., isotherms are nonlinear), and in many cases, relative humidity. Some models have been suggested for quantitative relationships between physicochemical parameters and experimental adsorption coefficients (3, 13, 16-18). However, these models only apply to small subsets of the existing experimental data, and they do not provide a sufficient theoretical understanding of the adsorption process. In particular the influence of the adsorbent has not yet been addressed. In previous work, a conceptual model that overcomes these shortcomings has been proposed and will be summarized in the following section (19). Unfortunately, the applicability of this model is limited by the restricted availability of the required parameters. Empirical relation* Author to whom correspondence should be addressed. Fax: +411-823 5471. E-mail: [email protected].

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ships will therefore be introduced here which allow the replacement of some of these parameters by more readily accessible data. A Conceptual Model for Predicting Gas Phase Adsorption Coefficients. The adsorption equilibrium between the gas phase and a surface is completely determined by the interactions between the adsorbate and the surface if the following conditions are met: the gas phase can be treated as ideal (i.e., no interactions between molecules in the gas phase) and there are no lateral adsorbate-adsorbate interactions (i.e., the adsorbed concentration is low ) zero coverage region). The interactions between the adsorbate and the surface consist of van der Waals interactions, which always are present and, in some cases, of Lewis acid-base interactions (a subclass of which are hydrogen bonds). Coulombic forces between a charged surface and an uncharged molecule are small and can be neglected for natural surfaces (surface potentials ξ typically between -15 and -60 mV). The van der Waals and acid-base interactions can and should be treated separately e so that the total free energy of adsorption ∆Gads can then be written as the sum of a van der Waals component ∆GvdW and an acid-base component ∆GAB (20, 21): e ∆Gads ) ∆GvdW + ∆GAB

(1)

e ∆Gads is related to the adsorption coefficient by the following equation (22):

e ∆Gads ) -RT ln[2.99 × 108 (m-1) K]

(2)

where R and T are the gas constant and the absolute temperature, respectively, K is the adsorption coefficient defined as K ) concn per unit surface area/concn in the gas phase (dim ) m), and the factor 2.99 × 108 (m-1) is given by the choosen standard state of adsorption (23, p 112) and the dimension of the adsorption coefficient K. As discussed in detail in ref 19, the free energy of adsorption e ∆Gads between an adsorbate molecule and a surface can be expressed by the following equation: e ∆Gads ) -2N[CA(1 - ro2/D2)x0.95xγvdW + γvdW 1 2 van der Waals interactions - + (3) CA′(xγ+ 1 γ2 + xγ1 γ2 )] (J/mol) Lewis acid-base interactions

where γvdW ) van der Waals component of the surface free energy of the adsorbate (1) and the adsorbent (2), γ+, γ- ) electron acceptor and electron donor parameters for calculating the corresponding acid-base interactions between the adsorbate (1) and the adsorbent (2), respectively; N ) Avogadro’s constant; CA, CA′ ) molecular contact area; ro ) equilibrium distance between molecule and surface; and D ) thickness of an adsorbed molecule. Comparison of experimental gas phase adsorption data from the literature with predicted data using eqs 2 and 3 has shown good agreement (19). These calculations provide valuable insight in the underlying intermolecular interactions since they do not use any empirical correlation or fitting parameter. However, there are severe restrictions in its applicability because of the limited knowledge on the surface parameters γvdW, γ+, and γ- for the adsorbate and the adsorbent. In the following paragraphs, these parameters will be discussed, first with respect to the adsorbate, and means to approximate them by other parameters will be evaluated.

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γvdW is the van der Waals component of the surface free energy. For liquids, the surface free energy is identical to the surface tension and the van der Waals component of the surface tension γvdW equals the total surface tension γ if a compound is non-self-associating (i.e., exhibits no internal acid-base interactions). For self-associating liquids, γvdW can be determined from the interfacial tension with an alkane since alkanes are known to interact by van der Waals interactions only (24, 25). Values of γvdW for a number of compounds can be found in the literature (24, 25). However, for many organic pollutants (e.g., PCBs, PAHs, pesticides, and others), these values are not tabulated and can also not readily be determined. The electron acceptor and donor parameters γ+ and γ- of a liquid compound can be determined from the interfacial tension with a reference Lewis acid and base provided that the γvdW values of all three compounds are already known (25). Literature values for γ+ and γ- are even more difficult to find than data for γvdW. Therefore, it is desirable to replace these parameters by others that are more readily available. Empirical correlations between γvdW , γ+ 1 1, and γof the adsorbate and well-known physicochemical 1 parameters are discussed in the following section first for the van der Waals and then for the acid-base interactions. Approximation of van der Waals Interactions. The van der Waals component ∆GvdW of the overall interaction free e energy ∆Gads is given by (see eq 3)

∆GvdW ) -2NCA(1 - ro2/D2)x0.95xγvdW (4) xγvdW 1 2 The term CA (γvdW )1/2 depends on the properties of the 1 adsorbate and shall be replaced in the following by a more easily available parameter. It has been common practice in the literature to use the saturated vapor pressure p°L of a liquid organic compound as a predictor for the adsorption from gas phase to a given surface. Although, in agreement with intuition, this procedure is actually not easily justified since the liquid vapor pressure of a compound depends solely on the internal interactions in the pure liquid, while adsorption depends on interactions with a surface which may represent a completely different material. In the following paragraph, it will be shown that the vapor pressure can only be used as a predictor for the ability of compounds to engage in van der Waals interactions with like or dislike molecules. In the process of evaporation, a molecule is taken out of its condensed phase and brought into the gas phase. Energetically, this process is equivalent to a process in which the surface of the condensed phase is increased by the surface area of an isolated molecule (26, p 22). Thus, the molecular free energy of evaporation ∆Gevap should be given by the surface tension (surface free energy) of the compound times the total surface area (TSA) of a molecule (26, p 22):

∆Gevap ) TSAγ

(5)

For all compounds whose van der Waals component of the surface tension γvdW is identical with the total surface tension γ, i.e., for all non self-associating compounds, one can substitute γ with γvdW. ∆Gevap is proportional to the logarithm of the saturation vapor pressure ln p°L, and with the assumption that the contact area (CA) of an adsorbed molecule is proportional to its total surface area (TSA), eq 5 can be written as

ln p°L ∝ CAγvdW 1

(6)

The surface tension of most organic compounds is between 20 and 40 mJ/m2. In this range, an approximately linear

relationship between γ and (γ)1/2 exists (r2 ) 0.998 for γ ) 20, 22, 24, ..., 40). It follows that eq 6 may also be expressed as

ln p°L ∝ CAxγvdW 1

(7)

Equation 7 may now be used to substitute the adsorbate specific term CA(γvdW )1/2 in eq 4 by the much better known 1 vapor pressure and since N and (1 - ro2/D2)(γvdW )1/2 can be 1 substituted by a constant (19), one gets

∆GvdW ) (b + m1 ln p°L) xγvdW 2

(8)

According to eq 8, ln p°L may be used to describe the van der Waals interactions of organic compounds with any surface if the coefficients b and m1, which are independent of adsorbate and adsorbent, are known. However, it follows from the derivation that this only works for compounds whose vapor pressure is not considerably affected by internal acidbase interactions. Thus, eq 8 will be valid for most organic compounds of environmental concern but it should not be applied for strongly self-associated compounds (e.g., carboxylic acids). Combining eqs 8 and 2 reveals that, in all cases where only van der Waals forces are active in the adsorption process e (∆GvdW ) ∆Gads ) a linear relationship between ln K and ln p°L is to be expected (no matter whether the compounds are from the same compound class or not). However, if acidbase interactions between the adsorbate and the adsorbent contribute significantly to the total free energy of adsorption, then additional parameters are needed for a prediction of ln K. This is why correlations that are based only on ln p°L cannot explain the variability of adsorption coefficients between compound classes of different polarity on a polar adsorbent (11, 27, 28). Approximation of Acid-Base Interactions. Acid-base interactions are represented in eq 3 by the following expression: + ∆GAB ) -2NCA′(xγ+ 1 xγ2 + xγ1 xγ2 )

(9)

Again, the aim is to substitute the parameters γ+ 1 , γ1 , and CA′ of the adsorbing molecule by others that are more readily available. The parameters γ+ 1 and γ1 represent the electron acceptor and donor properties of the adsorbate per unit contact area of the adsorbate. Multiplication with the contact area per molecule CA′ (for the difference between CA and CA′, see ref 19) and Avogadro’s constant N in eq 9 yields the same parameters on a per mole basis. Abraham has constructed a scale of hydrogen bond parameters R (electron acceptor parameter) and β (electron donor parameter), which also are on a per mole basis and Gibbs energy related and which are tabulated for several hundred compounds (29, 30). It appears that R and β should be suitable for a correlation 1/2 and CA′(γ-), respectively. Both correlations with CA′(γ+ 1) 1 have to go through the origin since R and β should be zero if ∆GAB is zero. Thus, eq 9 can be substituted by the following empirical expression:

∆GAB ) m2βxγ+ 2 + Rxγ2

(10)

Summarizing the above considerations the original model (eq 3) may be replaced by an empirical equation of the form e ∆Gads ) (b + m1 ln p°L)xγvdW + m2 βxγ+ 2 2 + m3 Rxγ2 (11)

This equation still contains the original parameters for the

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TABLE 1. Experimental Gas Phase Adsorption Coefficients for a Water Surface and Other Data Used in the Regression Analysis (All Values for 20 °C)

b

adsorbate

Kexpa (M)

∆Geexp (kJ/mol)

ln p°Lc (Pa)

rc

βc

n-pentane n-hexane n-heptane n-octane n-nonane n-decane 2-methylheptane 2,2,4-trimethylpentane cyclohexane cycloheptane cyclooctane cis-2-octene trans-2-octene 1,1,1-trichloroethane benzene toluene ethylbenzene isopropylbenzene fluorobenzene chlorobenzene 1,3-dichlorobenzene diethyl ether propylether methylformate ethyl acetate chloroform acetone dichloromethane tetrachloromethane 1,2-dichloroethane trichloroethylene tetrachloroethylene

6.50 × 1.39 × 10-7 2.85 × 10-7 6.70 × 10-7 1.47 × 10-6 3.14 × 10-6 6.09 × 10-7 4.18 × 10-7 1.23 × 10-7 3.51 × 10-7 7.37 × 10-7 1.33 × 10-6 1.30 × 10-6 3.43 × 10-7 5.91 × 10-7 1.55 × 10-6 3.38 × 10-6 5.37 × 10-6 7.62 × 10-7 1.66 × 10-6 3.49 × 10-6 7.06 × 10-6 1.99 × 10-5 2.84 × 10-6 3.89 × 10-5 4.68 × 10-7 2.58 × 10-5 2.63 × 10-7 2.03 × 10-7 1.01 × 10-6 3.13 × 10-7 3.94 × 10-7

-7.23 -9.09 -10.83 -12.93 -14.84 -16.68 -12.68 -11.76 -8.78 -11.34 -13.15 -14.60 -14.53 -11.29 -12.61 -14.95 -16.86 -17.99 -13.23 -15.13 -16.94 -18.66 -21.18 -16.43 -22.81 -12.04 -21.81 -10.64 -10.00 -13.93 -11.06 -11.62

10.95 9.70 8.46 7.24 6.03 4.78 7.63 8.54 9.25 7.71 6.57 7.58 7.59 9.49 9.22 7.98 6.86 6.10 9.01 7.10 5.20 10.99 8.78 11.07 9.20 9.96 10.12 10.77 9.41 9.03 8.96 7.52

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.15 0.04 0.10 0 0.10 ∼0 ∼0

0 0 0 0 0 0 0 0 0 0 0 0.07 0.07 0.09 0.14 0.14 0.15 0.15 0.10 0.07 0.02 0.45 0.45 0.38 0.45 0.02 0.49 0.05 0 0.11 ∼0 ∼0

10-8

a Experimental values from refs 58 and 13 extrapolated from 12.5 and 15 °C, respectively, to 20 °C. Average values were used where it applied. Ref 59. c Ref 29.

surface properties which cannot be replaced by more readily available data. These data will be discussed later on. Determination of the Empirical Regression Coefficients. In order to determine the parameters m1, m2, m3, and b, a multiple regression analysis has to be performed with experimental adsorption coefficients for compounds that cover all types of interactions and for a surface with known γvdW , γ+ 2 2 , and γ2 values distinctly different from zero. Data from the literature for the adsorption of vapors on a bulk water surface fulfill these requirements. Furthermore, the water surface is of importance in many environmental applications (31-33). The free energies of adsorption required for the regression analysis were calculated according to eq 2 from the experimental adsorption coefficients from Karger et al. (15) and Hoff et al. (13) after extrapolation from 12.5 and 15 °C, respectively, to 20 °C. The data used in the regression analysis for the adsorbates and the water surface are listed in Tables 1 and 2. Equation 11 proved to be very suitable in describing the experimental data (Figure 1). The mean deviation between experimental and calculated adsorption coefficients K is only 20%. The calculated regression e parameters, using ∆Gads in joules per mole, p°L in pascal at 20 °C, and R and β dimensionless, are

b ) -5092 ( 132 m1 ) 324.1 ( 16.6 m2 ) -5071 ( 153 m3 ) -3344 ( 656 It must be noted here that b depends on the standard state of adsorption chosen in eq 2 (here the standard state defined by de Boer). If a different standard state (e.g., Kimball-Rideal) is chosen for the calculation of adsorption coefficients K from e ∆Gads , then the parameter b would have to be recalculated. Validation of the Model with Other Surfaces. With the results of the above regression analysis, eq 3 can be replaced

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by the following semiempirical equation: e (J/mol) ) ∆Gads - 5071βxγ+ (-5092 + 324.1 ln p°L)xγvdW 2 2 - 3344Rxγ2 (12)

Although the empirical parameters were determined for the adsorption on a water surface, the model should, of course, be applicable to other surfaces. Unfortunately, there are no data sets for environmentally relevant surfaces other than water that would be suitable for a validation. Glycerol and thiodipropionitrile (TDPN) have surfaces for which experimental adsorption data exist and which possess surface parameters different from water but within the range that is likely to be encountered in the environment (Table 2). Comparison of experimental and calculated (using eqs 2 and 12) adsorption coefficients is displayed in Figure 2. This validation comprises 13 compounds (alkanes, alkenes, benzene, and diethyl ether) for TDPN (34) and 14 compounds (alkanes, alkenes, and alkylbenzenes) for glycerol (35) at 20 °C. Also shown are results for the adsorption of nine different chlorobenzenes on graphitized carbon black (GTCB) extrapolated to 20 °C (36). Graphite differs from the other tested surfaces in that it has an extremely high γvdW value and that 2 it is a solid and may therefore not be ideally homogeneous. The model calculations for graphite were based on a mean value of γvdW ) 120 mJ/m2 (from data in Table 2, assuming 2 a negligible change with temperature beteween 20 and 25 °C). Acid-base interactions between graphite and the adsorbing chlorobenzenes were assumed to be negligible. The good agreement between predicted and experimental adsorption coefficients in Figure 2 supports the conclusion that eq 12 together with eq 2 will generally allow the prediction

TABLE 2. Surface Parameters from the Literature Determined by Contact Angle or Interfacial Tension Measurements and by Inverse Gas Chromatography (IGC) surface watera 1-octanola glycerola TDPNa squalanea white oila icea watera teflon (FEP)a polypropylenea polyethylenea nylon 6,6a polystyrenea polyvinylchlorida wood pulp fibera cellulosea glucosea paraffin waxa graphitea TiO2 (anatase)a SiO2a coppera coppera leada leada irona irona washed haira washed haira carbon fibersb,d precipitated silicab silica grafted with hexadecanolb R-Al2O3b birch wood mealb

temp (°C)

γvdW (mJ/m2)

γ+ (mJ/m2)

γ- (mJ/m2)

ref

20 20 20 25 23 25 0 0 20 20 20 20 20 20

21.8 27.5 34 49.9 29.2 28.9 29.6 22.8 17.9 25.7 33 36.4 42 43 41.8 44 42.2 25.5 114-132 75.5 77.5 59.1 66.1 98.3 102.7 107.4 109.7 ∼29 ∼26 46.5 75.3 38.7 ∼100 43.8

25.5 0 3.92 ∼0c 0 0 14 ∼26.5 0 0 0 0.02 0 0.04 0.2 1.6 0 0 na na na na na na na na na na na 0.19e na na na 10e

25.5 0 57.4 na 0 0 28 ∼26.5 0 0 0 21.6 1.1 3.5 24.5 17.2 51.1 0 na na na na na na na na na na na 4.1e na na na 84e

25 25 25 60 24 20 25 25 25 25 25 25; RH unknown 25 25 37; RH unknown 25; RH unknown 25; RH ≈ 0% 20 20, 61 61; RH ≈ 0% 61; RH ≈ 0% 62; clean (reduced) 62; partly oxidized, RH ≈ 0% 62; clean (reduced) 62; partly oxidized, RH ≈ 0% 62; clean (reduced) 62; partly oxidized, RH ≈ 0% 63; 20-40% RH 63; ∼50-95% RH 64; ∼0% RH 65; ∼0% RH 65; ∼0% RH 43; ∼0% RH 66; ∼0% RH

20 20 25 25 25 25 25 25 25 25 25 21 21 29 20 20 60 50

a Contact angle or interfacial tension measurements. b IGC measurements at infinite dilution. c Estimated from the molecular structure. d Depending on the pretreatment of the fibers, significantly different values have been reported in the literature. e Calculated according to eq 12 from the data reported in the cited reference.

FIGURE 1. Comparison of experimental and fitted adsorption coefficients on a water surface for the data that were used in the regression analysis (20 °C). of adsorption coefficients of organic compounds from the gas phase to surfaces at low concentrations (i.e., in the linear part of the isotherm). Compared to eq 3, eq 12 has the advantage that the required adsorbate parameters are known for most compounds of environmental interest while at the same time the conceptual understanding of the adsorption

FIGURE 2. Comparison of experimental and calculated adsorption coefficients for different organic compounds on various surfaces (20 °C). process remains unaltered. Unfortunately, the surface parameters, which are also required for the calculations, are more difficult to get. Determination and Discussion of the Surface Parameters + γvdW 2 , γ2 , and γ2 . As indicated by the above results, it should

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TABLE 3. Comparison of Surface Parameters Determined at 40 °C from IGC at Infinite and Finite Dilution and from Contact Angle Analysis (CAA) (42) γvdW (mJ/m2) surface

IGC, infinite dil

IGC finite dil

CAA

poly[4,4′-cyclohexylidenebis(phenol)] carbonate polystyrene styrene/4-vinyl pyridine diblock polymer aluminum oxide coated pigment parylene blue (dye stuff)

19.3 30.5 31.6 55.4 38.4

16.1 27.5 28.1 37.7 22.0

16.6 28.3 27.7 na na

be possible to predict vapor adsorption to any surface whose γvdW , γ+ 2 2 , and γ2 values are known. These surface parameters can be determined from measurements of the contact angle (for solid surfaces) or the interfacial tension (for liquid surfaces) with at least three different reference liquids: one alkane for γvdW and one Lewis acid and base for γ2 2 and + γ2 , respectively (25). A compilation of such data is found in Table 2. However, there is a major problem involved in contact angle measurements on solid surfaces: usually the advancing and receding contact angles are not identical (contact angle hysteresis), and it is questionable which, if any, of the two contact angles represents the true thermodynamic equilibrium (26, p 324). In fact, it may be impossible to determine correctly surface free energies of solids by contact angle measurements (24). Other limitations of contact angle measurements are discussed in ref 37. As an alternative, in recent years, inverse gas chromatography (IGC) has become a widely used method for the determination of surface free energies of solids and liquids (38-40). In IGC, probe molecules with known properties are injected into an isothermal gas chromatographic system with the surface of interest as stationary phase. The surface properties can then be calculated from the retention of the adsorbates (for a detailed discussion see ref 19). In other words, vapor adsorption itself can be used to determine the surface parameters. Some surface data determined by IGC are also shown in Table 2. It should be pointed out that IGC at infinite dilution tends to give surface parameters that are higher than the surface average since dilute vapors preferably adsorb to those adsorption sites with the highest energy. In contrast, measurements of contact angles or interfacial tension represent mean values for the whole surface since they are based on the adhesion of a bulk liquid instead of isolated molecules (41, p 387). Obviously, both procedures should give the same results if the surface is homogenous (i.e., a liquid surface). This is corroborated by the above validation (Figure 2) where the experimental data came from adsorption of dilute vapors while the calculations were based on bulk measurements of mean surface parameters of water, TDPN, and glycerol. However, for solid surfaces, differences must be expected because of the always present chemical and/or morphological heterogeneities. Pure graphite is one of the most homogenous solid surfaces, and indeed, the surface parameters from contact angle measurements still gave good results when used for the estimation of adsorption of dilute vapors (Figure 2). In general, however, differences between surface parameters of solids determined by IGC and contact angle analysis (CAA) must be expected. These differences are shown exemplarily by data from Farard et al. (42) (Table 3). It can also be seen that, with increasing concentration of the vapors used in IGC, the resulting surface parameters approach those of contact angle analysis as is expected theoretically. If adsorption of dilute vapors in the linear range of the isotherm is to be predicted, it is obviously advisable to use surface parameters derived from IGC measurements at just these conditions. For predictions at higher gas phase concentrations on heterogeneous surfaces, the energy distribution of all three surface parameters should be known. This information can be obtained from measured adsorption

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isotherms of probe adsorbates which can also be determined by IGC (43-45). If the adsorbed concentration approaches monolayer coverage, the surface is best characterized by the average parameters resulting from contact angle measurements. In the latter case, lateral interactions between neighboring adsorbed molecules also have to be considered for a correct prediction of adsorption. This cannot yet be done by the current model but is principally possible assuming an Ising model (46, p 3.40). When using surface parameters, another important point has to be considered. Due to the strong decay of intermolecular interactions with distance, it is the outermost molecular layer of the surface and not its bulk properties that control adsorption. The formation of a surface film by oxidation, or the adsorption of a water film which cannot be displaced by organic vapors, may therefore significantly change the effective values of γvdW , γ+ 2 2 , and γ2 of the original surface (47, 48). Pure carbon and metal surfaces for example will readily be oxidized in contact with the atmosphere, and in addition, these oxide layers will adsorb considerable amounts of water. Unfortunately, it is not always stated in the literature under which conditions the surface parameters were measured. The alteration of surfaces by the adsorption of water from the atmosphere where it is usually available at rather high relative concentrations deserves some special attention. Most of the abundant minerals in the environment are hydrophilic and thus adsorb one or more molecular layers of water at ambient humidities. The mono- or even multilayer adsorption of water on a surface will shift the original surface parameters of the surface toward those of water. Much experimental evidence has been published for this phenomenon (27, 31, 49, 50). One can conclude from Table 2 that this implies a decrease in γvdW for almost all solids, while the 2 parameters γ+ 2 and γ2 may be shifted in either direction. The coverage of natural surfaces with adsorbed water under ambient conditions has several important consequences: (a) adsorbed water layers level out chemical and geometrical heterogeneities of the surface (51, p 87) so that average surface parameters may be used without problems; (b) adsorbed water layers also level out differences between different hydrophilic surfaces since the surface characteristics will approach those of bulk water and become independent from the underlying solid when the water layer becomes thick enough (52); and (c) in order to describe surfaces that adsorb considerable amounts of water, the values for γvdW , γ+ 2 2 , and γ2 have to be known as a function of relative humidity. Adsorption on Ice. For the fate of contaminants in colder climates, adsorption to ice is important (53). It is known that the ice surface is covered by a liquid-like transition layer at temperatures between 0 and about -30 °C (54-56), and it has been suggested that adsorption to ice and snow in this temperature range resembles adsorption to subcooled water (57). However, experimental values for the adsorption of organic vapors on ice at temperatures between 0 and -20 °C do not give a clear picture (14, 15). According to the surface parameters for ice and water at 0 °C in Table 2, the following conclusions emerge: compounds which can only interact by

van der Waals forces will exhibit a greater adsorption to ice than to water. However, with increasing electron donor ability of the adsorbate, this difference will decrease, and for strong electron donors, the adsorption to ice will be smaller than the adsorption to a water surface. Outlook. The semiempirical model represented by eq 12 allows a good conceptual understanding and prediction of adsorption from the gas phase to surfaces. However, serious restrictions are still imposed by our limited knowledge of the surface parameters, particularly for solid surfaces. Data displayed in Table 2 can serve as an orientation for the range of values that may be expected for different ambient surfaces. Measurements of surface parameters that better comply to the demands of environmental chemistry have to follow. Because of the problems involved in contact angle measurements discussed above, IGC should be the method of choice. For a number of mineral surfaces, such IGC data already exist (27, 31, 52). The derivation of surface parameters from these data will be presented elsewhere. In its current form, the model does not account for intermolecular interactions in the gas phase (assumption of an ideal gas phase) or lateral adsorbate-adsorbate interactions. A correction of the adsorption coefficients for gas phase nonidealities can easily be incorporated if the virial coefficients of the vapor are known. However, in general, such a correction will only be neccessary for systems where the pressure is much higher than under ambient conditions. Lateral interactions between adsorbed molecules which will lead to nonlinear isotherms at high relative gas phase concentrations, and the possibilities to predict the temperature dependence of the adsorption coefficients will be discussed in following papers.

Acknowledgments Special thanks are due to Beate Escher, Jo¨rg Klausen, and Rene´ Schwarzenbach for critical review of the manuscript. This work has been supported by the European Environmental Research Organisation (EERO).

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Received for review April 22, 1997. Revised manuscript received August 27, 1997. Accepted August 28, 1997.X ES970361N X

Abstract published in Advance ACS Abstracts, October 1, 1997.

VOL. 31, NO. 12, 1997 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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