CHAPTER 6: RESULTS
6.5 Viscosity of F-ILs
6.5.2 The QSPR model
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had an AARD% of 4.85% and 21.89% for ln(η) and η, respectively. According to the results, both can predict the viscosity of F-ILs more accurately compared with previous models.
All previous models were developed for few types of ionic liquids, except the model proposed by Gharagheizi et al. [91]. They used a dataset consisted of 1034 unique data points of which 724 were for F-ILs. By using only the data of F-ILs, that model showed an AARD% of 6.7%
and 59.7% for ln(η) and η which the latter is a very large deviation and calls the applicability of this model for F-ILs into question. As a result, their model has lower accuracy compared with models presented in this thesis.
The comparison between models proposed and previous models is shown in Table 6.31, at the end of next section. In addition, information for the entire dataset, as well as the values of the functional groups of the ILs for both developed models are available in the supplementary CD.
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Table 6.30. The results show that average absolute relative deviation (AARD%) of the model is 3.07% overall data points, 2.91% for the “training” set, and 3.61% for the “test”set. In addition, R2 is 0.983 for all data points, 0.985 for the “training” set and 0.980 for the “test”
set.
Table 6.29:Parameters of the QSPR model in equation (6.6).
No. Chemical structure Descriptions ai bi ci
Intercept 1.241
1 GGI5Cat topological charge index of order 5 -2.728 2 RDF035mCat Radial Distribution Function - 3.5 /
weighted by atomic masses 0.0648
3 R1v+Cat R maximal autocorrelation of lag 1 / weighted by atomic van der Waals volumes
-48.288 6.168
4 R3v+Cat R maximal autocorrelation of lag 3 / weighted by atomic van der Waals volumes
162.761 -58.990
5 B05[N-O]Cat presence of [N-(A)4-O] (value 0 or 1) 1.539 6 Mor32uAn 3D-MoRSE - signal 32 / unweighted -0.522 7 E3uAn 3rd component accessibility directional
WHIM index / unweighted 2.368
8 MSDCat mean square distance index (Balaban) -5.676
9 EEig02xCat Eigenvalue 02 from edge adj. matrix
weighted by edge degrees 0.227
10 EEig03xCat Eigenvalue 03 from edge adj. matrix
weighted by edge degrees -0.191
11 ESpm01dCat Spectral moment 01 from edge adj.
matrix weighted by dipole moments -0.614 0.3123 12 E3uCat 3rd component accessibility directional
WHIM index / unweighted 0.996
13 E3vCat 3rd component accessibility directional WHIM index / weighted by atomic van der Waals volumes
-3.220
14 RBFCat rotatable bond fraction 1.694
15 nR06Cat number of 6-membered rings 0.0389
16 PW2Cat path/walk 2 - Randic shape index 1.532
17 piPC07Cat molecular multiple path count of order 07 0.0189
18 EEig02dCat Eigenvalue 02 from edge adj. matrix
weighted by dipole moments -0.1547
19 L/BwCat length-to-breadth ratio by WHIM 0.0026
20 HATS2mCat leverage-weighted autocorrelation of lag
2 / weighted by atomic masses -0.5904
21 nBMAn number of multiple bonds -0.0178
22 Mor17pAn 3D-MoRSE - signal 17 / weighted by
atomic polarizabilities 0.6370
Table 6.30: The statistical error parameters for the ln(η) in equation (6.6).
Statistical Parameter
124 training set
R2 0.985
Average absolute relative deviation 2.91
Standard deviation error 0.15
Root mean square error 0.15
No. of data points 667
test set
R2 0.980
Average absolute relative deviation 3.61
Standard deviation error 0.20
Root mean square error 0.20
No. of data points 196
total
R2 0.983
Average absolute relative deviation 3.07
Standard deviation error 0.17
Root mean square error 0.17
No. of data points 863
Figure 6.30: Predicted versus experimental values of ln(η) (––– diagonal line).
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Figure 6.31: Relative deviation of predicted ln(η) from experimental data.
As illustrated in Figure 6.33, almost all data points are near the diagonal which indicates the robustness of the QSPR model for the calculation/prediction of the viscosity of F-ILs. In previous section it was explained that most of the data points with large deviations are for very low viscosity values or for temperatures over 330K, or possible impurity of ionic liquids [163].
To compare this model with the previous GC model more precisely, the linear scale values of viscosity are shown in Figure 6.32. In addition, the AARD% of linear scale data is 12.1%
which is close to AARD% of GC model (13.31)%. As discussed in section 4.2.2, the QSPR models have fewer parameters than the GC model of similar accuracy and it can be seen obviously for this model; but the number of parameters is relatively high compared with the QSPR models of other physico-chemical properties of compounds. The common QSPR models have less than 15 parameters and consequently, the larger models are not well accepted by cheminformatics researchers. As a result, further QSPR modeling of this property was ignored; because the model developed had 22 parameters for the refined dataset.
So the model would be larger if the complete dataset (1160 data points including unreliable data points) was used.
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Figure 6.32: Predicted versus experimental values of η in linear scale by the QSPR model (––– diagonal line).
Table 6.31: Summary of different models for predicting the ln(η) of ILs.
Model Model Type and parameters NILs Ndata AARD% Comments
Abbott [81] Correlation 11 n.a. 122 10 ILs contained fluorine atom.
Bandres et al.
[82]
Correlation 8 n.a. 4.5 7 ILs contained fluorine atom.
Gardas and Coutinho [83]
GC, 13 parameters, r 30 500 7.78* Only 19 ILs contained fluorine atom.
*AARD% is in linear scale.
Gardas and Coutinho [86]
GC, 12 parameters 25 482 7.50* Only 16 ILs contained fluorine atom.
*AARD% is in linear scale.
Tochigi and Yamomoto [89]
QSPR, 24 parameters 161 334 5.04 149 ILs contained fluorine atom.
Most of the ILs had just one data point.
Bini el al.
[90]
QSPR, 4 parameters. 33 66 n.a. Authors proposed two models for T = 293 K and T = 353 K.
Gharagheizi et al. [91]
GC, 47 parameters 443 1672 6.32 638 duplicated data points were used.
By removing the duplicates, the AD% was risen to 7.1%.
0 500 1000 1500 2000 2500 3000
0 500 1000 1500 2000 2500 3000
ηcalc/ cP
ηexp/ cP
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Model Model Type and parameters NILs Ndata AARD% Comments
724 data points were for F-ILs Valderrama
et al. [92]
ANN 58 327 n.a.
Billard et al.
[93]
ANN 99 99 10 The data were only at 298 K.
GC Model (1) GC, 35 parameters 85 863 3.23 The reliable data sources were used.
GC Model (2) GC, 36 parameters 332 1160 4.85 The entire database including unreliable data sources was used.
QSPR Model QSPR, 22 parameters 85 863 2.91 The reliable data sources were used.
6.6 γ∞ of solutes in ionic liquids