Environ. Sci. Techno/. 1995, 29, 1773-1780
Site Energy Distribution Analysis of Pieloaded Adsorbents MARGARET C. CARTER,+ JAMES E. KILDUFF, AND WALTER J. WEBER, JR.* Department of Civil and Environmental Engineering, The University of Michigan, Ann Arbor, Michigan 48109-2125
A methodology relating changes in the isotherm parameters for sorption of one solute by a heterogeneous sorbent to changes in the site energy distributions of that sorbent caused by prior irreversible sorption (preloading) of other solutes is proposed. Approximate site energy distributions underlying three isotherm models commonly used t o describe sorption of organic solutes from aqueous solutions are developed using the theory of heterogeneous surfaces. It is demonstrated that, regardless of the type of initial site energy distribution assumed, preloading by a non-desorbable solute results in a loss of surface heterogeneity. The loss occurs preferentially across sites having the highest energies, with the number of sites in the lowest energy ranges actually increasing in some cases. Activated carbon is used to demonstrate the methodology, but the approach is generally applicable to other heterogeneous adsorbents in both natural and engineered systems.
Introduction One of the more interesting and complex examples of competitive effects among solutes for sorption on energetically heterogeneous surfaces is that of the preloading of activated carbon in water treatment applications by macromolecular background organic matter, of which humic substances constitute the greatest proportion. Preloading occurs when the adsorption front(s) for humic substances move(s) ahead of adsorption fronts for target speciesin adsorber beds. Once adsorbed,humic substances do not readily desorb, nor are they readily displaced, and they thus mod@ the adsorptive properties of the carbon for subsequent uptake of target species. Preloading has been observed to reduce the abilityof the carbon to remove a variety of target compounds (1-6). This reduction has often been quantified in terms of changes in isotherm parameters for the target solute with extent of preloading. Prior studies of preloading effects have commonly limited analysis to simple assessments of changes in capacities and rates of sorption for target solute(s), producing little mechanistic information (3-7). Carter et al. (6) did hypothesize specific preloading mechanisms, but their study was limited to an examination of preloading effects on the parameters of only one isotherm model. Implicit in any isotherm model is an assumption of an underlying distributionof site energies (8). On a theoretical basis, isotherm parameters can thus be related to particular site energy distributions, and their empirically determined values can be interpreted with respect to the energetic character of a sorbent. Measurements of how isotherm parameters change in response to competitive solute preloading may then be used to postulate how the energetic characteristics of a sorbent are changed by such phenomena. This information may be valuable in forming hypotheses regardingthe actual physicochemical mechanisms underlying preloading phenomena. In this paper we develop and demonstrate a methodology to determine site energy distributions from isotherm parameters. Because the energy distributions of sorbents are generallynot known in practice, several isotherm models representing different distributions are examined. To demonstrate the approach, we focus on a rather simple bi-solute system, one that mimics the essential features of humic preloading but which is sufficiently well-characterized to allow a more mechanistic interpretation of the data. The essential feature of preloading is the fact that humic molecules, once adsorbed, show little tendency to desorb or be displaced. To identify a model bi-solute system that also exhibits such characteristics, we performed Ideal Adsorbed Solution Theory (IAST) calculations for several candidate compounds to evaluate their tendency to be displaced by trichloroethylene (TCE), the solute selected as our target compound. The IAST model and its application are well-documented elsewhere (9).Our calculations showed that 1,2,4-trichlorobenzene(TCB), a strongly adsorbing aromatic compound, would exhibit no significant * Author to whom all correspondence should be addressed; e-mail address:
[email protected];Fax: 313-763-2275. Present address: Amoco Chemical Company, 150 W. Warrenville Rd., Napenille, IL 60563-8460. +
0013-936W95/0929-1773$09.00/0
0 1995 American Chemical Society
VOL. 29. NO. 7,1995 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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displacement in the presence ofTCE over the concentration range of interest. Preloading of carbon by macromolecular humic substances in fiied-bed reactors (FBRs) involves both thermodynamic and mass transfer considerations. These large molecules are more slowly adsorbed than most target compounds, and this accounts for the more rapid movement of their wavefront(s) through FBR adsorbers. Once inside the microporous structure of the carbon, such macromolecules can become sterically lodged and thus not readily displaced by subsequently sorbing solutes. By choosing two molecularly discrete and similarly sized compounds, TCE and TCB, we essentially eliminate mass transfer as a significant preloading factor in our investigation. From apurelythermodynamic point ofview, the order of adsorption in such a system should have no bearing on the equilibrium distribution of adsorbates. It is not, however, our objective to characterize TCE/TCB bi-solute equilibria. Rather, we wish to examine the effect of anondisplacable species on the subsequent adsorption of another compound. In deference to the physical system being modeled, we do preload the carbon with TCB prior to adsorbing TCE. While not strictly necessary from a thermodynamic perspective, this approach accounts for any physical mechanisms of competition that develop as a consequence of the structural characteristics of the adsorbent. The approach described and demonstrated here offers potential for increasing our understanding of sorbent preloading at a fundamental level because it relates changes in experimentallymeasured isotherm parameters to changes in the energy characteristics of sorbent surfaces. In turn, site energy distribution changes may form the basis for hypotheses regarding specific mechanisms. As will be shown, the methodology potentially accounts for changes in the numbers, diversity and average energy of surface sites. The analysis implicitly includes the effects if any of adsorbent structure, such as pore blockage by preloaded solutes and restricted access to micropores, because these effects are reflected phenomenologically in adsorption isotherm model coefficients. As noted, structural effects are not expected to be significant for the TCBiTCE system examined here, but they are likely to be quite important in systems containing macromolecular dissolved organic matter 16).
Theory The basic integral equation underlying the theory of heterogeneous surfaces is
Equation 1 defines the total sorption (q,) of a solute by a heterogeneous surface as the integral of an energetically homogeneous isotherm ( q h ) multiplied by a site energy frequency distribution (F(E))over a range of energies, where Eis the differencebetween the solute and solvent adsorption energies for a given site. While the limits on the integral are most appropriately based on minimum and maximum adsorption energies (IO), these are typically not known a priori; it is generally assumed for convenience that they range from zero to infinity (10, I I ) . The Langmuir isotherm, which is predicated on sorption sites of uniform energy, is commonly used to represent q h 1774
ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 29, NO. 7.1995
in eq 1 (8);Le.
where Q" is the maximum adsorption capacity and b is a temperature-dependent parameter related to the energy of adsorption (12). Because it does assume uniform site energy, the Langmuir model applies strictly to homogeneous surfaces. Its general form, however, is useful for describing locally homogeneous surfaces comprising more generally heterogeneous sorbents. The model is used primarily in that sense here and is thus referred to as the local Langmuir model. If local sorption isotherm and site energy distribution functions are known or assumed, the integral given in eq 1 may be solved to yield a corresponding overall sorption isotherm. This approach has been used by Halsey and Taylor (13)to derive the Freundlich isotherm based on a local Langmuir isotherm model and an exponential site energy distribution. Conversely, if a set of data is found to conform to a particular isotherm model, the integral equation may be solved to derive the corresponding site energy distribution, an approach used by Misra (IO), Sips (14,15),andTothet al. (16). Allofthemodelsusedinthese latter efforts have been shown to represent simplifications of a more general isotherm relationship termed the generalized Langmuir model (GLM), which can be written (17
(3)
where Q; is the generalized isotherm maximum adsorption capacity, m and n are heterogeneity parameters, and b, is a generalized form of the Langmuir energy constant that incorporates a characteristic site energy, (Eo),the universal gas constant (R), and absolute temperature ( r ) :
The constant Eo is the energy corresponding to the maximum sitefrequency, and it determines the position of the energy distribution function on the energy axis. For a symmetric quasi-Gaussian distribution, E, represents the mean site energy,while for an exponential distribution, Eo represents the minimum site energy. The heterogeneity parameter m characterizes the shape of the site energy distribution in the direction of lower values of E, while the parameter n characterizes the shape of the site energy distribution in the direction of higher values of E (8). For various combinations of limiting values of m and n, the three-parameter Langmuir-Freundlich model (LFM) and thegeneralizedFreundlich model (GFM)can be derived from the four-parameter GLM equation. The LFM and GFM are chosen as specific derivatives of the GLM for this work because of their relationship to the common Freundlich model (CFM),which can be shown to be a low-concentration limit of the LFM, GFM and GLM equations. These several isotherm forms are given in Table 1. In general, the behavior of the heterogeneous isotherms differs sigmficantly from the local Langmuir isotherm. The GLM, LFM and GFM functions asymptotically approach a limiting capacity but do not exhibit linear behavior at low concentrations. The CFM equation does not have a linear region at low
TABLE 1
Generalized Langmuir Model and Its Simplifications model
equation
LFM
m (range)
n (range)
low c.
high C,
0,1
$( bg Ce)"
$
n=m
1
concentration, nor does it approach a limitingvalue at high concentration. It has, nevertheless, proven broadly useful for describing adsorption data over solute concentration ranges of common interest in environmental applications. Note that when the heterogeneity parameters are equal to unity, each of the model equations given in Table 1reduces to the local Langmuir model, the CFM being restricted to low-concentration regions. Exact site energy distributions for the GLM isotherm and its simplifications have been derived by solving the integral adsorption equation for FE) through application of a Stieltjes transform (8,10,14,15). The distributions are normalized, and their shape is determined by the values of the heterogeneity parameter (n),while their position on the energy axis is determined by the choice of the reference energy (Eo). The LFM equation has been found to have a symmetric quasi-Gaussiandistribution centered onEo.The GFM and CFM equations have been found to have exponential distributions, with Eo serving as the lower energy limit.
$( bg Ce)"
where C, is the maximum solubility of the solute in the solvent,E, is that value of the sorption energy corresponding to Ce = C,, R is the universal gas constant, T is absolute temperature and E* = E - E, (8, 18, 19). Equation 5 may also be obtained from Polanyi theory (20). The Esreference state for E represents the lowest physically realizable sorption energy, and its magnitude depends only on the solute; Le., it is independent of the sorbent (8). The parameter Es is analogous to Eo in that it determines the position of the distribution on the energy axis, but the position is not exact. Because the overall sorption isotherm is defined in terms of C,, substitution of eq 5 into any isotherm expression results in a sorption equation written in terms of a net energy, E*. By incorporating eq 5 into eq 1, it can be shown that an approximate site energy distribution, F(E*), is obtained by differentiating this isotherm, q,(E*), with respect to E*
Approximate Site Energy Distributions Cerofolini (20) proposed an alternative technique for determining site energy distributions based on a method referred to as the condensation approximation. The method involves generating approximate distribution functions from isotherm equations (8,9).The approximate distributions, unlike the exact distributions, are not normalized but rather are written directly in terms of the isotherm parameters (Q;b,, m,and n). For each of the isotherms presented, the area under the distribution is controlled by Q;,the position of the distributionon the energy axis relative to the reference energy is controlled by b,, and the spread of the distribution is controlled by m and n. Use of approximate energy distributions affords particular advantages for the type of analysis done here because it facilitates examination of how changes in experimentally determined isotherm parameters relate to changes in the distributions of site energies. Under the assumptions of the Cerofolini approximation, the equilibrium liquid phase concentration is related to the energy of adsorption by
Because the resulting site energy distributions are not normalized, the area under the distribution is equal to the maximum adsorption capacity Q;:
The Langmuir-Freundlich Model. Incorporation of eq 5 into the LFM equation presented in Table 1 followed by differentiation with respect to E* yields
Equation 8 corresponds to a quasi-Gaussian site energy distribution,like the exact distribution for the LFM isotherm.
Generalized Freundlich Model. Application of Cerofolini's method to the GFM equation followed by differentiation with respect to E*yields eq 9, the approximate VOL. 29. NO. 7, 1995 /ENVIRONMENTAL SCIENCE & TECHNOLOGY
1775
site energy distribution reflected by the GFM:
While the exact site energy distribution for the GFM isotherm is exponential, that for the approximate distribution is quasi-Gaussian, widened toward higher energy values. Common Freundlich Model. The common Freundlich isotherm, a simplification of the GLM, involves only two independent parameters. Applying Cerofolini's approximation and taking the first derivative with respect to E* then yields the approximate site energy distribution in terms of the corresponding sorption parameters:
Like the exact site energy distribution for the CFM, that for the approximate formulation is exponential. Although in its formal presentation the CFM incorporates all three isotherm parameters, it is effectively a twoparameter isotherm because it is not possible to uniquely determine Qg and b, from one set of sorption data. In fact, the CFM is more commonlv expressed explicitly as a twoparameter isotherm, i.e. qe = K J :
(11)
A comparison of eq 11 with the more rigorous formulation of the CFM isotherm given in Table 1 shows that the exponent n is consistent in both expressions as an indication of heterogeneity, but that the parameter KFis a composite parameter incorporating Q;, b,, and n:
K, = QibI
(12)
Experimental Section The activated carbon used in these studies was a bituminous coal-based material typically used in water treatment applications (F400, Calgon Corporation, Pittsburgh, PA). Carbon obtained from the manufacturer was crushed and mechanically sieved to a uniform particle size,which ranged from 150 to 180 pm. Sieved carbon was washed with deionized, distilled, filtered water (MQ water, Millipore Milli-Q system) and oven-dried to constant weight at 105 "C. The carbon was stored in a vacuum desiccator until used in an isotherm experiment. Trichloroethylene (TCE) was chosen as a model compound because it is a widespread environmental priority pollutant. 1,2,4-Trichlorobenzene (TCB) was chosen as a model preloading compound because preliminary studies showed that TCB is not displaced to any significant degree by TCE under the conditions of this study. Reagent-grade TCE (MallinckrodtSpecialty Chemical Co.)and TCB (Aldrich Chemical Co., Inc.) were used as received from the manufacturer. Working solutions were prepared by spiking background water with a desired amount of stock solution prepared in methanol to achieve the desired initial aqueous concentration of solute. Stock concentrations and spike volumes were designed so methanol concentrations were below mol fraction. At this concentration, no significant co-solvent effects are expected (21-23). 1776
ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 29, NO. 7 , 1995
The background solution consisted of M phosphate to buffer pH (Mallinckrodt), 100 mg/L sodium azide (Fluka, purum pea.) to control biological activity, and sodium chloride (J. T. Baker) to achieve an ionic strength of 0.01 M. All chemicals were reagent grade and used as received from the manufacturer. Experiments were conducted at room temperature (23 i 3 "C) at pH 7 f 0.2 with pH adjustment by either HCl or NaOH as required. Isotherm experiments were conducted using (CMBR) the completely mixed batch reactor (CMBR) method (6). The CMBRs consisted of 250-mL amber glass bottles filled completely and sealed headspace-free with screw caps and Teflon-lined silicone septa. The reactors were kept wellmixed by tumbling end-over-end on a rotary tumbler for a period of 2 weeks. Preliminary rate studies indicated that this time was sufficient to reach equilibrium for both TCE and TCB. After the carbon was preloaded with 22 pg/mg TCB, the reactors were carefully opened and spiked with TCE. A range of initial concentrations was chosen to yield equilibrium concentrations ranging from about 2 to about 2000 pglL. The reactors were then tumbled for a two-week TCE equilibration period, after which time the reactor contents were sampled. Aqueous samples were extracted into pesticide-free hexane (Ultra resi-analyzed, J. T. Baker Co., Inc.) and analyzed by gas chromatography with electron capture detection and electronic detector peak integration. Losses due to volatilization, sorption onto reactor components, and bacterial activity were assessed with control reactors that did not contain adsorbent. Losses in these experiments were consistently less than 5% for high concentrations of TCE and TCB (1000-4000 uglL). Because these losses were low and because the percentage of the initial mass adsorbed was high, no attempt was made to correct the amount adsorbed for losses. The 95%confidence limits for the TCE analytical method were determined to be f0.4 pg/L near concentrations of 10 pg/L up to f 5 pg/L near concentrations of 1000 pglL. For TCB, 95% confidence limits ranged from f 0 . 3 pg/L near concentrations of 10 pg/L up to about f 4 pglL for concentrations near 2000 pglL. Statistical error in the amount of solute adsorbed was estimated by propagating the error of experimental measurements through the mass balance expressions as described by Topping (24). Standard errors of the amount adsorbed for both TCE and TCB ranged from O.O5pg/mgat an equilibrium concentration of 1OpUglL to 1.2 pg/mg at 1000 pg/L. Error bars representing twice the standard error are therefore smaller than the symbols used to represent the data on log-log plots. Ideal adsorbed solution theory calculations indicated that the displacement of TCB by TCE over the range of concentrations examined would be insignificant and that TCB could be considered a non-displaceable solute. Experimental data verifymg the predictions are tabulated in Table 2 for several TCE equilibrium concentrations. The measured displacement of TCB is less than 1.2% for all concentrations of TCE examined.
Results and Discussion Figure 1 presents experimental data, isotherm model fits, and associated site energy distributions for sorption of TCE onto unpreloaded activated carbon. Similar results were obtained for isotherms fitted to data gathered for TCBpreloaded carbon. A nonlinear regression softwarepackage (SYSTAT,Systat, Inc., Evanston, IL) was used to determined isotherm parameters and 95% confidence limits for both
TABLE 2
TCB Displacement in Model P r e l d n g Systenf
c.TCE bsR1
G, TCB bSn) qe. TCB (cldmg) YO TCB desorbed
3.0
0.41 1 0.310 0.404 0.787 0.998 7.44 10.64
7.7 25.2 60.4 200 1146 1651
21.91 21.92 21.91 21.90 21.78 21.89 21.74
0.036 0.024 0.035 0.084 0.103 0.842 1.21
Tonfidence limits on C. and qe are discussed in the Experimental Section. lo00
I
4
Low C, Limit High C, Limit
I I
a
I I
I
I I
10
1
100
Ce
.. .!. .
1000
10000
(WL)
I
.
!
I
' . !! :H .
!
!
Low C, Limit High C, Limit
i
i!
I
*
:
i i i
!I
!I $1
i1 i ij i j
1 1.65
16.65
21.65
26.65
31.65
E' (kJ/mol) FIGURE 1. Experimental data, models, and site energy distributions for TCE sorption on unpraloaded carbon. (a) Experimental data and isotherm fits for the LFM (-1, GFM (- -1, and CFM (- -1. (b) Site energy distributionsfor the LFM (-1, GFM (- -1, and CFM (- -1.
cases using the LFM, GFM, and CFM models. Results are summarized in Table 3. Although a slight curvature can be detected in the data, each of the isotherm equations appears to fit the data well over the concentration range studied. Comparisons of the energy distributions corresponding to the unpreloaded and preloaded cases for each of the three isotherm models are plotted in Figure 2. The site energy distributions were obtained by inserting the designated isotherm parameters for the LFM, GFM, and CFM into eqs 8- 10, respectively, and calculatingthe frequency, F(E*), corresponding to each E*. As explained in the followingsection, energy distributionspresented in Figures 1 and 2 are limited to the E* range defined by the experimental concentrations. Practical Energy Limits and Choices of Isotherm Models. There are no mathematical restrictions on the range of E" values employed for calculation of site energy distributions from isotherm parameters. It is important to note, however, that negative energies do not have a true
physical meaning (18).Negative values of EL occur when the absolute energy, E, falls below$, the energy associated with the maximum solubility of the solute. This concept is illustrated in Figure 3, which depicts the relationship between concentrations and energy described by equation 5 for a hypothetical solute having an aqueous solubility of C,= 106pg/L.While the sorbent surfacemay indeed contain such low energy sites, the sites are not available to the solute because residual solution concentrations in excess of the solubility limit would be required to access them. For experimentaldata, high and low concentration limits imposed by factors such as analytical accuracy, solute volatilization, and experimental error are even more restrictive than those imposed by solubility. Practices employed for determination of sorption isotherm data for hydrophobic organic chemicals are frequently limited to residual concentration values above Ce = 1pg/L and below Ce = 10 000 pg/L. As shown in Figure 3, this experimental concentration range restricts the span of E* over which energy distributions can meaningfully be compared to approximately 11-34 kJ/mol. The limitation on E*results in the interesting fact that, over the concentration ranges of interest, the distribution functions for a given sorbent and therefore the applicable isotherm models are similar. As a consequence, it is often the case that a given set of data can be described by any one of the several isotherm equations based on heterogeneous site energy distributions, even though the overall shapes of the distributions are not the same (19,25). Part a of Figure 1shows clearly that the LFM, GFM, and CFM isotherms all provide good fits of the experimental data. It is evident in the corresponding site energy distributions given in part b of Figure 1that the concentration span covers regions of the distribution where they are most similar in shape. Over this practical E* range, both the LFM and GFM isotherms are log-linear,which explains why data over this range are described equally well by the two-parameter CFM equation. Indeed, as noted earlier, the common Freundlich model has enjoyed widespread use in environmental applications in which concentration ranges of interest commonly cover these same few orders of magnitude. Further analysis of Figure 1 indicates that the choice of an isotherm equation becomes more critical when experimental data cover a wider range, including very high concentrations. Significant deviations in the model traces can be seen to appear at the upper concentration range of the data, correspondingto marked differencesbetween site energy distributions at the lowest E* levels. In fact, any isotherm model is likely to give erroneous results if extrapolated beyond the experimental range in which it was determined (25). Alternatively, the observed model differences suggest it may be possible to isolate a "best-fit'' isotherm model if the data include very high concentrations. This was demonstrated by Seidel and Carl (191,who were able to iden@ one specific isotherm from three different equations to describe adsorption of phenol and indol onto Hydraffin 71 carbon after adding adsorptionpoints obtained at near-saturation concentrations to data previously determined at lower concentrations. TheoreticalInterpretation. As a prelude to examination of preloading phenomena, it is instructive to examine how changes in individual isotherm parameters reflect relative changes in the site energy distribution for a particular surface. The LFM is chosen for this purpose because its VOL. 29, NO. 7,1995 / ENVIRONMENTAL SCIENCE &TECHNOLOGY
1
1777
TABLE 3
Model Parameters Determined for TCE Adsorption in Presence of TCB on Unpreloaded and Preloaded Adsorbenta LFM adsorbent state
4(pglmg)
not preloaded 95% CI 144 f 33.3 preloaded 95% CI 125 i 94.2 a
bg (Ups) x 104 4.1 f 2.6 3.3 f 4.2
GFM
4(ps/me)
n
CFM
bg14pg) x 104
n
KF(Ipa)'l"(L)"/mgl
n
5.0 i 2.5 3.8 i 3.6
0.57 f 0.03 0.85 f 0.07
1.59 f 0.142 0.17 i 0.142
0.51 i 0.02 0.77 i 0.04
0.61 f 0.03 100 f 17.0 0.86 f 0.08 104 f 57.6
C, values ranged from 4 to 3000 pg/L. Preloading of TCB was at 22 pg/mg. 12
-
,
I
i
108
I
I
1
w,
20
10
30
E'
8"
\
40
(kJlmol)
-10
0
10
E'
b
20
10
30 E'
30
40
I
C
3
s
\
\
\ 0 CD
-
unpreloaded
10
w, LL
preloaded 0
10
20
30
E'
40
(kJ/rnol)
FIGURE 2. Site energy distributions for unpreloaded and TCB preloaded (qe= 22 mgg) carbons correspondingto different isotherm models. (a) The Langmuir-Freundlich model. (b) The generalized Freundlich model. (e) The common Freundlich model.
symmetrical shape permits straightfonvard illustration of the effects of parameter variations. For this analysis, qe and C, are chosen to have the units of micrograms per milligram and micrograms per liter, respectively. The site energy distributions for the LFM isotherm (eq 8) for variations in Q;, b,, and n are plotted respectively in parts a-c of Figure 4. The range of parameter values is representative of typical, strongly sorbing synthetic organic chemicals. The influence of the capacity parameter on the 1778
30
40
(kJlmol)
FIGURE 3. Residual solution concentration limits on net adsorption energy ranges.
(kJlmol)
I
20
ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 29. NO. 7 , 1995
area under the site energy distribution for Qg values of 700, 500, and 200 yglmg is illustrated in part a of Figure 4. The curves in this figure show successive decreases in areawith decreasing Qg, but no changes in either the shape or the mean of the distribution. The area under the site energy distribution curve can be interpreted as the maximum number of sites available for sorption. Thus, as Q; decreases, it reflects a decrease in the number of sites available for sorption. Part b of Figure 4 depicts changes in the mean of the site energy distribution as the affinity parameter (b,) is varied through values of 1.0 x 1.0 x lo-*, and 1.0 x 10-I L/pg. These curves showthat increases in b, shift the mean of the distribution to higher values but do not alter either the shape or the area of the curve. The position of the distribution mean on the energy axis can be used as a measure of the affinity of the solute for the sorbent surface. For example, for two surfaces having different b, values, sorption by that with the higher value would have the higher average energy and thus be more favorable for sorption reactions than the lower affinity surface. Changes in b, for the same sorbent then may be representative of mechanisms that alter the average energies of sites on a sorbent surface. Part c of Figure 4 shows the influence of the heterogeneity parameter (n)on the width of the site energy distribution for dimensionless n values of 0.4, 0.7, and 1.0. Increases in n cause a marked narrowing of the distribution, although the mean and the area of the curves do not change. The width of the site energy distribution may be interpreted to relate to the diversity of energysites, Le., to the heterogeneity of surface site energies. Processes that increase the value of n for a given sorbent can be interpreted as decreasing surface heterogeneity. Effects of Preloadingon Site Energy Distributions. The preceding discussion has focused on how isotherm pa-
,
50
-20
I
20
0
E* 50 ..
40
(kJ/mol)
.
-20
20
0 E'
40
1 60
60
(kJ/mol) i
-20
40
20
0 E*
60
(kJ/mol)
FIGURE 4. Variations in site energy distributions as functions of changes in the adsorption equilibrium parameters associated with the Langmuir-Freundlich model. (a) Changes in for 4 = Upg and n = 0.7. (b) Changes in bg for = 500 pg/mg and n = 0.7. (c) Changes in n for = 500 p g h g and 4 = lo-* Upg.
Qi
Qi
Qi
rameters may be related to the energy distributions of sorbent surfaces in terms of the quantities, energies, and heterogeneities of sorption sites. It is evident from this discussion that any alterations to the site energy distributions, such as those hypothesized to occur during competitive solute preloading, can be analyzed in terms of changes in isotherm parameters. It is generally not possible to determine the exact energy distribution that best characterizes a given sorbent surface over the relatively limited concentration ranges which typify environmental sorption data. However, this is not a limitation to the methodology because it is still possible to examine relative changes in energy distributions over environmentally relevant concentration ranges. To fully interpret these changes, careful analysisof experimentaldata using several different conceptual isotherm models may be necessary. The LFM site energy distribution shown in part a of Figure 2 clearly shows an overall narrowing of the site energy
distribution with preloading, as reflected by a decrease in the number of high energy sites and an increase in lower energy sites. This decrease in the heterogeneity of surface sites remaining after preloadingis quantified as a statistically significant increase in the value for n from 0.61 to 0.86. Moreover, the loss of sites to the preloaded solute occurs preferentially at the higher adsorption energies, a fact consistent with the laws of thermodynamics. These data support the hypothesis, previously proposed by Carter et al. (Q, that preloading tends primarily to reduce higher energy sites. The increase in lower energy sites caused by preloading suggests that some higher energy sites are not completely eliminated but have somehow had their net adsorption energiesreduced. As an alternative explanation, it is possible that new, low energy adsorption sites are created as a result of molecular association with the adsorbed TCB. The n values for the GFM isotherm also show a statistically significant increase with preloading, although a visual inspection of the distributions in part b of Figure 2 shows this model to be less sensitive to changes due to preloading than is the LFM. This may indicate that the GFM is not a suitable model for the system under study. The two-parameter CFM isotherm shows results similar to those for the LFM in terms of changes in heterogeneity due to preloading. The n value is increased significantly from 0.51 to 0.77. Similar to the LFM, this shift is reflected graphically in part c of Figure 2 by a loss in higher energy sites and an increase in lower energy sites. Examination of the LFM and GFM data in Table 3 indicates that values of bg,a parameter which characterizes the average surface energy, are lower for preloaded carbon. This result is consistent with the hypothesis that preloading tends to reduce higher energy sites and with the observed trend in the site energy heterogeneity parameter n. However, an examination of the contidence intervals reveals that the differences are not large enough to be statistically significant. One explanation for the lack of statistical significance is that the data does not span a sufficiently wide range of concentration to permit a reliable estimate of the b, parameter. In the low concentration range, the isotherm is relatively insensitive to changes in the energy parameter. In contrast, the isotherm is quite sensitive to changes in the heterogeneity parameter, n, and therefore this parameter can be estimated more reliably. Another explanation for the lack of statistical significanceis that the average energy of the surface under study is not impacted greatly by the preloading. While a decrease in the high energy sites has been noted, this is accompanied by an increase in the lower energy sites. Therefore, the change in the average energy of the surface is rather small. A small change in the average surface energy is consistent with the likelihoodthat the fraction ofhigh energysites on the surface is small. Therefore, while the adsorption of TCB has a significant impact on the site energy heterogeneity as a result of depleting high energy sites, the impact on the average energy is small. Finally, little change in the average site energy is consistent with the degree of TCB loading. The liquid-phase concentration of TCB is in the low parts per billion range, and a loading of 22 pglmg is rather low. Higher TCB loadings would be expected to result in further decreases in the average site energy. It is important to note that measurable differences in average surface energies for adsorption of phenol onto different carbonaceous adsorbents have been reported (8). These results suggest VOL. 29, NO. 7,1995 I ENVIRONMENTAL SCIENCE & TECHNOLOGY
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that at a given loading, b, may be largely a function of the specific adsorbent and its characteristic site energy distribution. The capacity parameter relating to the maximum number of adsorption sites (Q;) for the LFM isotherm was determined to decrease from 144 to 125 pg/mg with preloading; however, the result is not statisticallysignificant. The Q,“value estimatedusing the GFM model was essentially unchanged by preloading. The factors which contribute to the lack of statistical significanceof changes in the average site energy parameter b, also contribute to the relative constancy of the Qg parameter. Q; is a quantity representative of very high surface coverages associated with high solute concentrations. In this study, the maximum aqueous phase concentration is less than 1% of solubility. While this concentration is relatively low, we note that the concentration range studied in this work is typical of many environmental systems, particularly those which employ activated carbon adsorption. Despite the relatively small changes in the average site energy and the maximum capacity parameters, the surface heterogeneity parameter was nonetheless greatly affected by preloading. This result indicates that low loadings of TCB significantly change the site energy distribution, and the mechanism is a depletion of the highest energy sites. The data further suggests that the high energy sites preferentially occupied by the TCB do not comprise a large fraction of the total number of sites. On the basis of the impact of preloading on the value of Q;, it might be expected that the KF value for the CFM model, which is commonly interpreted as a “capacity” parameter, would also exhibit minimal changes in response to preloading. On the contrary, the Kr value shows a 10fold decrease from 1.59 to 0.17 due to preloading. Examination of the area under the curve shown in part c of Figure 2 for the preloaded adsorbent visually shows a reduction relative to that for the unpreloaded sorbent. A rigorous interpretation of Kr is difficult because as indicated in eq 12, this parameter is in reality a combination of parameters; Le., it is a “lumped”parameter. Regardless of its mechanistic interpretation, however, the value of Kb represents the adsorption capacity at unit concentration. A large change in capacity at low concentration is consistent with the foregoing discussion of the impact of preloading on LFM and GFM parameters. In the low-concentration range, higher energy sites are needed to effect adsorption of the target solute. The data suggest that it is precisely these higher energy sites that have been eliminated by preloading. Therefore, the impact of preloading is to deplete the surface preferentially of high energy sites. This, in turn, causes a significant decrease in the site energy heterogeneity as indicated by an increase in the heterogeneity parameter ( n ) .A loss of high energy sites causes a significant reduction
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in the amount adsorbed at low aqueous phase concentrations, which is reflected in a significant decrease in the Kr. parameter for the CFM.
Acknowledgments The authors thank Ping Yuan and Xu Min for their assistance in the collection of the laboratory data reported herein. This publication is a result of work sponsored in part by the National Science Foundation (Grant CES8702786) and by the National Institute of Environmental and Health Sciences (Grant 5P42E504911-02).
Literature Cited (1) Hand, D. W.; Crittenden, J. C.; Arora, H.; Miller, J. M.; Lykins, B. W., Jr. I.-Am. Water WorksAssoc. 1989, 81 (11, 67-77. (2) Smith, E. H.; Weber, W. J., Jr. Enuiron. Sci. Technol. 1989, 23, 713-722. (31 Speth, T. F.; Miltner, R. J.J.-Am,Water WorksAssoc. 1989,81 (41, 141-148. (4) Summers, R. S.; Haist, B.; Koehler, J.; Ritz, 7.; Zimmer, G.; Sontheimer, H. J.-Am. Water WorksAssoc. 1989, 81 (51, 66-74. (5) Speth, T. F. J. Environ. Eng. Diu.(N.Y.) 1991, 117, 66-79. (61 Carter, M. C.; Weber, W. J., Jr,; Olmstead, K. P. J.-Am. Water Works Assoc. 1992, 84 (e), 81-91. (7) Zimmer, G.; Crittenden, J. C.; Sontheimer, H.; Hand, D. W. In Proceedings of the A W A Annual Conference, Orlando, FL; ANWA Denver, CO, 1988; pp 211-220. ( 8 ) Detylo-Marczewska,A,; Jaroniec,M.; Gelbin, D.; Seidel,A. Chern. Scr. 1984, 24, 239-246. (9) Sontheimer, H.; Crittenden, J. C.; Summers, R. S.Activated Carbon for Water Treatment, 2nd ed.; DVGW-Forschungsstelle: Germany, 1989. (10) Misra, D. N. J. Chem. Phys. 1970, 52, 5499-5501. (11) Jaroniec, M. SurJ Sci. 1975, 50, 553-564. (12) Weber, W. J., Jr. Physicochemical Processes for Water Qualiy Control; Wiley: New York, 1972. (13) Halsey, G.; Taylor, H. S. J. Chem. Phys. 1947, 15, 624-630. (14) Sips, R. I. Chem. Phys. 1948, 16, 490-495. (15) Sips, R. J. Chem. Phys. 1950, 18, 1024-1026. (16) Toth, I.; Rudinski, W.; Waksmundzki, A,; Jarionic,M.; Sokolowski. S. Acta Chim. Acad. Sci. Hung. 1974, 82. (17) Jaroniec, M. Adu. Colloid Interface Sci. 1983, 18, 149-225. 118) Cerofolini, G. F. Localized Adsorption o n Heterogeneous Surfaces. Thin Solid Films 1974, 23, 129-152. (191 Seidel, A.; Carl, P. S. Chem. Eng. Sci. 1989, 44, 189-194. 1201 Manes, M.; Hofer, J. E. J. Phys. Chem. 1969, 73, 584-590. (21) Curtis, G. P. Sorption of Halogenated Organic Solutes on to Aquifer Materials: Comparisons Between Laboratory Results and Field Observations. Thesis, Department ofcivil Engineering, Stanford University, Stanford, CA, 1984. (22) Wauchope, R. D.; Savage, K. E.: Koskinen, W. C. Weed Sci. 1983, 31, 744-751. (23) NkediKizza, P.; Rao, P. S. C.; Hornsby, A. G. Enuiron. Sci. Technol., 1985, 19, 975-979. (24)Topping, J. Errors of Observation and Their Treatment;Chapman and Hall: London, 1972. (251 Kinniburgh, D.G. Enuiron. Sci. Technol. 1986, 20, 895-904.
Received f o r review A u g u s t 11, 1994. Revised m a n u s c r i p t received March 23, 1995. Accepted April 11, 1995.@
ES9405150 Abstract published in Advance ACS Abstracts, May 15, 1995
