_{1}

^{*}

An experimental characterization of the Van der Waals forces involved in volatile organic compounds (VOC) dissolved into stationary phases of gas liquid chromatography (GLC) has been started at the beginning of the seventies. This field has been reactivated from 1994 thanks to a fruitful cooperation between our CNRS team and the group of Ervin Kováts at the Federal Polytechnic School of Lausanne. The applied strategy can be summarized, in the first instance, as the experimental measurement of accurate and superabundant mutual affinities of a limited number of VOC and stationary phases and their processing using an original tool named Multiplicative Matrix Analysis (MMA). Then, in the second stage, the obtained results have been compared with molecular properties well established, as the Van der Waals molecular volume, the refraction index and the polar surface area (PSA), in order to get generalized values for any compound. The present study summarizes the positive results developed in our three last papers on this topic (2013, 2016 and 2018), as well as the attempt to overcome the negative ones using enthalpies of vaporization.

One of our activity axes for various decades in our CNRS group and personally recently pursued, has been to characterize the intermolecular forces involved in solute-solvent interactions. This, in the purpose of getting accurate numerical values reflects these forces. We have preferred until now the GLC (Gas-Liquid Chromatography) approach, but the purpose of the present study is to explore, possibly more fruitfully, the enthalpy of vaporization splitting.

It has been recently published two papers on the intermolecular forces involved in GLC, respectively focused on solutes and on stationary phases acting as solvents [

It can be summarized in three steps:

· Establishment of accurate and superabundant databases of retention indices in GLC. Let us highlight the importance of expressing the retention in terms of Kováts indices (RI), the only one mapping out the observation of Rohrschneider [

RI − RI CH4 = δ D + ω W + ε E + α A + β B (1)

where the acronyms are those of _{CH4} being the retention index of methane, always equal to 100.

The first database we used in 1972 and 1976 [

[^{th} phase, the Hyprose SP-80. We did not hear about the achievement of this plan (McReynolds deceased in 1976).

Shortly after our publication [^{th} phase [

· Multiplicative Matrix Analysis (MMA). The operating principle of this data processing, initially developed in cooperation with Robin [

· Attempts of extending the accurate obtained results to a larger number of compounds. Two avenues have been explored. The first one is the experimental method using five selected stationary phases in filled columns. It could be quite easy to consider an automated device including five columns in parallel. In the publication [

The second avenue we have explored for extending the accurate results get for a few number of compounds is a Simplified Molecular Topology (SMT). This tool will be summarized in the Materials and Methods section since it is again applied in the present study, in spite of various relatively unsatisfactory results in the past [

They are detailed in [

· The induction-polarizability descriptor ε of solutes. This descriptor, or parameter named ε as reminiscent of electron, has firstly be drawn in previous studies [

ε 2016 = 10 f n R V W − 2.828 V W + 62.67 (2)

with: f n R = ( n R 2 − 1 n R 2 + 2 ) (3)

in which n_{R} stand for the refractive index at 20˚C, and V_{w} for the intrinsic molecular volume according to Molinspiration [

Because the refractive index is not always available in liquid state, an alternative expression of ε_{2016} has been proposed on the basis of 14 molecular features which can be named ε_{2016-SMT} (see its complete definition on the bottom of _{2016} and ε_{2016-SMT} has been found equal to 0.978 for 447 VOC in liquid state at room temperature.

· The dispersion descriptor δ of solutes. Similarly, in its more recent expression the δ_{2016} descriptor has been taken from the product fn_{R}V_{w}, and in its alternative version δ_{2016-SMT} from an equation including 10 molecular features (see its complete definition on the top of _{2016} and δ_{2016-SMT} has been found equal to 0.997 for 447 VOC in liquid state at room temperature.

· The solute descriptors α and β involved in hydrogen bonding. The solute parameters of acidity and basicity according to Abraham in 1993 [

· The orientation descriptor ω of solutes. As shown in _{2016}), as a function of 11 molecular features.

At this stage, it should however be underlined that this expression of ω, based on the results shown in

· The solvent parameters. The only accurate and available database of solvent parameters involved in Van der Waals forces we have found appears noticeably smaller than for solutes. It is limited to W and E for 11 stationary phases, as it can be seen in

We can see on the present

The three main observations to be retained about the solvent parameters as they are summarized in [

- Their prominent proximity with the Polar Surface Area (PSA), particularly for McR-b, but not only. Therefore PSA, promoted as of pharmacological interest ( [

- All the molecular features, including PSA, involved in a prediction model of solvent solvation parameters of GLC stationary phases should be divided by their intrinsic molecular volume on the contrary to that observed for solutes [

- The observation by the Kováts group [

ID | GLC Stationary Phases | Formula | McR-b | D | W | E |
---|---|---|---|---|---|---|

Kov_01 | 19, 24-dioctadecyldotetracontan (C78) | C78 H158 | 0.293 | 204.0 | 66.2 | 283.2 |

Kov_02 | infinite carbon atoms (Cinf) | Cinf Hinf | 0.288 | 204.2 | 68.3 | 306.6 |

Kov_03 | 18, 23-dioctadecyl-1-untetracontanol (POH) | C77 H156 O | 0.291 | 204.1 | 86.8 | 291.5 |

Kov_04 | 19, 24-bis-(18, 18, 18-trifluorooctadecyl)-1, 1, 1, 42, 42, 42-hexafluorodotetracontane (TTF) | C78 H146 F12 | 0.288 | 204.2 | 141.4 | 284.8 |

Kov_05 | 1, 1, 1-trifluoro-19, 24-dioctadecyldotetracontane (MTF) | C78 H155 F3 | 0.291 | 204.1 | 88.1 | 283.0 |

Kov_06 | 1-chloro-18, 23-dioctadecyluntetracontane (PCl) | C77 H155 Cl | 0.293 | 204.2 | 85.0 | 290.1 |

Kov_07 | 1-bromo-18, 23-dioctadecyluntetracontane (PBr) | C77 H155 Br | 0.291 | 204.2 | 83.9 | 291.5 |

Kov_08 | 17, 22, bis-(16-methoxyhexadecyl)-1, 38-dimethoxyoctatricontane (TMO) | C74 H150 O | 0.291 | 204.2 | 122.7 | 305.8 |

Kov_09 | 18, 23-dioctadecyl-1-untetracontanethiol (PSH) | C77 H156 S | 0.286 | 204.1 | 81.4 | 293.5 |

Kov_10 | 1-cyano-18, 23-dioctadecyluntetracontane (PCN) | C78 H155 N | 0.291 | 203.9 | 124.6 | 301.2 |

Kov_11 | 18,23-dioctadecyl-7-hentetracontanol (SOH) | C77 H156 O | 0.290 | 204.1 | 87.2 | 289.1 |

Mean value | 0.290 | 204.0 | ||||

Standard deviation | 0.002 | 0.1 |

Let us mention an erratum in the

As mentioned above, the main observed difference between solute and solvent parameters is that the former can be expressed as functions of one or various molecular features, whereas the latter as functions of similar features but divided by their intrinsic molecular volume. This finding may be seen slightly surprising but a priori acceptable.

The main question comes from our publication of 2013 [

On the other hand, it has also be shown in 1989 by Patte et al. [

Because the superimposition of the 59 odorant curves on the same diagram would be difficult to interpret, these authors have parameterized the experimental points for each of the 59 odorants, using the Hill model [

R = ( C / C x ) n R M 1 + ( C / C x ) n (4)

in which R stands for the electroantennogram amplitude of response, R_{M} for the maximal amplitude, C for the concentration, n for the power law exponent and C_{x} for the concentration corresponding to the inflexion point in the log-linear sigmoid curve.

This model appears often suitable in life sciences, each time the experimental curves present a sigmoid shape in linear-log coordinates and a hyperbolic shape in log-log coordinates, as it is the case in

It can also be considered an anchor point (C_{0}, R_{0}) in the bottom of the slanted almost straight line of the log-log drawing as in

log C 0 = 1 n log R 0 R M − R 0 + log C X (5)

One of the Hill model main advantages is that it easily allows iterative procedures resulting to an optimal fitting between experimental points and curvilinear drawings like in _{M}, C_{X} and C_{0}. (In the Patte et al. experimentation on the Honey Bee, R_{0} has been fixed to 0.1 mV, as the minimal electrophysiological value distinct from the base-line).

That has allowed Patte et al. to characterize the 59 studied odorants using these four olfactory parameters and to observe two things: 1) their strong mutual correlations and 2) high improvements of these correlations when the concentrations are expressed in fractions of saturated vapor pressure, as reflected by Equation (6) and Equation (7):

log C x = log SVP + log R M n − 2.33 ( r = 0.99 ; N = 59 ; F = 946 ; without outliers) (6)

log C 0 = log SVP + log R 0 n − 2.33 ( r = 0.97 ; N = 59 ; F = 404 ; without outliers) (7)

in which SVP stands for the saturated vapor pressure expressed in bars and the constant −2.33 as the abscissa C_{C} of the convergent (and comfort) point.

It should be underlined that this type of statistical results is unusual in life sciences.

In fact, the original Equation (7) from [

log C 0 = log SVP + log R 0 n − log R C n − 2.33 (8)

in which R_{C} stands for the response at the convergence point, and that by chance in the present case, as it can be verified in _{C} = 1 mV, and therefore logR_{C}/n = 0

Without deeply entering into the physical chemistry of solutions, the role played by the saturated vapor pressure at very different concentrations consists to say that the odorants reach the olfactory dendrites through a dry route into pores-tubules until the immediate proximity of the olfactory cilia, as it is shown in various anatomic studies on Insects [

Furthermore, the high mutual correlations between the olfactory parameters C_{X}, R_{M} and n, or C_{0}, R_{0} and n, respectively observed in the Equation (6) and Equation (7), reflect the intersection of the 59 curves for the abscissa −2.33 of the log fraction of saturated vapour pressure, as it is exemplified in

From psychophysical studies (i.e. human responses), it has also be shown for a long time [_{0} and the power law exponents n. This has been partially interpreted as the fact that the olfactory dendrites of neuroreceptors in Vertebrates are immersed in olfactory aqueous mucus at least 30 times thicker than the water layer in Insects mentioned above, where the VOC (volatile organic compounds) can not obey to the Raoult law. We have proposed in 2013 [

v e r t o l f = 7.406 MR 100 + 3.604 PSA2 V w (9)

in which MR stands for the molar refraction, V_{w} for the Van der Waals molar volume and PSA2 for one of the slightly modified expressions of the original polar surface area, specified in the Material and Methods section.

The equation analogous to (7) valid for psychophysical data, as it appears in 2013 [

log C 0 = − v e r t o l f − 0.8177 n − 2.3 ( r = 0.77 , N = 186 , F = 89 , without outliers) (10)

At this stage, in spite of the moderate value of the resulting correlation coefficient with the Equation (10), the analogy between Equation (7) and Equation (10) must be underlined. It however remains a difficulty concerning the definition of vertolf in Equation (9), which appears as the sum of two terms: one as suitable for solutes (7.406MR/100) and another one as suitable for solvents (3.604PSA2/V_{w}). Indeed, as seen in §1.1.2, molecular features (here MR and PSA2) have to be divided by their intrinsic molecular volume only for solvents. The principal purpose of this study is to overcome this apparent inconsistency in definition of vertolf.

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 be presented and detailed elsewhere [_{4}, OH_{2}, NH_{3}, SH_{2}) are excluded. In addition, a connectivity parameter due to Zamora [

Let us specify that the calculations using the SMT procedure have been made manually in this study, using 2D molecular drawings from ChemSpider [

One of the ways to overcome the apparent contradiction between our three last publications mentioned in the Introduction could be at the first sight the use of molecular surface area instead of the molecular volume. In the presentation of the Molecular Surface Area Plugin by Chemaxon, it is specified that two types of available molecular surface area calculations are available: the Van der Waals surface area and its Solvent Accessible Surface Area (SASA), both being expressed in Ǻ^{2} [_{w} (both from Chemaxon [

Nevertheless, we have tested in the present study the property we propose to call the Global Spherical Surface (GSS), expressed as derived from the molecular volume as follows:

GSS = ( 36 π ) 1 / 3 V w 2 / 3 ≡ 4.836 V w 2 / 3 (in Ǻ^{2} when V_{w} is expressed in cubic angstroms) (11)

This expression means that solute molecules are considered as small spheres disseminated in the solvent.

We have considered until now three variants of PSA:

- The most classical, only including the polar atoms N and O. We have selected the values named TPSA (T as topological) established by Molinspiration [

- The variant including the same polar atoms N and O as in TPSA, but also the various divalent S according to Ertl et al. [

- In 2013 we have named PSA2 a third variant initially identical to PSA3, but diminished of the pentavalent N present in nitrates according to [

All the sources of PSA come from Molinspiration [

We have adopted in the present study the values of molecular volume according to Molinspiration [_{w} (w as Van der Waals), in order to avoid any confusion with V_{20}, the molecular volume at 20˚C (molar mass/density) which is not an additive property [

Most of those applied here are from ChemSpider [

1) The two descriptors of solutes δ and ε (see meaning of acronyms in _{R}) and Van der Waals molecular volume (V_{w}), according to the Equation (12) and Equation (13) from [

δ 2016 = f n R V w with f n = n R 2 − 1 n R 2 + 2 (12)

ε 2016 = 10 f n R V w − 2.828 V w + 62.67 (13)

In addition to these definitions, named “theoretical” in [

2) The descriptors of solvents. The predicted W and E descriptors in [

Otherwise, two updated predictions of the McR-b descriptor using PSA (unpublished until now) are given for the database on the study (75 phases on 86 columns), by the Equation (14) and Equation (15)):

McR-b 2019 = 0.299 − 0.253 PSA V W r = 0.946 , F = 710 (14)

McR-b 2019 = 0.302 − 0.229 PSA V W − 0.992 O11 V W r = 0.959 , F = 472 (15)

[ F = 548 ] [ F = 26 ]

whatever the chosen molecular features are (e.g. with or without PSA, with 66 columns as in 2011 or with 86 as presently), all the higher tests values of validation are obtained with the ratio molecular feature over V_{w}. And when it is included with other features, PSA always plays a central role in the regressions.

Let us note that variants of PSA mentioned in the Material and Methods section are equally validated in the Equation (14) and Equation (15), since among the phases selected in the database of McReynolds no one includes sulfur nor nitro compounds.

3) The ω descriptor for solutes. As it results from the Introduction, the principal effort remaining to do in the present topic is related to an improvement in the characterization of the ω descriptor for solutes.

As a last development of our GLC approach, in _{2020-SMT} seems clearly preferable to the one including V_{w}. Indeed, in addition of the absence of outlier, the ω_{2020-SMT} model appears preferable to the ω_{2016-SMT} one on the basis of a visual comparison of the two correspondent correlograms in

The results obtained using the enthalpy of vaporization have been based on a databank of 445 volatile organic compounds (VOC) in liquid state at room temperature (more often at 20˚C), chosen as including numerous chemical functions: alcohols, aldehydes, ketones, carboxylic acids, ethers, amides, lactones, nitro-compounds, nitriles, amines, esters, various types of halogen and sulfur compounds and hydrocarbons, both of saturated or unsaturated types, with and without mono and polycycles. A similar set of 447 VOC was used in 2016 [

[

The enthalpy of vaporization values for the 445 VOC under study come from ChemSpider [_{vap} of these 445 VOC is as follows:

H_{vap} = :

· 0.4840 f n R V W + 17.23 [ F = 2554 ] (δ_{2020} + 17.23) (16)

· _{2020}) (17)

· _{2020}) (18)

· _{vap}_{ 2020}) (19)

in which S_{vap} stands for the entropy of vaporization and T_{BP} for the boiling point expressed in kelvins.

Comments

· The predictive regressions of enthalpy values as the sum of Equations (16)-(19) applied to the 116 hydrocarbons taken alone and to the all 445 compounds of the database under study are visualized in

· The constant 2.25 attributed to the ε_{2020} definition has been chosen to provide zero values for the normal alkanes.

· The comparison between the 2016 and 2020 versions of the VOC characteristics is as follows:

(by definition) (20)

(, also from their definitions) (21)

· By contrast, ω_{2020} could not be assimilated to ω_{2020-SMT} (definition recalled in _{2020}.

· The constant 17.23 greatly reflects the product PV of vaporization included in the corresponding enthalpy (H = U + PV). Taking into account the important difference of molar volume in liquid and gas phases (respectively 0.1 liter in average and 24 liters) associated to a constant pressure of one atmosphere, a product value in the range 23 - 24 was expected rather than 17.23. This difference of values could be due, among others, to the predictive function of V_{w} including a constant, i.e. providing positive values for hypothetic compounds without any atom (see

· According to a study of Goss and Schwarzenbach [_{vap}_{-2020} descriptor proposed here appears rather convincing for characterizing the entropy of vaporization, and thus in some way validates the general definitions of δ_{2020}, ε_{2020} and ω_{2020} which together reflect the free internal energy of vaporization U_{vap} (

The Equations (16)-(19) have been applied to another data set of 180 compounds for which interesting results have been obtained in an olfactory QSAR study as mentioned above. On the contrary to the 445 compounds dataset including only liquids at room temperature, the 180 compounds dataset includes 27 solids and 8 gases (the redundancy between these two datasets concerns about 60 compounds). As it can be seen in

The author is greatly indebted to the Royal Society of Chemistry for its free ChemSpider database of chemical structures and physicochemical properties, including values of the named “enthalpies of vaporization” on which the present study is based.

We understand that this last expression is an abbreviation of “difference of enthalpy at the boiling point and at room temperature (usually 20˚C or 25˚C)”. It is also named “boiling enthalpy”.

The present study confirms some results on the intermolecular forces based on GLC experimentation previously published (the London and Debye forces), as stated in the Introduction of this paper. It also improves the results previously obtained on the molecular polarity strictly speaking (Keesom forces) as stated in the Results section. However, we believe that at this stage a dialog with colleagues involved in theoretical and experimental thermodynamics would be fruitful to go even further in the present field.

Some particular comments

· The descriptors of molecular polarity strictly speaking for solutes, via a GLC approach and the enthalpy of vaporization one, present some similarities but not complete.

· The first interesting convergence observed in the present study on the ω descriptor is summarized in _{vap} or GLC: the former with one of the PSA variants described in the Material and Methods section (PSA1), and the latter with 10 different molecular features including three with strong coefficients and strong partial F ratios (N3, O2 and F1) (see

· One hypothesis can be suggested to explain this phenomenon: some molecular proximity in the molecular aptitudes to be polar and to be proton acceptor, and a consecutive wrong rearrangement of the input values in the MMA processing of the GLC experimental data (see _{vap} data, since proton donor and proton acceptor abilities are neutralized in mutual hydrogen bonding between the molecules of a given compound. Therefore the ω values obtained from H_{vap} seems to be preferable.

· Another difficulty arises from the role played by the divalent sulfur compounds in our QSAR study of 2013 [_{vap} (Equation (18),

· To conclude, it can be considered that the splitting of enthalpy of vaporization for liquids into δ_{2020}, ω_{2020}, ε_{2020} and [S_{vap}_{-2020} + 17.23] using Equations (16)-(19) correctly reflects the Van der Vaals and the hydrogen bonding forces. It appears to be a quite robust answer entirely based on well established and easily available molecular properties. Only the three first terms are expected to be involved in some physiological phenomena, not the entropic plus the constant part.

The author reiterates its gratitude to ChemSpider for having inspired the new approach of the Van der Waals forces characterization described here. He also warmly thanks David Laffort for his strongly needed writing assistance.

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

The authors declare no conflicts of interest regarding the publication of this paper.

Laffort, P. (2020) Interest of Splitting the Enthalpies of Vaporization in Four Distinct Parts Reflecting the Van der Waals and the Hydrogen Bonding Forces. Open Journal of Physical Chemistry, 10, 117-137. https://doi.org/10.4236/ojpc.2020.102007