Concentration-Dependent Polyparameter Linear Free Energy Relationships to Predict Organic

Concentration-dependent polyparameter linear free energy relationships to predict organic compound sorption on carbon nanotubes

Qing Zhao1,2, Kun Yang2,3, Wei Li2,4,and Baoshan Xing2,★

1 Institute of Applied Ecology, Chinese Academy of Sciences, Shenyang 110016,China

2Stockbridge School of Agriculture, University of Massachusetts, Amherst, MA 01003, USA

3Department of Environmental Science, Zhejiang University, Hangzhou 310058, China

4Laboratory for Earth Surface Processes, College of Environmental Sciences, Peking University, Beijing 100871, China

★e-mail:

1. Details on the data collection

Table S1. Physical/Chemical parameter values of compounds that were used to develop the correlations.

Sorbents / Compound / Cs* (mg/L) / R** / V** / π** / α** / β**
MWCNT15 / aniline / 34160 / 0.955 / 0.8162 / 0.96 / 0.26 / 0.41
4-chloroaniline / 2755 / 1.06 / 0.9386 / 1.13 / 0.3 / 0.31
2-nitroaniline / 1260 / 1.18 / 0.9904 / 1.37 / 0.3 / 0.36
3-nitroaniline / 900 / 1.2 / 0.9904 / 1.71 / 0.4 / 0.35
4-nitroaniline / 600 / 1.22 / 0.9904 / 1.93 / 0.46 / 0.35
phenol / 80190 / 0.805 / 0.7751 / 0.89 / 0.6 / 0.3
2-chlorophenol / 28500 / 0.853 / 0.8975 / 0.88 / 0.32 / 0.31
4-chlorophenol / 26300 / 0.915 / 0.8975 / 1.08 / 0.67 / 0.2
2,4-dichlorophenol / 4600 / 0.96 / 1.0199 / 0.84 / 0.53 / 0.19
2-nitrophenol / 2100 / 1.015 / 0.9493 / 1.05 / 0.05 / 0.37
3-nitrophenol / 14000 / 1.05 / 0.9493 / 1.57 / 0.79 / 0.23
4-nitrophenol / 16000 / 1.07 / 0.9493 / 1.72 / 0.82 / 0.26
4-methylphenol / 23000 / 0.82 / 0.916 / 0.87 / 0.57 / 0.31
naphthalene / 31.7 / 1.34 / 1.0854 / 0.92 / 0 / 0.2
phenanthrene / 1.29 / 2.055 / 1.4544 / 1.29 / 0 / 0.29
pyrene / 0.135 / 2.06 / 1.5846 / 1.29 / 0 / 0.29
P-MWCNTs
G-MWCNTs
COOH-MWCNTs
OH-MWCNTs / nitrobenzene / 1936 / 0.871 / 0.8906 / 1.11 / 0 / 0.2
1,2-dinitrobenzene / 133 / 1.17 / 1.0648 / 1.7 / 0 / 0.28
1,3-dinitrobenzene / 574.9 / 1.15 / 1.0648 / 1.6 / 0 / 0.38
1,4-dinitrobenzene / 69 / 0.93 / 0.9474 / 1.92 / 0 / 0.47
1,3,5-trinitrobenzene / 278 / 1.43 / 1.239 / 2.42 / 0 / 0.1
naphthalene / 31.7 / 1.34 / 1.0854 / 0.92 / 0 / 0.2
4-nitroaniline / 600 / 1.22 / 0.9904 / 1.93 / 0.46 / 0.35
4-nitrophenol / 16000 / 1.07 / 0.9493 / 1.72 / 0.82 / 0.26
4-chloroaniline / 2755 / 1.06 / 0.9386 / 1.13 / 0.3 / 0.31
4-chlorophenol / 26300 / 0.915 / 0.8975 / 1.08 / 0.67 / 0.2

* Cs: aqueous solubility, obtained from refs1-3. ** [R, V, π, α, β]: solvation descriptors of the probe compounds, provided by the Absolv program in the ADME Suite software (Advanced Chemistry Development).

1. Details on the concentration-dependent pp-LFER modeling

2.1 Goodness-of- fit and robustness of pp-LFER in different solute concentration

Table S2 shows that the pp-LFER approach can be applied in a wide range of concentrations (from -5 to 0 of log Ce/Cs, where Ce represents the equilibrium concentration and Cs is the solubility of the compounds) in MWCNT15, as shown by the values of correlation coefficient (R2 > 0.8), the Root Mean Square Error of Calibration (RMSEC < 0.5), the cross-validated correlation coefficient (> 0.7) and cross-validated root mean square error (RMSECV < 1).

Table S2. R2, RMSEC, and RMSECV values of the application of pp-LFER approach under various concentrationsforMWCNT15.

log Ce/Cs / pp-LFER equation / R2 / RMSEC / / RMSECV
-5.00 / log ki = 2.98-0.56Ri+1.88πi–3.39αi-10.9βi+1.13Vi / 0.820 / 0.448 / 0.705 / 0.779
-4.78 / log ki = 2.04-0.56Ri+1.76πi–3.13αi-9.97βi+1.80Vi / 0.864 / 0.398 / 0.766 / 0.833
-4.57 / log ki = 1.16-0.55Ri+1.65πi–2.89αi-9.10βi+2.41Vi / 0.899 / 0.352 / 0.831 / 0.713
-4.35 / log ki = 0.35-0.54Ri+1.55πi–2.67αi-8.29βi+2.96Vi / 0.926 / 0.311 / 0.846 / 0.650
-4.13 / log ki =-0.39-0.53Ri+1.46πi–2.48αi-7.54βi+3.45Vi / 0.946 / 0.275 / 0.890 / 0.563
-3.91 / log ki =-1.07-0.51Ri+1.37πi–2.32αi-6.85βi+3.88Vi / 0.960 / 0.242 / 0.922 / 0.486
-3.670 / log ki =-1.69-0.48Ri+1.29πi–2.18αi-6.22βi+4.26Vi / 0.970 / 0.215 / 0.945 / 0.418
-3.48 / log ki =-2.25-0.46Ri+1.21πi–2.06αi-5.65βi+4.58Vi / 0.978 / 0.192 / 0.961 / 0.360
-3.26 / log ki =-2.74-0.43Ri+1.14πi–1.96αi-5.14βi+4.85Vi / 0.983 / 0.173 / 0.972 / 0.313
-3.04 / log ki =-3.18-0.40Ri+1.08πi–1.89αi-4.68βi+5.07Vi / 0.986 / 0.158 / 0.979 / 0.277
-2.83 / log ki =-3.56-0.36Ri+1.03πi–1.83αi-4.28βi+5.24Vi / 0.988 / 0.147 / 0.983 / 0.251
-2.61 / log ki =-3.89-0.32Ri+0.98πi–1.80αi-3.93βi+5.36Vi / 0.990 / 0.140 / 0.986 / 0.235
-2.39 / log ki =-4.16-0.28Ri+0.94πi–1.79αi-3.64βi+5.44Vi / 0.991 / 0.136 / 0.987 / 0.227
-2.17 / log ki =-4.39-0.24Ri+0.90πi–1.79αi-3.41βi+5.47Vi / 0.991 / 0.134 / 0.988 / 0.227
-1.96 / log ki =-4.57-0.20Ri+0.87πi–1.82αi-3.23βi+5.47Vi / 0.991 / 0.134 / 0.987 / 0.231
-1.74 / log ki =-4.70-0.16Ri+0.84πi–1.87αi-3.10βi+5.43Vi / 0.991 / 0.136 / 0.987 / 0.238
-1.52 / log ki =-4.79-0.11Ri+0.83πi–1.93αi-3.02βi+5.35Vi / 0.991 / 0.138 / 0.985 / 0.254
-1.30 / log ki =-4.84-0.07Ri+0.81πi–2.01αi-3.00βi+5.24Vi / 0.991 / 0.142 / 0.984 / 0.323
-1.09 / log ki =-4.85-0.02Ri+0.80πi–2.10αi-3.03βi+5.10Vi / 0.990 / 0.146 / 0.984 / 0.268
-0.870 / log ki =-4.83+0.02Ri+0.80πi–2.21αi-3.12βi+4.93Vi / 0.990 / 0.150 / 0.982 / 0.291
-0.652 / log ki =-4.77+0.07Ri+0.80πi–2.34αi-3.26βi+4.74Vi / 0.989 / 0.156 / 0.981 / 0.288
-0.435 / log ki =-4.69+0.11Ri+0.81πi–2.47αi-3.45βi+4.53Vi / 0.988 / 0.162 / 0.979 / 0.306
-0.217 / log ki =-4.59+0.16Ri+0.82πi–2.61αi-3.71βi+4.30Vi / 0.987 / 0.169 / 0.977 / 0.322
0 / log ki =-4.47+0.21Ri+0.84πi–2.76αi-4.06βi+4.07Vi / 0.986 / 0.177 / 0.976 / 0.328

2.2Polynomial regressions between pp-LFER parameters and log Ce/Cs

The Incremental Order Polynomial Regression results are presented in Table S3. From Table S3, we selectedquadraticregression for all pp-LFERs with log Ce/Cs (P normality testing > 0.05, P constant variance testing > 0.05 and Pincre < 0.001).

Table S3 Incremental Order Polynomial Regression Results between pp-LFERs and log Ce/Cs.

pp-parameter / Polynomial Order / P normality testing / P constant variance testing / Fincre / Pincre**
c / 0 / 0.000405 / 0.0130 / —* / —
1 / 0.0252 / 0.934 / 86.4 / <0.001
2 / 0.504 / 0.419 / 2649 / <0.001
3 / 0.498 / 0.670 / 2423 / <0.001
r / 0 / 0.0492 / 0.0130 / — / —
1 / 0.0456 / 0.0636 / 729 / <0.001
2 / 0.299 / 0.561 / 6101 / <0.001
3 / 0.446 / 0.126 / 243191 / <0.001
p / 0 / 0.00116 / 0.0130 / — / —
1 / 0.0195 / 0.856 / 123 / <0.001
2 / 0.391 / 0.709 / 39934 / <0.001
3 / 0.0707 / 0.166 / 4908475 / <0.001
a / 0 / 0.0163 / 0.0130 / — / —
1 / 0.0237 / 0.869 / 2.83 / 0.106
2 / 0.449 / 0.228 / 2212 / <0.001
3 / 0.348 / 0.518 / 86987 / <0.001
b / 0 / 0.000621 / 0.0130 / — / —
1 / 0.0140 / 0.777 / 65.3 / <0.001
2 / 0.159 / 0.635 / 105994 / <0.001
3 / 0.079 / 0.526 / 26.0 / <0.001
v / 0 / 0.000867 / 0.0130 / — / —
1 / 0.0277 / 0.749 / 15.3 / <0.001
2 / 0.502 / 0.555 / 1824 / <0.001
3 / 0.387 / 0.545 / 2922 / <0.001

* —: cannot calculate.

**Pincre: The incremental P value is the change in probability of being wrong that the added independent variable order improves the prediction of the dependent variable. It is the value calculated from Fincre.

2.3Splitting data for a training and validation set

In order to obtain appropriate validation, we split the data into the training and the external validation set (Table S4). First, we sorted 16 compounds based on decreasing maximum log ki value. Second, the data were split into three sets:pyrene and aniline which have the highest and the lowest log kimax value were grouped into the validation set V2 to represent the compounds that are not within the range of the training set. The rest 14 compounds were split into two sets: training set (T) and the validation set (V1). In order to ensure V1set isevenly distributed within the range of log kimax valuein training set, we utilized the following pattern of splitting: T-T-T-V1-T-T-T-V1T-T-T-V1-T-T.

Table S4 Training and validation set for modeling

Compounds / log kimax / set
pyrene / 4.00 / V2
phenanthrene / 3.72 / T
naphthalene / 2.94 / T
4-nitroaniline / 1.76 / T
2-nitroaniline / 1.64 / V1
2-nitrophenol / 1.54 / T
2,4-dichlorophenol / 1.53 / T
3-nitrophenol / 1.35 / T
4-nitrophenol / 1.15 / V1
3-nitroaniline / 1.02 / T
4-chloroaniline / 0.987 / T
2-chlorophenol / 0.715 / T
4-chlorophenol / 0.572 / V1
4-methylphenol / 0.370 / T
phenol / -0.393 / T
aniline / -0.710 / V2

2.4Internal validation, statistical measures of goodness-of-fit and robustness of new model

Four parameters were used in this section. R2 and RMSEC were used as the two measures of the goodness of fit. and RMSECV were used to measure the robustness of the new model on the presence/absence of particular probe compound in the training set T. The results were shown in Table S5.The R2 value (>0.967) and RMSEC (<0.201) suggest the good fit of new model. The cross-validated coefficient (>0.949) and the cross-validated root mean square error RMSECV (<0.428) reveal the robustness of the predictive model.

Table S5 goodness-of-fit and robustness of new model for training set (T)

Compounds / n / R2 / RMSEC / / RMSECV
phenanthrene / 24 / 1.000 / 0.035 / 0.983 / 0.387
naphthalene / 24 / 1.000 / 0.084 / 0.999 / 0.428
4-nitroaniline / 24 / 0.997 / 0.183 / 0.992 / 0.369
2-nitrophenol / 24 / 0.997 / 0.094 / 0.997 / 0.195
2,4-dichlorophenol / 24 / 0.998 / 0.083 / 0.993 / 0.222
3-nitrophenol / 24 / 0.995 / 0.164 / 0.981 / 0.362
3-nitroaniline / 24 / 0.998 / 0.183 / 0.996 / 0.265
4-chloroaniline / 24 / 0.985 / 0.140 / 0.976 / 0.166
2-chlorophenol / 24 / 0.967 / 0.201 / 0.949 / 0.266
4-methylphenol / 24 / 0.996 / 0.138 / 0.984 / 0.265
phenol / 24 / 0.997 / 0.062 / 0.971 / 0.398

2.5 External validation and measures of predictive ability

We used external validation to test the predictability of the model by using data of both validation set V1 (within the range of log kimax valuein training set) and validation set V2(out of the range). The value of R2 (>0.938) and RMSEC (<0.380) suggest satisfactory predicting powerfor the external validation compounds (Table S6).

Table S6 goodness-of-fit and robustness of new model for validation set (V1 and V2)

Compounds / n / R2 / RMSEC
2-nitroaniline / 24 / 0.994 / 0.244
4-nitrophenol / 24 / 0.968 / 0.192
4-chlorophenol / 24 / 0.924 / 0.205
pyrene / 24 / 0.999 / 0.169
aniline / 24 / 0.938 / 0.380

3Model performance

Figure S1 Sorption isotherms of chemical compounds on G-MWCNT. Open squares (□) obtained from original reference; Dash lines (---) predicted based on the newpp-LFERs model.

Figure S2 Sorption isotherms of chemical compounds on P-MWCNT. Open squares (□) obtained from original reference; Dash lines (---) predicted based on the newpp-LFERs model.

Figure S3 Sorption isotherms of chemical compounds on COOH-MWCNT. Open squares (□) obtained from original reference; Dash lines (---) predicted based on the newpp-LFERs model.

Figure S4 Sorption isotherms of chemical compounds on OH-MWCNT. Open squares (□) obtained from original reference; Dash lines (---) predicted based on the newpp-LFERs model.

4Relative contribution of molecular-interface interactions

Table S7. Measured and predicted logki values for EDCs and pharmaceuticals sorption on MWCNT15.

Compounds / Measured
log ki * / Ce/Cs / R** / π** / α** / β** / V** / Predicted
log ki
Norfloxacin / 4.14 / 0.01 / 1.98 / 2.43 / 0.73 / 1.64 / 2.472 / 4.15
Norfloxacin / 3.35 / 0.1 / 1.98 / 2.43 / 0.73 / 1.64 / 2.472 / 3.11
Bisphenol A / 4.11 / 0.01 / 1.59 / 1.56 / 1 / 0.79 / 1.864 / 2.38
17 alpha-ethinyl estradiol / 5.82 / 0.01 / 2.07 / 2.43 / 0.9 / 1.02 / 2.395 / 5.40
Oxytetracycline / 2.01 / 0.01 / 3.73 / 3.83 / 2.04 / 3.06 / 3.158 / 1.82
Carbamazepine / 1.31 / 0.01 / 2.15 / 2.11 / 0.53 / 1.1 / 1.811 / 2.28
Ofloxacin / 3.38 / 0.01 / 2.26 / 2.58 / 0.57 / 2.05 / 2.504 / 3.35
Ofloxacin / 2.57 / 0.1 / 2.26 / 2.58 / 0.57 / 2.05 / 2.504 / 2.48

* Data were obtained from ref. 4-6. ** [R, V, π, α, β]: solvation descriptors of the probe compounds, provided by the Absolv program in the ADME Suite software (Advanced Chemistry Development).

4.1 Relative contribution of molecular-interface interactions

The sorption energy can be described as follows:

Gsorb = -RTlnki

where R is the universal gas constant, 8.314 × 10-3 KJ/(mol·K); T (K) is the absolute temperature. Combining the equation with the new model, thus we can obtain following equations:

Gsorb=-RT(ƒ1 + ƒ2Ri + ƒ3πi + ƒ4αi+ ƒ5βi+ ƒ6Vi)ln10 = Gc+GR+Gπ+Gα+Gβ+GV

where Gc (-RTƒ1ln10) is the sorption energy caused by unknown interactions; GR (-RTƒ2Riln10) represents the energy caused by the molecular force of long-pair electrons; Gπ(-RTƒ3πiln10) represents the energy contributed by solute dipolarity/polarizability; Gα(-RTƒ4αiln10) is the sorption energy from hydrogen-bond acidity; Gβ (-RTƒ5βiln10) represents the sorption energy contributed by hydrogen-bond basicity; GV(-RTƒ6Viln10) represents the sorption energy from London dispersion. The predicted sorption energy of Guanine on MWCNT15 is shown in Fig. 5c. We can concludethat the main interactions that control Guanine arethe hydrophobic interactions and π-π stacking interactions, which is consistent with several previous studies7-9. At low equilibrium concentrations (log Ce/Cs < -4.725, that is Ce < 0.000753 mg/L), the relative contribution of interactions followed the order: π-π stacking interactions > hydrophobic interactions > the molecular force of long-pair electrons interaction > hydrogen-bond acidity interaction > hydrogen-bond basicity interaction. At equilibrium concentration equals to 0.000753 mg/L, the interactions followed the order: π-π stacking interactions = hydrophobic interactions > the molecular force of long-pair electrons interaction > hydrogen-bond acidity interaction > hydrogen-bond basicity interaction; while at Ce > 0.000753 mg/L, hydrophobic interaction became the most dominating interaction.

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