Article Estimating Equivalent Alkane Carbon Number Using Abraham Solute Parameters William E. Acree, Jr. 1 , Wei-Khiong Chong 2 , Andrew S.I.D. Lang 3, * 1 2 3 * and Hamed Mozafari 3 Department of Chemistry, University of North Texas, Denton, TX 76203, USA Advent Polytech Co., Ltd., Taipao City 61249, Taiwan Department of Computing & Mathematics, Oral Roberts University, Tulsa, OK 74136, USA Correspondence: alang@oru.edu Abstract: The use of equivalent alkane carbon numbers (EACN) to characterize oils is important in surfactant-oil-water (SOW) systems. However, the measurement of EACN values is non-trivial and thus it becomes desirable to predict EACN values from structure. In this work, we present a simple linear model that can be used to estimate the EACN value of oils with known Abraham solute parameters. We used linear regression with leave-one-out cross validation on a dataset of N = 80 oils with known Abraham solute parameters to derive a general model that can reliably estimate EACN values based upon the Abraham solute parameters: E (the measured liquid or gas molar refraction at 20 ◦ C minus that of a hypothetical alkane of identical volume), S (dipolarity/polarizability), A (hydrogen bond acidity), B (hydrogen bond basicity), and V (McGowan characteristic volume) with good accuracy within the chemical space studied (N = 80, R2 = 0.92, RMSE = 1.16, MAE = 0.90, p < 2.2 × 10−16 ). These parameters are consistent with those in other models found in the literature and are available for a wide range of compounds. Keywords: equivalent alkane carbon number (EACN); Abraham solute parameters; hydrophobicity; oils Citation: Acree, W.E., Jr.; Chong, W.-K.; Lang, A.S.I.D.; Mozafari, H. Estimating Equivalent Alkane Carbon Number Using Abraham Solute Parameters. Liquids 2022, 2, 318–326. https://doi.org/ 10.3390/liquids2040019 Academic Editor: Slobodan Žumer Received: 19 August 2022 Accepted: 26 September 2022 Published: 2 October 2022 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Copyright: © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 1. Introduction Considerable attention has been given in recent years to development of better surfactant-based microemulsions and foam systems for enhanced oil recovery in petroleum processes, for removal of oil from contaminated soil and industrial machinery surfaces, and for the solubilization of fragrances in water-based formulations. Many factors including the temperature, electrolyte concentration, and the hydrophobicities of both the surfactant and oil contribute to the overall efficiency of the extraction system. Experimental determination of the optimum set of conditions for a given surfactant-oil-water system is both expensive and very time-consuming. Fortunately, empirical equations have been proposed to describe how the various factors affect microemulsion formation. One such expression is based on the hydrophilic-lipophilic difference (HLD) framework [1,2]. Ionic surfactant: HLD = ln(S) − k · EACN + Cc − α · (T − Tref ) (1) Nonionic surfactant: HLD = b · S − K · EACN + Cc + CT · (T − Tref ) (2) where S is the salinity (not to be confused with Abraham’s S parameter) and the terms ln(S) and b · S take into account the electrolyte concentration (usually in grams per 100 mL) of the system, b is electrolyte and surfactant specific, EACN is the equivalent alkane carbon number of the oil phase, Cc represents the hydrophilicity of the surfactant, and the last two terms, α · (T − Tref ) and CT · (T − Tref ) are related to the temperature effect. The application of HLD in predicting the type and microemulsion phase behavior is described in greater detail elsewhere [1–3]. 4.0/). Liquids 2022, 2, 318–326. https://doi.org/10.3390/liquids2040019 https://www.mdpi.com/journal/liquids Liquids 2022, 2 319 Our interest in the current study is in developing a predictive method for the equivalent alkane carbon number (EACN), which for simple alkanes is numerically equal to the number of carbons (ACN), and for other liquids it is equal to the number of carbons of the n-alkane exhibiting a similar phase behavior in a reference surfactant-oil-water (SOW) system. EACNs can be determined by comparing the oil’s fish-tail-temperature (T*) in a reference SOW to standard calibration curves for n-alkanes [4]. The experimental determination of EACN values for novel oils may be time consuming and the ability to predict EACN values is advantageous. Bouton et al. [5] have developed a two-descriptor model based upon experimental data for 43 oils using the proprietary Molecular Operating Environment (MOE) software: EACN = −19.84 + 2.88 · average negative softness + 0.88 · KierA3 (3) where KierA3 is the third alpha modified shape index and “average negative softness”—which is related to polarizability. Lukowicz et al. [6] have developed a three-descriptor model based upon 70 oils using COSMO-RS σ-moments: EACN = −4.85 − 0.23 · M2 − 0.33 · Macc + 0.06 · M0 , (4) where M2 is molecular polarity, Macc is hydrogen bond basicity, and M0 is total molecular surface area. This extends previous work in this area [7]. Most recently, Delforce et al. [8] have developed both a graph machine model using SMILES codes and a neural network model using COSMO-RS-computed σ-moments based on reliable EACN values for 111 molecules. This work develops a model for EACN based upon experimental EACN values for 80 liquids using the five Abraham solute parameters E, S, A, B, and V which encode physicochemical properties related to those already found to be important-namely size and shape, polarizability, and hydrogen bond basicity, i.e., we propose the following model: EACN = c + e · E + s · S + a · A + b · B + v · V (5) where E is the solute excess molar refractivity-the measured liquid or gas molar refraction at 20 ◦ C minus that of a hypothetical alkane of identical volume-in units of (cm3 /mol)/10, S is the solute dipolarity/polarizability, A and B are the overall or summation hydrogen bond acidity and basicity, and V is the McGowan characteristic volume in units of (cm3 /mol)/100. 2. Materials and Methods Experimentally measured EACN values, collected by Aubry et al. [4,8], were combined with their experimentally determined Abraham solute parameters, primarily from the UFZ-LSER database [9], with the values for decylcyclohexane taken from a paper by Chung et al. [10], and the values for dodecylcyclohexane and bis(2-ethylhexyl) adipate new to this work (from an unpublished database of measured Abraham parameters original to Professor Abraham dated December 2020 shared with one of the authors before Professor Abraham’s passing on the 19 January 2021), see Table 1. A modeling dataset was created from these data by: 1. Using median EACN values for compounds with multiple experimental measurements. 2. Only keeping compounds with all 5 Abraham parameters available (measured, not predicted) [9]. This dataset of N = 86 compounds with EACN values and Abraham parameters is available under a CC0 license from figshare [11]. Modeling was performed using R v4.2.0 (R Core Team, Vienna, Austria) [12]. Liquids 2022, 2 320 Table 1. Measured EACN values with available Abraham Solute Parameters. Compound EACN E S A B V EACN Ref. 2.4 1.7 1.8 2.5 3.5 2.8 4.6 4.5 4.5 4.5 3.7 4.1 3.9 2.6 5.8 6.3 5.5 5.6 5.7 4.5 7.2 7.9 6.9 5.6 5.3 10.0 11.2 10.1 4.3 3.9 6.3 6.7 4.6 14.4 17.5 11.7 14.8 24.5 13.8 0.305 0.305 0.305 0.305 0.244 0.244 0.191 0.191 0.263 0.263 0.263 0.409 0.320 0.320 0.257 0.257 0.257 0.283 0.283 0.283 0.255 0.255 0.255 0.474 0.544 0.000 0.000 0.000 0.421 0.421 0.270 0.270 0.270 0.243 0.300 0.000 0.000 - 0.10 0.10 0.10 0.10 0.06 0.06 0.17 0.17 0.10 0.10 0.10 0.10 0.23 0.23 0.14 0.14 0.14 0.07 0.07 0.07 0.14 0.14 0.14 0.10 0.25 0.00 0.00 0.00 0.12 0.12 0.07 0.07 0.07 0.23 0.23 0.00 0.00 - 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 - 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.13 0.13 0.00 0.00 0.00 0.00 0.00 0.00 0.00 - 0.8454 0.8454 0.8454 0.8454 0.9863 0.9863 1.1272 1.1272 1.1272 1.1272 1.1272 1.1272 1.1272 1.1272 1.2681 1.2681 1.2681 1.2681 1.2681 1.2681 1.4090 1.4090 1.4090 1.4090 1.3004 1.5176 1.5176 1.5176 1.3004 1.3004 1.4090 1.4090 1.4090 2.2544 2.5362 1.7994 2.2221 - [13] [13] [14] [15] [13] [13] [13] [13] [13] [13] [16] [6] [16] [13] [13] [13] [16] [13] [13] [13] [13] [17] [16] [18] [18] [5,19] [6,20] [13] [6,20] [6,20] [6,20] [6,20] [6,20] [21] [16] [7] [7] [21] [22] −3.4 1.0 3.5 6.3 5.6 5.8 8.0 7.3 9.8 9.0 0.340 0.191 0.185 0.366 0.181 0.181 0.176 0.176 0.173 0.173 0.37 0.40 0.40 0.40 0.40 0.41 0.41 0.42 0.42 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.12 0.09 0.09 0.10 0.10 0.10 0.10 0.10 0.10 0.8472 1.3582 1.6400 1.7624 1.9218 1.9218 2.2036 2.2036 2.4854 2.4854 [18] [23] [18] [24] [18] [23] [18] [23] [18] [23] Branched and cyclic alkanes Cyclohexane Cyclohexane Cyclohexane Cyclohexane Methylcyclohexane Methylcyclohexane 1,4-Dimethylcyclohexane 1,4-Dimethylcyclohexane Ethylcyclohexane Ethylcyclohexane Ethylcyclohexane Cyclooctane 1,2-Dimethylcyclohexane 1,2-Dimethylcyclohexane Propylcyclohexane Propylcyclohexane Propylcyclohexane Isopropylcyclohexane Isopropylcyclohexane Isopropylcyclohexane Butylcyclohexane Butylcyclohexane Butylcyclohexane Cyclodecane cis-Decalin Myrcane Myrcane Myrcane Pinane Pinane p-Menthane p-Menthane p-Menthane Decylcyclohexane Dodecylcyclohexane Isododecane Hemisqualene Squalane Squalene Halogenated alkanes 1-Bromo-2-methylpropane 1-Chlorooctane 1-Chlorodecane 1,10-Dichlorodecane 1-Chlorododecane 1-Chlorododecane 1-Chlorotetradecane 1-Chlorotetradecane 1-Chlorohexadecane 1-Chlorohexadecane Liquids 2022, 2 321 Table 1. Cont. Compound EACN E S A B V EACN Ref. −1.2 −3.1 −4.1 0.8 −0.8 0.6 −0.5 0.4 −1.4 −3.2 3.9 1.5 −1.8 −2.4 5.5 0.1 0.4 −3.3 3.6 3.4 3.1 3.6 2.9 2.0 2.3 2.0 2.0 1.6 1.9 1.4 1.5 0.8 1.3 0.1 −0.3 −1.3 8.1 2.0 3.9 4.0 10.3 6.6 7.3 5.7 6.2 6.0 14.4 7.8 0.395 0.515 0.501 0.391 0.391 0.347 0.347 0.360 0.360 0.495 0.094 0.460 0.155 0.613 0.093 0.143 0.600 0.438 0.438 0.350 0.350 0.492 0.492 0.515 0.515 0.501 0.501 0.522 0.522 0.526 0.526 0.590 0.590 0.607 0.607 0.089 0.133 0.579 0.757 0.757 0.720 0.720 0.579 0.079 0.571 0.28 0.38 0.46 0.18 0.18 0.22 0.22 0.20 0.20 0.32 0.08 0.24 0.22 0.52 0.08 0.22 0.51 0.20 0.20 0.12 0.12 0.22 0.22 0.19 0.19 0.31 0.31 0.29 0.29 0.25 0.25 0.31 0.31 0.49 0.49 0.08 0.22 0.48 0.20 0.20 0.15 0.15 0.47 0.08 0.47 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.09 0.00 0.00 0.09 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.09 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.09 0.12 0.16 0.10 0.10 0.10 0.10 0.10 0.10 0.11 0.07 0.10 0.10 0.16 0.07 0.10 0.15 0.14 0.14 0.07 0.07 0.14 0.14 0.15 0.15 0.23 0.23 0.22 0.22 0.23 0.23 0.20 0.20 0.19 0.19 0.07 0.10 0.15 0.22 0.22 0.25 0.25 0.15 0.07 0.15 0.8024 0.7594 0.7594 0.9433 0.9433 0.9433 0.9433 0.9433 0.9433 0.7919 1.1928 1.0842 1.1498 0.9982 1.4746 1.4316 1.2800 1.2574 1.2574 1.3660 1.3660 1.2574 1.2574 1.2574 1.2574 1.3230 1.3230 1.3230 1.3230 1.3230 1.3230 1.3230 1.3230 1.2800 1.2800 1.7564 1.7134 1.8436 1.8533 1.8533 1.9189 1.9189 2.1254 2.6018 2.4072 [13] [13] [13] [13] [13] [13] [13] [13] [13] [13] [18] [18] [18] [18] [18] [18] [18] [18] [6,20] [6,20] [19] [6,20] [6,20] [6,20] [6,20] [6,20] [6,20] [6,20] [6,20] [6,20] [6,20] [6,20] [6,20] [6,20] [6,20] [6,20] [18] [18] [18] [16] [6,20] [20] [6,20] [6,20] [6,20] [25] [18] [25] Alkenes, terpenes, alkynes and aromatics Cyclohexene 1,3-Cyclohexadiene 1,4-Cyclohexadiene 1-Methyl-1-cyclohexene 1-Methyl-1-cyclohexene 4-Methyl-1-cyclohexene 4-Methyl-1-cyclohexene 3-Methyl-1-cyclohexene 3-Methyl-1-cyclohexene 2,5-Norbornadiene 1-Octene cis-Cycloctene 1-Octyne p-Xylene 1-Decene 1-Decyne Butylbenzene Phenyl-1-butyne alpha-Pinene alpha-Pinene p-Menth-2-ene p-Menth-2-ene Delta-3-carene Delta-3-carene beta-Pinene beta-Pinene Limonene Limonene gamma-Terpinene gamma-Terpinene alpha-Terpinene alpha-Terpinene Terpinolene Terpinolene p-Cymene p-Cymene 1-Dodecene 1-Dodecyne 1-Tetradecyne Octylbenzene 2,6,10-Trimethylundecane-2,6-diene Longifolene Longifolene Caryophyllene Caryophyllene Decylbenzene 1-Octadecene Dodecylbenzene Liquids 2022, 2 322 Table 1. Cont. Compound EACN E S A B V EACN Ref. 2.2 2.4 3.3 3.2 –3.4 −1.7 4.2 1.9 1.7 −2.1 −0.6 −1.3 1.8 2.3 2.2 6.2 −0.6 0.3 3.8 5.0 6.2 8.0 5.2 7.2 8.1 10.3 6.8 7.2 7.3 6.8 9.3 7.3 7.1 9.7 12.2 13.8 13.0 15.7 18.5 21.2 23.9 21.2 −0.063 0.000 0.000 0.000 0.108 0.162 0.000 0.108 0.156 0.101 0.013 0.013 0.013 0.000 0.103 0.132 0.002 0.002 0.000 −0.010 0.000 −0.062 −0.062 0.000 −0.010 −0.040 - 0.17 0.25 0.25 0.25 0.68 0.90 0.25 0.51 0.68 0.90 0.68 0.58 0.58 0.58 0.25 0.68 0.90 0.58 0.56 0.58 0.06 0.25 0.53 0.53 0.58 1.10 1.25 - 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 - 0.57 0.45 0.45 0.45 0.51 0.36 0.45 0.51 0.36 0.51 0.45 0.45 0.45 0.45 0.51 0.36 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.45 1.13 1.28 - 1.0127 1.2945 1.2945 1.2945 1.2515 1.2500 1.5763 1.6350 1.5333 1.5320 1.6742 1.8738 1.8738 1.8738 1.8581 1.8151 1.8132 2.1556 2.1556 2.4374 2.4374 2.4217 2.5783 2.5783 2.7192 3.3572 8.3631 - [26] [22] [25] [27] [22] [22] [22] [27] [27] [22] [22] [22] [17] [20] [18] [22] [22] [22] [6] [6] [6] [22] [6] [6] [6] [22] [6] [6] [25] [6] [20] [6] [28] [6] [6] [6] [25] [5] [5] [5] [5] [5] −1.5 −1.6 −1.7 −3.1 0.4 −0.2 −0.1 0.8 0.322 0.380 0.674 0.154 0.154 0.154 0.154 0.61 0.33 0.86 0.49 0.49 0.49 0.49 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.62 0.76 0.57 0.45 0.45 0.45 0.45 1.4247 1.3591 1.3390 1.5490 1.5490 1.5490 1.5490 [21] [21] [21] [21] [29] [29] [29] [29] Ethers, esters, nitriles and ketones Diisopropyl ether Dibutyl ether Dibutyl ether Dibutyl ether 2-Octanone Octanenitrile Dipentyl ether C3-O-C4-O-C3 C4-O-C2-O-C4 2-Decanone Decanenitrile 2-Undecanone Ethyl decanoate Ethyl decanoate Ethyl decanoate Dihexyl ether 2-Dodecanone Dodecanenitrile Ethyl dodecanoate Decyl butyrate Hexyl octanoate Diheptyl ether Ethyl myristate Butyl dodecanoate Octyl octanoate Dioctyl ether Myristyl propionate Isopropyl myristate Isopropyl myristate Ethyl palmitate Hexyl dodecanoate Ethyl oleate Ethyl oleate Bis(2-ethylhexyl) adipate Tricaprilin Tricaprin Tricaprin Trilaurin Trimyristin Tripalmitin Tristearin Triolein Fragrances, acrylates and miscellaneous Menthone Eucalyptol Rose oxide D-Carvone Hexyl methacrylate Hexyl methacrylate Hexyl methacrylate Hexyl methacrylate Liquids 2022, 2 323 Table 1. Cont. Compound EACN E S A B V EACN Ref. 0.7 −0.2 1.5 0.2 −0.4 −0.1 −0.2 −0.6 −0.9 −1.3 −1.7 −1.9 −1.1 3.5 1.0 0.154 0.154 0.154 0.154 0.154 0.243 0.198 0.368 0.331 0.340 0.892 - 0.49 0.49 0.49 0.49 0.49 0.65 0.59 0.65 0.65 1.53 0.78 - 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 - 0.45 0.45 0.45 0.45 0.45 0.54 0.64 0.68 0.65 0.97 0.76 - 1.5490 1.5490 1.5490 1.5490 1.5490 1.7652 1.8308 1.7878 1.7878 1.9218 1.7614 - [29] [29] [29] [29] [29] [6,20] [21,22] [21,22] [21,22] [21] [21] [17] [21] [21] [21] Fragrances, acrylates and miscellaneous Hexyl methacrylate Hexyl methacrylate Hexyl methacrylate Hexyl methacrylate Hexyl methacrylate Menthyl acetate Citronellyl acetate Geranyl acetate Linalyl acetate alpha-Damascone Methyl dihydrojasmonate beta-Ionone Ethylene brassylate Methyl cedryl ether Ambrettolide 3. Results The standard Abraham solute descriptor-based model is represented by Equation (6), where c is the intercept, E, S, A, B, and V are the Abraham solute descriptors, and e, s, a, b, v are their coefficients obtained by linear regression: EACN = c + e · E + s · S + a · A + b · B + v · V (6) When using all the data, we found a moderate correlation (R2 = 0.61) between S and B. Removing S-parameter outliers bis(2-ethylhexyl) adipate, tristearin, and methyl dihydrojasmonate (S > 1) resulted in a dataset where all pairwise correlations had coefficients of determination lower than 0.50 and the coefficients of determination of each parameter against all others was lower than 0.80. Removing S-parameter outliers provides a greater reliability to the model, but may limit its application to a smaller chemical space. Performing linear regression with leave-out-out (LOO) cross-validation showed that dodecylcyclohexane, decylcyclohexane, and octyl octanoate were clear outliers. Removing the three outliers, and again using LOO linear regression, we found that EACN can be estimated with similar accuracy (LOO measures) using Abraham solute parameters (N = 80, R2 = 0.92, RMSE = 1.16, MAE = 0.90, p < 2.2 × 10−16 ) as compared to previous models [5–8], at least within the chemical space represented in the study: EACN = −2.16 − 2.08 · E − 9.51 · S − 50.91 · A − 5.41 · B + 6.83 · V (7) Analyzing the EACN estimates for each compound type, we see that the model performs the best for alkenes, terpenes, alkynes, and aromatics (N = 31, ME = 0.37, MAE = 0.57, RMSE = 0.76). Good performance is seen for the four other types: branched and cyclic alkanes (N = 16, ME = −0.81, MAE = 0.85, RMSE = 1.11); halogenated alkanes (N = 6, ME = 0.99, MAE = 0.99, RMSE = 1.16); fragrances, acrylates, and miscellaneous (N = 9, ME = −0.16, MAE = 0.94, RMSE = 1.18); and ethers, esters, nitriles, and ketones (N = 18, ME = −0.17, MAE = 1.16, RMSE = 1.32)—with consistent over-prediction for halogenated alkanes and consistent under-prediction for branched and cyclic alkanes, see Figure 1. Liquids Liquids 2022, 2022, 22, FOR PEER REVIEW 324 7 Figure 1. Measured EACN EACN values values colored colored by Figure 1. Estimated Estimated vs. vs. Measured by type: type: alkenes, alkenes, terpenes, terpenes, alkynes, alkynes, and and aromatics (dark cyclic alkanes (orange); ethers, esters, nitriles, and ketones (red); aromatics (darkblue); blue);branched branchedand and cyclic alkanes (orange); ethers, esters, nitriles, and ketones (red); fragrances, acrylates, and miscellaneous (light blue); and halogenated alkanes (green). fragrances, acrylates, and miscellaneous (light blue); and halogenated alkanes (green). 4. Discussion Discussion 4. We have We have demonstrated demonstrated that that EACN EACN can can be be estimated estimated using using the the standard standard Abraham Abraham solute parameter model, see Equation (7). The first four parameters all have solute parameter model, see Equation (7). The first four parameters all have negative negative coefficients where EEisisthethe solute excess molar refractivity-the measured liquidliquid or gasor molar coefficients where solute excess molar refractivity-the measured gas ◦ C minus that of a hypothetical alkane of identical volume-in units of refraction at 20 molar refraction at 20 °C minus that of a hypothetical alkane of identical volume-in units (cm3 /mol)/10, solute dipolarity/polarizability, A and B are the overall or summaof (cm3/mol)/10,S is S the is the solute dipolarity/polarizability, A and B are the overall or tion hydrogen bond acidity and basicity, and V is the McGowan characteristic volume in summation 3hydrogen bond acidity and basicity, and V is the McGowan characteristic units of (cm /mol)/100. These results align with previous results [5–8], using different volume in units of (cm3/mol)/100. These results align with previous results [5–8], using parameter systems, but showing similar accuracy and that EACN has contributions from different parameter systems, but showing similar accuracy and that EACN has shape (size and branching) [5–8], polarity/polarizability [5–8], and hydrogen bond basiccontributions from shape (size and branching) [5–8], polarity/polarizability [5–8], and ity [6–8]. Our addition of hydrogen bond acidity, represented by the A descriptor, leads to hydrogen bond basicity [6–8]. Our addition of hydrogen bond acidity, represented by the superior estimation of EACN values for alkynes something not seen in previous models. A descriptor, leads to superior estimation of EACN values for alkynes something not seen We began with a dataset of N = 86 oils with both measured EACN values and meain previous models. sured Abraham solute descriptors. During modeling we removed six compounds: bis(2We began with a dataset of N = 86 oils with both measured EACN values and ethylhexyl) adipate, tristearin, methyl dihydrojasmonate, decylcyclohexane, dodecylcyclomeasured Abraham solute descriptors. During modeling we removed six compounds: hexane, and octyl octanoate. bis(2-ethylhexyl) tristearin, methyl because dihydrojasmonate, decylcyclohexane, The first threeadipate, compounds were removed they had large S-values which dodecylcyclohexane, and octyl octanoate. resulted in an artificially high collinearity with the B parameter. The second set of three The firstwere three compounds werefrom removed they had largeanalysis. S-valuesEven which compounds removed as outliers a firstbecause LOO cross-validation so, resulted in an artificially high collinearity with the B parameter. The second set of three Equation (7)-predicted EACN values for these compounds are generally of the right order, compounds werevalues removed as outliers from[11]. a first LOO cross-validation analysis. so, see the predicted in the open dataset The utility of Equation (7) can alsoEven be seen Equation (7)-predicted EACN values for these compounds are generally of the right order, by using it to predict EACN values of compounds that have measured EACN values but see the predicted values in the open dataset [11]. The utility of Equation (7) can also be Liquids 2022, 2 325 that do not have measured Abraham solute parameters. Using predicted Abraham solute parameters [9], we predicted the EACN values of several of these compounds without measured Abraham solute parameters from Table 1, see Table 2. For the compounds listed in Table 2, Equation (7) performs relatively well, with statistics similar to those found for the estimated EACN results above, specifically: N = 11, ME = 0.17, MAE = 1.13, RMSE = 1.61. Table 2. Equation (7)-predicted EACN values using predicted Abraham solute parameters. Compound 1-Tetradecyne 2,6,10-Trimethylundecane-2,6-diene Decyl butyrate Butyl dodecanoate Myristyl propionate Diheptyl ether Hexyl dodecanoate Ethyl oleate Ethyl oleate Methyl cedryl ether Ambrettolide alpha-Damascone EACN E S A B V Predicted EACN 3.9 10.3 5.0 7.2 6.8 8.0 9.3 7.1 7.3 3.5 1.0 −1.3 0.150 0.350 0.000 0.010 0.050 0.000 0.010 0.130 0.130 0.650 0.540 0.680 0.24 0.23 0.56 0.56 0.56 0.18 0.56 0.72 0.72 0.23 0.68 0.71 0.05 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.12 0.34 0.55 0.52 0.53 0.46 0.52 0.68 0.68 0.22 0.76 0.54 1.9952 2.1361 2.1556 2.4374 2.5783 2.1399 2.7192 2.9580 2.9580 2.0959 2.2858 1.7614 5.7 7.7 4.3 6.3 7.2 8.3 8.3 7.2 7.2 7.4 1.8 −1.2 The most recent paper by Delforce et al. [8] notes that the measured EACN of 2.2 for diisopropyl ether reported previously [26] is an outier for their model. Our model estimates the EACN value of diisopropyl ether to be 0.2 which is in line with their newly measured EACN value of 0.6. Our approach provides a useful tool for estimating equivalent alkane carbon numbers as Abraham solute parameters are available for a significant number of compounds [9,10]. While a general model is presented, models for specific families of compounds can be easily created using our open dataset [11]. We also note that the estimated EACN values of individual hydrocarbons from Equation (7) will allow estimation of EACN values of heavy hydrocarbon mixtures, EACNmix , using the mathematical expression proposed by Cayias et al. [30] and Cash et al. [31]: EACNmix = N ∑i=1 xi EACNi (8) where xi and EACNi denote the mole fraction and numerical EACN value of the individual hydrocarbon component i, respectively. Future research directions include measuring the EACN values of more diverse compounds, especially those with known non-zero A-parameter values. Author Contributions: Conceptualization, W.-K.C.; methodology, W.E.A.J., A.S.I.D.L. and H.M.; data collection and curation, A.S.I.D.L. and H.M.; writing—original draft preparation, W.E.A.J., W.-K.C., A.S.I.D.L. and H.M.; writing—review and editing, W.E.A.J., W.-K.C., A.S.I.D.L. and H.M. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Data Availability Statement: Data used in this study is available from figshare under a CC0 license [8]. Conflicts of Interest: The authors declare no conflict of interest. References 1. 2. Salager, J.L.; Morgan, J.C.; Schechter, R.S.; Wade, W.H.; Spe-Aime, M.; Vasquez, E. Optimum formulation of surfactant/water/oil systems for minimum interfacial tension or phase behavior. Soc. Pet. Eng. AIME J. 1979, 19, 107–115. [CrossRef] Ghayour, A.; Acosta, E. Characterizing the oil-like and surfactant-like behavior of polar oils. Langmuir 2019, 35, 15038–15050. [CrossRef] [PubMed] Liquids 2022, 2 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 326 Virin Kittithammavong, V.; Charoensaeng, A.; Khaodhiar, S. A Normalized HLD (HLDN ) tool for optimal salt-concentration prediction of microemulsions. Appl. Sci. 2021, 11, 9151. [CrossRef] Aubry, J.-M.; Ontiveros, J.F.; Salager, J.L.; Nardello-Rataj, V. Use of the normalized hydrophilic-lipophilic-deviation (HLDN) equation for determining the equivalent alkane carbon number (EACN) of oils and the preferred alkane carbon number (PACN) of nonionic surfactants by the fish-tail method (FTM). Adv. Colloid Interface Sci. 2020, 276, 102099. [CrossRef] Bouton, F.; Durand, M.; Nardello-Rataj, V.; Borosy, A.P.; Quellet, C.; Aubry, J.M. A QSPR model for the prediction of the “fish-tail” temperature of C i E4/water/polar hydrocarbon oil systems. Langmuir 2010, 26, 7962–7970. [CrossRef] Lukowicz, T.; Illous, E.; Nardello-Rataj, V.; Aubry, J.M. Prediction of the equivalent alkane carbon number (EACN) of aprotic polar oils with COSMO-RS sigma-moments. Colloids Surf. A Physicochem. Eng. Asp. 2018, 536, 53–59. [CrossRef] Lukowicz, T.; Benazzouz, A.; Nardello-Rataj, V.; Aubry, J.-M. Rationalization and Prediction of the Equivalent Alkane Carbon Number (EACN) of Polar Hydrocarbon Oils with COSMO-RS σ-Moments. Langmuir 2015, 31, 11220–11226. [CrossRef] Delforce, L.; Duprat, F.; Ploix, J.-L.; Ontiveros, J.F.; Goussard, V.; Nardello-Rataj, V.; Aubry, J.-M. Fast Prediction of the Equivalent Alkane Carbon Number Using Graph Machines and Neural Networks. ACS Omega 2022, in press. Ulrich, N.; Endo, S.; Brown, T.N.; Watanabe, N.; Bronner, G.; Abraham, M.H.; Goss, K.-U. UFZ-LSER Database v 3.2.1 [Internet], Leipzig, Germany, Helmholtz Centre for Environmental Research-UFZ. 2017. Available online: http://www.ufz.de/lserd (accessed on 31 December 2021). Chung, Y.; Vermeire, F.H.; Wu, H.; Walker, P.J.; Abraham, M.H.; Green, W.H. Group Contribution and Machine Learning Approaches to Predict Abraham Solute Parameters, Solvation Free Energy, and Solvation Enthalpy. J. Chem. Inf. Modeling 2022, 62, 433–446. [CrossRef] Acree, W.E.; Chong, W.; Lang, A.S.I.D.; Mozafari, H. Dataset: EACN and Abraham Parameter Values. Figshare. Dataset 2022. [CrossRef] R Core Team. R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria. 2022. Available online: https://www.R-project.org/ (accessed on 31 December 2021). Bouton, F. Influence of Terpenes and Terpenoids on the Phase Behavior of Micro-and Macro-Emulsions. Ph.D. Thesis, University of Lille, Lille, France, 2010. Kahlweit, M.; Strey, R.; Busse, G. Effect of alcohols on the phase behavior of microemulsions. J. Phys. Chem. 1991, 95, 5344–5352. [CrossRef] Burauer, S.; Sottmann, T.; Strey, R. Nonionic microemulsions with cyclic oils-Oil penetration, efficiency and monomeric solubility. Tenside Surfactants Deterg. 2000, 37, 8–16. Queste, S.; Salager, J.L.; Strey, R.; Aubry, J.M. The EACN scale for oil classification revisited thanks to fish diagrams. J. Colloid Interface Sci. 2007, 312, 98–107. [CrossRef] [PubMed] Lukowicz, T. Synergistic Solubilisation of Fragrances in Binary Surfactant Systems and Prediction of Their EACN Value with COSMO-RS. Ph.D. Thesis, Université Lille, Lille, France, 2015. Tchakalova, V.; Testard, F.; Wong, K.; Parker, A.; Benczédi, D.; Zemb, T. Solubilization and interfacial curvature in microemulsions: I. Interfacial expansion and co-extraction of oil. Colloids Surf. A Physicochem. Eng. Asp. 2008, 331, 31–39. [CrossRef] Bouton, F.; Durand, M.; Nardello-Rataj, V.; Serry, M.; Aubry, J.M. Classification of terpene oils using the fish diagrams and the Equivalent Alkane Carbon (EACN) scale. Colloids Surf. A Physicochem. Eng. Asp. 2009, 338, 142–147. [CrossRef] Ontiveros, J.F.; Pierlot, C.; Catté, M.; Molinier, V.; Pizzino, A.; Salager, J.L.; Aubry, J.M. Classification of ester oils according to their Equivalent Alkane Carbon Number (EACN) and asymmetry of fish diagrams of C10E4/ester oil/water systems. J. Colloid Interface Sci. 2013, 403, 67–76. [CrossRef] Gradzielski, M.; Langevin, D.; Sottmann, T.; Strey, R. Droplet microemulsions at the emulsification boundary: The influence of the surfactant structure on the elastic constants of the amphiphilic film. J. Chem. Phys. 1997, 106, 8232–8238. [CrossRef] Tchakalova, V.; Testard, F.; Wong, K.; Parker, A.; Benczédi, D.; Zemb, T. Solubilization and interfacial curvature in microemulsions: II. Surfactant efficiency and PIT. Colloids Surf. A Physicochem. Eng. Asp. 2008, 331, 40–47. [CrossRef] Israelachvili, J.N.; Mitchell, D.J.; Ninham, B.W. Theory of self-assembly of hydrocarbon amphiphiles into micelles and bilayers. J. Chem. Soc. Faraday Trans. 2 Mol. Chem. Phys. 1976, 72, 1525–1568. [CrossRef] Deen, G.R.; Pedersen, J.S. Phase behavior and microstructure of C12E5 nonionic microemulsions with chlorinated oils. Langmuir 2008, 24, 3111–3117. [CrossRef] Engelskirchen, S.; Elsner, N.; Sottmann, T.; Strey, R. Triacylglycerol microemulsions stabilized by alkyl ethoxylate surfactants—A basic study: Phase behavior, interfacial tension and microstructure. J. Colloid Interface Sci. 2007, 312, 114–121. [CrossRef] [PubMed] Wormuth, K.R.; Kaler, E.W. Microemulsifying polar oils. J. Phys. Chem. 1989, 93, 4855–4861. [CrossRef] Tanford, C. The Hydrophobic Effect: Formation of Micelles and Biological Membranes, 2nd ed.; J. Wiley: Hoboken, NJ, USA, 1980. Kahlweit, M.; Busse, G.; Faulhaber, B.; Eibl, H. Preparing nontoxic microemulsions. Langmuir 1995, 11, 4185–4187. [CrossRef] van Os, N.M.; Haak, J.R.; Rupert, L.A.M. Physico-Chemical Properties of Selected Anionic, Cationic and Nonionic Surfactants; Elsevier: Amsterdam, The Netherlands, 2012. Cayias, J.L.; Schechter, R.S.; Wade, W.H. Modeling crude oils for low interfacial tension. Soc. Pet. Eng. J. 1976, 16, 351–357. [CrossRef] Cash, L.; Cayias, J.L.; Fournier, G.; Macallister, D.; Schares, T.; Schechter, R.S.; Wade, W.H. The application of low interfacial tension scaling rules to binary hydrocarbon mixtures. J. Colloid Interface Sci. 1976, 59, 39–44. [CrossRef]