It is currently admitted that the intermolecular forces implicated in Gas Liquid Chromatography (GLC) can be expressed as a product of parameters (or descriptors) of solutes and of parameters of solvents. The present study is limited to those of solutes, and among them the three ones are involved in the Van der Waals forces, whereas the two ones involved in the hydrogen bonding are left aside at this stage. These three studied parameters, which we call δ , ω and ε , respectively reflect the three types of Van der Waals forces: dispersion, orientation or polarity strictly speaking, and induction-polarizability. These parameters have been experimentally obtained in previous studies for 121 Volatile Organic Compounds (VOC) via an original Multiplicative Matrix Analysis (MMA) applied to a superabundant and accurate GLC data set. Then, also in previous studies, attempts have been made to predict these parameters via a Simplified Molecular Topology procedure (SMT). Because these last published results have been somewhat disappointing, a promising new strategy of prediction is developed and detailed in the present article.
The present study takes place at the continuation of a series of six papers started in 2005 by our group, in which we have focused our efforts on a better knowledge of the intermolecular forces involved in GLC (Gas-Liquid Chromatography) between solutes (VOC or Volatile Organic Compounds) and stationary phases [
・ Van der Waals, subdivided in London, Keesom, and Debye types,
・ hydrogen bonding, subdivided in proton donor and proton acceptor types.
According to Rohrschneider [
in which RI stands for the Kováts retention index of the solute on the stationary phase under study, and
Among the results obtained in our series of six quoted studies, those useful for the present are summarized in
The physicochemical characterization of our solute parameters is partially similar to that adopted by various authors starting with the study of Abraham et al. in 1990 [
Three out of our four polar solute parameters are very similar to those of Abraham and co-authors: those we are calling ε, α and β. By contrast, our ω parameter (as orientation or polarity strictly speaking) is quite different of the corresponding parameter according to Abraham and co-authors (equations have however been provided to transform one system into the other one [
・ dispersion (London),
・ orientation or polarity strictly speaking (Keesom),
・ polarizability-induction (Debye), (ε as electrons involvement),
・ acidity (proton donor according to Brønsted),
・ basicity (proton acceptor according to Brønsted).
Based on a strong cooperation between our group and the Kováts group, accurate values of solute parameters have solely been established applying an original algorithm presently called MMA (as Multiplicative Matrix Analysis) to a set of retention indices of 127 compounds on 11 phases [
An improvement of this step has been the reduction of the number of needed stationary phases without losing accuracy. The most satisfactory result has been obtained with two apolar phases of very different molecular weight and same structure, and three polar phases, respectively poly-fluorinated, polyether and primary mono alcoholic. Because these five phases have been synthesized by the Kováts group and are not commercially available, a procedure has been proposed to calibrate the commercial phases using six VOC references [
In 1982 [
It should be relatively easy to reach the above mentioned goal using filled columns. The purpose could however be harder with open tubular columns, particularly for the proton donor phase and the two apolar phases of very different molecular weight, as suggested, for example, by the results of Poole et al. [
The 100% GLC determination of solutes parameters not seemingly being anymore developed, an alternative way has been followed consisting in the pooling of those presently available with those published by Abraham and co-authors [
In the above mentioned step, simultaneously to the solute parameters for 127 compounds, were obtained the accurate values of solvent parameters named D, W, E, A and B for 11 stationary phases.
On another hand, from the important collection of GLC retention indices published by Mc Reynolds in 1970 (207 stationary phases on 226 columns and 10 VOC) [
As for solutes, we pooled these two data sets into a more extended data set of 66 phases (56 ? 1 + 11) [
We added in this pooled data set, according to [
The results are clear and contrasted. On one hand their identification is almost evident (to a solute proton donor property correspond a solvent proton acceptor property and reciprocally). On the other hand their values predicted on the basis of a simplified molecular topology (which is summarized in the Material and Methods section of the present paper) fail to be satisfactory each time intramolecular hydrogen forces are suspected. The solution could perhaps be to extend the molecular topology presently applied, to a larger neighboring of a given atom. However, that solution would need considerably more experimental data than the presently available ones.
The results are more satisfactory. Out of the three molecular parameters of solutes, those of dispersion δ and of induction-polarizability ε are clearly related to equations including the molar refractivity and the Van der Waals molar volume, both being easily and accurately predictable, even for solids and gases, using a simplified molecular topology.
Similarly, out of the solvent parameters of phases, the parameters b of McReynolds and E have appeared related to equations including the Van der Waals molar volume and the PSA (polar surface area), both being easily and accurately predictable, even for solids and gases, using a simplified molecular topology. By contrast, the cases of the orientation or polarity strictly speaking parameter of solutes ω, and of its associated solvent parameter W have remained open.
The present study, therefore, is limited to intent an optimal characterization of the solute parameters related to the Van der Waals forces, those related to the hydrogen bonding forces being (temporarily?) left aside.
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 presented elsewhere [
In addition to the 34 atom characteristics kept, we also consider three additional topological features:
・ Chlorine linked to carbon C11.
・ Amines linked to (a carbon linked to O2). This feature is present in amides.
・ A connectivity parameter due to Zamora [
In
As shown in the Introduction, four sets of solvation parameters have been established along the last decade: two for VOC as solutes and two for GLC stationary phases as solvents [
For solutes, one set exclusively comes from GLC experimentation and can be considered as accurate (127 compounds), and the other one, only partially from chromatographic origin and less precise, covers a greater variety of VOC (456 compounds). Some compounds have been excluded from these two initial experimental data sets of solutes:
・ Those which include Si or Sn,
・ Those which include a given atom only linked to hydrogen (e.g. CH4, OH2, NH3, SH2),
・ Those in gas or solid state at room temperature.
Structural elements | Bonds | Topological features |
---|---|---|
Carbon | ≤4 | C0, C1, C11, C111, C1111, C2, C12, C112, C22, C3, C13 |
Oxygen | ≤2 | O0, O1, O11, O2 |
Nitrogen trivalent | ≤3 | N0, N1, N11, N111, N12, N3 |
Nitrogen pentavalent | ≤5 | N122 |
Phosphor pentavalent | ≤5 | P1112 |
Fluorine | 1 | F1 |
Chlorine | 1 | Cl1 |
Bromine | 1 | Br1 |
Lodine | 1 | L1 |
Sulfur divalent | ≤2 | S0, S1, S11, S2 |
Sulfur hexavalent | ≤6 | S111111, S1122 |
Hydrogen | 1 | H1 = sum (maximal bonds-explicit bonds) |
ADDITIONAL | ||
Cl1^C11 | Chlorine linked to C11 | |
NCO | N1 or N11 or N111 linked to (a carbon linked to O2) | |
SSSR | Smallest sum of the smallest rings |
*See explanation in the text. Italicized elements are not involved in the present study.
Finally, the number of VOC kept in these two data sets under study becomes respectively 121 for the accurate one and 447 for the extended one.
These four data sets thus specified are reported in the Supplementary Material, excluding the parameters α, β, A and B, which are involved, as we saw, in the hydrogen bonding forces.
The polar surface area of a molecule (PSA) is currently defined as the surface sum over all polar atoms, primarily oxygen and nitrogen, also including their attached hydrogens [
These interesting results have tended to consider PSA as a strictly pharmacological property not applicable in the physicochemical field as a general criterion of polarity, since, for example, strongly polar elements such as halogens, particularly fluorine, have always been excluded of its definition. We have however recently shown that PSA, associated with the Van der Waals molecular volume Vw, appears strongly implicated in the characterization of one of the polarities observed in GLC: the McReynolds b parameter already quoted [
Few authors also include sulphur and phosphor in an alternative definition of PSA [
A second purpose of the present study is therefore an attempt to elucidate what appears, at the first view, as a contradiction: is it PSA a pharmacological property strictly speaking or a more general tool characterizing the molecular polarity? That involves a clarification, on experimental basis, about its most suitable definition among the various ones already proposed: is it or not a unique one valid in all circumstances?
In their early applications [
In the present study, the TPSA values have been collected, for the extended set of 447 VOC, from Molinspiration [
The various expressions supposed to be reflecting 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 then in the present study, the values of molecular volumes (expressed in cubic angstroms) proposed by the freely interactive calculator of Molinspiration [
These properties are the measure of the total polarizability of one mole of a given compound. According to the Lorentz and Lorenz equation, MR can be determined as follows:
with
and
in which M, d and n stand respectively for the molar mass, the density at 20˚C and the refractive index at 20˚C. Initiated by Abraham et al. [
The molar refractivity values are generally expressed in ml∙mol−1.
Applying a multiple linear regression analysis (MLRA) to the ω values of the 121 VOC data set, as possible functions of the molecular features of
As a reminder, F ratio value can be obtained from the correlation coefficient r, the number of observations N (here the number of VOC) and the number of independent variables, according to Abdi [
Obviously, the quality of the prediction differs according to the considered statistical test; r or F (both statistical tests are supposed to be as high as possible).
Most statisticians often prefer the second criterion, particularly when the number of independent variables increases in large proportion relatively to the number of observations.
As a result, we consider for further uses, and perhaps as a first approach, the SMT model reported in
An interesting observation is the discarding of the molecular feature N122 (present in nitrates) by the MLRA program, confirming our previous hypothesis that the pentavalent N is non polar [
Let us specify that in
The best molecular property well established, related to the solute parameter of dispersion δ obtained via an experimental GLC, has been found to be the molar refractivity we have named MRw in Equation (5) [
The theoretical induction-polarizability parameter εtheoret is obtained via a bilinear relationship between the molar refractivity and the molar volume, such as its values equals zero for n-alkanes, according to the following equation:
In order to express it in a similar scale of sizes than δ2016 and ω2016, we define henceforward ε2016 as follows:
No significant improvements have been found in the present study, comparatively to
[
・ the three parameters appear partially related, in addition to other molecular features, to PSA,
・ each molecular feature concerned, including PSA, appears involved in a ratio of this feature to the molar volume Vw, on the contrary of what is observed for solute parameters. In other words, the various types of solvent polarities appear in some way, as densities of polarity,
・ more precisely, the parameters McR b and E can be expressed via two different equations including both PSA/VW and 1/VW.
At this stage, there is no new argument concerning the inclusion or not of other polar elements than N and O in the definition of PSA. By contrast, the observation already made [
The results on solute parameters presented here, compared to those previously published on the same topic, show real improvements, as summarized in
Let us recall that the difference in the N values between 2008 and the present study for δ and ε not at all results from an elimination of outliers in the MLRA of data, but from objective facts detailed in the Materials and Methods section. Concerning ω, the important difference value of N is principally interpreted as a lack of accuracy in the more extended data set, as we already saw.
The improvements observed in the present study are principally due to a pragmatic approach summarized in
・ starting with only accurate and superabundant experimental data submitted to an MMA;
・ physicochemical characterization when possible, with molecular properties well established for a large amount of compounds, as it is the case, for example, for VW, MRW and PSA;
・ if it is successful, applying SMT to these well established properties, in order to overcome some inappropriate situations (e.g. refraction index for solids and gases); this step has been applied to δ2016 and ε2016;
・ if it is unsuccessful, applying SMT to chromatographic accurate and less numerous data (this step has been applied to ω2016).
It should be of interest to note the high mutual independence of these parameters, as it can be seen in
The absence of improvements for solvent parameters is very probably due to a too small amount of accurate and superabundant chromatographic measurements. One of the consequences is the uncertainty about possible presence of polar elements in the definition of PSA, other than N and O. The only conclusive fact seems to be the absence
r | N | F | ||
---|---|---|---|---|
δ | 2008 (ref. [ | 0.981 | 456 | 944 |
present study | 0.997 | 447 | 6136 | |
ω | 2008 (ref. [ | 0.861 | 456 | 145 |
present study | 0.976 | 121 | 197 | |
ε | 2008 (ref. [ | 0.954 | 456 | 351 |
present study | 0.978 | 447 | 691 |
of pentavalent N and P and of hexavalent S.
The present study does not provide any improvements in the separation of components of solutions nor the identification of such components, both being the principal followed purposes in chromatographic sciences. On the other hand, the results obtained in this study and in some other ones we have previously conducted in a similar way, would not be reached without the strongly help of GLC experimentation. We have presently the key to determine with simplicity and a relatively not too bad accuracy, the three parameters, for solutes, of Van der Waals forces in solutions. And we strongly believe that these labile forces could be implicated in some pharmacological and chemo sensorial properties. Our next effort will be to test this hypothesis.
It should be difficult to conclude this study without quoting an important recent review on the “Determination of solute descriptors by chromatographic methods” by Poole et al. [
Concerning the possible objection against our ω2016 model, because only based on 121 solutes, it should be noted that this data set includes numerous chemical functions: alcohols, aldehydes, ketones, ethers, nitro-compounds, nitriles, secondary and tertiary amines, esters, various types of halogen and sulfur compounds and hydrocarbons, both of saturated or unsaturated types, with or without mono and polycycles… are however absent (and present in the set of 447 solutes) primary amines, carboxylic acids, amides and lactones. Also, substances with more than one chemical function are sparingly represented in this 121 data set. As a conclusion, the strictly speaking polarity descriptor proposed here, of purely pragmatic and not at all of theoretical nature, could be considered as a first approach, and possibly improvable in the future with the help, among others, of semi empirical quantum chemical methods already applied in this topic (e.g. [
The author warmly thanks David Laffort for his writing assistance. He also sincerely thanks the Royal Society of Chemistry for its free Chem Spider database of chemical structures [
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. http://dx.doi.org/10.4236/ojpc.2016.64009
Databases associated with this article are freely available, on request to the author:<paul.laffort@sfr.fr>
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