Abraham Solvation Parameter Model: Calculation of L Solute Descriptors for Large C₁₁ to C₄₂ Methylated Alkanes from Measured Gas–Liquid Chromatographic Retention Data

Abstract

Abraham model L solute descriptors have been determined for 149 additional C₁₁ to C₄₂ monomethylated and polymethylated alkanes based on published Kovat’s retention indices based upon gas–liquid chromatographic measurements. The calculated solute descriptors, in combination with previously published Abraham model correlations, can be used to predict a number of very important chemical and thermodynamic properties including partition coefficients, molar solubility ratios, gas–liquid chromatographic and HPLC retention data, infinite dilution activity coefficients, molar enthalpies of solvation, standard molar vaporization and sublimation at 298 K, vapor pressures, and limiting diffusion coefficients. The predictive computations are illustrated by estimating both the standard molar enthalpies of sublimation and the enthalpies of solvation in benzene for the monomethylated and polymethylated alkanes considered in the current study.

1. Introduction

Scientists and engineers in both academia and the industrial manufacturing sector must rely upon empirical and semi-theoretical models to predict the thermodynamic and physical properties required in process design calculations. Even with today’s modern instrumentation it is not feasible to experimentally determine the properties for the more than 60 million known chemical compounds [1]. Chemical manufacturing processes rarely contain only a single compound. Experimental measurements become even more challenging when one takes into account the number of possible binary, ternary and higher-order multicomponent mixtures that can be prepared from existing compounds. The number of possible combinations increases annually as new compounds are synthesized, found and identified.

Over the last 50 years numerous predictive methods have been developed based upon either quantitative structure–property relationships (QSPRs) or group contribution concepts. QSPR methods [2,3,4,5,6,7,8] identify mathematical relationships between the desired property that one wishes to calculate and other physical properties or from compound descriptor values that can be derived from molecular structure and/or quantum mechanical considerations. For some published QSPR studies [2,6,8] more than 1000 different descriptors have been considered before narrowing the descriptor set down to those yielding the desired predictive accuracy. Group contribution methods [9,10,11,12,13,14,15,16], on the other hand, fragment the given molecule into atoms or functional groups. A numerical value is then assigned to each atom or fragment group. In the simplest case the desired property would be calculated as the summation of the product of the number of occurrences each fragment group appears in the molecule times its respective numerical group value. Naturally the method would be limited to those molecules having known functional group values.

The predictive method that we have been using to predict thermodynamic and physical properties is based upon the Abraham solvation parameter model [17,18,19,20] which defines solute transfer between two immiscible (or partly miscible) phases in terms of a linear free energy relationship (LFER). The first LFER:

Solute Property = e₁ × E + s₁ × S + a₁ × A + b₁ × B + v₁ × V + c₁

(1)

describes solute transfer between two condensed phases, while the second LFER:

Solute Property = e₂ × E + s₂ × S + a₂ × A + b₂ × B + l₂ × L + c₂

(2)

describes solute transfer into a condensed phase from the gas phase. Specific properties that have been successfully described include partition coefficients [20,21,22], molar solubility ratios [19,23,24], aquatic toxicities [25,26,27], nasal pungencies [28], gas–liquid chromatographic and HPLC retention data [18,29,30,31,32,33], Draize scores and eye irritation thresholds [34,35], human and rat intestinal adsorption data [36,37], human skin permeability [38,39], infinite dilution activity coefficients [40,41], molar enthalpies of solvation [42,43,44], standard molar vaporization [45] and sublimation [46] at 298 K, vapor pressures [47], and limiting diffusion coefficients [48,49].

Unlike many of the QSPRs that have been proposed in the published chemical and engineering literature, Equations (1) and (2) are based upon a fundamental understanding of how molecules interact in solution. The first five terms on the right-hand side of both Equations (1) and (2) represent a different type of molecular interaction that is described by the product of a solute property (E, S, A, B, V and L) times its complimentary solvent or process property (e₁, s₁, a₁, b₁, v₁, c₁, e₂, s₂, a₂, b₂, l₂ and c₂). The uppercase alphabetical characters in both Abraham model correlations are called solute descriptors, and are defined in the following manner: A and B represent the respective overall hydrogen-bond donating and accepting abilities of the dissolved solute; E denotes the given solute’s excess molar refraction referenced to that of a linear alkane having a comparable molecular size; L refers to the logarithm of the solute’s gas-to-hexadecane partition coefficient determined at 298.15 K; S corresponds to a combination of the electrostatic polarity and polarizability of the solute; and V is the solute’s McGowan molecular volume calculated from known sizes of the constituent atoms and chemical bond numbers. The numerical values of the lowercase solvent or process property are determined by a least-squares analysis that involves curve-fitting the measured property for a series of solutes with known descriptor values in a given solvent (or for a given process) in accordance with Equations (1) and (2) of the Abraham model. The calculated numerical values of solvent/process equation coefficients depend upon the organic solvent or process under consideration. In other words, the equation coefficients that describe the enthalpy of solvation of organic solutes dissolved in benzene are numerically different than the values that describe the enthalpy of solvation of organic solutes in dimethyl sulfoxide. The Abraham model is described in greater detail elsewhere [17,18,50,51,52].

One major advantage that the Abraham model offers over most predictive QSPRs is that the same numerical values of the solute descriptors are used in every Abraham model correlation, irrespective of the chemical property being predicted. This feature avoids having to calculate a new set of solute descriptors every time that one wishes to predict a different chemical property. A common set of solute descriptors for every correlation also permits one to directly compare the solubilizing properties of different organic solvents and two-phase partitioning systems through Principal Component Analysis, the Euclidean distance formula and other computational methods. Such comparisons might be used to assist design engineers in identifying less toxic, more environmentally compatible solvent alternatives to replace the more hazardous organic solvents currently used in industrial manufacturing processes, or to help in identifying partition systems that might mimic biological response properties. These latter comparisons have involved skin permeation and water-to-organic solvent systems [38], parallel artificial membrane permeability assays and biological systems [53], and aquatic toxicity and water-to-organic solvent systems [25,27]. Each of the fore-mentioned comparisons described both the specified biological and chemical process in terms of an Abraham model correlation.

At present, experimental-based solute descriptors are available for more than 8500 different molecular organic and organometallic compounds and for more than 300 different ionic species (such as tetraalkylammonium and substituted-pyridinium cations, substituted-phenolate and substituted-benzoate anions), which is only a tiny fraction of the known chemical compounds. Recognizing that it will never be possible to perform a sufficient number of experimental measurements to calculate experimental-based Abraham model solute descriptors for every known chemical compound, researchers have searched for alternative methods to estimate the numerical values. Published group contribution [53,54,55,56] and machine learning methods [55,56] have exhibited remarkable promise in that both the molar enthalpies of solvation (ΔH_solv) and molar Gibbs energies of solvation (ΔG_solv) of molecular organic solutes and inorganic gases in a wide range of organic solvents of varying polarity and hydrogen-bonding character could be reasonably predicted by the estimated solute descriptors. In the study by Chung and coworkers [56] the authors used an “inhouse” solute descriptor database containing 8366 unique chemical compounds. The compounds were fragmented into atom-centered (AC) functional groups. Each solute descriptor was then calculated by:

$$E, S,A,B\mathrm{or}L={\displaystyle \sum }_{i=1}^{N_{atom}}A{C}_i+{{\displaystyle \sum }}_{j=1}^{}RS{C}_j+{{\displaystyle \sum }}_{k=1}^{}LD{I}_k$$

(3)

summing the contributions from all AC groups, with special ring strain corrections (RSC) and long-distance interaction (LDI) groups being added to account for any more advanced structural features that were not fully captured by the atom-centered approach. Halogenated molecules required a slightly different estimation scheme in that the halogenated atoms were replaced by hydrogen atoms prior to the fragmentation. The correction(s) for the halogen atom(s) were added at the end to the calculated solute descriptor of the “non-halogenated compound”:

$$E,S,A,B\mathrm{or}L={\displaystyle \sum }_{i=1}^{N_{atom*}}A{C}_i+{{\displaystyle \sum }}_{j=1}^{}RS{C}_j+{{\displaystyle \sum }}_{k=1}^{}LD{I}_k+{{\displaystyle \sum }}_{l=1}^{N_{halogen}}Haloge{n}_l$$

(4)

where N_atom* and N_halogen denote the number of non-halogen heavy atoms and the number of halogen atoms in the given molecule, respectively. The numerical values of the individual AC groups, as well as all RSC, LDI and Halogen values, were determined by regressing the known descriptor values in accordance with Equations (3) and (4). The authors developed a machine learning method for estimating solute descriptors. Both predictive methods are very easy to use as the authors provided a link to the computational software. Users simply enter the canonical SMILES code of the molecule into the software. The results of the authors’ calculations showed that solute descriptors estimated by the machine learning method provided the better test set predictive values for both ΔH_solv and ΔG_solv with mean absolute errors of MAE = 3.89 kJ/mole and MAE = 4.184 kJ/mole, respectively. Slightly larger test set errors of MAE = 4.73 kJ/mole (ΔH_solv) and MAE = 4.94 kJ/mole (ΔG_solv) were noted in the case of the solute descriptors estimated by the authors’ group contribution method. The study by Ulrich and Ebert [57] used the slightly smaller Abraham Absolv solute parameter database found on the UFZ-LSER internet website [58] in developing their group contribution and deep machine learning methods for estimating solute descriptors. Methods aimed at predicting the Abraham model process coefficients have had mixed success; in part, because experimental-based correlations have been developed for relatively few organic solvents and biphasic partition systems [59,60,61,62].

The continued development of predictive group contribution and machine learning methods for the Abraham model requires the determination of both experimental-based solute descriptors and experimental-based solvent/process correlations. Additional experimental measurements are also needed for testing the limitations and applications of new predictive methods. To aid in future endeavors, we have recently reported solute descriptors for an additional 174 monomethyl branched alkanes [63], for an additional 127 C₉–C₂₆ mono-alkyl alkanes and polymethyl alkanes [64], for an additional 33 linear C₇–C₁₄ alkynes [65], and for several important active pharmaceutical ingredients and intermediates [23,66,67,68]. Abraham model correlations have also been recently determined for two practical partitioning systems, water-methyl ethyl ketone (MEK) [21] and water-methyl isobutyl ketone (MIBK) [22], and for solute transfer into isopropyl acetate [69], anisole [70] and cyclohexanol [71]. In the current communication we have calculated Abraham model L solute descriptor values for an additional 149 C₁₁ to C₄₄ methylated alkanes from measured gas–liquid chromatographic retention data gathered from a compilation by Katritzky and coworkers [72].

2. Calculation of Abraham Model Solute Descriptors for Methylated Alkanes

Normally the determination of Abraham model solute descriptors involves constructing a series of mathematical expressions for the measured solute properties of the given solute in a series of solvents and/or for a series of processes for which the lowercase equation coefficients are known. The solute properties used in past descriptor calculations have included logarithms of the measured solubility ratio of the solute in several different organic mono-solvents, the logarithms of the measured water-to-organic solvent partition coefficients, measured gas–liquid chromatographic retention data, and/or experimental enthalpies of solvation for the solute dissolved in several different organic solvents. Each of these solute properties will hopefully have very little experimental error. Aquatic toxicities and biological response factors generally have too much experimental error to be used effectively in solute descriptor calculations.

The Abraham model expressions for each of the fore-mentioned processes contain a common set of solute descriptors. The series of mathematical expressions are then solved for the “best” set of descriptor values that minimizes the overall squared-summed difference between the measured properties and the respective back-calculated values based on Equations (1) and (2). For the methylated hydrocarbons listed in

Table 1. Kovat’s retention indices, KRI, and Abraham model L solute descriptors for linear alkanes and for methylated alkanes.

Compound Name	KRI/100	L Value Database	L Value Calculated
Linear Alkanes
Heptane	7.000	3.173	3.172
Octane	8.000	3.677	3.676
Nonane	9.000	4.182	4.180
Decane	10.000	4.686	4.684
Undecane	11.000	5.191	5.188
Dodecane	12.000	5.696	5.692
Tridecane	13.000	6.200	6.196
Tetradecane	14.000	6.705	6.700
Pentadecane	15.000	7.209	7.204
Hexadecane	16.000	7.714	7.708
Heptadecane	17.000	8.218	8.212
Octadecane	18.000	8.722	8.716
Nonadecane	19.000	9.226	9.220
Eicosane	20.000	9.731	9.724
Heneicosane	21.000	10.236	10.228
Docosane	22.000	10.740	10.732
Tricosane	23.000	11.252	11.236
Tetracosane	24.000	11.758	11.740
Pentacosane	25.000	12.264	12.244
Hexacosane	26.000	12.770	12.748
Heptacosane	27.000	13.276	13.252
Octacosane	28.000	13.780	13.756
Nonacosane	29.000	14.291	14.260
Triacontane	30.000	14.794	14.764
Hentriacontane	31.000	15.321	15.268
Dotriacontane	32.000	15.787	15.772
Tritriacontane	33.000	16.303	16.276
Tetratriacontane	34.000	16.818	16.780
Pentatriacontane	35.000	17.223	17.284
Hexatriacontane	36.000	17.736	17.788
Heptatriacontane	37.000	18.211	18.292
Octatriacontane	38.000	18.686	18.796
Nonatriacontane	39.000	19.270	19.300
Tetracontane	40.000	19.853	19.804
Monomethylalkanes
2-Methylnonane	9.665	4.453	4.515
3-Methylnonane	9.730	4.486	4.548
2-Methylundecane	11.665	5.516	5.523
3-Methylundecane	11.725	5.550	5.553
2-Methyltridecane	13.665	6.528	6.531
3-Methyltridecane	13.730	6.563	6.564
2-Methylpentadecane	15.665	7.539	7.539
3-Methylpentadecane	15.737	7.577	7.575
2-Methylheptadecane	17.658	8.551	8.544
3-Methylheptadecane	17.740	8.591	8.585
2-Methylnonadecane	19.660	9.563	9.553
3-Methylnonadecane	19.743	9.607	9.594
10-Methylnonadecane	19.430	9.449	9.437
2-Methylheneicosane	21.660	10.571	10.561
3-Methylheneicosane	21.745	10.621	10.603
11-Methylheneicosane	21.410	10.449	10.435
2-Methyltricosane	23.640	11.586	11.559
3-Methyltricosane	23.745	11.635	11.611
8-Methyltricosane	23.670	11.468	11.574
12-Methyltricosane	23.370	11.449	11.422
2-Methylpentacosane	25.630	12.599	12.562
3-Methylpentacosane	25.744	12.651	12.619
13-Methylpentacosane	25.345	12.454	12.418
2-Methylheptacosane	27.630	13.611	13.570
3-Methylheptacosane	27.744	13.666	13.627
14-Methylheptacosane	27.330	13.458	13.418
2-Methylnonacosane	29.622	14.626	14.573
3-Methylnonacosane	29.740	14.680	14.633
15-Methylnonacosane	29.315	14.464	14.419
2-Methylhentriacontane	31.615		15.578
3-Methylhentriacontane	31.741		15.641
4-Methylhentriacontane	31.575		15.558
5-Methylhentriacontane	31.500		15.520
6-Methylhentriacontane	31.432		15.486
7-Methylhentriacontane	31.400		15.470
13-Methylhentriacontane	31.308		15.423
16-Methylhentriacontane	31.298		15.418
2-Methyltritriacontane	33.620		16.588
3-Methyltritriacontane	33.745		16.651
4-Methyltritriacontane	33.575		16.566
5-Methyltritriacontane	33.500		16.528
6-Methyltritriacontane	33.437		16.496
13-Methyltritriacontane	33.285		16.420
17-Methyltritriacontane	33.285		16.420
2-Methylpentatriacontane	35.620		17.596
3-Methylpentatriacontane	35.743		17.658
18-Methylpentatriacontane	35.273		17.422
Dimethylalkanes
3,9-Dimethyltricosane	24.100		11.790
5,9-Dimethyltetracosane	24.850		12.168
3,11-Dimethylpentacosane	26.090		12.793
3,15-Dimethylpentacosane	26.050		12.773
5,11-Dimethylpentacosane	25.820		12.657
5,17-Dimethylpentacosane	25.850		12.672
7,11-Dimethylpentacosane	25.770		12.632
2,6-Dimethylhexacosane	27.040		13.272
4,8-Dimethylhexacosane	26.950		13.227
5,11-Dimethylhexacosane	26.820		13.161
6,10-Dimethylhexacosane	26.780		13.141
7,11-Dimethylhexacosane	26.750		13.126
3,7-Dimethylheptacosane	28.090		13.801
3,15-Dimethylheptacosane	28.050		13.781
5,11-Dimethylheptacosane	27.820		13.665
5,17-Dimethylheptacosane	27.860		13.685
7,13-Dimethylheptacosane	27.740		13.625
9,19-Dimethylheptacosane	27.650		13.580
2,6-Dimethyloctacosane	29.050		14.285
2,10-Dimethyloctacosane	28.990		14.255
4,10-Dimethyloctacosane	28.950		14.235
5,15-Dimethyloctacosane	28.820		14.169
7,13-Dimethyloctacosane	28.730		14.124
3,7-Dimethylnonacosane	30.080		14.804
3,13-Dimethylnonacosane	30.040		14.784
5,13-Dimethylnonacosane	29.820		14.673
5,19-Dimethylnonacosane	29.830		14.678
7,17-Dimethylnonacosane	29.730		14.628
2,6-Dimethyltriacontane	31.050		15.293
2,10-Dimethyltriacontane	30.990		15.263
2,12-Dimethyltriacontane	30.950		15.243
3,7-Dimethyltriacontane	31.080		15.308
4,10-Dimethyltriacontane	30.940		15.238
6,10-Dimethyltriacontane	30.750		15.142
3,7-Dimethylhentriacontane	32.090		15.817
3,13-Dimethylhentriacontane	32.030		15.787
3,15-Dimethylhentriacontane	32.090		15.817
5,13-Dimethylhentriacontane	31.805		15.674
5,17-Dimethylhentriacontane	31.820		15.681
7,11-Dimethylhentriacontane	31.702		15.622
11,21-Dimethylhentriacontane	31.629		15.585
2,8-Dimethyldotriacontane	32.970		16.261
4,8-Dimethyldotriacontane	32.920		16.236
6,10-Dimethyldotriacontane	32.730		16.140
8,12-Dimethyldotriacontane	32.660		16.105
9,21-Dimethyldotriacontane	32.620		16.084
14,18-Dimethyldotriacontane	32.575		16.062
3,9-Dimethyltritriacontane	34.030		16.795
3,15-Dimethyltritriacontane	34.090		16.825
5,16-Dimethyltritriacontane	33.800		16.679
5,19-Dimethyltritriacontane	33.820		16.689
7,17-Dimethyltritriacontane	33.700		16.629
11,23-Dimethyltritriacontane	33.624		16.590
2,10-Dimethyltetratriacontane	34.940		17.254
4,16-Dimethyltetratriacontane	34.890		17.229
6,10-Dimethyltetratriacontane	34.738		17.152
8,12-Dimethyltetratriacontane	34.650		17.108
12,22-Dimethyltetratriacontane	34.614		17.089
13,17-Dimethyltetratriacontane	34.550		17.057
3,7-Dimethylpentatriacontane	36.095		17.836
3,15-Dimethylpentatriacontane	36.010		17.793
5,9-Dimethylpentatriacontane	35.800		17.687
5,19-Dimethylpentatriacontane	35.805		17.690
7,17-Dimethylpentatriacontane	35.697		17.635
9,21-Dimethylpentatriacontane	35.610		17.591
2,12-Dimethylhexatriacontane	36.950		18.267
5,17-Dimethylhexatriacontane	36.800		18.191
13,23-Dimethylhexatriacontane	36.610		18.095
3,15-Dimethylheptatriacontane	38.010		18.801
5,19-Dimethylheptatriacontane	37.790		18.690
5,17-Dimethylheptatriacontane	37.800		18.695
13,23-Dimethylheptatriacontane	37.590		18.589
5,17-Dimethyloctatriacontane	38.780		19.189
Trimethylalkanes
4,8,12-Trimethyltetracosane	25.200		12.345
5,9,13-Trimethylpentacosane	26.100		12.798
4,8,12-Trimethylhexacosane	27.190		13.348
3,7,11-Trimethylheptacosane	28.380		13.948
4,8,12-Trimethyloctacosane	29.180		14.351
3,7,11-Trimethylnonacosane	30.370		14.950
5,13,17-Trimethylnonacosane	30.070		14.799
6,14,18-Trimethyltriacontane	31.000		15.268
3,7,11-Trimethylhentriacontane	32.365		15.956
5,13,17-Trimethylhentriacontane	32.054		15.799
7,13,17-Trimethylhentriacontane	31.913		15.728
11,15,19-Trimethylhentriacontane	31.810		15.676
2,10,16-Trimethyldotriacontane	33.240		16.397
4,12,16-Trimethyldotriacontane	33.160		16.357
6,14,18-Trimethyldotriacontane	32.990		16.271
12,16,20-Trimethyldotriacontane	32.810		16.180
3,7,15-Trimethyltritriacontane	34.365		16.964
5,13,17-Trimethyltritriacontane	34.050		16.805
7,11,15-Trimethyltritriacontane	33.890		16.725
11,15,19-Trimethyltritriacontane	33.796		16.677
2,10,16-Trimethyltetratriacontane	35.240		17.405
4,8,12-Trimethyltetratriacontane	35.155		17.362
6,14,18-Trimethyltetratriacontane	34.970		17.269
8,12,16-Trimethyltetratriacontane	34.864		17.215
12,16,20-Trimethyltetratriacontane	34.780		17.173
3,7,15-Trimethylpentatriacontane	36.363		17.971
5,9,13-Trimethylpentatriacontane	36.050		17.813
7,11,15-Trimethylpentatriacontane	35.883		17.729
13,17,21-Trimethylpentatriacontane	35.770		17.672
13,17,23-Trimethylpentatriacontane	35.830		17.702
4,8,16-Trimethylhexatriacontane	37.150		18.368
8,12,16-Trimethylhexatriacontane	36.850		18.216
14,18,22-Trimethylhexatriacontane	36.760		18.171
3,7,15-Trimethylheptatriacontane	38.350		18.972
5,13,17-Trimethylheptatriacontane	38.030		18.811
7,13,19-Trimethylheptatriacontane	37.840		18.715
15,19,23-Trimethylheptatriacontane	37.750		18.670
15,19,23-Trimethyloctatriacontane	38.735		19.166
5,13,17-Trimethylnonatriacontane	40.010		19.809
15,19,23-Trimethylnonatriacontane	39.724		19.665
14,18,22-Trimethyltetracontane	40.710		20.162
Tetramethylalkanes
3,7,11,15-Tetramethylnonacosane	30.620		15.076
3,7,11,15-Tetramethylhentriacontane	32.610		16.079
4,8,12,16-Tetramethylhentriacontane	32.490		16.019
3,7,11,15-Tetramethyltritriacontane	34.590		17.077
4,8,12,16-Tetramethyltritriacontane	34.480		17.022
3,7,11,15-Tetramethylpentatriacontane	36.580		18.080
7,11,15,19-Tetramethylpentatriacontane	36.280		17.929
9,13,17,21-Tetramethylpentatriacontane	36.170		17.874
11,15,19,24-Tetramethylpentatriacontane	36.050		17.813
6,10,12,16-Tetramethylhexatriacontane	37.230		18.408
8,12,16,20-Tetramethylhexatriacontane	37.130		18.358
10,14,18,22-Tetramethylhexatriacontane	37.035		18.310
3,7,11,15-Tetramethylheptatriacontane	38.550		19.073
7,11,15,19-Tetramethylheptatriacontane	38.230		18.912
9,13,17,21-Tetramethylheptatriacontane	38.130		18.862
11,15,19,24-Tetramethylheptatriacontane	38.030		18.811
10,14,18,22-Tetramethyloctatriacontane	39.000		19.300

, the computational process is greatly simplified in that the E, S, A and B solute descriptors are all equal to zero. The V solute descriptor is readily calculated from the solute’s molecular structure, the atomic volumes of the constituent atoms contained in the solute molecule, and the number of chemical bonds in the solute molecule as described by Abraham and McGowan [73]. This leaves only the L solute descriptor to be calculated.

To calculate the L solute descriptor based on the gas–liquid chromatographic data retrieved from the published paper by Katritzky and coworkers [72], we first must establish a mathematical relationship correlation between the reported Kovat’s retention indices, KRI, and the L solute descriptor for alkane solute molecules. Numerical values KRI are available for 178 methylated alkanes [73]; however, for most of the molecules the L solute descriptor is not known. We can increase the number of compounds used in establishing the Abraham model correlation by noting that by definition the KRI values of linear alkanes is simply 100 times the number of carbon atoms. This allows us to add an additional 34 alkanes (heptane through tetracontane) to the regression data set. By combining the 34 linear alkanes and the 29 monomethyl alkanes with known L descriptor values from the Katritzky et al. compilation [72], we have 63 experimental data points to use in developing our Abraham model KRI versus L descriptor correlation.

Analysis of the values in the second and third columns of Table 1 yielded the following Abraham model expression:

L = 0.504 (0.001) × (KRI/100) − 0.356 (0.012)
(N = 63, SD = 0.034, R² = 1.000 and F = 942,023)

(5)

where N is the number of experimental data points used in the linear least-squares analysis, SD is the standard deviation, R² is the squared correlation coefficient, and F is the Fisher F-statistic. Standard errors in the slope and intercept are given in parentheses immediately following the respective equation coefficient. Equation (5) back-calculates the L values used in the least-squares analysis to within an average absolute deviation of AAE = 0.025 and an average error of AE = −0.006. Figure 1 depicts the linear plot of the L descriptor values versus KRI/100 values for the 63 data points used in deriving Equation (5). The derived mathematical relationship then allows the calculation of the L solute descriptors of the remaining 149 methylated alkanes. These calculations are summarized in the last column of Table 1. As an informational note, Katritzky et al. identified the different alkanes by a numerical labelling scheme where the first two digits in the number indicated the length of the longest carbon chain, and each of the next two-digit pairs showed the location of the methyl substituent on the carbon-atom backbone. We named the compounds labelled 22_0822 and 38_162024 as 8-methyltricosane and 15,19,23-trimethyloctatriacontane, respectively. For the first alkane, the placement of a methyl substituent on the 22nd carbon atom would increase the carbon backbone by one carbon atom. For the second alkane, we renumbered the carbon atoms starting at the other end of the carbon backbone to obtain a smaller set of numerical values.

3. Calculation of Thermodynamic Properties of Large Methylated Alkanes Using Abraham Model Solute Descriptors

The L solute descriptors that are tabulated in the last column of Table 1 provide researchers with an additional 149 chemical compounds to use in developing group contribution and machine learning methods for predicting Abraham model solute descriptors. Remember that the E, S, A and B solute descriptors of the tabulated compounds are equal to zero, and that the V solute descriptor values can be easily obtained using the method described by Abraham and McGowan [73]. The tabulated values given in Table 1 can also be used in conjunction with published Abraham model correlations to predict a wide range of physical, biological and thermodynamic properties including vapor pressures, enthalpies of vaporization and sublimation, enthalpies of solvation, aquatic toxicities and other properties. In the next few paragraphs, we will illustrate the computational methodology by calculating the standard molar enthalpies of sublimation, ΔH_sub,298K, and of vaporization at 298 K, ΔH_vap,298K, as well as discussing how the former values might be combined with measured enthalpy of solution data, ΔH_soln,298K, to obtain a second set of predicted ΔH_sub,298K values. While our computations are focused on the large, methylated alkanes studied in the current communication, we note that the computational method can be applied to other organic compounds as well. All that is needed for the predictions is knowledge of the Abraham model solute descriptors for the given compound and the Abraham model correlation for the property/process that one wishes to predict. This is the driving force behind the development of group contribution and machine learning methods to predict Abraham model solute descriptors.

For the methylated alkane compounds studied in the current communication, the numerical values of ΔH_sub,298K are calculated according to Equation (6) [46].

ΔH_sub,298K = 13.93 + 13.57 L − 0.05 L × L

(6)

For the convenience of the journal readers, we have removed the e_k × E, s_k × S, a_k × A and b_k × B terms from Equation (2) as these terms will not contribute to the calculated ΔH_sub,298K values because the E, S, A and B solute descriptors of the methylated alkane compounds are set equal to zero. The second column in

Table 2. Comparison of the enthalpies of sublimation, ΔH_sub,298K (in kJ mol⁻¹), predicted by the Abraham model Equation (6) and the group-additivity method of Naef and Acree (Equation (8)).

Compound Name	ΔHsub,298K Equation (6)	ΔHsub,298K Equation (8)
Monomethylalkanes
2-Methylnonane	73.4	77.3
3-Methylnonane	73.8	77.3
2-Methylundecane	87.3	90.0
3-Methylundecane	87.7	90.0
2-Methyltridecane	100.4	102.7
3-Methyltridecane	100.8	102.7
2-Methylpentadecane	113.4	115.4
3-Methylpentadecane	113.9	115.4
2-Methylheptadecane	126.3	128.1
3-Methylheptadecane	126.8	128.1
2-Methylnonadecane	139.1	140.8
3-Methylnonadecane	139.7	140.8
10-Methylnonadecane	137.7	140.8
2-Methylheneicosane	151.8	153.5
3-Methylheneicosane	152.4	153.5
11-Methylheneicosane	150.3	153.5
2-Methyltricosane	164.4	166.2
3-Methyltricosane	165.1	166.2
8-Methyltricosane	163.0	166.2
12-Methyltricosane	162.7	166.2
2-Methylpentacosane	177.0	178.9
3-Methylpentacosane	177.6	178.9
13-Methylpentacosane	175.2	178.9
2-Methylheptacosane	189.4	191.6
3-Methylheptacosane	190.0	191.6
14-Methylheptacosane	187.5	191.6
2-Methylnonacosane	201.7	204.3
3-Methylnonacosane	202.4	204.3
15-Methylnonacosane	199.8	204.3
2-Methylhentriacontane	213.2	217.0
3-Methylhentriacontane	214.0	217.0
4-Methylhentriacontane	213.0	217.0
5-Methylhentriacontane	212.5	217.0
6-Methylhentriacontane	212.1	217.0
7-Methylhentriacontane	211.9	217.0
13-Methylhentriacontane	211.3	217.0
16-Methylhentriacontane	211.3	217.0
2-Methyltritriacontane	225.3	229.7
3-Methyltritriacontane	226.0	229.7
4-Methyltritriacontane	225.0	229.7
5-Methyltritriacontane	224.6	229.7
6-Methyltritriacontane	224.2	229.7
13-Methyltritriacontane	223.3	229.7
17-Methyltritriacontane	223.3	229.7
2-Methylpentatriacontane	237.2	242.4
3-Methylpentatriacontane	238.0	242.4
18-Methylpentatriacontane	235.2	242.4
Dimethylalkanes
3,9-Dimethyltricosane	167.0	167.0
5,9-Dimethyltetracosane	171.7	173.4
3,11-Dimethylpentacosane	179.4	179.7
3,15-Dimethylpentacosane	179.1	179.7
5,11-Dimethylpentacosane	177.7	179.7
5,17-Dimethylpentacosane	177.9	179.7
7,11-Dimethylpentacosane	177.4	179.7
2,6-Dimethylhexacosane	185.2	186.1
4,8-Dimethylhexacosane	184.7	186.1
5,11-Dimethylhexacosane	183.9	186.1
6,10-Dimethylhexacosane	183.6	186.1
7,11-Dimethylhexacosane	183.4	186.1
3,7-Dimethylheptacosane	191.7	192.4
3,15-Dimethylheptacosane	191.4	192.4
5,11-Dimethylheptacosane	190.0	192.4
5,17-Dimethylheptacosane	190.3	192.4
7,13-Dimethylheptacosane	189.5	192.4
9,19-Dimethylheptacosane	189.0	192.4
2,6-Dimethyloctacosane	197.6	198.8
2,10-Dimethyloctacosane	197.2	198.8
4,10-Dimethyloctacosane	197.0	198.8
5,15-Dimethyloctacosane	196.2	198.8
7,13-Dimethyloctacosane	195.6	198.8
3,7-Dimethylnonacosane	203.9	205.1
3,13-Dimethylnonacosane	203.6	205.1
5,13-Dimethylnonacosane	202.3	205.1
5,19-Dimethylnonacosane	202.3	205.1
7,17-Dimethylnonacosane	201.7	205.1
2,6-Dimethyltriacontane	209.8	211.5
2,10-Dimethyltriacontane	209.4	211.5
2,12-Dimethyltriacontane	209.2	211.5
3,7-Dimethyltriacontane	210.0	211.5
4,10-Dimethyltriacontane	209.1	211.5
6,10-Dimethyltriacontane	207.9	211.5
3,7-Dimethylhentriacontane	216.1	217.8
3,13-Dimethylhentriacontane	215.7	217.8
3,15-Dimethylhentriacontane	216.1	217.8
5,13-Dimethylhentriacontane	214.3	217.8
5,17-Dimethylhentriacontane	214.4	217.8
7,11-Dimethylhentriacontane	213.7	217.8
11,21-Dimethylhentriacontane	213.3	217.8
2,8-Dimethyldotriacontane	221.4	224.2
4,8-Dimethyldotriacontane	221.1	224.2
6,10-Dimethyldotriacontane	219.9	224.2
8,12-Dimethyldotriacontane	219.5	224.2
9,21-Dimethyldotriacontane	219.3	224.2
14,18-Dimethyldotriacontane	219.0	224.2
3,9-Dimethyltritriacontane	227.7	230.5
3,15-Dimethyltritriacontane	228.1	230.5
5,16-Dimethyltritriacontane	226.4	230.5
5,19-Dimethyltritriacontane	226.5	230.5
7,17-Dimethyltritriacontane	225.8	230.5
11,23-Dimethyltritriacontane	225.3	230.5
2,10-Dimethyltetratriacontane	233.2	236.9
4,16-Dimethyltetratriacontane	232.9	236.9
6,10-Dimethyltetratriacontane	232.0	236.9
8,12-Dimethyltetratriacontane	231.5	236.9
12,22-Dimethyltetratriacontane	231.2	236.9
13,17-Dimethyltetratriacontane	230.9	236.9
3,7-Dimethylpentatriacontane	240.1	243.2
3,15-Dimethylpentatriacontane	239.6	243.2
5,9-Dimethylpentatriacontane	238.3	243.2
5,19-Dimethylpentatriacontane	238.3	243.2
7,17-Dimethylpentatriacontane	237.7	243.2
9,21-Dimethylpentatriacontane	237.2	243.2
2,12-Dimethylhexatriacontane	245.1	249.6
5,17-Dimethylhexatriacontane	244.2	249.6
13,23-Dimethylhexatriacontane	243.1	249.6
3,15-Dimethylheptatriacontane	251.4	255.9
5,19-Dimethylheptatriacontane	250.1	255.9
5,17-Dimethylheptatriacontane	250.2	255.9
13,23-Dimethylheptatriacontane	248.9	255.9
5,17-Dimethyloctatriacontane	255.9	262.3
Trimethylalkanes
4,8,12-Trimethyltetracosane	173.8	174.2
5,9,13-Trimethylpentacosane	179.4	180.6
4,8,12-Trimethylhexacosane	186.2	186.9
3,7,11-Trimethylheptacosane	193.5	193.3
4,8,12-Trimethyloctacosane	198.4	199.6
3,7,11-Trimethylnonacosane	205.6	206.0
5,13,17-Trimethylnonacosane	203.8	206.0
6,14,18-Trimethyltriacontane	209.5	212.3
3,7,11-Trimethylhentriacontane	217.7	218.7
5,13,17-Trimethylhentriacontane	215.8	218.7
7,13,17-Trimethylhentriacontane	215.0	218.7
11,15,19-Trimethylhentriacontane	214.4	218.7
2,10,16-Trimethyldotriacontane	223.0	225.0
4,12,16-Trimethyldotriacontane	222.5	225.0
6,14,18-Trimethyldotriacontane	221.5	225.0
12,16,20-Trimethyldotriacontane	220.4	225.0
3,7,15-Trimethyltritriacontane	229.7	231.4
5,13,17-Trimethyltritriacontane	227.9	231.4
7,11,15-Trimethyltritriacontane	226.9	231.4
11,15,19-Trimethyltritriacontane	226.3	231.4
2,10,16-Trimethyltetratriacontane	235.0	237.7
4,8,12-Trimethyltetratriacontane	234.5	237.7
6,14,18-Trimethyltetratriacontane	233.4	237.7
8,12,16-Trimethyltetratriacontane	232.7	237.7
12,16,20-Trimethyltetratriacontane	232.2	237.7
3,7,15-Trimethylpentatriacontane	241.7	244.1
5,9,13-Trimethylpentatriacontane	239.8	244.1
7,11,15-Trimethylpentatriacontane	238.8	244.1
13,17,21-Trimethylpentatriacontane	238.1	244.1
13,17,23-Trimethylpentatriacontane	238.5	244.1
4,8,16-Trimethylhexatriacontane	246.3	250.4
8,12,16-Trimethylhexatriacontane	244.5	250.4
14,18,22-Trimethylhexatriacontane	244.0	250.4
3,7,15-Trimethylheptatriacontane	253.4	256.8
5,13,17-Trimethylheptatriacontane	251.5	256.8
7,13,19-Trimethylheptatriacontane	250.4	256.8
15,19,23-Trimethylheptatriacontane	249.9	256.8
15,19,23-Trimethyloctatriacontane	255.7	263.1
5,13,17-Trimethylnonatriacontane	263.1	269.5
15,19,23-Trimethylnonatriacontane	261.5	269.5
14,18,22-Trimethyltetracontane	267.2	275.8
Tetramethylalkanes
3,7,11,15-Tetramethylnonacosane	207.2	206.8
3,7,11,15-Tetramethylhentriacontane	219.2	219.5
4,8,12,16-Tetramethylhentriacontane	218.5	219.5
3,7,11,15-Tetramethyltritriacontane	231.1	232.2
4,8,12,16-Tetramethyltritriacontane	230.4	232.2
3,7,11,15-Tetramethylpentatriacontane	242.9	244.9
7,11,15,19-Tetramethylpentatriacontane	241.2	244.9
9,13,17,21-Tetramethylpentatriacontane	240.5	244.9
11,15,19,24-Tetramethylpentatriacontane	239.8	244.9
6,10,12,16-Tetramethylhexatriacontane	246.8	251.3
8,12,16,20-Tetramethylhexatriacontane	246.2	251.3
10,14,18,22-Tetramethylhexatriacontane	245.6	251.3
3,7,11,15-Tetramethylheptatriacontane	254.6	257.6
7,11,15,19-Tetramethylheptatriacontane	252.7	257.6
9,13,17,21-Tetramethylheptatriacontane	252.1	257.6
11,15,19,24-Tetramethylheptatriacontane	251.5	257.6
10,14,18,22-Tetramethyloctatriacontane	257.2	264.0

contains our calculated ΔH_sub,298K values for the 178 compounds gathered from the Katritzky et al. [72] paper.

In our search of the published chemical and engineering literature we did not find experimental ΔH_sub,298K data to compare our calculated values against. The sublimation enthalpies of large, nonvolatile compounds are difficult to measure due to the compound’s very small vapor pressures; however, these quantities are often needed in the design of high-temperature industrial processes and in the calculation of gas-phase standard molar enthalpies of formation from enthalpy of combustion measurements. What we offer in the way of a comparison is to compare our Abraham model predictions against the calculated values from the Naef and Acree group-additivity method [14]. The group-additivity method has been shown to predict ΔH_sub,298K values for approximately 1866 molecular compounds to within a standard deviation of SD = 10.33 kJ mol⁻¹. The basic method estimates a given thermodynamic or physical property by:

$$Property={\displaystyle \sum }_i{A}_i{a}_i+{\displaystyle \sum }_j{B}_j{b}_j+Constant$$

(7)

summing the contributions that each individual atom group makes to the overall property. In Equation (7), A_i denotes the number of occurrences of the ith atom group, B_j is the number of times each special group occurs, and a_i and b_j are the numerical values of each atom group and special group.

For monomethylated and polymethylated alkanes, the atom group-additivity method proposed by Naef and Acree [14] fragments molecules into three distinct kinds of sp³ hybridized carbon atoms based on the number of each type of atoms directly bonded to the carbon atom. The first carbon-atom group will be bonded to three hydrogen atoms and one carbon atom (CH₃ group), the second carbon-atom group will be attached to two hydrogen and two carbon atoms (CH₂ group), and the third carbon-atom group has a single hydrogen and three carbon-atom nearest neighbors (CH group). The method also includes one special group that is defined as the total number of carbon atoms in the alkane molecule.

In Equation (8) below we have inserted the numerical group values and constants into Equation (7) for predicting ΔH_sub,298K of C_nH_2n+2 monomethylated and polymethylated alkanes:

ΔH_sub,298K (kJ mol⁻¹) = 5.99 n_CH3 + 6.88 n_CH2 + 2.28 n_CH − 0.53 n_carbons + 21.03

(8)

We note that the predicted values based on Equation (6) of the Abraham model are similar to the predictions based on the group-additivity model of Naef and Acree [14] for the “smaller” of the large polymethylated alkanes as shown by the numerical entries in the last two columns of Table 2. The differences become more pronounced with increasing carbon-atom chain length. The group-additivity method is unable to distinguish between the placement of the alkyl-substituent group along the large carbon-atom chain, and yields the same predicted values for a common set of number of different atom types. In other words, the predicted values of all dimethylhexacosane isomers in Table 2 are the same. Every dimethylhexacosane isomer considered in this study has 4 CH₃-type carbon atoms, 22 CH₂-type carbon atoms, 2 CH-type carbon atoms, and 28 total carbon atoms. The only dimethylhexacosane isomers that would be different would be those in which both methyl groups were situated on the same carbon atom. The predicted values of these latter dimethylhexacosane isomers would be identical to each other, but different from the dimethylhexacosane isomers in Table 2. Identical predicted values for isomeric compounds are a common feature of most published group-additivity and group contribution methods for predicting thermodynamic properties of organic compounds. The Abraham model, on the other hand, will give different predicted values for each dimethylhexacosane isomer, and does not require that the molecule be fragmented into atom groups or functional groups.

The enthalpies of vaporization would be calculated in similar fashion using the mathematical correlation developed by Churchill and coworkers [45]:

ΔH_vap,298K (kJ mol⁻¹) = 6.100 + 9.537 L

(9)

and the group-additivity method proposed by Naef and Acree [14]:

ΔH_vap,298K (kJ mol⁻¹) = 3.07 n_CH3 + 4.67 n_CH2 + 3.57 n_CH + 0.09 n_carbons + 8.61

(10)

As before, only the terms needed in the calculation of the ΔH_vap,298K values for the polymethylated alkanes studied in the current communication are given. The standard molar enthalpies of vaporization of large alkanes can be experimentally determined using correlation gas chromatography [74,75,76]. The experimental method is applicable to both solid and liquid compounds, and moreover, does not require highly purified chemical samples as the chromatographic retention times corresponding to the dissolved impurities in the samples can be distinguished from the desired chemical compound by their much smaller peak areas.

Solomonov and coworkers [77,78,79,80,81] recently devised an indirect method for determining both standard molar enthalpies of vaporization and sublimation from measured enthalpies of solution, ΔH_soln, and predicted enthalpies of solvation, ΔH_solv, for the given chemical compound dissolved in a suitable organic solvent. Numerical values of ΔH_vap,298K and ΔH_sub,298K were calculated from:

ΔH_vap,298K = ΔH_soln,298K − ΔH_solv,298K

(11)

ΔH_sub,298K = ΔH_soln,298K − ΔH_solv,298K

(12)

Equations (11) and (12), respectively, depending upon whether the dissolved solute is a liquid or crystalline compound. The standard molar vaporization/sublimation enthalpies of vaporization and sublimation based upon the proposed solution calorimetry approach of Solomonov and coworkers were found to be in good agreement (within experimental uncertainties) with the values determined by the more direct calorimetric, gas saturation and vapor pressure methods. The Abraham general solvation model was one of the predictive methods used by the authors [81] to calculate the solvation enthalpies. Abraham model correlations are available for calculating ΔH_solv, values for solutes dissolved in water and in more than 30 different organic solvents of varying polarity and hydrogen-bonding character. Group contribution and atom-additivity methods for predicting enthalpies of solvation are currently available for only a handful of organic solvents. In

Table 3. Predicted gas-to-benzene enthalpies of solvation, ΔH_solv,298K (in kJ mol⁻¹) for 178 monomethylated and polymethylated alkanes based upon Equation (13).

Compound Name	ΔHsolv,298K (kJ mol−1)	Compound Name	ΔHsolv,298K (kJ mol−1)
Monomethylalkanes		Dimethylalkanes
2-Methylnonane	−42.6	3,9-Dimethyltricosane	−104.1
3-Methylnonane	−42.8	5,9-Dimethyltetracosane	−107.3
2-Methylundecane	−51.5	3,11-Dimethylpentacosane	−112.6
3-Methylundecane	−51.8	3,15-Dimethylpentacosane	−112.4
2-Methyltridecane	−60.0	5,11-Dimethylpentacosane	−111.4
3-Methyltridecane	−60.3	5,17-Dimethylpentacosane	−111.5
2-Methylpentadecane	−68.5	7,11-Dimethylpentacosane	−111.2
3-Methylpentadecane	−68.8	2,6-Dimethylhexacosane	−116.6
2-Methylheptadecane	−76.9	4,8-Dimethylhexacosane	−116.2
3-Methylheptadecane	−77.3	5,11-Dimethylhexacosane	−115.6
2-Methylnonadecane	−85.4	6,10-Dimethylhexacosane	−115.5
3-Methylnonadecane	−85.8	7,11-Dimethylhexacosane	−115.3
10-Methylnonadecane	−84.5	3,7-Dimethylheptacosane	−121.0
2-Methylheneicosane	−93.9	3,15-Dimethylheptacosane	−120.8
3-Methylheneicosane	−94.3	5,11-Dimethylheptacosane	−119.9
11-Methylheneicosane	−92.9	5,17-Dimethylheptacosane	−120.0
2-Methyltricosane	−102.4	7,13-Dimethylheptacosane	−119.5
3-Methyltricosane	−102.8	9,19-Dimethylheptacosane	−119.2
8-Methyltricosane	−101.4	2,6-Dimethyloctacosane	−125.1
12-Methyltricosane	−101.3	2,10-Dimethyloctacosane	−124.8
2-Methylpentacosane	−110.9	4,10-Dimethyloctacosane	−124.7
3-Methylpentacosane	−111.4	5,15-Dimethyloctacosane	−124.1
13-Methylpentacosane	−109.7	7,13-Dimethyloctacosane	−123.7
2-Methylheptacosane	−119.4	3,7-Dimethylnonacosane	−129.4
3-Methylheptacosane	−119.9	3,13-Dimethylnonacosane	−129.3
14-Methylheptacosane	−118.1	5,13-Dimethylnonacosane	−128.3
2-Methylnonacosane	−127.9	5,19-Dimethylnonacosane	−128.4
3-Methylnonacosane	−128.4	7,17-Dimethylnonacosane	−128.0
15-Methylnonacosane	−126.6	2,6-Dimethyltriacontane	−133.5
2-Methylhentriacontane	−135.9	2,10-Dimethyltriacontane	−133.3
3-Methylhentriacontane	−136.5	2,12-Dimethyltriacontane	−133.1
4-Methylhentriacontane	−135.8	3,7-Dimethyltriacontane	−133.7
5-Methylhentriacontane	−135.4	4,10-Dimethyltriacontane	−133.1
6-Methylhentriacontane	−135.2	6,10-Dimethyltriacontane	−132.3
7-Methylhentriacontane	−135.0	3,7-Dimethylhentriacontane	−137.9
13-Methylhentriacontane	−134.6	3,13-Dimethylhentriacontane	−137.7
16-Methylhentriacontane	−134.6	3,15-Dimethylhentriacontane	−137.9
2-Methyltritriacontane	−144.4	5,13-Dimethylhentriacontane	−136.7
3-Methyltritriacontane	−144.9	5,17-Dimethylhentriacontane	−136.8
4-Methyltritriacontane	−144.2	7,11-Dimethylhentriacontane	−136.3
5-Methyltritriacontane	−143.9	11,21-Dimethylhentriacontane	−136.0
6-Methyltritriacontane	−143.6	2,8-Dimethyldotriacontane	−141.7
13-Methyltritriacontane	−143.0	4,8-Dimethyldotriacontane	−141.4
17-Methyltritriacontane	−143.0	6,10-Dimethyldotriacontane	−140.6
2-Methylpentatriacontane	−152.9	8,12-Dimethyldotriacontane	−140.3
3-Methylpentatriacontane	−153.4	9,21-Dimethyldotriacontane	−140.2
18-Methylpentatriacontane	−151.4	14,18-Dimethyldotriacontane	−140.0
Trimethylalkane		3,9-Dimethyltritriacontane	−146.1
4,8,12-Trimethyltetracosane	−108.8	3,15-Dimethyltritriacontane	−146.4
5,9,13-Trimethylpentacosane	−112.6	5,16-Dimethyltritriacontane	−145.2
4,8,12-Trimethylhexacosane	−117.2	5,19-Dimethyltritriacontane	−145.3
3,7,11-Trimethylheptacosane	−122.2	7,17-Dimethyltritriacontane	−144.7
4,8,12-Trimethyloctacosane	−125.6	11,23-Dimethyltritriacontane	−144.4
3,7,11-Trimethylnonacosane	−130.7	2,10-Dimethyltetratriacontane	−150.0
5,13,17-Trimethylnonacosane	−129.4	4,16-Dimethyltetratriacontane	−149.8
6,14,18-Trimethyltriacontane	−133.3	6,10-Dimethyltetratriacontane	−149.1
3,7,11-Trimethylhentriacontane	−139.1	8,12-Dimethyltetratriacontane	−148.8
5,13,17-Trimethylhentriacontane	−137.8	12,22-Dimethyltetratriacontane	−148.6
7,13,17-Trimethylhentriacontane	−137.2	13,17-Dimethyltetratriacontane	−148.3
11,15,19-Trimethylhentriacontane	−136.8	3,7-Dimethylpentatriacontane	−154.9
2,10,16-Trimethyldotriacontane	−142.8	3,15-Dimethylpentatriacontane	−154.5
4,12,16-Trimethyldotriacontane	−142.5	5,9-Dimethylpentatriacontane	−153.6
6,14,18-Trimethyldotriacontane	−141.7	5,19-Dimethylpentatriacontane	−153.6
12,16,20-Trimethyldotriacontane	−141.0	7,17-Dimethylpentatriacontane	−153.2
3,7,15-Trimethyltritriacontane	−147.6	9,21-Dimethylpentatriacontane	−152.8
5,13,17-Trimethyltritriacontane	−146.2	2,12-Dimethylhexatriacontane	−158.5
7,11,15-Trimethyltritriacontane	−145.5	5,17-Dimethylhexatriacontane	−157.9
11,15,19-Trimethyltritriacontane	−145.2	13,23-Dimethylhexatriacontane	−157.1
2,10,16-Trimethyltetratricontane	−151.3	3,15-Dimethylheptatriacontane	−163.0
4,8,12-Trimethyltetratriacontane	−150.9	5,19-Dimethylheptatriacontane	−162.0
6,14,18-Trimethyltetratriacontane	−150.1	5,17-Dimethylheptatriacontane	−162.1
8,12,16-Trimethyltetratriacontane	−149.7	13,23-Dimethylheptatriacontane	−161.2
12,16,20-Trimethyltetratriacontane	−149.3	5,17-Dimethyloctatriacontane	−166.2
3,7,15-Trimethylpentatriacontane	−156.0	Tetramethylalkane
5,9,13-Trimethylpentatriacontane	−154.7	3,7,11,15-Tetramethylnonacosane	−131.7
7,11,15-Trimethylpentatriacontane	−154.0	3,7,11,15-Tetramethylhentriacontane	−140.1
13,17,21-Trimethylpentatriacontane	−153.5	4,8,12,16-Tetramethylhentriacontane	−139.6
13,17,23-Trimethylpentatriacontane	−153.8	3,7,11,15-Tetramethyltritriacontane	−148.5
4,8,16-Trimethylhexatriacontane	−159.3	4,8,12,16-Tetramethyltritriacontane	−148.0
8,12,16-Trimethylhexatriacontane	−158.1	3,7,11,15-Tetramethylpentatriacontane	−156.9
14,18,22-Trimethylhexatriacontane	−157.7	7,11,15,19-Tetramethylpentatriacontane	−155.7
3,7,15-Trimethylheptatriacontane	−164.4	9,13,17,21-Tetramethylpentatriacontane	−155.2
5,13,17-Trimethylheptatriacontane	−163.1	11,15,19,24-Tetramethylpentatriacontane	−154.7
7,13,19-Trimethylheptatriacontane	−162.3	6,10,12,16-Tetramethylhexatriacontane	−159.8
15,19,23-Trimethylheptatriacontane	−161.9	8,12,16,20-Tetramethylhexatriacontane	−159.3
15,19,23-Trimethyloctatriacontane	−166.0	10,14,18,22-Tetramethylhexatriacontane	−158.9
5,13,17-Trimethylnonatriacontane	−171.4	3,7,11,15-Tetramethylheptatriacontane	−165.3
15,19,23-Trimethylnonatriacontane	−170.2	7,11,15,19-Tetramethylheptatriacontane	−163.9
14,18,22-Trimethyltetracontane	−174.4	9,13,17,21-Tetramethylheptatriacontane	−163.5
		11,15,19,24-Tetramethylheptatriacontane	−163.1
		10,14,18,22-Tetramethyloctatriacontane	−167.2

we have tabulated the ΔH_solv values for 178 different polymethylated alkanes dissolved in benzene based upon:

ΔH_solv,298K (kJ mol⁻¹) = −5.175(0.354) − 8.393(0.103) L

(13)

the updated Abraham model correlation reported by Lu et al. [82] The above correlation contains only the terms needed to predict values for the compounds studied in the current communication.

4. Conclusions

The current study is a continuation of our ongoing research involving the calculation Abraham model solute descriptors based on experimental water-to-organic solvent partition coefficients, infinite dilution activity coefficients, molar solubilities and gas–liquid chromatographic and high-performance liquid chromatographic retention data. Abraham model L solute descriptors have been calculated for an additional 149 C₁₁ to C₄₂ monomethylated and polymethylated alkanes based on the measured Kovat’s gas–liquid chromatographic retention indices retrieved from the published chemical literature. The calculated solute descriptors, in combination with previously published Abraham model correlations, can be used to predict a number of very important chemical and thermodynamic properties including partition coefficients, molar solubility ratios, gas–liquid chromatographic and HPLC retention data, infinite dilution activity coefficients, molar enthalpies of solvation, standard molar vaporization and sublimation at 298 K, vapor pressures, and limiting diffusion coefficients. The predictive computations are illustrated by estimating both the standard molar enthalpies of sublimation and the enthalpies of solvation in benzene for the monomethylated and polymethylated alkanes considered in the current study. The standard molar enthalpy of sublimation predictions were also performed using the group-additivity method proposed by Naef and Acree. Experimental thermodynamic data are not currently available for many of the larger monomethylated and polymethylated alkanes. Predictive methods provide practicing chemists and engineers working in the industrial manufacturing sector with a means to estimate the physical and thermodynamic properties needed in process design calculations.

A comparison of the two methods revealed that the ΔH_sub,298K predictions based on the Abraham model are similar to predictions based on the group-additivity model of Naef and Acree [14] for the “smaller” of the large polymethylated alkanes. The differences became more pronounced with increasing carbon-atom chain length. The group-additivity method was not able to distinguish between the placement of the alkyl-substituent group attached to the large carbon-atom chain, and yielded the same predicted values for a given molecular formula. In other words, the predicted values of all dimethylhexacosane isomers were the same. This limitation is a common feature of most group-additivity and group contribution methods. The Abraham model, on the other hand, provides different predicted values for the different dimethylhexacosane molecules, and does not require fragmentation of the molecule into atom groups or functional groups.

The solute descriptors determined in the current study further the development of group contribution and machine learning methods by providing experimental-based values for an additional 149 chemical compounds. Published group contribution [53,54,55,56] and machine learning methods [55,56] have shown some promise along these lines in that the estimated descriptor values provide reasonably accurate predictions for both the molar enthalpies of solvation (ΔH_solv) and molar Gibbs energies of solvation (ΔG_solv) of organic solutes and inorganic gases in a wide range of organic solvents of varying polarity and hydrogen-bonding character.