The Kováts retention indices (RI) in Gas Liquid Chromatography (GLC) can be expressed by a linear equation of terms, each term being a product of a solute parameter and of a solvent parameter, according to Rohrschneider in 1966  . If five terms are considered, as most authors since 1976 have done so   , this equation can be written as follows:
in which RICH4 stands for the retention index of methane (always equals to 100). The lower case Greek letters stand for the solvation parameters of solutes, and the Latin upper case letters stand for the solvation parameters of stationary phases.
The first three terms correspond to the Van der Waals forces:
・ → dispersion (London)
・ → orientation or polarity strictly speaking (Keesom)
・ → polarizability-induction (Debye)
And the fourth and fifth terms correspond to the hydrogen bonding forces:
・ → proton donor of solute and acceptor of solvent according to Brønsted
・ → proton acceptor of solute and donor of solvent according to Brønsted
We have recently published a revisited definition, on experimental basis, of the three solute parameters or descriptors δ, ω and β, related to the Van der Waals forces in solutions, as they are involved in GLC  . The present study reflects a similar attempt for the solvent descriptors D, W and E. The comparison with previous results on this topic will be stated in the Discussion and Perspectives section.
2. Materials and Methods
2.1. Statistical Tools
In addition to the Microsoft Excel Windows facilities for drawing diagrams and handling data sets, the SYSTAT 12® for Windows has been applied for stepwise MLRA (Multidimensional Linear Regression Analysis).
2.2. SMT, A Simplified Molecular Topology
The principle of this tool has already been presented elsewhere   . In the version used here, it only takes into account, for each atom of a molecule, its nature and the nature of its bonds, leaving aside the nature of its first neighbors with the exception of four cases specified hereafter. Each atom is provided with an index comprising a series of digits. Their sum is at most equal to its valence. The value of the digits define the type of bonds (1 for a single, 2 for a double bond, etc.), but the bonds with hydrogen are excluded. In the present version, the nature of atoms kept is limited to C, H, O, N, P, S, F, Cl, Br, I. In addition, the compounds which include a given atom only linked to hydrogen (e.g. CH4, OH2, NH3, SH2) are excluded. The additional topological features are:
・ Chlorine linked to carbon C11
・ Oxygen linked to carbon C11 (primary alcohols)
・ Oxygen linked to carbon C111 (secondary alcohols)
・ A connectivity parameter due to Zamora  called the “smallest set of smallest rings” (SSSR). According to this concept, for the naphthalene for example, which contains two individual C-6 rings and one C-10 ring embracing them, only the two six numbered rings are considered. Two six numbered rings corresponding to 12 carbon atoms, the SSSR value of naphthalene is therefore be taken as equal to 12.
Let us specify that the calculations using the SMT procedure have been made manually in this study, using 2D molecular drawings from ChemSpider  .
2.3. Molar and Molecular Volume
The various expressions which reflect the “intrinsic molecular volume” or the “Van der Waals molecular volume”, are all additive properties (which it is not the case for the ratio molar mass/density at 20˚C). We have selected among them in various studies, the values of molecular volumes (expressed in cubic angstroms) proposed by the freely interactive calculator of Molinspiration  . The authors of this calculator have used, in a first step, a semi-empirical quantum chemistry method to build 3D molecular geometries for a training set of about 12 000 molecules. In a second step, they have fitted the sum of fragment contributions to the supposed real volumes of the training set. We name this expression Vw (as Van der Waals volume).
We have applied in the present study, a predictive tool for Vw using the SMT procedure described in 2.2, which appears rather satisfactory as shown in Figure 1, and alternatively applicable to the values from Molinspiration (and easier to handle for polymers). This predictive method of the molecular volume can be considered as very similar to the one that we published in 2011  , but slightly refined. In this last quoted publication, it was shown that the van der Waals molecular volume appears strongly involved in the solvent properties.
2.4. Polar Surface Area (PSA)
According to Palm et al.  , who have strongly promoted this molecular
Figure 1. Correlogram between Van der Waals molecular volumes obtained using two methods. The SMT method appears more suitable for great molecules (i.e. polymers). The unique bust scarcely noticeable visible outlier in this figure corresponds to cyclodecane.
property in pharmacology, the polar surface area can be simply and accurately defined as “the area occupied by nitrogen and oxygen atoms, and hydrogen atoms attached to these heteroatoms”. Presently, this property is considered as one of the popular molecular properties, available in various sources of chemical data banks like ChemSpider  , Molinspiration  or Chemaxon  . However, because in some cases the values are not available, we have used in the present study a predicted method reported in Figure 2, which can be considered as a refined version of our 2011 publication  .
It should be noted that out of the 447 compounds applied here for establishing the SMT model, the five outliers (clearly visible in the diagram) all correspond to 5-ring arylic (or “aromatic”) compounds: furfural, furan, 2-methylfuran, benzofuran and pyrrole. The observed differences for these 5-ring arylic molecules can be easily explained: two single bonds for the heteroatom in one case and two aromatic bonds in the other case. This difficulty does not appear for 6-ring molecules, where the mean adjacent bonds of heteroatoms equal 1.5 bonds in both representations. Let us emphasise that the general consistency of the SMT procedure is based on the 2D Kekulé representation.
2.5. Experimental Solvent Descriptors of the Van der Waals Forces Involved in GLC Stationary Phases
As already seen in the Introduction, the present study is similar to our 2016 study for solutes, of descriptors prediction for solvents using the SMT procedure  . The principal observation in this last publication for solutes, was that in order to mitigate previous disappointing published results, the optimal approach was to limit those experimental descriptors to very accurate ones, more precisely those derived from a matrix of 127 solutes × 11 phases established by the Kováts group, using an original algorithm presently called MMA (as Multiplicative Matrix Analysis)   . In order to follow the same strategy for stationary phases properties, are reported in Table 1 the D, W and E values as reported in  for the 11 phases under study.
The first observation in view of the right columns of Table 1 is that D descriptor is almost a constant. That is a consequence of using the Kováts retention
Figure 2. Correlogram between the PSA values established using two methods. The SMT method appears more suitable for great molecules (i.e. polymers). See text.
Table 1. Solvent descriptors D, W and E of the van der Waals forces involved in GLC, according to  , and McReynolds b parameter according to  for 11 stationary phases studied by the Kováts group.
indices, which are relative expressions to n-alkanes of affinities of given solutes to given solvents, rather than absolute expressions.
Before going further, a few words of explanation on the column of Table 1 on McReynolds b parameter (or shortly McR b) are needed. In its study of 1970  , this author published various expressions of the polarity for 226 GLC columns (207 phases). This b descriptor or parameter allows for a quick transforming Kováts retention indices into absolute retention indices directed related to the solute/solvent affinity, according to West  :
in which RSL stands for relative slope (the reference phase being squalane in most cases)
in which RI and RIabs respectively stand for Kováts retention index strictly speaking and absolute retention index.
Unfortunately, in the particular case shown in Table 1, the McR b values are also constant and consequently a possible predicting model of McR b, and then of Dabs, has to be established using another experimental data set. We have selected for that the pooled McR b values from Table 1 and from McReynolds in 1970  , both reported in Table 2.
In our last publication devoted to the solvent properties of GLC stationary
Table 2. Experimental McReynolds b descriptors values for 86 GLC identified stationary columns (75 phases) from McReynolds  and from the Kováts group as reported above in Table 1. Highlighted columns correspond to duplicated phases from different suppliers.
phases  , a number of general trends were observed:
・ the descriptors McR b, W and E appeared related to PSA, in addition to other molecular features.
・ each molecular feature concerned, including PSA, appeared to be involved in a ratio of this feature to the molecular volume, Vw, contrary to the observations for solute descriptors. In other words, the various types of solvent polarities appeared in some way as densities of polarity.
・ the predicting equation for E, even not excellent (r = 0.85 for 11 phases), implied a confirmation of the previous observation of the Kováts group     that the alkanes, in order to be completely apolar phases, should be of infinite carbon atom numbers.
・ the predicting equation for McR b, relatively acceptable (r = 0.91 for 66 phases), was seemingly the first one proposed reflecting its physicochemical meaning. It also confirmed the observation pointed out in various studies, of an abnormal chromatographic behaviour of diglycerol     .
As outlined in the Introduction, the following presented Results aim to confirm the results above, and where possible improve on them.
3.1. McReynolds b Descriptor
Let us firstly recall the model proposed in 2011  :
with: r = 0.908; N = 74 columns (66 phases); F = 166.
After observing that with the slightly extended experimental data set in Table 2, both r and F values appear slightly improved with this 2011 model, finally an optimal model is presently shown in Figure 3.
It should be noted that using only two molecular features (PSA/V and O2/V), we obtained a very similar correlogram (r = 0.956, but F = 443). That can be interpreted as follows: the coefficients for O1/V, O11/V and N3/V are directly proportional in the PSA/V prediction and in the McR b prediction. In contrast,
Figure 3. Optimal prediction to date of the McReynolds b descriptor using the experimental values from Table 2 and the SMT procedure.
O2/V is out of this proportionality. It also should be specified that the compounds including F, Cl, Br, S, N111, present in Table 2, have not be kept by the MLRA program. In contrast, various other molecular features of N, present in the prediction of PSA, are absent in Table 2. For this reason we prefer to consider as temporarily valid the model shown in Figure 3, rather than the alternative one including PSA.
3.2. W and E Descriptors
Apart from the spectacular (and unexpected) match of experimental points to the models in Figure 4 and Figure 5 compared to similar attempts in 2011, let us firstly emphasise the important role played by the reverse of the molecular volume in Figure 5 (and its absence in Figure 3 and Figure 4). That confirms our observation in 2011, and above all the already mentioned previous observation of the Kováts group     , that the alkanes, in order to be completely “non polar” in the chromatographic sense, should be of infinite carbon atom numbers. That is not the case for squalane, generally chosen as a reference stationary phase.
Figure 4. Predictive model of the W solvent descriptor, based on Table 1 and the SMT procedure.
Figure 5. Predictive model of the E solvent descriptor, based on Table 1 and the SMT procedure.
Another observation is the important role played by the fluorine compounds in the W descriptor, and its total absence in the other two. It is also worth highlighting the important difference of coefficients for primary and secondary alcohols in the E descriptor, and the absence of difference for the other two descriptors.
4. Discussion and Perspectives
The publication of McReynolds in 1970  principally includes two types of experimental chromatographic data: 1) a matrix of retention indices of 10 solutes on 226 columns (207 phases), 2) the McR b descriptors for the same 226 columns. The first cited data set has been applied by number of authors in a purpose of classification the stationary phases, e.g.:      , but, as above mentioned, the polar descriptor McR b has only previously studied in a QSPR prospect in our study of 2011  and have been refined in the present one.
Compared with the results here presented using the experimental data from the Kováts group, those obtained from the 226 × 10 matrix of McReynolds can be considered as less satisfactory, whatever the authors are. In contrast, of course, the variety of the molecular structures on which the Kováts data are based is narrowed.
On the other hand and more generally speaking as already underlined  , all the studies based on the so called Abraham molecular descriptors are difficult to be compared with those based on mutually independent solute descriptors, as we are proposing since 2005  .
It is not easy to foresee the fruitful development of the results here presented. The author has been along all his activity time, interested by the olfaction in a broadest sense of the term, and involved in parallel in physicochemical and physiological aspects. The reason is that he is convinced that the recognition of the odorants by the olfactory receptors is not at all similar to the internal chemoreception, which is based on very specific key and cue mechanisms of recognition. The olfactory recognition, in contrast, is very probably based on a great amount of weakly specific receptors and a powerful system of information processing. The implicated labile intermolecular forces could be the Van der Waals forces … Some few results have been obtained in this sense, the last one in 2013  .
Taking into account the presently available experimental and accurate descriptors values for solvents, the results here presented appear rather satisfactory. They could be summarized as:
・ the confirmation of some broad trends previously published, as the role played by the molecular volume taken alone in the descriptor E, and the involvement of all the other molecular features expressed as ratios to the molecular volume;
・ the involvement of PSA has also be partially confirmed, but alternative regressive equations only based on SMT procedure presently provide much more better fitting with experimental values;
・ the results obtained for the McR b descriptor are obviously not so good than for W and E, but the explanation could be due to experimental material established in 1970 for McR b, and at the end of the nineties for W and E. Indeed, the chromatographic technology has greatly progressed in the time interval.
The challenge remains to know if, as they are, these results can be applied in purely physical chemistry and in other fields such as pharmacology or sensory physiology.
6. Supporting Information
Supporting information associated with this article is freely available by contacting the author at: firstname.lastname@example.org.
The eight latter publications we have signed or co-signed, including the present one, have been all based on an important collective work of the Kováts group in
The author warmly thanks Annick Aspirot for his writing assistance. He also sincerely thanks the Royal Society of Chemistry for its free ChemSpider database of chemical structures  and the Molinspiration Company for its freely interactive calculator  . This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.
 Karger, B.L., Snyder, L.R. and Eon, C. (1976) An Expanded Solubility Parameter Treatment for Classification and Use of Chromatographic Solvents and Adsorbents: Parameters for Dispersion, Dipole and Hydrogen Bonding Interactions. Journal of Chromatography A, 125, 71-88.
 Laffort, P. and Patte, F. (1976) Solubility Factors in Gas-Liquid Chromatography: Comparison between Two Approaches and Application to Some Biological Studies. Journal of Chromatography A, 126, 625-639.
 Laffort, P. (2016) A Revisited Definition of the Three Solute Descriptors Related to the Van der Waals Forces in Solutions. Open Journal of Physical Chemistry, 6, 86-100.
 Laffort, P. and Héricourt, P. (2006) Solvation Parameters. 2. A Simplified Molecular Topology to Generate Easily Optimized Values. Journal of Chemical Information and Modeling, 46, 1723-1734.
 Laffort, P. and Héricourt, P. (2009) Solvation Parameters. Part 4: What Is the Impact of Recent Chromatographic Data Update? The Open Applied Informatics Journal, 3, 12-21.
 ChemSpider, Search and Share Chemistry. (2017)
 Molinspiration, Calculation of Molecular Properties and Bioactivity Score. (2017)
 Laffort, P. (2011) Solvation Parameters. Part 5: Physico-Chemical Interpretation of Experimental Solvent Values for Stationary Phases of Gas-Liquid Chromatography. Journal of Chromatography A, 1218, 4025-4033.
 Palm, K., Luthman, K., Ungell, A.L., Strandlund, G. and Artursson, P. (1996) Correlation of Drug Absorption with Molecule Surface Properties. Journal of Pharmacological Sciences, 85, 32-39.
 ChemAxon Ltd. (2017)
 Laffort, P., Chauvin, F., Dallos, A., Callegari, P. and Valentin, D. (2005) Solvation Parameters: Part 1. Mutual Improvements of Several Approaches and Determination of Two First Sets of Optimized Values. Journal of Chromatography A, 1100, 90-107.
 West, S.D. (1989) Correlation of Retention Indices with Resolution and Selectivity in Reversed-Phase HPLC and GC. Journal of Chromatographic Sciences, 27, 2-12.
 Fritz, D.F. and sz. Kováts, E. (1973) Activity Coefficient for Gas Chromatography. Influence of the Molecular Weight of the Stationary Phase on Gas Chromatographic Data. Analytical Chemistry, 45, 1175-1179.
 Défayes, G., Fritz, D.F., Gorner, T., Huber, G., De Reyff, C. and sz. Kováts, E. (1990) Organic Solutes in Paraffin Solvents. Influence of the Size of the Solvent Molecule on Solution Data. Journal of Chromatography A, 500, 139-184.
 SUPELCO, Bellefonte, PA, USA (2017) Bulletin 880. Online Catalog.
 Li, J., Zhang, Y. and Carr, P.W. (1992) Novel Triangle Scheme for Classification of Gas Chromatographic Phases Based on Solvatochromic Linear Solvation Energy Relationships. Analytical Chemistry, 64, 210-218.
 Zenkevich, I.G. and Makarov, A.A. (2005) A New Application of McReynolds Constants to the Characterization of the Chromatographic Properties of Stationary Phases. Journal of Analytical Chemistry, 60, 845-850.
 Hoffmann, E.A., Fekete, Z.A., Rajkó, R., Pálinkó, I. and Kortvélyesi, T. (2009) Theoretical Characterization of Gas-Liquid Chromatographic Stationary Phases with Quantum Chemical Descriptors. Journal of Chromatography A, 1216, 2540-2547.
 Hoffmann, E.A., Rajkó, R., Fekete, Z.A. and Kortvélyesi, T. (2009) Quantum Chemical Characterization of Abraham Solvation Parameters for Gas-Liquid Chromatographic Stationary Phases. Journal of Chromatography A, 1216, 8535-8544.
 Reddy, K.S., Dutoit, J.C. and sz. Kováts, E. (1992) Pair-Wise Interactions by Gas Chromatography: Part I. Interaction Free Enthalpies of Solutes with Non Associated Primary Alcohol Groups. Journal of Chromatography A, 609, 229-259.
 Cloux, R., Défayes, G., Fóti, K., Dutoit, J.C. and sz. Kováts, E. (1993) Pair-Wise Interactions by Gas Chromatography: Part III. Synthesis of Isosteric Stationary Phases for Gas-Chromatography. Synthesis, 09, 909-919.
 Reddy, K.S., Cloux, R. and sz. Kováts, E. (1994) Pair-Wise Interactions by Gas Chromatography: Part IV. Interaction Free Enthalpies of Solutes with Trifluoromethyl-Substituted Alkanes. Journal of Chromatography A, 673, 181-209.
 Défayes, G., Reddy, K.S., Dallos, A. and sz. Kováts, E. (1995) Pair-Wise Interactions by Gas Chromatography: Part V. Interaction Free Enthalpies of Solutes with Primary Chloro- and Bromo-Alkanes. Journal of Chromatography A, 699, 131-154.
 Reddy, K.S., Cloux, R. and sz. Kováts, E. (1995) Pair-Wise Interactions by Gas Chromatography: Part VI. Interaction Free Enthalpies of Solutes with Primary Methoxyalkane, Cyanoalkane, and Alkanethiol Groups. Journal of Chromatography A, 704, 387-436.
 Dallos, A., Sisak, A., Kulcsár, Z. and sz. Kováts, E. (2000) Pair-Wise Interactions by Gas Chromatography: VII. Interaction Free Enthalpies of Solutes with Secondary Alcohol Groups. Journal of Chromatography A, 904, 211-242.