w a t e r r e s e a r c h 5 9 ( 2 0 1 4 ) 2 9 5 e3 0 3

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Prediction of sorption of aromatic and aliphatic organic compounds by carbon nanotubes using poly-parameter linear free-energy relationships Thorsten Hu¨ffer a,b,c,*, Satoshi Endo d, Florian Metzelder a, Sarah Schroth a, Torsten C. Schmidt a,c a

Instrumental Analytical Chemistry, University of Duisburg-Essen, Universita¨tsstrasse 5, 45141 Essen, Germany Department of Environmental Geosciences, University of Vienna, Althanstrasse 14, 1090 Vienna, Austria c Centre for Water and Environmental Research ZWU, University of Duisburg-Essen, Universita¨tsstrasse 2, 45141 Essen, Germany d Helmholtz Centre for Environmental Research UFZ, Permoserstrasse 15, 04318 Leipzig, Germany b

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Article history:

The accurate prediction of distribution coefficients of organic compounds from water to

Received 22 January 2014

carbon-based nanomaterials (CNM) is of major importance for the understanding of environ-

Received in revised form

mental processes and a risk assessment of released CNM. Poly-parameter linear free-energy

10 April 2014

relationships (ppLFER) have previously been shown to offer such an accurate prediction of

Accepted 11 April 2014

sorption processes. The aim of this study was to identify and quantify the contribution of in-

Available online 24 April 2014

dividual molecular interactions to overall sorption by multi-walled carbon nanotubes (MWCNTs). To this end, a large data set of experimental sorption isotherms by MWCNTs of 20


aliphatic and 14 aromatic compounds covering various relevant molecular interactions was

Carbon nanomaterials

produced. A thermodynamic cycle was used to obtain MWCNT-air distribution coefficients


(KMWCNT/a) for the interpretation of direct sorbate-MWCNTs interactions. The thereby derived

Organic compounds

ppLFER log KMWCNT/a ¼ (0.59  0.59)E þ (2.23  0.59)S þ (3.90  0.67)A þ (3.23  0.71)B þ (0.98  0.17)


L  (0.05  0.50) shows the contribution of non-specific interactions, represented by the hexadecane-air partitioning constant (L), and specific interactions related to the solute polarity (S) as well as the H-bond interactions (A, B). Measured MWCNT-water distribution coefficients were clearly more accurately calculated by the ppLFER equations (R2 0.85e0.86) compared to the classical prediction by single parameter model based on the octanolewater partitioning constant (R2 0.64e0.78). In addition, the ppLFER presented here allow a more accurately prediction of sorption by MWCNTs compared to literature ppLFER, especially for aliphatic compounds and at environmentally relevant concentrations. ª 2014 Elsevier Ltd. All rights reserved.

* Corresponding author. Department of Environmental Geosciences, University of Vienna, Althanstrasse 14, 1090 Vienna, Austria. Tel.: þ43(1) 4277 53383; fax: þ43(1) 4277 9533. E-mail address: [email protected] (T. Hu¨ffer). http://dx.doi.org/10.1016/j.watres.2014.04.029 0043-1354/ª 2014 Elsevier Ltd. All rights reserved.



w a t e r r e s e a r c h 5 9 ( 2 0 1 4 ) 2 9 5 e3 0 3


In recent years, research on the environmental behaviour of carbon-based nanomaterials (CNM) has received growing attention, while, among others, the impact of CNM on the fate and transport of organic contaminants has been in the focus of researchers. In general, CNM are characterized by strong interactions with organic compounds (Pan and Xing, 2008); however, the influence of molecular structure on overall sorption are yet poorly understood. For example, specific p-pelectron donor-acceptor interactions have been discussed to be responsible for the strong interaction (Pan et al., 2008; Chen et al., 2008, 2007), while sorption of cyclohexane, which can only undergo non-specific interactions, was found to be stronger than of aromatic benzene (Chen et al., 2007). These contradictory observations emphasize the need for a more comprehensive approach to investigate sorption by CNM. There have been few attempts for the quantitative and qualitative determination of the contribution of multiple types of interactions to overall sorption by CNM (Apul et al., 2013; Xia et al., 2010; Zhao et al., 2014). However, such an approach would be required for a priori prediction of sorption of diverse organic compounds by CNM. Poly-parameter linear free-energy relationships (ppLFER) present a promising approach, as they offer the opportunity to capture all relevant molecular interactions that influence the sorption coefficient. Thus, they have higher predictive power than commonly used one-parameter LFER (opLFER) based, e.g., on the octanolewater partitioning constant (Kow) (Goss and Schwarzenbach, 2001). Abraham’s ppLFER equations consist of terms describing the individual contributions of molecular interactions using both the properties of the sorbate (solute descriptors) and the sorbent (phase descriptors) (Abraham, 1993; Abraham et al., 2004), which are given by: log Ki;1=a ¼ e1a Ei þ s1a Si þ a1a Ai þ b1a Bi þ l1a Li þ c1a


log Ki;1=w ¼ e1w Ei þ s1w Si þ a1w Ai þ b1w Bi þ v1w Vi þ c1w


where log Ki,1/a and log Ki,1/w represent the logarithmic distribution coefficients of a given sorbate i between phase 1 and air and between phase 1 and water, respectively. The uppercase letters in Eqs. (1) and (2) denote the solute descriptors representing the solute’s capability of exerting individual types of interactions: Ei, the excess molar refraction; Si, dipolarity/polarizability; Ai, solute hydrogen (H)-bond acidity; Bi, solute H-bond basicity; Li, logarithmic hexadecane-air partitioning constant; and Vi, McGowan volume of the solute. Ei, Vi, and Li are descriptors representing non-specific interactions as the cavity formation energy and dispersive van-der-Waals interactions, whereas Si, Ai, and Bi indicate specific interaction (Goss and Schwarzenbach, 2001). It should be noted that non-specific interactions cannot be fully separated by the ppLFER model, because of inherent correlations between the descriptors. The corresponding lowercase letters denote the phase descriptors and are derived by multiple regression analysis (MRA), and c denotes the regression constant. Sorption mechanisms have successfully been determined by ppLFER, for example, from the aqueous phase to activated carbon (Shih and Gschwend, 2009) and to natural organic

matter in soils and sediment (Endo et al., 2008a; Bronner and Goss, 2011). Most recently, Apul et al. developed a ppLFER model for the prediction of sorption of aromatic compounds by multiwalled carbon nanotubes (MWCNTs) (Apul et al., 2013). However, the developed ppLFER has certain drawbacks. Firstly, only aromatic compounds have been used for the model development. Inaccurate description of sorption properties of MWCNTs can result from the use of a biased probe sorbate set that does not include aliphatic compounds. Secondly, the reported ppLFER did not contain the term for excess molar refraction (E), which also accounts for the contribution of nonspecific interactions (Nguyen et al., 2005). A comprehensive discussion of the relevant interactions may not be possible without taking all descriptors into account. As a consequence, there is still improvement necessary for a comprehensive ppLFER development. Thus, the aim of the study presented here was to derive ppLFER for sorption by MWCNTs in order to investigate the contribution of individual intermolecular interactions to overall sorption and, furthermore, to characterize the sorption properties of MWCNTs. For ppLFER modelling, a probe set of 34 compounds was selected including aliphatic and aromatic compounds featuring various functionalities.


Materials and methods



Multi-walled carbon nanotubes (C150HP) were purchased from Bayer Material Science (Leverkusen, Germany). Properties of MWCNTs are given elsewhere (Hu¨ffer et al., 2013a). Amorphous carbon was removed by heating MWCNTs to 350  C for 1 h (Chen et al., 2007). Thirty-four sorbates were selected as probe compounds based on previous publications (Endo et al., 2008a, 2009a) covering a broad range of various substance classes including the following: apolar aliphatics (alkanes), monopolar aliphatics (ethers and halogenated alkenes), bipolar aliphatics (alcohols), non-polar aromatics (BTEX and PAHs), monopolar aromatics (e.g., anisole), and bipolar aromatics (phenols). Note that the present study vastly extends the diversity of chemicals from previous works (Apul et al., 2013; Xia et al., 2010). The probe compound set used in this study did not cover very large hydrophobic compounds, multifunctional polar compound (e.g., pesticides), and polyfluorinated chemicals, which are thus out of the calibration domain of the resulting models from this study. Basic physico-chemical properties and ppLFER descriptors of used sorbates are given in Tables S1 and S2 of the Supplementary Material, respectively. Stock solutions of sorbates were prepared weekly in methanol by dissolving the pure compound and kept at 4  C in the dark.


Sorption batch experiments

MWCNTs (2e5 mg) were weighted into 20-mL amber headspace screw vials. Then, 10e20 mL of 10 mM CaCl2 as background solution were added into the vials, which were then closed with screw caps with butyl/PTFE-lined septa. After the


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vials were shaken for 24 h to wet the sorbent (Chen et al., 2007), samples were spiked with methanolic sorbate standard solutions, resulting in equilibrium concentrations ranging over 3e4 orders of magnitude. The amount of sorbent was adjusted to achieve 30e90% of sorbate sorbed at equilibrium. The methanol content did not exceed 0.25% (v/v) in water to minimize co-solvent effects. Duplicate measurements were performed for each sorbate and each concentration to assure reproducibility. Samples were shaken for equilibration at 25  C in a temperature-controlled room for no longer than 5 days. Equilibration times of probe sorbates were pre-determined and equilibration times are in accordance with previous publications on sorption by CNTs (Shen et al., 2009; Yang et al., 2006). Subsequently, the vials were removed from the shaker and the sorbate concentration in the aqueous phase was determined. For volatile sorbates (as indicated by HS in Table S1), batch sorption experiments were conducted in a three-phase system (gaseous, liquid, and solid), where vials contained 10 or 15 mL of the background solution. After equilibration, vials were placed in the tray of the autosampler at least 2 h prior to analysis in order to reach equilibrium between liquid and gaseous phase (Endo et al., 2008a). Sorbate concentrations in the gas phase were then determined by direct injection of 1000 mL of the vial headspace into GCeMS by the autosampler using an external calibration for quantification. After each measurement, the syringe was flushed with nitrogen for 4 min for cleaning. For less volatile sorbates (indicated by ITEX2 in Table S1), vials contained 20 mL of the background solution leaving minimal headspace. After equilibration, samples were centrifuged at 2500 rpm for 20 min. Subsequently, 10 mL of the supernatant were transferred to clean vials and the headspace concentration of analytes in the samples was analysed after 2 h airewater equilibration using in-tube microextraction (ITEX2). The ITEX2 option for the CombiPal autosampler was received from CTC Analytics (Zwingen, Switzerland) and consisted of a heated syringe holder, a trap heater, a 1.3 mL Hamilton syringe with side port (Hamilton, Bonaduz, Switzerland), and a single magnet mixer (SMM, Chromtech, Idstein, Germany). Tenax GR (BGB Analytik AG, Schlossboeckelheim, Germany) was used as trap material. The ITEX2 extraction procedure was generally adapted from Laaks et al. (2010). For extraction, samples were transferred to the SMM, where the samples were heated to 40e70  C and stirred at 500 rpm for 10 min, and 30e50 extraction strokes with an aspiration and dispensing volume of 1 mL at a flow of 50 mL s1 were performed. The temperatures of the trap and the syringe were 40 and 70  C, respectively, to avoid condensation of water in the syringe. After the extraction, 500 mL helium was aspirated as desorption gas from the injector. The trap was then heated for desorption to 280e300  C and the aspired desorption gas was injected into the GC injector at 50 mL s1. To avoid cross contamination, the trap was heated to 330  C for 10 min while flushed with nitrogen at 5 mL min1 after injection. For all samples, quantification was achieved using an external calibration; 12e16 calibration standards were prepared in 10 mL background solution one day prior to analysis. All analyses were conducted using a Trace GC Ultra (Thermo Electron Corporation, Austin (Texas), USA) coupled to a DSQ

single quadrupole mass spectrometer (Thermo Electron Corporation, Austin (Texas), USA) equipped with a split/splitless injector (SSL) and a CombiPAL autosampler (CTC Analytics, Zwingen, Switzerland). An HP-5 capillary column (30 m  0.32 mm  0.25 mm, J&W Scientific) and isothermal oven temperatures between 70 and 150  C were used depending on the analyte retention. Helium was used as carrier gas at a flow of 1.5 mL min1. The temperature of the SSL was set to 200e250  C. The temperatures of the transfer line and the ion source of the mass spectrometer were set to 250 and 220  C, respectively. The mass spectrometer was operated in electron ionization mode with ionization energy of 70 eV. Quantification of analytes was done in scan mode. The sorbed concentrations by MWCNTs were calculated by mass balance. Loss of analytes during the experimental procedure was monitored by preparing spiked samples without sorbent. The loss of analytes was incorporated in the calculations. The calculated sorbed concentration and the aqueous concentration were log-converted, plotted, and then fitted to the log-converted Freundlich model equation: log Cs ¼ log KF þ n log Cw 1

(3) 1

where Cs [mg kg ] and Cw [mg L ] denote the sorbed and aqueous concentration of sorbates, respectively, and KF [(mg kg1)/(mg L1)1/n] and n [e] are the Freundlich coefficient and exponent, respectively. Model fits were performed with Sigma Plot 12.0 for Windows.


Data analysis

The aqueous distribution coefficients Kd/w [L kg1] of all sorbates were then interpolated at a constant sorbate loading of 1000 mg/kg on MWCNTs using the Freundlich equation (3). This concentration was chosen since experimental isotherm data for most of the sorbates were available around this concentration and least extrapolations had to be made. However, for 1-octanol, 4-methyl-4-heptanol, naphthalene, and ethylbenzoate short range extrapolation (i.e., 0.97). The goodness of fit for sorption of tetrachloromethane (TeCM), 2-octanone, 4-methyl-4-heptanol, propylbenzene, and anisole was lower (R2 0.93e0.97). Thus, the influence of Freundlich parameters was evaluated for the 4 compounds on the calculation of logarithmic distribution coefficients (log Kd/ w) and consequently on the ppLFER development by a sensitivity analysis. Changes in KF of 0.1 log units and 0.03 in sorption linearity (n) did not result in statistically significant differences in phase descriptors obtained by ppLFER (ANOVA test, p > 0.25, not shown). Therefore, we do not further discuss the influences of isotherm fitting errors on the ppLFER modelling results. The isotherms data fits indicate that the Freundlich exponent n of aliphatic compounds was significantly higher (p < 0.001), i.e., closer to linear sorption, than for aromatic compounds. In particular, the sorption isotherms of methyl tert.-butyl ether (MTBE) and TeCM were almost linear (n ¼ 0.9e1) over the investigated concentration range, which was not observed for any other sorbate within this work. All sorption experiments were performed at least twice with good reproducibility; thus, these observations may indicate particular sorption mechanisms for these compounds. Overall, the following discussions on ppLFER development are based on a large consistent data set for sorption of diverse compounds by MWNCTs covering wide sorbate concentration ranges, which was not available before.

Material. Log Kd/a values experimentally determined and calculated by the ppLFER are shown in Fig. S1. Sorption by MWCNTs could accurately be calculated using the ppLFER (R2 ¼ 0.96) and scattering around the 1:1 prediction line was generally small, which shows that the ppLFER approach covers the relevant interactions well. In order to investigate the contribution of specific and nonspecific interactions to overall sorption, log Kd/a values were plotted against sorbate descriptors representing non-specific interactions (i.e., L and E); and only a significant correlation between log Kd/a and L was observed, which indicates a minor contribution of E. Fig. 2 shows that sorption of alkanes was generally similar in terms of sorption strength; however, sorption of cyclic alkanes and iso-hexane was slightly lower compared to their linear homologues. Sorption of C6 alkanes decreased following the order: n-hexane > cyclo-hexane > isohexane. This decrease in sorption is interesting as ppLFER descriptors for n-hexane and iso-hexane suggest similar sorption. Thus, it can be concluded that in addition to nonspecific interactions other factors may need to be considered for sorption of alkanes by MWCNTs. The ratio of sorption coefficients for linear and cyclic alkanes (Kn/Kc) can be used as an indicator for the dominant sorption mode (i.e., adsorption vs. absorption) (Endo et al., 2008b; Goss, 2004). Kn/Kc ratios for C6, C7, and C8 alkanes were 1.15, 1.09, and 0.99, respectively, showing that i) adsorption is the dominant sorption mode by MWCNTs and ii) steric effects, such as size exclusion effects can be neglected since Kn/Kc ratios for sorption of the three alkane pairs are w1 (Endo et al., 2009b). Furthermore, Fig. 2 shows that Kd/a of alkanes was generally lower than Kd/a of any other compounds with similar values for L and that the difference in Kd/a between alkanes and other compounds are more than one order of magnitude, with only one exception (TeCM). This difference in sorption strength can be attributed to specific interactions since alkanes generally can only undergo non-specific interactions. Thus, the contribution of specific interactions to overall sorption was calculated for compounds other than alkanes as: Dlog K ¼ log Kd=a  c  lL  eE

3.2. Interpretation of direct sorbate-MWCNTs interactions The derived ppLFER phase descriptors for log Kd/a (direct sorbate-MWCNTs interactions) are given in the Supplementary

Fig. 1 e Sorption isotherms of 34 probe compounds used in this study. Sorbate abbreviations are given in Table S1.

Fig. 2 e Correlation of log Kd/a and L descriptors of (C) alkanes and (B) non-alkane sorbates indicating the contribution of specific interaction to overall sorption.


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Fig. 3 e Comparison between calculated and measured log Kd values for sorption by MWCNTs at 10L2 (A) and 10L4 (B) of sorbates aqueous solubility. Solid lines represent 1:1 fits, and dashed lines indicate 0.3 log unit deviations from measured values. R2: regression coefficient; SE: standard error of estimates; RMSE: root mean squared error; N: number of data points.

Dlog K was then correlated to sorbate descriptors representing specific interactions S and B, while A was excluded from this analysis since the probe compound set included only few strong H-bond donors. When considering all compounds, no clear relationship was obtained (as shown in Fig. S2). Conversely, when considering only compounds with a low H-bond basicity (B < 0.2), the relationship between Dlog K and S improved (R2 ¼ 0.87). S may thus be a good indicator for specific interactions other than H-bonding, e.g., pep-electron donoreacceptor interactions, which are commonly assigned to be responsible for the strong interaction between CNM and hydrophobic organic compounds (Pan and Xing, 2008). In conclusion, the contribution of specific interactions to overall sorption by MWCNTs cannot be assigned to a single sorbate descriptor.


Comparison with literature data

The sorption data obtained in this study were compared with the data in the previous studies where ppLFER that were derived only for aromatic compounds (Apul et al., 2013; Xia et al., 2010). To this end, log Kd/w values were calculated for sorption by MWCNTs at concentrations of 102 and 104 of the sorbates aqueous solubility (Ci,sat) using the Freundlich parameters obtained above. These concentration levels were chosen in accordance to previous reports. The resulting log Kd/ w values were then fitted to Eq. (2). log Kd/w values obtained from the Freundlich isotherms (which are derived from experimental data) and those calculated by ppLFER for both concentration levels are compared in Fig. 3. For 25 out of 34 probe sorbates at the higher concentration level, the deviation between ppLFER calculated and experimentally derived log Kd/ w was below 0.3 log units, which shows the adequately good fit of the ppLFER model. At the lower concentration level, the scattering around the 1:1 prediction line slightly decreased, and 27 out of 34 compounds were within the 0.3 log unit deviation range. The outliers could not be assigned to a certain compound class. The scattering is relatively large compared to a typical range observed when ppLFER is used for homogeneous phases (e.g., polymers) (Endo et al., 2011a,b; Sprunger et al., 2007), which suggests heterogeneous sorption by MWCNTs. Sorption linearity of some probe sorbates was

much higher than that of the rest of the probe sorbate set (e.g., MTBE), which corroborates this interpretation. The ppLFER phase descriptors for MWCNTs are shown in Table 1. Statistical details of the regression analyses are given in the Supplementary Material Tables S7eS12. The v phase descriptor was the largest positive descriptor with v ¼ 3.91 and 4.83 for high and low concentration levels, respectively. This is qualitatively in agreement with previous publications (Apul et al., 2013; Xia et al., 2010), whose phase descriptors are also shown in Table 1. To ensure comparability between the ppLFER from this study with previous reports, the ranges of solute descriptors used for ppLFER development are shown in Fig. S3. The b phase descriptor for MWCNTs was negatively correlated with sorption (Table 1), which indicates that the Hbond donating capability of MWCNTs to the probe compounds is lower than that of water (Xia et al., 2010). This is generally plausible since there are in principle no potential H-bond donating functional groups on the sorbent surface. Comparing b descriptors of pristine and surface modified MWCNTs (e.g., hydroxyl- or carboxyl-MWCNTs) should yield further information on the H-bond donoreacceptor ability of MWNCTs, but goes beyond the scope of this study. As pointed out by Apul et al., a discrimination between H-bond and peH-bond by ppLFER is not possible because the b phase descriptors may include interactions between H-bond donating functionalities of sorbates and p electrons on MWCNTs surface. As mentioned above, Apul et al. (2013) did not take the eEterm into account for ppLFER development. It was previously concluded that hydrophobicity and non-specific interactions most significantly contribute to sorption by MWCNTs (Apul et al., 2013; Xia et al., 2010). However, the eE-term by definition incorporates non-specific interactions (Nguyen et al., 2005) (i.e., excess molar refraction), which involves induction of dipoles within the solute (Abraham et al., 2004, 1999). A comprehensive discussion of the contribution of individual interactions may thus be difficult without taking all descriptors into account. Re-calculating the ppLFER given by Apul et al. taking the eE-term into account indicates that the significance of the contribution of eE was concentration dependent (as shown in the Supplementary material). The contribution of eE was insignificant for infinite dilution, while an e coefficient of 1.20 was calculated to significantly (p < 0.05)


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Table 1 e ppLFER for sorption by MWCNTs developed in the present study and obtained from previous reports. e log Kd=a;106 SE log Kd=w;102 SE log Kd=w;102 (Apul et al.)b SE log Kd=w;104 SE log Kd=w (Xia et al.)c

0.59 0.59 0.37 0.35 e 0.43 0.33 0.04

s 2.34 0.59 0.26 0.39 0.67 0.47 0.46 0.38 1.75

a 3.90 0.67 0.93 0.41 1.31 0.56 0.79 0.40 0.37

b 3.23 0.71 3.53 0.50 2.86 1.22 3.66 0.48 2.78

v l ¼ 0.98 0.17 3.91 0.40 4.41 0.70 4.83 0.39 4.18








0.35 0.40 3.81 0.78 0.10 0.39 1.33










For log Kd/a lL is used as descriptor instead of vV. b Taken from Apul et al. (2013). Note that KN d,10 refers to infinite dilution conditions at an average of 0.2% of the sorbate aqueous solubility. c Taken from Xia et al. (2010). Kd values were determined at an average of 104 of the sorbates aqueous solubility. N: number of compounds. SE: standard errors of coefficients.

contribute in the ppLFER at a concentration level of 102 Ci,sat (as shown in the Supplementary Material). From the discussion above it becomes apparent that the significance of all descriptors should be evaluated for a comprehensive discussion of the relevant molecular interactions. Internal cross validation (leave-many-out; as described in Gramatica, 2007) of ppLFER derived at concentrations of 102, 103, and 104 of the sorbates aqueous solubility was performed. The details of this validation are given in the Supplementary material. In brief, the probe compound set was ranked by decreasing log Kd/w values (Zhao et al., 2014). Then, nine sorbates were selected for internal validation of a ppLFER derived by the remaining 26 sorbates. The crossvalidated correlation coefficients Q2LMO-CV > 0.90 indicate the robustness and predictivity of the sorption models derived here. However, low Q2LMO-CV alone may not be sufficient to indicate the robustness and predictive power of a model (Gramatica, 2007); therefore, the ppLFER derived here were further validated externally using literature data by a mutual comparison (as performed by Endo et al., 2009a). Fig. 4A compares the measured log Kd/w values of this study at 102 Ci,sat predicted using the ppLFER from Apul et al. (2013). The deviation between the predicted and measured log Kd/w values of aliphatic compounds was significantly smaller for the ppLFER developed here (R2 for aliphatic compounds of 0.91 using the ppLFER from this study compared to 0.58 using the ppLFER by Apul et al., 2013). Additionally, most data points were located below the 1:1 prediction line indicating an underestimation of the distribution coefficients by ppLFER from the literature. The comparison between log Kd/w collected by Apul et al. and predictions by the ppLFER calibrated with experimental log Kd/w values measured in this study is shown in Fig. 4B. Log Kd/w of most sorbates used by Apul et al. could be predicted well with our ppLFER (R2 ¼ 0.81). The ppLFER developed here could generally predict literature values with higher precision at this concentration level, as indicated by the lower linear regression parameters. Furthermore, this comparison was extended to a lower concentration level of 103 Ci,sat. This concentration was chosen since an average of 0.2% of the probe sorbate solubility was used by Apul et al. to develop a ppLFER at infinite dilution conditions (Apul et al., 2013). Fig. 4CeD shows that the ppLFER presented here predicts literature data with higher precision than vice versa. At this concentration level previous models

clearly tend to underestimate sorption by MWCNTs by around one log unit. Considering only aliphatic compounds the higher precision of the ppLFER from this work (R2 ¼ 0.85) compared to the ppLFER from Apul et al. (R2 ¼ 0.28) is more pronounce than at the high concentration level. Scattering around the 1:1 prediction line in Fig. 4D shows that almost 50% of the compounds used by Apul et al. could be predicted by the ppLFER from this work with a deviation of 0.3 log units or lower. The decrease in concentration generally resulted in lower precision in prediction of sorption (Apul et al., 2013). However, for the data set presented here, this trend was less pronounced, which shows the robustness of the experimental isotherm data used for ppLFER development. The results of internal and external validation of the ppLFER presented here therefore provides a substantial improvement of the prediction of log Kd/w for sorption by MWCNTs, especially at low concentrations typically found in the environment.

3.4. Comparison of sorption properties of MWCNTs with activated carbon In the literature, CNM have been proposed as superior sorbents; thus, sorption by CNM is often compared to that of other carbonaceous materials, such as activated carbon (AC) (Kim and Agnihotri, 2008; Ji et al., 2009; Zhang et al., 2010). This is mainly due to the fact that with increasing production rate and consequently decreasing cost, may become at least competitive to traditionally used AC, for example, in water treatment processes (Mauter and Elimelech, 2008; Upadhyayula et al., 2009). Differences in sorption affinity between CNM and AC were often assigned to molecular sieving effects from pore-filling mechanisms of CNM and AC (Ji et al., 2009; Zhang et al., 2010). ppLFER should be able to qualitatively and quantitatively display the observed difference in interaction strength that were mainly assigned to non-specific van-der-Waals and specific electron donor-acceptor (EDA) interactions (Zhang et al., 2010). The ppLFER derived here were thus compared to previously reported ppLFER for sorption by AC. Shih and Gschwend used a ppLFER to investigate the contribution of individual interactions to overall sorption of organic compounds by granular AC at various levels of sorbate saturation (Shih and Gschwend, 2009). For reason of comparability, only the ppLFER derived at a concentration level of 102 Ci,sat is discussed here:

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Fig. 4 e Comparison of the predicted and measured log Kd/w. (A) Prediction by the ppLFER from Apul et al. (2013) vs log Kd=w;10L2 measured in this study. (B) Prediction by the ppLFER calibrated in this study vs. log Kd=w;10L2 collected by Apul et al. (2013). (C) Prediction by the ppLFER from Apul et al. (2013) vs log Kd=w;10L3 measured in this study. (D) Prediction by the ppLFER calibrated in this study vs. log Kd=w;10L3 collected by Apul et al. (2013). Solid lines represent the 1:1 agreement, and dashed lines indicate 0.3 log unit deviations. R2: regression coefficient; RMSE: root mean squared error; N [ number of data points.

log KAC=w;102 ¼0:33E0:12S0:52A4:52Bþ4:59V þ0:79  R2 ¼ 0:97; N ¼ 14


It is apparent that sorption of organic compounds by activated carbon is influenced by similar interactions since the descriptors in ppLFER Eq. (6) and those derived in the present study (Table 1) are qualitatively comparable. ppLFER descriptors for both AC and MWCNTs substantially differ from those for example reported for sorption by natural organic matter (Nguyen et al., 2005). However, there are quantitative differences in phase descriptors observable for AC and MWCNTs (i.e., larger v and smaller b for AC than for MWCNTs). These differences were found to be statistically insignificant due to large standard errors. The ppLFER currently available for sorption by AC and MWCNTs are therefore not able to explain the aforementioned differences observed in sorption between the two sorbents. Possible reasons of the relative large standard errors include: the number of probe sorbates is still small for both AC and MWCNTs; heterogeneity of the sorbent site is very high; and ppLFER does not take the geometry of the sorbate molecule and the carbon surface into account. ppLFERs were initially derived to describe the partitioning of compounds between two bulk

phase; even though they were later proposed for a number of adsorbents (Goss and Schwarzenbach, 2001) and have successfully been used to describe sorption processes by typical adsorbents (Apul et al., 2013; Xia et al., 2010; Shih and Gschwend, 2009).


Comparison of ppLFER with opLFER

Distribution coefficients are often predicted based on opLFER with aqueous solubility or hydrophobicity parameters of sorbates, such as the octanolewater partitioning constant (Kow) (Schwarzenbach et al., 2003). Such correlations have to be considered with caution since for example Kow refers to absorption between two bulk phases, whereas sorption by MWCNTs is thought to be an adsorption process. In addition, the prediction of sorption of organic compounds by various sorbents may not be accurate by Kow (Pan and Xing, 2008; Chen et al., 2007), especially at environmentally relevant low concentrations (Endo et al., 2009a). To emphasize the advantage of ppLFER for an accurate prediction of sorption, experimental distribution coefficients at both concentration levels were related to distribution data calculated by an opLFER using log Kow. Fig. S5 shows that compared to ppLFER the prediction


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of sorption data by opLFER was less accurate (R2 ¼ 0.78 at 102 Ci,sat and 0.64 at 104 Ci,sat). Especially in the low concentration range the ability of ppLFER to predict sorption coefficients clearly exceeds that of Kow correlation. In order to ensure that the quality of sorption prediction by ppLFER is not due to the higher degree of freedom, Akaike’s Information Criterion (AIC) was calculated for opLFER and ppLFER at high and at low concentration levels (for details of AIC calculation see Hu¨ffer et al., 2013b). AIC values were 164 and 175 for ppLFER and 157 and 150 for opLFER at high and low concentrations, respectively. Therefore, the improved prediction of sorption using ppLFER was not due to overparameterization. The derived linear regression in Fig. S4 shows that Kow underestimated measured Kd/w values by one order of magnitude at high concentration, while discrepancies increase up to almost three orders of magnitude at low concentrations. Kah et al. (2011) established a log Kd/welog Kow correlation for sorption of 13 PAHs by the same kind of MWCNTs used in this study and obtained a fairly good linear regression (R2 ¼ 0.90) with a slope of 0.36 and y-intercept of 5.72 (Kah et al., 2011). The slopes of the log Kd/welog Kow correlations obtained here are clearly higher and closer to 1, and are well comparable to the relationships derived by Xia et al. for sorption of aromatic compounds covering various polarities (Xia et al., 2010). As previously pointed out by Endo et al., care must be taken when extrapolating from the commonly stated class-specific agreement of Kow correlation to class-comprehensive conclusions since a clear discrimination of the contribution of individual interaction properties requires quantitative indicators (Endo et al., 2009a). It must be stressed at this point that a consistent correlation of Kd/w values to Kow is further complicated by the fact that Kow values reported in literature vary to some extent. Overall, the comparison between opLFER with Kow and ppLFER emphasizes the advantage of ppLFER for a comprehensive discussion of sorption properties of MWCNTs.



Sorption properties of multi-walled carbon nanotubes were characterized using poly-parameter linear free-energy relationships (ppLFER):  A clear discrimination between specific and non-specific interaction and their contribution to overall direct sorbate-MWCNTs interaction could be shown using ppLFER.  The probe sorbate set used in this study for ppLFER calibration resulted in a significant improvement in prediction of distribution coefficients.  The ppLFER approach allows the characterization of sorption properties compared to commonly used log Kd/ welog Kow correlations.  MWCNTs showed similar sorption properties in term of ppLFER phase descriptors compared to activated carbon. Based on their surface chemistry (if one considers that MWCNTs are highly aggregated and thereby reduce their effective surface area), this implies that MWCNTs have similar sorption properties as activated carbon.

Acknowledgement This work was financed by the German Research Foundation (SCHM 1372/10-1). The comments by the anonymous reviewers significantly improved our manuscript.

Appendix A. Supplementary data Supplementary data related to this article can be found at http://dx.doi.org/10.1016/j.watres.2014.04.029.


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Prediction of sorption of aromatic and aliphatic organic compounds by carbon nanotubes using poly-parameter linear free-energy relationships.

The accurate prediction of distribution coefficients of organic compounds from water to carbon-based nanomaterials (CNM) is of major importance for th...
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