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).

The principle of this tool has already been presented elsewhere [5] [6] . 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 [7] 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 [8] .

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 [9] . 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 [10] , 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.

According to Palm et al. [11] , who have strongly promoted this molecular

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 [8] , Molinspiration [9] or Chemaxon [12] . 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 [10] .

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.

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 [4] . 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) [6] [13] . 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 [6] 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

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 [14] , 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 [15] :

RSL = McRb McRb reference (2)

in which RSL stands for relative slope (the reference phase being squalane in most cases)

and RI abs = RI × RSL (3)

in which RI and RI_abs 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 D_abs, 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 [14] , both reported in Table 2.

Let us firstly recall the model proposed in 2011 [10] :

McRb 2011 = 0.29 − 0.26 PSA V + 6.22 V (4)

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,

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.

The results obtained on the basis of Table 1 for the W and E descriptors are summarized in Figure 4 and Figure 5.

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 [16] [17] [18] [19] , 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.

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.