Energy & Fuels 1989,3,730-734
730
sponsible for the activation of methane. From the TPD studies, we can conclude that, for the perovskite-type catalysts examined, a strong binding of oxygen to the surface site is essential to selectively produce Cz+hydrocarbons from methane as opposed to complete oxidation leading to undesirable carbon dioxide. Present results suggest a possibility that TPD technique can be
utilized to find more effective catalysts by selecting a proper combination of A and B site substitution in perovskite-type catalysts. Registry NO.L%$I%.lMn03,1133784&6; CHI,7482-8;CZH4, 74-85-1; c ~ H 74-84-0; ~ , coz,124-38-9;co,63048-0;HCHO, 5000-0;Sq9N%,lMn03, 123183-49-3; H O ~ , ~ N % , ~123183-50-6 M~O~, Gdo.9N~,lMn03, 123183-51-7; La,,&,Mn03, 113378-47-5.
Investigation of Structure/Property Relationships of Selected C5-Clo Hydrocarbons Using Canonical Correlation Analysis of Multisource Data Barbara L. Hoesterey,? Henk L. C. Meuzelaar,*vf and Ronald J. Pugmire1 Center for Microanalysis and Reaction Chemistry and Department of Fuels Engineering, University of Utah, Salt Lake City, Utah 84105 Received October 26, 1988. Revised Manuscript Received August 21, 1989
Twelve physicochemicaland thermodynamic properties including molecular weight, boiling point, flash point, density, refractive index, volumetric, gravimetric, and molar heats of combustion, atomic H/C, carbon number, hydrogen number, and the fuel-related threshold sooting index for 47 C5-Cl0 hydrocarbons were subjected to factor analysis. Two factors with eigenvalues greater than 1.0 were found, accounting for 95% of the variance. The major groups of variables were interpreted as arising from either molecular size (boiling point, flash point, molar heat of combustion, molecular weight, and carbon number) or degree of unsaturation (density, refractive index, volumetric heat of combustion, threshold sooting index, H/C, and gravimetric heat of combustion). Canonical correlation analysis of the properties factor space with mass spectrometry/Kovats retention index data showed that characteristic mass spectral variables correlated closely with the degree of unsaturation by differentiating aliphatic from aromatic compounds. The Kovats retention index variable, not unexpectedly, modeled molecular-size-related parameters such as carbon number.
Introduction There is current interest in determining structure/ property relationships for fuels and fuel components. Structure/property relationships have typically been determined for homologous series of hydrocarbons, such as n-alkane~.'-~Properties have been correlated with topological indices by using both raw data and logarithmic transforms of one or both of the parameter^.^^^ This structure/property correlation approach has been used widely in the form of structure/activity relationships for assessing the effectiveness of drugs of similar carbon skeleton.6J Many of the techniques are general and may apply to fuels. Especially important to fuel studies are correlations related to combustion properties such as between octane number,* heats of formation,l heats of combustion, and various topological indices or correlations related to sooting properties and structural parameters derived from spectroscopic measurement~.~J~ We have recently become interested in extending multivariate analysis techniques to properties of hydrocarbons and their relationship to structure. Our approach is somewhat different from that of most other procedures in which intuitively derived topological indices are tested against selected properties. We first determine the int Center
for Microanalysis and Reaction Chemistry.
* Department of Fuels Engineering.
terrelationships among the properties using multivariate analysis techniques. This is useful in a way directly related to structure since it helps decide how many structural parameters may be needed to fully describe the suite of properties of interest. Factor analysis creates linear combinations of variables based on correlation. A data set can be constructed by using the properties of interest, and this can be examined for correlations among the properties. This can also be done for a set of structural parameters derived from topological indices, spectroscopy, or other sources. Then, from canonical correlation analysis, the properties data and the structural data can be related. Canonical correlation analysis determines the relationship between a group of variables (e.g. physicochemical properties) and another (1)Wiener, H. J. Am. Chem. SOC.1947,69,17-20. (2)Rouvray,D. H.; Pandey, R. B. J. Chem.Phys. 1981,85,2286-2290. (3)Trinajstic, N.Chemical Graph Theory; CRC Press: Boca Raton, FL,1983;Vol. 2. (4)Rouvray, D. H.; Crafford, B. C. S. Afr. J. Sci. 1976,72,47-51. (5)Hansen, Peter J.; Jurs, Peter C. Anal. Chem. 1987,59,2322-2327. ( 6 ) Jurs, Peter C. Science 1986,232,1219-1224. (7)Rouvray, D. H.In Chemical Applications of Topology and Graph Theory; King, R. B., Ed., Elsevier: Amsterdam, The Netherlands, 1983; pp 159-177. (8) Balaban, A.; Motoc, I. Math. Chem. 1979,5,197. (9)Pugmire, Ronald J.; Grant, David M. Unpublished data. (10)Hamblen, D. G.; Solomon, P. R.; Tarentul, K. S.; Carangelo, R. M. Prep?.-Am. Chem. SOC.Diu. Pet. Chem. 1987,32(2),530-533.
0887-0624/89/2503-0730$01.50/00 1989 American Chemical Society
Energy & Fuels, Vol. 3, No. 6, 1989 731
Canonical Correlation Analysis of D a t a Table I. C d l nCompounds Used in the Test Set carbon no. 2 no. compd 5 +2 n-pentane 2-methylbutane 0 1-pentene cyclopentane -2 1-pentyne trans-2-methyl-1,3-butadiene 6 +2 n-hexane 2-methylpentane 3-methylpentane 1-hexene 0 cyclohexane methylcyclopentane -2 1-hexyne cyclohexene -6 benzene 7 +2 n-heptane 2-methylhexane 3-methylhexane 2,3-dimethylpentane 2,4-dimethylpentane 0 1-heptene -2 1-heptyne -6 to1uen e a +2 n-octa ne 2-methylheptane 2,2,4-trimethylpentane 2,3,4-trimethylpentane 0 1-octene trans-1,2-methylcyclohexane -2 1-octyne -6 ethylbenzene o-xy 1ene styrene -a n-nonane 9 4-2 0 1-nonene -6 1,2,3-trimethylbenzene 1,3,5-trimethylbenzene n-propylbenzene isopropylbenzene 10 +2 n-decane 0 1-decene -2 cis-decahydronaphthalene trans-decahydronaphthalene -4 endo-tricyc10[5.2.1.0~~~]decane -6 n-butylbenzene p-isopropyltoluene -8 1,2,3,4-tetrahydronaphthalene
group of variables (e.g. structural information). I t m n also assess how much correlating information (variance) is represented by each group of variables in the analysis. Our initial goal was to use factor analysis to test the dimensionality of the physicochemical properties data to determine the number of independent measurements needed to describe these properties. The data set selected for this study shows that factor analysis is not limited to drawing inferences from homologous series of hydrocarbons, but can handle a wide variety of types of compounds at the same time while still deriving useful equations that relate variables to each other. Finally, we wanted to begin to develop other methods of deriving structural indices, especially using spectroscopic data. Spectroscopic data, such as mass spectra, provide the information necessary to determine the structure of a compound, and combined with gas chromatography, the technique is suitable for mixture analysis. Any characterization of a fuel necessarily involves mixtures of many compounds, principally hydrocarbons. In recent years gas chromatography/mass spectrometry (GC/MS) has been increasingly used to characterize fuels. Development of GC/MS-based structural indices could eventually enable prediction of physicochemical and thermodynamic properties of complex mixtures directly from GC/MS data.
Table 11. Twelve Physicochemical Properties Used for Multivariate Analysis 1 atomic hydrogen to carbon ratio (H/C) 2 boiling point at 1 atm (bp) density at 25 "C ( d ) 3 4 flash point at 1 atm (Fp) 5 heat of combustion per gram ( A H c / g ) 6 index of refraction at 20 O C (RI) 7 molar heat of combustion (AH,/mol) 8 molecular weight (MW) 9 number of carbon atoms (no. of C) 10 number of hydrogen atoms (no. of H) 11 threshold sooting index (TSI) 12 volumetric heat of combustion (AHc/mL)
Experimental Section The compounds chosen were those C5-Cio hydrocarbons with data readily available on the threshold sooting index and molar heats of combustion. Threshold sooting is related to smoke point and the burning efficiency of a fuel." C5-Cio hydrocarbons were used because they are included in the class of compounds in the gasoline range. Threshold sooting and volumetric heats of combustion (calculated from molar heat of combustion using density) were used by Pugmire and Grant to investigate the structural dependence of these proper tie^.^ The compounds used here include both straight and branched chain alkanes and compounds with one to five units of unsaturation in both rings and double bonds (see Table I). Note especially the presence of decalin and tricyclodecane, of interest since structural isomers of these compounds have different melting and boiling points. The properties used are listed in Table 11. Many of these properties are important for fuels. Compounds used in this study were all liquids at room temperature and were chosen because the selected property information was readily available. No attempt was made to represent all possible hydrocarbons in the C5-Cl0 range. Data on boiling point, refractive index, density, and flash point were obtained from ref 12, which uses ref 13 as a source for the first three properties. The Aldrich Chemical Co. determined flash points in-house. In some cases, data were obtained directly from ref 13. Molar heats of combustion were obtained from API-RP-44 tabled4 or ref 15. Gravimetric and volumetric heats of combustion were calculated. Threshold sooting indices were obtained from a paper by Olsen.'l A few of the sooting indices were estimated; the index for cyclohexane was used for tricyclodecane, l,&dimethylcyclohexane was used as the index for 1,2-dimethylcyclohexane and butadiene was used as the index for isoprene (2-methyl-l,3-butadiene). Boiling point and flash point were entered in kelvin. Molar heats of combustion were divided by 10 before entering the values in order to fit our strict data input format. Mass spectra were obtained from the NIH/EPA mass spectral library of 58000 compounds. Studies of the optimal representation of mass spectral data have been done on series of related compounds (e.g., ref 16). We coded the m/z-intensity information and scaled each spectrum to 100% total ion current. To simulate a combined gas chromatography/mass spectroscopy experiment, Kovats retention indices for the compounds were found for a standard squalane column." Kovats indices for alkynes and a few of the benzenes were estimated by using McReynolds con-
(11) Olsen, D. B.; Pickens, J. C.; Gill, R. J. Combust. Flame, 1985,62,
43-60.
(12) Aldrich Catalog Handbook of Fine Chemicals; Aldrich Chemical Company, Inc.: Milwaukee, WI, 1987. (13) Weast, Robert C., Ed. Handbook of Chemistry & Physics, 51st ed.; The Chemical Rubber Company: Cleveland, OH, 1970-1971. (14) API-RP-44 Tables; Thermodynamics Research Center, Texas A&M University: College Station, TX, 1986. (15) Technical Data Book-Petroleum Refining, 2nd ed.; American Petroleum Institute: Baltimore, MD, 1971; Chapter 1-14, pp 1-52-1-80. (16) Rozett, R. W.; Petersen, E. M. Anal. Chem. 1975,47,2377. Jurs, Peter C.; Isenhour, Thomas L. Applicationsof Pattern Recognition;John Wiley and Sons: New York, 1975. (17) Schupp, 0. E.; Lewis, J. S., Eds. Compilation of Gas Chromatographic Data; American Society for Testing and Materials: Philadelphia, PA, 1967. Ibid., 2nd ed.; Supplement 1; 1971.
732 Energy & Fuels, Vol. 3, No. 6, 1989
Hoesterey et al. n-alkanes branched alkanes cyclic aliphatics alkenes alkynes aromatics miscellaneous
o / /
Table 111. Factor Loadings (Correlation Coefficients) of
Property Variables with
Fl/F2 property
space
atomic H/C boiling point density flash point gravimetric heat of combustion molar heat of combustion molecular weight no. of carbon atoms no. of hydrogen atoms refractive index threshold sooting index volumetric heat of combustion
0.973 0.997 0.973 0.979 0.983 0.995 0.995 0.995 0.990 0.989 0.900 0.924
correln with GC/MS1 (CV1) -1.00 0.50 0.94 0.50 -0.98 0.00 0.17 0.30 -0.58 0.94 1.00 0.69
with data (CV2) 0.00 0.87 0.34 0.87 -0.17 0.90 0.89 0.85 0.69 0.34 0.00 0.58
correlation analysis was performed by using the factor scores from the physicochemical properties and combined mass spectrometry-Kovats index data matrices. -2.4
0 FACTOR I (64% variance)
1
2.4
( 900 1
(1H
1 1001
Figure 1. (a, top) Score plot of the first two factors of the physicochemical and thermodynamic properties data set. Note the high percentage (95%)of variance explained. Compare with the corresponding loading plot in part b. (b, bottom) Loading plot of the first two factors of the physicochemical and thermodynamic properties data set. Note the high degree of correlation among many variables, as well as the high percentage of variance explained in F1/F2 space (compare also with part a and Table 111).
stants from either an Apiezon L or tricresyl phosphate column obtained from ref 18. The Kovats indices were added to the scaled mass spectrometry data as an additional variable, after dividing them by 100 to achieve a similar order of magnitude as the mass spectral peak intensities. The SIGMA program package developed in-house was used for factor analysis and canonical correlation ana1y~is.l~Vector representations of variance diagrams were generated according to the technique described by Windig et al." Since an orthogonal set of factor scores is used as input for the canonical correlation analysis, the resultant canonical correlation space can be considered as a rotation of the original factor space. Canonical
Results and Discussion Factor analysis was performed on the physicochemical properties data from the 47 hydrocarbon compounds. Three factors were found with percent variance greater than 1.0, accounting for 98.4% of the total variance. The first two factors had eigenvalues greater than 1.0. Eigenvalue greater than 1.0 is a frequently used criterion for data reduction applications.21 Figure l a shows the factor score plot on F1 vs F2 (95% variance). Visual examination of the plot shows two trends. Homologous series of hydrocarbons fall roughly along straight lines (some with different slopes) in order of increasing carbon number in this factor space. Branched alkanes appear very close to the n-alkanes, implying that many of their properties are similar. The other direction in the data, roughly perpendicular to the "carbon number" trend appears to be associated with increasing units of unsaturation, or z number as defined by the equation CnH2n+r.The relationship is not exact, however, since alkynes (z = -2) and cycloalkanes ( z = 0) fall along the same line. The parameters carbon number and z number have been suggested before from regression analysis.22 The vector representation of the variance diagram methodZ0shows the directions in the factor space in which maximum correlation occurs among variables. The polar variance diagram for the F1/F2 factor space in Figure l b shows that parameters such as carbon number, heat of combustion per mole, molecular weight, flash point, and boiling point are all found within the Fl-/F2+ quadrant of the diagram. The high loadings (greater than 0.9-see Table 111) show that these variables are well represented in this factor space. The small differences in rotation demonstrate the high degree of correlation among these variables. It is well-known that these variables are highly correlated; for example, parameters such as boiling point and molecular weight show linear behavior in the C5-Cl0 range and beyond for homologous ~ e r i e s . ~ JCarbon ~ number and molecular weight correlate for hydrocarbons, since carbons contribute the bulk of the weight. Molar
~~
(18) McReynolds, W. 0. J . Chromatogr. Sci. 1970,8, 685. (19) Windig, Willem; Chakravarty, Tanmoy; Richards, Joseph M.; Nguyen, Van T.; Dedes, Apostolos; Meuzelaar, Henk L. C. SIGMA, System for Integrated Graphics-Oriented Multivariate Analysis. In Proceedings of the 34th A.S.M.S. Conference;American Society of Mass Spectrometry: Cincinnati, OH, 1985; pp 64-65. (20) Windig, Willem; Meuzelaar, Henk L. C. Anal. Chem. 1984, 56,
2297-2303.
(21) Dillon, William R.; Goldstein, Matthew. Multiuariate Analysis, Methods and Applications; John Wiley & Sons, Inc.: New York, 1984; pp
48-49.
(22) Bunger, James W.; Prasad, D. A. V.; Russell, C. P.; Oblad, Alex G. Prepr.-Am. Chem. SOC.,Diu. Pet. Chem. 1987, 32(2),540-544. (23) Morrison R. T.; Boyd, R. N. Organic Chemistry, 2nd ed.; Allyn & Bacon, Inc.: Boston, MA, 1966; pp 107-108.
Energy & Fuels, Vol. 3, No. 6,1989 733
Canonical Correlation Analysis of Data heat of combustion also shows the expected correlation since well-known additivity rules have been developed for heats of combustion based on functional groups.23 Flash point is apparently a property that is strictly related to boiling point. The vector diagram also reveals a group of strongly correlating variables in the inferred “increasing z number” direction in the Fl-/F2- quadrant, namely volumetric heat of combustion, density, refractive index, and threshold sooting index. This group of variables is separated by about 60° from the carbon number direction. A 90° difference between variables (“orthogonality”) implies a complete absence of correlation. Smaller differences imply that the variables are correlated to some extent. For example, the projection of density (at 200O) on molecular weight (130O) gives a loading (=correlation coefficient) of 0.3, thus showing a very low level of correlation. Refractive index was chosen as a physicochemical property variable since it is related to molar polarizability and dipole moment, and extensive tables of refractive index values are readily available. In this data set, it can be seen that a component of the refractive index increases with increasing carbon number, as well as with increasing ring number or degree of unsaturation. Atomic H/C and heat of combustion per gram are found almost in the opposite direction from threshold sooting index and the “increasing z number” direction, thus revealing a strong negative correlation. That H/C increases in a linear fashion as z number decreases makes this property a good single predictor of the z number, which is an important descriptor of the relative position of a compound in this space. The hydrogen number parameter lies directly between molecular weight (and carbon number) and H/C, as would be expected. Threshold sooting index was one of the few properties that did not load as strongly within the F1/F2 space as the other parameters, having a 0.9 loading. Inspection of factor 3 showed that sooting index correlates less strongly with density than was apparent with factors 1and 2. Since we were interested in this variable because of previous factor 3 was included in the subsequent canonical correlation analyses in order to provide more information on the threshold sooting index. The residual variance in factors 4 and higher was very small and probably can be largely accounted for by measurement uncertainties in the values of the properties taken from the literature or estimated by us. Our interest in modeling physicochemical properties of hydrocarbons arises from interest in correlating properties with structure and vice versa. The hydrocarbon properties data showed that at least two independent measures of structure are needed to describe the properties data, since two (orthogonal) factors with eigenvalues greater than 1.0 were found in the factor analysis. Extraction of correlated directions with the variance diagram revealed two physically meaningful parameters, n and z, that described nearly all the significant variance in the properties data set. An empirical approach to the development of structural parameters that describe physicochemicalproperties is to use spectroscopically derived data. For example, the mass spectrum of a pure compound often contains enough information to unambigously determine the structure of that compound. Furthermore, retention indices obtained by gas-liquid chromatography (GLC) are often used as an adjunct to structural identification. Our long-term goal in modeling properties using spectroscopic and/or chromatographic data is to derive physicochemical property information on mixtures by using relationships between
I
2
3
4
5 6 FACTOR
7
8
9
IO
Figure 2. Scree plot of eigenvalues of the first 10 factors from
the combined mass spectrometry-Kovats index data set. Note the slow leveling trend, indicating a relatively high dimensionality of the data. spectroscopic parameters and properties established for pure compounds. Mass spectra and Kovats retention indices for 46 of the 47 compounds used for properties determination were available in the literature, the exception being endo-tricycl0[5.2.1.0~~~]decane. Factor analysis was performed on the combined mass spectral and Kovats data from these compounds, and 23 factors with eigenvalue greater than 1.0 were obtained. The eigenvalues of the first 10 factors are shown in the “scree” plot21 in Figure 2. The high dimensionality of the data is due to unique characteristic fragmentation patterns for compounds. Many papers showing the application of factor analysis to electron ionization mass spectra are available in the literature (e.g. ref 16). A brief description of the factor analysis results from these mass spectrometry data is in order. Factor 1 (not shown) differentiated aromatic compounds on Fl+ from the alkanes, alkenes and alkynes on F1-. Variables that were associated with nonaromatic compounds included the lower m/z fragments, such as m/z 27,29,41, 43, and 57. Higher m / z fragments were correlated with these variables, but with lower loadings on this factor. This is not unexpected, since the smallest aliphatics were C6 compounds, and no MS signals are expected above m / z 72 for C5compounds. Diagnostic variables for the aromatic compounds (principally alkylbenzenes) were m / z 50, 51, 63,65, and 74-77. Benzene and styrene were somewhat removed from the main aromatic cluster on the F2+ side, and toluene was nearer the F2+ side. Low loadings for the Kovats index showed that this variable was not important in differentiating compounds on factor 1 or 2. The distribution of scores and loadings on higher factors (nos. 3-6) showed that individual compounds and their characteristic mass variables were separated from the others, such as cisand trans-decalin separated from all the rest in F3/F4 space (not shown here). The Kovats index variable was also found in the F3/F+ space with high loadings, pointing in the direction of the decalin isomers and tetralin. Some distribution by molecular weight was seen in the Kovats variable direction. Prior to canonical correlation analysis, factor analysis was performed on the properties data with tricyclodecane excluded. The factor space was unchanged from the one previously described. Canonical correlation between physicochemical properties data and mass spectral-Kovats data was performed by using the first 3 factors from the
734 Energy & Fuels, Vol. 3, No. 6, 1989
Hoesterey et al.
Table IV. Results of Canonical Correlation Analysis of Physicochemical Properties Data and Mass Spectrometry-Kovats Data Sets canonical 5% variance variate eigencanonical (MSfunction value correln (phys prop) Kovats) 1 1.00 >0.99 50.47 14.43 2 0.99 0.98 40.97 6.75 3 0.80 0.89 4.43 5.42
,-.
u
properties data (98% variance) and 10 factors (program limit) from the mass spectral-Kovats data (69% variance). We chose to use 10 factors since the scree plot did not clearly indicate a lower number of “significant” factors, as shown in Figure 2. Canonical variates 1and 2 showed correlations of greater than 0.95 (see Table IV). This CVlICV2 space contained 91% of the variance in physicochemical properties and 21 70of the variance from the mass spectral-Kovats data. This implies that the total mass spectral data is, in a sense, too rich in information to be used in its entirety to model the dimensionalityof the limited number of properties and compounds used in the test set. However, the mass spectral variables (values of m / z ) that load strongly in this canonical variate space can be used as diagnostic variables that relate to chemical and physicochemical properties. The CV1 mass spectral axis was found to model z number, as can be seen by the ordering of compounds in Figure 3 along that axis. Variables along CV1- include m / z 29 (C2H5+),41 (C3H5+)and 43 (C3H7+),from alkanes, alkenes, and monocyclics and m/z 51 (C4H3+),63 (C5H3+),and 77 (C6H5+)from aromatic fragments on CV1+. Properties loading strongly on CV1- (more aliphatic) include H/C and gravimetric heat of combustion, whereas threshold sooting, density, and refractive index load strongly on the CV1+ (aromatic) direction. Volumetric heat of combustion, a variable correlating with sooting in the original properties factor space, loads less strongly on this axis. Its projected loading on CV1 is 0.69. The complete equation for the CV1 and CV2 directions using the properties data are given in Table 111. The CV2 direction generally models carbon number. For example the carbon number variable loading is 0.85 on CV2 and the Kovats variables from the GC/MS data loads at 0.79 on CV2. The Kovats variable is not strictly related to carbon number because of the cyclic Clo compounds cis and trans-decalin and tetralin, with Kovats indices in the 1080-1150 range where Cll acyclic compounds characteristically occur.
Acknowledgment. This work was sponsored (in part) by the Advanced Combustion Engineering Research Center. Funds for this center are received from the National Science Foundation, the State of Utah, 23 industrial participants, and the US. Department of Energy. The Consortium for Fossil Fuel Liquefaction Science (DOE Contract No. UKRF 4 21816 87 69) also supported this research. Registry No. n-Pentane, 109-66-0;2-methylbutane, 78-78-4;
Conclusions For the 12 physicochemical properties used in this limited study of 47 hydrocarbon compounds only two orthogonal factors (“dimensions”)were necessary to describe nearly all variance in the data set or, in other terms, to model the full range of properties. Closer examination of the variance diagram for these factors showed that carbon number appeared to determine one dimension and that degree of unsaturation ( z number) determined the second dimension. Canonical correlation of combined mam spectral/Kovats index data, such as typically obtainable by GC/MS methods, with physicochemical properties data gave two canonical variate functions with correlation coefficients >0.9. The two orthogonal canonical variate functions accounted for 91‘70 of the physicochemical properties
1-pentene, 109-67-1; cyclopentane, 287-92-3; 1-pentyne, 627-19-0; 2-methyl-l,3-butadiene, 78-79-5; n-hexane, 110-54-3; 2-methylpentane, 107-83-5; 3-methylpentane, 96-14-0; 1-hexene, 592-41-6; cyclohexane, 110-82-7; methylcyclopentane, 96-37-7; 1-hexyne, 693-02-7; cyclohexene, 110-83-8; benzene, 71-43-2; n-heptane, 142-82-5; 2-methylhexane, 591-76-4; 3-methylhexane, 589-34-4; 2,3-dimethylpentane, 565-59-3; 2,4-dimethylpentane, 108-08-7; 1-heptene, 592-76-7; 1-heptyne, 628-71-7; toluene, 108-88-3; noctane, 111-65-9; 2-methylheptane, 592-27-8; 2,2,4-trimethylpentane, 540-84-1; 2,3,4-trimethylpentane, 565-75-3; 1-octene, 111-66-0; trans-1,2-dimethylcyclohexane, 6876-23-9; 1-octyne, 629-05-0; ethylbenzene, 100-41-4; o-xylene, 95-47-6; styrene, 100-42-5; n-nonane, 111-84-2; 1-nonene, 124-11-8; 1,2,3-trimethylbenzene, 526-73-8; 1,3,5-trimethylbenzene, 108-67-8; npropylbenzene, 103-65-1; isopropylbenzene, 98-82-8; n-decane, 124-18-5; 1-decene,872-05-9; cis-decahydronaphthdene,493-01-6; trans-decahydronaphthalene, 493-02-7; endo-tricyclo[5.2.1.0z~6]decane, 2825-83-4; n-butylbenzene, 104-51-8;p-isopropyltoluene, 99-87-6; 1,2,3,4-tetrahydronaphthalene, 119-64-2.
0 0. 0
0 0
0
06 @@
0
0
a
0
. i z=-6
O
z=+2
e
z=o
Generalized C V I Scores (corr. coeff >0.99)
Figure 3. Score plot of the f i t two generalized canonical variate functions representing the combined physicochemical properties/mass spectrometry Kovata index data sets. Note excellent fit on CV1 (correlation coefficient >0.995; see also Table IV), corresponding to the z number (degree of unsaturation).
+
variance and represented both the molecular size parameters and degree of unsaturation parameters. Diagnostic variables from the mass spectral/Kovats data set were associated with both the molecular size and degree of unsaturation dimensions.
