Reconstruction of Adsorption Potential in Polanyi ... - ACS Publications

May 9, 2014 - The equilibrium Polanyi adsorption potential was reconstructed as ε = −RT ln(Ca(or H)/δ) to correlate the characteristic energy (E) of ...
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Reconstruction of Adsorption Potential in Polanyi-Based Models and Application to Various Adsorbents Bingjun Pan and Huichun Zhang* Department of Civil and Environmental Engineering, Temple University, 1947 North 12th Street, Philadelphia, Pennsylvania 19122, United States S Supporting Information *

ABSTRACT: The equilibrium Polanyi adsorption potential was reconstructed as ε = −RT ln(Ca(or H)/δ) to correlate the characteristic energy (E) of Polanyi-based models (qe = f [ε/E]) with the properties or structures of absorbates, where qe is the equilibriumn adsorption capacity, Ca(or H) is the converted concentration from the equilibrium aqueous concentration at the same activity and corresponds to the adsorption from the gas or nhexadecane (HD) phase by the water-wet adsorbent, and “δ” is an arbitrary divisor to converge the model fitting. Subsequently, the modified Dubinin− Astakhov model based on the reconstructed ε was applied to aqueous adsorption on activated carbon, black carbon, multiwalled carbon nanotubes, and polymeric resin. The fitting results yielded intrinsic characteristic energies Ea, derived from aqueous-to-gas phase conversion, or EH, derived from aqueous-to-HD phase conversion, which reflect the contributions of the overall or specific adsorbate−adsorbent interactions to the adsorption. Effects of the adsorbate and adsorbent properties on Ea or EH then emerge that are unrevealed by the original characteristic energy (Eo), i.e., adsorbates with tendency to form stronger interactions with an adsorbent have larger Ea and EH. Additionally, comparison of Ea and EH allows quantitative analysis of the contributions of nonspecific interactions, that is, a significant relationship was established between the nonspecific interactions and Abraham’s descriptors for the adsorption of all 32 solutes on the four different adsorbents: (Ea − EH) = 24.7 × V + 9.7 × S − 19.3 (R2 = 0.97), where V is McGowan’s characteristic volume for adsorbates, and S reflects the adsorbate’s polarity/polarizability.

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INTRODUCTION Adsorption of organic compounds from aqueous phase by adsorbents such as activated carbon,1,2 zeolite,3,4 synthetic polymeric adsorbent,5,6 carbon nanomaterial,7,8 and black carbon9,10 is environmentally significant due to its application in environmental remediation and water treatment and its important role in the fate of pollutants. Understanding adsorption processes is indispensable for settling a specified separation problem and evaluating the environmental impacts of organic pollutants. In the absence of direct spectroscopic evidence, an appropriate adsorption model can provide insights into the adsorption process. The Polanyi potential theory of adsorption has been widely accepted as a powerful theory for dealing with physical adsorption of both vapor and solutes toward energetically heterogeneous adsorbents.2,11−13 Essentially, it defines an adsorption potential (Z) that is equal to the energy required to remove a molecule at a particular location in the adsorption space to a point outside the attractive force field; the magnitude of the adsorption potential varies within the adsorption space and depends on the proximity of the adsorbate molecule to the solid surface. The Polanyi theory postulates that condensation of an adsorbate to its pure solute state in the adsorption space will take place wherever the adsorption potential (Z) is greater than a critical value. For the case of aqueous adsorption, the © 2014 American Chemical Society

critical value (i.e., the equilibrium adsorption potential) can be mathematically calculated as12 εo = −RT ln(Cw /Cwsat)

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where R (8.314 × 10−3 kJ/mol·K) is the universal gas constant, T (K) is the absolute temperature, Csat w is the aqueous solubility of the pure solute, and Cw is the aqueous equilibrium concentration. εo has been thermodynamically interpreted as the difference in solute’s Gibbs free energy upon adsorption relative to its pure (or subcooled) liquid state at the temperature T.14 Connection of points in the adsorption space with the same adsorption potential (Zi) can form equipotential surfaces, and the equipotential surface with the adsorption potential of εo and the micropore walls of the adsorbent define the boundaries of the adsorbed adsorbate at the equilibrium concentration Cw. According to the theory of volume filling of micropores, there is a fixed available adsorption space for any solute at a given value of εo/β,15 where β is a solute-specific “affinity coefficient” and is related to solute’s molecular structure or properties. Received: Revised: Accepted: Published: 6772

August May 2, May 9, May 9,

30, 2013 2014 2014 2014

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fundamental understanding of the modified D−A model which is critical to its further application to various adsorption processes. In the present study, we further conceptually converted original aqueous adsorption to the corresponding “gas-phase adsorption” by water-wet adsorbents and subsequently proposed another equilibrium adsorption potential (εa). By using εa in the modified D−A model, we can obtain intrinsic characteristic energy (Ea) which is expected to represent the energy contribution of the overall adsorbate−adsorbent interactions. This is because the contributions of solute− water and water−water interactions to the overall adsorption have been completely eliminated and there are no solute− solute interactions in the gas phase. Otherwise, solute−water contributions can significantly interfere with the contributions of adsorbate−adsorbent interactions, as indicated in our previous study25 where the contributions of H-bonding interactions were negative in the original aqueous sorption but positive after converting to the gas-phase adsorption. Comparison of Ea and EH will also shed light on nonspecific adsorbate−adsorbent interactions. Note that water−adsorbent interactions are intrinsically specific for different adsorbents due to their different surface properties. Because the water− adsorbent interactions fall outside the scope of this paper, they were not separately addressed; consequently, the adsorbate−adsorbent interactions herein mean the interactions between adsorbates and water-wet adsorbents. In addition, the effect of both the artificial divisor and the range of equilibrium concentrations of adsorption isotherms on Ea and EH values was tested. At last, Abraham’s polyparameter linear free energy relationships (pp-LFERs)26,27 were applied to quantitatively analyze contributions of individual interactions to Ea or EH. Literature data of adsorption of various apolar and polar organic compounds on four different adsorbents including multiwalled carbon nanotube material (MWCNT),20 black carbon (charcoal, BC),9 activated carbon (AC),28−30 and polymeric resin (MN200)25 were evaluated in this paper.

The Polanyi theory initially dealt with vapor adsorption on the surface of activated carbon where nonspecific dispersion interactions (London forces) are primarily responsible for the adsorption. According to the London theory, molecular polarizability can approximately reflect nonspecific interaction forces. Dubinin and Timofeyev further approximated that the polarizability of a molecule is proportional to its molar volume (Vm) in the liquid form.2,16 Thus, Vm can represent the affinity coefficient β. However, when specific interactions are also responsible for the adsorption, molar volume is not sufficient to capture all adsorption forces. Dubinin and Astakhov proposed a more general energy term (Eo) and developed the Dubinin− Astakhov (D−A) model to describe adsorption isotherms,17,18 ⎛ εo ⎞b log qe = log Q − ⎜ ⎟ ⎝ Eo ⎠ o

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Here qe and Qo are the equilibrium and maximum adsorption capacity, respectively, Eo is the characteristic energy whose value depends on the definition of εo, was believed to account for all possible interaction forces responsible for the adsorption, 18 and hence might permit comparison of adsorption forces among different adsorbates, and b is the D−A model heterogeneity parameter. Up to now, plenty of studies have applied the D−A model to gain insights into different adsorption processes, because the model parameters can reflect the physicochemical properties of both adsorbates and adsorbents.7,18−21 The definition of the equilibrium adsorption potential (εo, eq 1) chooses the respective pure (or subcooled) liquid state of each solute as the reference state for determining the change of Gibbs free energy upon adsorption. However, such a choice will inevitably introduce different baselines for different adsorbates.22,23 For example, apolar or monopolar compounds can undergo only nonspecific solute−solute interactions, while additional specific solute−solute interactions exist within bipolar compounds. Solute−solute interactions are obviously different among different compounds and have been captured by the pure (or subcooled) liquid state. With such a reference state, information on the compound-specific solute−solute interactions is actually involved in the adsorption potential (εo). Consequently, the corresponding Eo values for different compounds (particularly for polar compounds) will not be able to provide quantitative information regarding the differences in adsorbate−adsorbent interactions. To eliminate or minimize the impact of different reference states, a new equilibrium adsorption potential, εH, was proposed in our previous study, based on the concept of theoretically converting aqueous adsorption to the corresponding adsorption from nhexadecane (HD).24 Using εH, we obtained a new characteristic energy (EH) which was believed to exclusively reflect the contribution of specific adsorbate−adsorbent interactions to the overall adsorption energy.24 However, several key factors about this modification still remain unclear: (1) the theoretical base of the proposed equilibrium adsorption potential; (2) the effect of the artificial divisor (see Theoretical Approach below) on the model fitting parameters; (3) the possibility of quantifying both nonspecific and specific adsorbate−adsorbent interactions; (4) the equilibrium concentration range of adsorption isotherms required for an accurate model fitting; (5) the applicability of the modified D−A model to other adsorbents besides polymeric adsorbents. The primary goal of this work was thus to address these questions to achieve a

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THEORETICAL APPROACH We propose that the characteristic energy E (Eo, Ea, or EH) in the D−A model can be principally recognized as the average excess energy of a solute upon adsorption as compared to the energy at the reference state (e.g., pure solute state for Eo, Figure 1). Specifically, for any adsorbed molecule in the adsorption space, its adsorption potential (Z) at any point

Figure 1. Illustration of the characteristic energy (E), which reflects the average excess energy of an adsorbate at the adsorbed state as compared to that at the reference state. The dashed lines indicate equipotential surfaces. 6773

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Table 1. Original D−A Model Fitting Parameters for the Adsorption Isotherms of MN200, MWCNT, AC, and BC. (Surface Area-Normalized Qo: μmol/m2; Eo: kJ/mol) MN200

MWCNT

solute

Qo

Eo

b

NB phenol 4-MP 2-CP 4-CP 2-NP 3-NP 4-NP 24-DCP aniline 4-CA 2-NA 3-NA 4-NA

4.55 4.36 4.11 − 4.33 − 3.81 3.73 − 4.92 4.12 4.14 3.58 3.69

17.2 20.1 20.4 − 23.0 − 20.5 20.6 − 17.8 17.8 15.4 14.5 13.6

2.17 2.08 1.80 − 1.75 − 1.74 1.81 − 1.88 1.77 1.81 1.54 1.48

Qo 4.11 3.93 5.83 3.32 3.70 3.66 2.81 3.44 6.35 3.98 2.74 2.10 2.10

Eo 18.6 19.5 19.1 21.8 17.3 23.9 24.9 21.1 12.2 14.5 19.3 16.9 20.0

AC

BC

b

solute

Qo

Eo

b

solute

Qo

Eo

b

1.81 1.77 1.39 2.30 1.26 1.46 2.25 1.84 1.51 1.22 1.47 1.64 1.77

1-PTNL PHTH DIEE EACE PROP 12-DCE DCM 4-NP − − − − − −

4.88 3.58 6.09 5.94 7.27 6.01 8.28 3.68 − − − − − −

17.5 26.2 14.8 13.8 10.9 14.0 11.0 35.5 − − − − − −

1.68 1.22 1.57 1.39 1.36 1.42 1.49 1.19 − − − − − −

BEN BNTL 12-DCB 124-TMB 124-TCB MNT DNT TNT TOL 14-XYL NAPH − − −

6.85 3.68 2.46 1.54 2.42 2.05 1.46 1.13 2.10 2.31 1.47 − − −

11.1 22.1 18.4 19.0 16.8 22.6 23.7 21.0 17.9 18.1 20.1 − − −

1.03 1.69 1.46 1.56 1.89 2.42 2.59 2.19 1.68 1.55 1.84 − − −

adsorption potential (eq 4) into eq 2 yields the modified D−A model,

should be greater than or equal to the energy (ε) required to condense the molecule from the bulk phase (e.g., aqueous phase, HD phase, or gas phase). This excess energy (Z − ε) varies with location, i.e., (Z − ε) is equal to zero for the adsorbates located on the equipotential surface (Z = ε) and gradually increases when approaching the micropore walls/ surfaces. Also, (Z − ε) varies with equilibrium concentration. The characteristic energy (E) in the D−A model should reflect the average value of all (Z − ε) over the adsorption space at various equilibrium concentrations. As mentioned, the determination of the original εo for each solute is based on its respective pure solute state at the temperature of adsorption which would inevitably render quantitative comparison of the corresponding characteristic energy (Eo) among solutes problematic. To compare the adsorbed solutes based on a unified reference state, a phase conversion method was applied to eliminate the interference of complex adsorbate−adsorbate, adsorbate−water, and water− water interactions when analyzing adsorbate−adsorbent interactions. The concept of phase conversion has been elaborated by other researchers23,31 and in our previous study.25 Briefly, the equivalent gas or HD-phase concentration (Ca or CH) can be calculated from the corresponding aqueous concentration by25

⎛ ε ⎞b ⎛ ε ⎞b log qe = log Q a − ⎜ a ⎟ or log qe = log Q H − ⎜ H ⎟ ⎝ EH ⎠ ⎝ Ea ⎠ (5)

where Ea and EH herein are the intrinsic characteristic energies based on the gas- and HD-phase conversion and reflect the average excess energy of the adsorbate when adsorbing by water-wet adsorbents from the gas- and HD-phase, respectively. Thus, Ea actually represents the energy contribution of the overall adsorbate−adsorbent interactions because no interactions take place in the gas phase, and EH represents the energy contribution of specific adsorbate−adsorbent interactions because only nonspecific interactions take place in the HD phase. Note that Qa and QH actually mean the maximum gas or HD-phase adsorption capacity when the equilibrium concentration reaches “δ”, so we still rely on Q0 (eq 2) for the maximum aqueous adsorption capacity.

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DATA SOURCES AND SOLUTE PHYSICOCHEMICAL PARAMETERS The adsorption isotherms of substituted phenols and anilines on multiwalled carbon nanotubes (MWCNT) were collected from the work of Yang et al.,20 sorption data of a series of aromatic compounds by black carbon (BC) were obtained from Zhu and Pignatello’s work,9 the data for activated carbon (AC) were derived from Manes’s series papers,28−30 and the adsorption of various aromatic compounds on MN200 were reported in our previous study.25 The abbreviations and relevant physicochemical properties of all solutes, including aqueous solubility (Csat w ), hexadecane−water partition coefficient (KHW), gas−water partition coefficient (i.e., Henry’s constant, KaW), and Abraham’s solute descriptors are listed in Table S1, SI.

Thus, εa (or H) means the Gibbs free energy change upon adsorption from the gas (or HD) phase to the water-wet adsorbent, and the artificial divisor “δ” is common for all adsorbates (its goal is to converge the model fitting). Note that the value of “δ” should always be larger than any converted equilibrium concentrations. Substitution of the new equilibrium

RESULTS AND DISCUSSION Original Aqueous Adsorption on Different Adsorbents. All the original adsorption isotherms on the four adsorbents are depicted in Figure S1, SI. Apparently, the adsorption capacities of AC and MN200 are larger than those of BC and MWCNT, although different compounds were

Ca(or H) = Cw exp[( −ΔGa(or H) ‐ W,i + C T)/RT ]

(3)

where ΔGa(or H)‑W,i is the net Gibbs free energy change of transfer of solute i from the aqueous phase to the gas or HD phase, and CT is the correction term for the calculation of net free energy change of adsorption from the aqueous phase to the adsorbent. Detailed calculations of ΔGa(or H)‑W,i and CT are in Text S1 in the Supporting Information (SI). On the basis of eq 3, we can reconstruct a new equilibrium adsorption potential, εa(or H) = −RT ln[Ca(or H)/δ]

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Figure 2. (a) Comparison of two sets of simulated isotherm curves with two different divisors (δ versus δ × 102) at different b values. Solid lines are the fitting curves with the divisor δ = 106 at Qa = 5000, E = 25, and b = 1−5; dashed lines are the fitting curves with the divisor δ × 102 at Qa × 1.1, E +11, and b × 1.4; all the lines intersect at the point ε = E. (b) Relationship between the slope of a typical type-I isotherm curve (S = d[log qe]/d[log Cw]) and equilibrium concentration on the log scale.

the effect of “δ” values on the modeling results was evaluated. Based on the modified D−A model after the gas-phase conversion (eq 5), the fitting parameters (Ea and b) of the adsorption on MN200 and MWCNT at three different “δ” values (104, 106, and 108) are listed in Table S2, SI. Numerically, increasing “δ” by 2 orders of magnitude caused an increase in Ea, b, and Qa by about 11 kJ/mol, 1.4 times, and 1.1 times, respectively. Figure 2a illustrates two sets of simulated isotherm curves at different b values; one set (the dashed lines) is with the divisor δ1, Ea1, Qa1, and b1, and the other (the solid lines) is with the divisor δ2 = δ1 × 102, Ea2 = Ea1 + 11, Qa2 = Qa1 × 1.1, and b2 = b1 × 1.4. As shown, the two sets of isotherm curves almost completely overlap except when the b1 value is equal to 1, where the adsorption capacities of the solid line are smaller at high equilibrium concentrations. Fortunately, the b values for the modified D−A model are mostly greater than 2 (Table 2). Similar effects of “δ” values on the fitting parameters were also observed after the HD phase conversion (i.e., EH, QH, and b) and for the adsorptions on AC and BC. Thus, selection of “δ” values will not influence the relative values of E among various adsorbates but will affect their absolute values. In this study, we used a fixed value of δ = 108 for the subsequent fitting of all adsorption isotherms. As shown above, the modified D−A model is not applicable to adsorptions whose b value of the D−A model fitting is close to 1. In this case, the increase in Ea (or EH) is much smaller than 11 kJ/mol when increasing “δ” by 2 orders of magnitude. For example, the b value for benzene adsorption on BC is 1.03 (Table 1), and the increase in Ea is only about 3 kJ/mol. The heterogeneity parameter, b, was believed to reflect the standard deviation of the sizes of all available micropores, that is, the more heterogeneous micropores would yield smaller b values and vice versa.35 Because the size of micropores is also associated with adsorption energy,16 parameter b might also be viewed as the heterogeneity of adsorption energy. So it is possible that fitting adsorption isotherms with the model may encounter difficulty in obtaining an averaged E value if the associated adsorption energies are highly heterogeneous. Another possibility for a small increase in Ea (or EH) values with increasing “δ” is that the range of equilibrium concentrations of the isotherm is not wide enough, such that the model fitting parameters cannot accurately reflect the characteristics of the adsorption. To avoid large deviations, Yang and Xing7 suggested that the sorption experiments should

tested. The surface areas of AC (1140 m2/g)28 and MN200 (1021 m2/g)25 are much larger than those of BC (430 m2/g)9 and MWCNT (174 m2/g).20 The corresponding surface areanormalized isotherms were recalculated and are illustrated in Figure S2, SI. When plotted this way, the adsorption capacities on different adsorbents become more comparable. The adsorption isotherms for 4-nitrophenol on AC, MN200, and MWCNT nearly overlap. It can be thus inferred that surface area is an important factor for determining adsorption capacities on these adsorbents. Also, because the majority of the surface area of MN200, AC, and BC exists in micropores (0.5) of benzene adsorption on BC at all equilibrium concentrations indicate the adsorption is far from saturation. The dependency of the D−A model parameters on the range of equilibrium concentration was tested, and we found that for any adsorbate/ adsorbent combination in this article, the changes in the fitting parameters are statistically insignificant if the slope at the highest equilibrium concentration is less than 0.2 (based on the log scale, data not shown), and the range between the highest and the lowest equilibrium concentration is more than 3 orders of magnitude (Figure 2b). Thus, a concentration range from C0.2 (the equilibrium concentration at which the slope is 0.2) to C0.2 × 10−3 and more than 10 data points well-distributed in such a range are suggested for an ideal D−A model fitting. Interaction Analysis Based on the Modified D−A Model. The converted isotherms that conceptually represent adsorption of solutes from the gas or HD phase by the four water-wet adsorbents (i.e., MN200, MWCNT, BC, and AC) were calculated (Figure S4, SI), and the corresponding fitting parameters based on the modified D−A model (eq 5) are listed in Table 2. As compared with the original aqueous isotherms, substantial differences in the converted isotherms among various solutes can be detected, especially for the gas-phase converted isotherms. Also, distinct differences in the characteristic energies (Ea or EH) emerge after using the newly defined equilibrium adsorption potentials. Generally, the compounds exhibiting greater equilibrium adsorption capacities in the converted isotherms have larger Ea or EH values, e.g., the greatest adsorption of 4-NP (on MN200, MWCNT or AC; Figure S4) yields the largest Ea or EH values, while this is not necessarily the case for the original aqueous isotherms. As shown, the substituent effect on the Ea or EH values consistently follows the trend: nitro > chloro > methyl substitution for the substituted phenols, anilines, or benzenes. Such an effect corresponds to the electronic effects of these substituents on the aromatic ring, where nitro groups have an electronwithdrawing ability stronger than that of chloro groups, and methyl groups have a weak electron-donating effect. Additionally, o-nitrophenol (2-NP) and o-nitroaniline (2-NA) have characteristic energies smaller than those of their meta- and para-isomers, resulting from intramolecular interactions in the ortho-isomers, which would reduce their H-bonding donating ability in intermolecular H-bonding.36 p-Nitro substitutions have larger Ea or EH values relative to those of meta-isomers due to the additional electron-accepting resonance effect of the nitro groups. Also, 2,4,6-trinitrotoluene (TNT) with more nitro groups has an Ea or EH value higher than that of 2,4dinitrotoluene (DNT) and p-nitrotoluene (MNT). As previously mentioned, parameter b can be viewed as the heterogeneity of adsorption energy over the range of equilibrium concentrations. Yang et al.20 observed a linear relationship between b and E, implying that b intrinsically depends on the interactions between solutes and adsorbents. As shown in Table 2, for the adsorption on MWCNT and BC, the chemicals with larger Ea or EH values usually but not necessarily

a

44.1 44.9 46.6 − 53.5 − 64.2 67.2 − 41.4 49.9 54.3 59.6 61.1 NB phenol 4-MP 2-CP 4-CP 2-NP 3-NP 4-NP 24-DCP aniline 4-CA 2-NA 3-NA 4-NA

The results for aniline on MWCNT and benzene on BC are not included (Ea or EH: kJ/mol; see Table S3, SI, for the standard errors of Ea and EH).

− 43.8 38.0 40.9 42.2 54.9 66.3 71.2 33.5 35.5 48.9 − − − BEN BNTL 12-DCB 124-TMB 124-TCB MNT DNT TNT TOL 14-XYL NAPH − − − 3.27 2.91 2.14 2.31 2.70 2.23 2.68 2.73 − − − − − − 33.0 41.0 20.9 23.2 22.6 22.4 19.2 54.7 − − − − − − 3.87 3.24 2.18 2.47 2.78 2.49 2.74 3.18 − − − − − − 39.5 57.7 21.4 25.1 23.3 25.6 19.7 74.7 − − − − − − 1-PTNL PHTH DIEE EACE PROP 12-DCE DCM 4-NP − − − − − − − 3.32 3.10 2.54 4.04 2.57 2.59 4.81 3.02 − 2.88 2.80 4.28 4.82 − 4.09 4.01 3.28 5.55 3.34 3.54 6.79 4.31 − 3.32 3.92 6.38 7.05 29.0 36.1 35.4 − 38.7 − 43.2 46.1 − 30.1 33.5 35.4 38.1 39.5

3.37 3.57 3.18 − 3.08 − 3.68 3.84 − 2.99 3.27 3.83 3.46 3.37

− 42.8 45.3 39.9 53.2 42.8 64.1 72.5 52.5 − 43.2 56.2 64.2 71.6

− 34.2 34.3 28.4 38.2 28.4 44.2 51.1 35.4 − 29.4 37.9 42.1 48.8

b EH b

gas phase

Ea solute

4.83 4.33 4.12 − 4.19 − 5.31 5.34 − 3.98 4.69 5.60 5.00 4.76

gas phase

Ea solute b

HD phase

EH b

gas phase

Ea b EH b

gas phase

Ea b

HD phase

EH

HD phase

solute

AC MWCNT MN200

Table 2. Modified D−A Model Fitting Parameters for the Adsorption Isotherms of MN200, MWCNT, AC, and BC with δ = 108 a

BC

b

HD phase

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Table 3. Dependence of Ea and EH on the Solute Descriptors for MN200, MWCNT, and BCa Ea

EH

adsorbent

e

MN200 MWCNT BC MN200 MWCNT BC

− − − − − −

s 14.2 25.4 17.3 6.7 15.7 6.4

± ± ± ± ± ±

a 1.6 2.1 5.5 0.7 1.6 4.1

15.8 16.0 − 15.6 15.3 −

± 2.0 ± 3.0 ± 1.0 ± 2.6

b

v

c

R2

− − 17.0 ± 9.9 − − 21.2 ± 8.0

30.0 ± 2.4 15.1 ± 3.0 25.7 ± 3.6 − − −

− − − 20.9 ± 0.9 10.4 ± 2.2 20.8 ± 2.5

0.975 0.973 0.949 0.983 0.948 0.884

a The best regression models were determined by the lowest Mallow’s Cp value while keeping the p-value of each parameter less than 0.1 to ensure each involved term is statistically significant.

have larger b values. However, such a trend is not obvious for the adsorption on MN200 and AC. As compared with MWCNT and BC, MN200 and AC have more abundant micropores whose sizes are commensurate with the size of the adsorbed molecules. Perceivably, molecular sieving effects on microporous adsorbents can take place, while MWCNT provides adsorption sites only along the external surfaces and consequently has little steric effects.7 In our previous study, we observed that the solutes with larger molecules have larger b values when adsorbed on a microporous adsorbent,24 meaning that steric effects could affect b values. Thus, parameter b likely depends not only on solute−adsorbent interactions but also on solute size and adsorbent pore size distribution. The contribution of individual interactions to the overall interaction can be quantitatively interpreted based on the ppLFERs developed by Abraham’s group.26,27 Briefly, five solute descriptors, i.e., E, S, A, B, and V, were introduced to describe the ability of each solute to form respective interactions with the sorbent. E is intended to capture London dispersive forces and Debye forces; V accounts for cavitation energy and part of London dispersive forces beyond what is captured by the E term; S is believed to reflect predominantly the effects of stable polarity and some effects of induced dipole; A and B are the descriptors for the overall H-bonding donating and accepting abilities, respectively. All the solute descriptors for the tested chemicals are listed in Table S1, SI. By conducting multiple linear regression analysis for a diverse range of solutes: Ea or E H = eE + sS + aA + bB + vV + c

the adsorbate−adsorbent interactions. MN200 is synthesized by copolymerization of styrene (monomer) and divinylbenzene (cross-linking agent). The electron-rich π-systems of the styrene−divinylbenzene matrix can serve as potential electron-donating sites; thus, electron acceptor−donator interactions can take place if the adsorbate has H-donating abilities (i.e., electron acceptor). MWCNT comprises highly polarizable graphite sheets that also can have electron acceptor−donator interactions with H-donating adsorbates. Thus, MN200 and MWCNT both have positive coefficients of term A. The coefficient of term S for MWCNT is larger than that of MN200 because the polarizability of multiple and condensed ring systems (i.e., graphite in MWCNT) is much higher than that of single aromatic ring systems (MN200). Consequently, MWCNT can form stronger S-type interactions. Additionally, the adsorption on both adsorbents has large coefficients of term V. Obviously, cavitation energy is not responsible for the positive contribution of term V because no free energy cost is required for cavity formation in the gas phase. Thus, the contributions of term V might arise from London dispersive forces. The polarizability of MWCNT is higher than MN200, and consequently MWCNT should form dispersive forces with adsorbates stronger than that of MN200. Instead, the obtained V coefficient (Table 3) for MWCNT is much smaller, which means dispersive forces are not the only cause for the V contribution. Unfortunately, the exact reasons for term V contributions remain unidentified. The adsorption mechanism on BC is different from that on MN200 and MWCNT. In particular, the contribution of B stands out while that of A vanishes. Almost all the tested chemicals for BC are without H-bonding-donating abilities (A = 0); thus, the A-type interactions cannot take place. The surface of BC contains H-donor groups including carboxylic acid (COOH), hydroxyl (OH), and traces of thiol (SH) and ammonium (NH3+)39 which can potentially provide hydrogen to form H-bonding with H-accepting chemicals. However, Sander and Pignatello39 ruled out H-bonding interactions between the surface functional groups of BC and adsorbates based on the observation that the relative position of the nitrobenzene isotherm to that of benzene and toluene isotherms is not significantly affected by elevating the pH from 6.5 to 11. Although the contribution of H-bonding interactions to the aqueous adsorption may be very weak, adsorbate−adsorbent H-bonding interactions can still exist because they may be counteracted by adsorbate−water Hbonding interactions. Indeed, there is a significant linear relationship between the contribution of specific interactions (EH) and term B (R2 = 0.84), indicating that the H-bonding between the H-donating groups of BC and H-accepting adsorbates is a component of the specific interactions.

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the dependence of the interactions on these solute descriptors can be obtained.25,37,38 Here e, s, a, b, and v are regression coefficients that describe the difference in each interaction force between the gas- or HD-phase and the adsorbent phase. The fractional contributions of individual interactions to Ea and EH for each adsorbent were obtained by the developed ppLFERs (Table 3). Note that Ea or EH increases to the same degree for any solute with an increasing value for the divisor “δ”, such that the regression coefficients (e, s, a, b, and v) of the pp-LFERs are not influenced by “δ”; only the constant c will be impacted. The obtained coefficients can serve to characterize respective contributions of multiple interactions to the overall or specific adsorbate−adsorbent interactions. The constant c of pp-LFERs has lost its physical significance due to its fluctuation with “δ”. The results of AC were not included, because only eight organic compounds were selected from Manes’s papers, the other reported isotherms do not meet the requirements for the D−A model fitting, and regression analysis of eight data points with five parameters is not statistically meaningful. As shown in Table 3, the dependence of Ea on the solute descriptors are similar for the adsorption on MN200 and MWCNT, that is, terms S, A, and V are jointly responsible for 6777

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As compared with the regression results of Ea (Table 3), the contribution of term V to the specific interactions (EH) disappears as expected because V exclusively contributes to nonspecific interactions. The contributions of term A or B almost stay the same, because the two terms are classified as specific interactions, and the contribution of another specific interaction, S, is reduced, as explained in detail below. As shown in Table 2 and Table S3, SI, the differences between Ea and EH values are statistically insignificant for the adsorption of nonpolar compounds and compounds with low polarity, such as the adsorption of dichloromethane (DCM), diethyl ether (DIEE), and propionitrile (PROP) on AC but are substantial for the adsorption of highly polar compounds, such as the adsorption of 1-pentanol (1-PTNL), phthalide (PHTH), and p-nitrophenol (4-NP) on AC. Because Ea represents the overall adsorbate−adsorbent interactions, and EH reflects the contributions of specific interactions, the difference between them should represent the contribution of nonspecific interactions. Note that the difference is independent of the “δ” value because the influences of “δ” on Ea and EH values are the same. The dependence of (Ea − EH) on the solute descriptors was tested. As shown in Figure 3, almost all (Ea −

as compared to the gas phase or to the HD phase. The dependence of the net Gibbs free energy change ΔGH‑a,i (transfer of solute i from the gas phase to the HD phase) on the solute descriptors was also tested, and we found that the dependence is almost identical (i.e., −ΔGH‑a,i = 27.0 × V + 9.5 × S − 20.2, R2 = 0.97), suggesting that our approach is valid. HD is an inert solvent that can undergo only nonspecific interactions with all solutes, irrespective of their polarity.23 Zhu and Pignatello believed that the HD-based nonspecific interactions encompass V- and E-type interactions.40 Actually, hexadecane cannot form E-type interactions with any solute because its E value is zero.41 In addition, HD can undergo weak S-type interactions with organic molecules through its polarizability because the S term also captures some effects of induced dipole. This can explain why the contribution of term S to EH is less than to Ea. Additionally, the constant in eq 7 is considered to contain entropy contributions that represent differential “freedom” of molecules between the gas phase and the HD phase. Perceivably, the motion of molecules would be freer in the gas phase relative to in the HD phase, such that there is an entropy loss and the constant is negative.

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ENVIRONMENTAL IMPLICATION A fundamental understanding of the adsorption mechanisms between contaminant molecules and an adsorbent is indispensable for settling a specified pollution problem and evaluating environmental behaviors. The Polanyi adsorption potential theory has proven to be a powerful available theory for dealing with vapor or aqueous adsorption processes on various adsorbents. By reconstruction of the equilibrium adsorption potential (ε) and elimination of the interference of complex adsorbate−adsorbate, adsorbate−water, and water− water interactions, the modification adopted in this work yields intrinsic characteristic energies that can facilitate interpretation of the direct interaction forces between adsorbates and adsorbents. Subsequently, quantitative comparison of the interactions among various solutes and adsorbents is likely which allows the elucidation of the effects of solute structures and adsorbent properties, whereas the characteristic energy given by the original adsorption potential is somewhat obscured. Such valuable information can be used to guide the adsorbent selection process for a given contaminant and facilitate evaluation of the fate of pollutants in the environment. The insights into nonspecific and specific interactions from Ea and EH will also be useful in considering competitive adsorption among different adsorbates in multisolute adsorption systems, because adsorbates with stronger specific interactions with the adsorbent are generally more competitive.

Figure 3. Relationship of nonspecific interactions (Ea − EH) with terms V and S for MN200, MWCNT, BC, and AC. Almost all the data points (Ea − EH) are located on the same plane surface based on the equation: (Ea − EH) = 24.7 × V + 9.7 × S − 19.3 (R2 = 97.1, mean weighted square error = 0.049); the short lines pointing away from the data points indicate the distance of the data points from the surface.

EH) points are located on the same V−S plane surface for the adsorption on all four adsorbents (R2 = 0.97; mean weighted square error = 0.049), meaning that the dependence of nonspecific interactions on the solute descriptors is practically identical for different adsorbents and only related to terms V and S. The integrated pp-LFER for the four adsorbents is shown in eq 7, which is similar to the individual pp-LFERs for each adsorbent (Text S2, SI). (Ea − E H) = 24.7 × V + 9.7 × S − 19.3

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ASSOCIATED CONTENT

S Supporting Information *

Additional information as noted in the text. This material is available free of charge via the Internet at http://pubs.acs.org.

(R2 = 0.97)

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(7)

Term V is primarily responsible for nonspecific interactions, term S provides relatively less contribution, and the constant is negative. From the principle of the phase conversion method, (Ea − EH) should represent the free energy change of transfer of solute i from the gas phase to the HD phase, if the obtained intrinsic characteristic energies (Ea and EH) can accurately reflect the excess energy of adsorbate i in the adsorption space

AUTHOR INFORMATION

Corresponding Author

*Phone: (215) 204-4807; fax: (215) 204-4696; e-mail: [email protected]. Notes

The authors declare no competing financial interest. 6778

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