TopoIogicaI A naIysis of Gas-Liquid Chromatographic Behavior of Alkenes J. R. ChrBtien and J. E. Dubols” Laboratoire de Chimle Organique Physique de I ’ Universitg Paris VU, AssocI6 au C .N.R. S . , 75005 Paris, France
Topologlcal analysis of Kovets indices of an alkene populatlon analyzed on five different statlonary phases Is presented. Attentlon Is focused only on topological anaiysls In gas chromatography for physicochemlcal appllcatlons and not for predlction of retention data. An evident chromatography meaning is given to the calculated topology-lnformatlon correlatlon by the DARC-PELCO method, Le., to the contrlbutlon of topological sites which approxlmately correspond to every skeleton carbon atom. The variations of these parameters are related to the internal effects of environment arislng from the structure of the solute and to the external effects of environment arising from the speclflc solute-statlonary phase interactlons. Furthermore, for alkene Kovirts indices on P,/Y-ODPN, the correlation parameters are related to the T electron net charge dlstributlons.
Exploitation of Kovlts indices by factorial analysis (1-4) or information theory and numerical taxonomy ( 5 , 6 )chiefly stresses stationary phase behavior. Physicochemical data, when calculated, are always given for the whole solute ( 1 , 3 ) . In this paper we intend to show how topological analysis together with topology-information correlations can grasp solute chromatographic behavior on practically every skeleton carbon atom. In most cases, published topology-informationcorrelations exploit independent physicochemical data and independent populations of compounds: IR vibration of the group C-0 (7), 13C NMR chemical shift (B), alkene bromination rate constants (9), heats of formation of ketones (101, pharmacodynamic activity (11),retention data in GC (12-19). The independence of these correlations has excluded any comparison between them. These correlations, established for a purely previsional purpose, bring out the coherence in the information relative to the various compounds of each population, by breaking down the molecular information on a structural model related to the studied population. Thus, until now, we have only given a limited phenomenological interpretation to the values of the perturbation terms associated with the sites of the structural model: determination of the active environment next to the functional group, particular influence of sites corresponding to certain ramifications. In trying to extend the phenomenological interpretation of the topology-information correlations within the framework of the DARC (DARC stands for description, acquistion, restitution and conception; topological analysis, by means of topology-information correlations, takes place chiefly within the framework of the last point, i.e., conception) topological system (20, 21), we were rapidly faced with the question: “Is it possible to give these empirical relationships a real physicochemical meaning?” In answer to this question, our attention was drawn by the retention data in GC, since they offer the possibility of obtaining microvariationsin the behavior of the same population of compounds analyzed on stationary phases of varied polarity.
Furthermore, for structurally comparable populations (alkanes, alkenes, alcohols, esters, iodides, ...) analyzed on the same stationary phase, it is possible to follow the influence of the progressive variation of the “polarity” of the functional group by following the variations of the different parameters of the correlation. Various prediction oriented topology-information correlations in GC have already been published: relative retention times for ketones (12,13)and esters (14,15), relative retention volumes for aldehydes (16),Kov6ts indices for aldehydes alkanes (18), alkenes (18), dibromo- and bromomethoxyalkanes (19). Chastrette et al. (16) have already compared and regrouped, within the same population, two populations of relative retention times for ketones and esters, thereby stressing the comparable influence of certain sites of the molecular environment. However, for a physicochemical interpretation, using retention times relative to a compound of a population, partially shadows the particular role played by the functional group in its interactions with the stationary phase. Although the Kovgts indices are also relative data, using n-alkanes as a reference avoids the above-mentioned drawback. Furthermore, by taking certain precautions, their precision is greater than that of the other chromatographic data (22,23). Thus, we have recently shown the predictive possibilities offered by a topological analysis of Kovlts indices (24):interpolation and extrapolation of retention data within a given structural population; the use of information dealing with other compound populations to increase the predictive aptitude of correlations established with a reduced compound population; the extension of this analysis to Kovlts indices determined under different chromatographic conditions (stationary phase, temperature). The exploitation of these possibilities can be obtained only by a simultaneous in depth study of the physicochemical significance of the topologyinformation correlation parameters used. Topological Analysis of Kovits Indices. The physicochemical exploitation of the topology-information correlations of the Kovlts indices is not self-evident because these relative data are rather complex by definition. The index of a solute X is defined, with respect to two n-alkanes with 2 and 2 + 1 carbon atoms, with the help of the corresponding specific retention volumes V , (25) as
(In,
.
In fact, the Kovlts index is simultaneously extensive and intensive in character, in other words, this property is simultaneously diffused all over the molecule and localized on the focus. Some examples will clarify this point. The molecular weight of a compound is the classical example of a n extensive molecular property. It is proportional to the number and mass of every type of atom. The extensiue character of the Kovcits index is related to its defined relationship, e.g., lengthening of an n-alkyl chain far enough away from the functional group contributes 100 IU per methylene group. ANALYTICAL CHEMISTRY, VOL. 49, NO. 6,MAY 1977
747
In the contrary alkenes IR absorption about 1650 cm-l is chiefly an intensive molecular property. It is characteristic of most alkenes, insensible enough to the environment, and not proportional to the carbon atom number. So, spectroscopic data (S(13C)in NMR, -v in IR) (7,8) and kinetic data (rate constants for alkene bromination) (9),which also led to a topological analysis, are almost exclusively of an intensive character. The property is above all localized on the focus (13C, C=O, C=C) and the environment only contributes perturbations which most often vanish after the f i t two layers of atoms around this focus. T h e intensive character of the Kovdts index is all the more marked since the functional group (usually assimilated to the focus) as well as the stationary phase used are more “polar”. This is illustrated by Ettre (26), according to Wherli and Kovlts, by indicating as a scale the large dispersion of the retention contributed by the functional group grafted onto the same n-alkyl chain R. This contribution by the focus is expressed as increments of the Kovlts indices, AI, and varies nearly 400 IU when going from the hydrocarbon RH to the corresponding alcohol ROH; this behavioral variation being the calculated difference between the Kovlts indices on the Emulphor 0 phase and on the Apiezon-L one. To summarize, in a first approximation, the following assumptions are taken: the extensive character of the Koudts index is related to the characteristics of solutes, that is to their ideal behavior; the intensive character of the Kovdts index is related to the specific solute-stationary phase interactions, that is, to the nonideal behavior of solute molecules. These specific interactions take place in a more preponderate manner at the level of the functional group but also, to a lower extent, at the level of every topological site. So, if we want to give the empirical relationships of topological analysis a real physicochemical meaning it becomes necessary to separate the previously defined extensive and intensive characters of the Kovlb index. I n other words, from a structural point of view, our problem boils down to determine the sensitivity of the perturbation terms to the internal and external effects of environment, the first arising f r o m the structure of the solutes and the latter from the solute-stationary phase interactions. Before confronting this problem, arising from the dual nature of the Kovlts index, it should be stressed that a discussion, on a physicochemical basis, of the values of the perturbation terms of these topology-informationcorrelations brings up another difficulty which, this time, is due to the data processing method and not to the information studied. In fact, the values obtained for the structural parameters (Le., the perturbation terms associated with the topological sites) depend not only on the characteristics of the information‘ studied, but also on the conventional structural model envisaged. Thus, any discussion should take into account the ordering of the topological sites, i.e., the priority introduced by the description code of the DARC topological system (18,20,27). Topological Site Ordering. With this in mind, we consider briefly, using two examples, the conventions required in order to follow the topological site distribution in an environment defined with respect to an origin or focus (here
C=C). In Figure l a we have a set of nine 1-alkeneslinear, branched, or geminated. A graph is associated with each of these alkenes. The topological sites correspond to the nodes of the graph. These nodes are identified with the skeletal carbon atoms of the alkene molecules. Superposition of these elementary graphs gives the characteristic imprint (E,) of this set of compounds. This imprint corresponds most often to the graph of a compound which has not been studied experimentally; 748
ANALYTICAL CHEMISTRY, VOL. 49, NO. 6, MAY 1977
a Ethylene
FO
Propene 1- Butene
FO-O FO-a-O
iso-Butene
FOq.
/
I-Pentene
-
2-Me -1 bu tene 2-Me -1 -pen tene 2,3-diMe -1-butene
-
2- Et -1 butene
Ea trans -2 - Butene
b ? -FO-?
cis-2-Butene cis -2 -Pent e ne 2 - M e - 2 - butene
2 -Me - 2 -pentene
3-Me-2- pentene t rans-3-Heptene
Eb *
I
DD? DD1
*
Flgure 1. Principle of the superposition of the elementary graph of some alkenes to give an imprint E, or E,: E, has only one development direction DD,; Eb also has a second development direction DD,
in this case we speak of a dummy target compound whose purpose is to characterize the extent of a structural population. Let us now consider another set of seven compounds comprising cis- and trans-2-butene, cis-2-pentene, trans3-heptene, 2-methyl-2-butene, a-methyl-&-pentene,and 3methyl-2-pentene. By convention: the graphs are superimposed as shown in Figure lb; the two development directions, DD1 and DD2, are nonequivalent (DD1 is given precedence); disubstitution on an sp2carbon takes precedence over chain lengthening. Thus a 180° rotation of the graph of 2-methyl-2-pentene would be in contradiction with this convention. Figure 2a gives the imprint of the population of 49 alkenes (Table I). The arrowed line in Figure 2b indicates the generation order of all sites whose appropriate information contribution must be taken into account. These conventions are expressed by the concept of an environment which is limited, concentric, and ordered (ELCO) (20). Each site is localized univocally in the ELCO by a linear order labeling
ANALYTICAL CHEMISTRY, VOL. 49, NO. 6, MAY 1977
749
a
a
\
\ R
=
0.993
I = 0.06
____
ILT
alkene
1 -hexene
1-pentene cH~cH~,c=c,C
CH~CH ( C H ~ ~ - C HCTCH-CH~-CH' ,
Flgure 2. (a) Imprint of the population of 49 compounds of Table I having 3 to 8 carbon atoms; (b) topological site ordering
Ai or Bij and its influence is herein interpreted as a perturbation term. EXPERIMENTAL We have exploited the Kovbts indices of an alkene population having at most 49 compounds analyzed on different stationary phases: squalane, Apiezon-L,dimethylsulfolane, I-octadecene, and P,@'-oxydipropionitrile. The corresponding data and sources appear in Table I. Several practical reasons motivated our retaining this particular population from among all those hereto published the possibility of choosing a relatively small focus (Le., one limited to the ethylenic function or extended to site AI), the variety of stationary phase polarities used in analyzing the alkene population, the possibility of comparing it with an isotopological population of alkanes analyzed on squalane at 80 "C (18). For the discussion of the relative variations of the perturbation terms, the variations of the indices with the temperature are negligible, in a first approximation, in comparison to those with the nature of the stationary phase. This approximation becomes more valid with decreasing ramification, e.g., on squalane in the 50-70 O C interval, the variation of the index with the temperature, d l / d t , is 0.017,0.050, and 0.117 I U / O C for 1-pentene,4-methyl-l-pentene, and 3,3-dimethyl-l-pentene, respectively (31). The topological analyses by a monofocalized treatment (18) of the alkenes Kovbts indices on the five stationary phases are presented as topology-information diagrams. The use of such diagrams is shown by an example; the topology-information diagram of the Kovtits indices for 47 alkenes analyzed on squalane at 80 "C (Figure 3a) allows us to calculateeasily the Koviits indices for particular alkenes, such as 1-hexene,4-methyl-l-pentene, and cis-4,4-dimethyl-2-pentene(Figure3b). The correlation coefficient, R , and the Exner J/ test (28) are given. The average deviation between the values calculated on the basis of these topology-informationcorrelations (Table I) and the experimental values is from 4 to 7.5 IU (i.e., ~ 1 % ) . The standard deviation goes from 5.7 IU on squalane to 10.6 IU on LIP-ODPN. Although this precision could be improved by various means, we have not done so in order to simplify the structural model, and thereby the first physicochemical exploitation by topological analysis, as much as possible. To justify this we cite two examples we have published recently: for a population of 70 alkenes analyzed on acetyltributylcitrate at 70 "C the standard deviation 750
ANALYTICAL CHEMISTRY, VOL. 49, NO. 6, MAY 1977
1
In
ex
~
calf exper
-
;;;
1
talc exper
-
'cy1
;;:
H'
1
caic exper
r C H 3
'li 'cH3! CH3
:::", 5
Figure 3. Topology-information diagram for a population of 47 alkene Kovits indices determined on squalane at 80 "C. (a)This dlagram shows the values of the focus (FO) and of the perturbation terms associated to the topological skes (A,andB,,), (b) Calculation principle of the Kovits index of 3 alkenes on the basis of the preceding topology-information
diagram. An asterisk indicates sites covered only once
is 3.0 IU; for a population of polar compounds, 36 dibromoalkanes, the standard deviation is 3.6 IU (24). In addition, these standard deviations can be reduced by additional structural parameters.
RESULTS AND DISCUSSION (A) Perturbation Terms and Internal Environment Effects. Rohrschneider (32,33)and McReynolds (35) have chosen squalane as the reference for the stationary phase. We shall do likewise in studying the behavior of the alkene population, so as to determine the sensitivity of the perturbation terms to the internal effects of environment. We shall suppose, in this case, that the coefficient of activity is almost identical to that of the n-alkane reference. In other words the relative coefficient of activity y;,, 1;the behavior of the solutes is then almost ideal and depends only on their particular structural effects. (a) n-Alkenes Subpopulation. Understanding the values o f the perturbation terms, from a study of the values of the Kouiits indices, is rather intuitive in the specific case of the n-alkene homologous series. This is exemplified by the topological analysis of the Kovfits indices for n-alkenes on squalane (schematized in Figure 4) which underscores the fact that the Kovfits index is a molecular datum which is mainly extensive. The lengthening of the n-alkyl chain introduces perturbation terms whose value nears 100 Iu as it gets further away from the focus; this is in agreement with the definition of the Kovkts indices. However, it should be remembered that for intensive properties, such as the chemical shift of 13C (8), the value of the perturbation terms nears zero starting from EB2,the second environment.
-
L
I
.o/ O
1 cis-2-alkenes
2
n-alkanes
3
trans-2-alkenes
L
cis-3-alkenes
0 0
strong,
A weak
n
100 I . u .
a v e r a g e 90-100 I U. c
90 I . U .
Figure 5. The topology-information correlation of Kovk indices on squalane (cf. Figure 3a) shows that there are three zones corresponding to strong, average, and weak perturbation term values
of an index when passing from an n-1-alkene to its trans2-alkene isomer while adhering to the priority orders of the DARC description code. The difference in ordinates is approximately 16 IU at the origin of the straight lines of the n-1-alkenes and trans-2-alkenes. The 6.1 IU cis term corresponds schematically to the average of the increases of the index while passing from the geometric trans isomers to the cis ones. Thus, the calculated index for cis-2-hexene is I
Treatment of the Kovats indlces for nalkenes analyzed on squalane at 80 'C. (a)Graphlc exploitation of the homologous series. (b) Topology-information correlation. In this reduced population of compounds the perturbation terms of the sites In the first development direction DDl express the lengthening of the nalkyl chain. The values associated respectively to sites Ai and Bli In the second development direction DD2 express the change to the n2-alkenes and to the n 3-alkenes. (The values are expressed in index units, IU). The asterisk indicates sltes covered only once Figure 4.
Let us consider the classical graphical exploitation of the Kovdts indices of this n-alkene population on squalane. All the information contributed by these homologous series is contained in the following type of linear relationship: ni
=an
+ bj
where n is the number of carbon atoms of compound Xi in the i series; a and b, are constants in the same i series. This information is expressed by the five straight lines in Figure 4a. The straight line for the n-1-alkenes is clearly below the one for the reference n-alkanes. Among the different positional isomers, the 1-alkenes have the shortest retention and the &-&alkenes have the longest. A straight line above the one for the n-alkanes corresponds to the latter isomers, whereas the straight line for the trans-2-alkenes of the geometric isomers is just below it. The deviation between the cis- and trans-3-alkene is smaller ("1 IU) and the value of the cis isomer is slightly greater. Their two corresponding straight lines, practically together for the indices, determined on the nonpolar phase, lie below the one for the trans-2alkenes while being above the ones for the n-1-alkenes. The chromatographist is accustomed to the graphic exploitation of such data in the form of linear relationships (eq 1). Analogous information to In,i and bi appears in the correlation of Figure 4b. The 290 IU value of the focus extended to site AI, and the 93 IU value of site B1l, for the n-1-alkenes, are smaller than the corresponding 300 and 100 IU values for the n-alkanes. These two values take into account the systematically smaller values of -17 IU of an n-alkene with respect to the corresponding n-alkane. In the second development direction, DD2, the site Al value of 116 IU is 16 IU greater than the value for the methylene group of an alkane, It takes into account the observed average increase
Icalcd =
290 + 93 i99 + 116 + 6.1 = 604.1 IU
whose value is practically identical to the experimental one 604 IU. Whenever the double bond migrates from position 2 to position 3, the index becomes smaller thus yielding a decrease of 9 IU for site Bll of DD2 when compared to the 100 IU contribution by a -CH2- group of an n-alkane. Furthermore, when compared to a 1-alkene having the same carbon skeleton, the n-3-alkenes show a relative increase of 16 IU for site Al in DD2. The calculated Kovdta index of an n-3-alkene is therefore greater than its n-1-alkene positional isomer; Le., 16 - 9 = 7 IU. The experimental difference between trans-3-heptene and 1-heptene (5 IU) illustrates this point. It should be specified that the topological exploitation takes best into account the nonlinearity of the indices with the first terms of the homologous series. However, any justification of the topology-information correlations aims at surpassing the narrow framework of homologous series by an analysis and synthesis of the set of information of any population of compounds whatsoever in an n-dimensional space. (b) Population of Linear and Ramified Alkenes. The topological analysis of the Kovdts indices of the entire population of alkenes on squalane by a monofocalized treatment (Figure 3a) shows the relative variations of the perturbation terms associated to the sites of the environment which is limited, concentric, and ordered (ELCO). These variations allow the distinguishing of three zones corresponding to the three degrees of perturbation (Figure 5): strong >lo0 IU, average 90-100 IU, and weak
