Gas-Chromatographic Retention and Molecular Structure An Extension of the James-Martin Rule Andrzej W. Ladon and Samuel Sandler Department of Chemical Engineering, University of Toronto, Toronto, Ontario, Canada
The relation between carbon number of members of an homologous series and the logarithm of their chromatographic retention established in the fundamental work of James and Martin has been useful to many workers in the field. It will be demonstrated in this paper how such a relationship can be extended to apply to some classes of substances beyond the bounds of a single homologous series. For each one of a given class of substances containing the same kind and number of functional groups such as alkanes, cycloalkanes, alkenes, cycloalkenes, and alkadienes, an equation of the following form is proposed
n
=
c, + c, log
t,
+ c,
log t2 +
c3
log t3
where n is the number of carbon atoms, CO,C1, Cz, C3 are constants and 1 1 , t 2 , t 3 retention times on each of three carefully selected stationary phases. A linear regression upon three variables has been used to test this formula.
From Martin’s (1) theoretical work, it appears that distinct correlations can be made between the structure of molecules and their chromatographic behavior. The relationship between the carbon number of members of an homologous series and the logarithm of their gas-chromatographic retention which was established in the fundamental work of James and Martin (2) has been frequently u,sed. The pioneers of gas chromatography have also foreseen the application of several stationary phases to the problems of identification (3). The present work demonstrates how such a relationship can be extended to some classes of substances beyond the bounds of a single homologous series. The general approach involves the determination of structural parameters, as represented by integers, from chromatographic retention. Much research has already been done on the reverse problem, that is, the determination of retention behavior from molecular structure. Special attention should be directed to the work of Rohr(1) A. J. P. Martin, Biochern. SoC. Symposia. 3, 7 ( 1948). (2) A . T. James and A . J. P. Martin, Biochern. J . , 50,679 (1952). (3) A. T. James and A. J. P. Martin, J. Appi. Chem.. 6, 105 (1956)
schneider (4, 5 ) and the use in his mathematical model of “polarity” rather than conventional structural parameters. He postulated the existence of polarity factors for both solutes and solvents, and on this basis was able to predict the retention indices for substances of different classes on a multiplicity of stationary phases. McReynolds (6) applied these concepts quite successfully to his own collection of retention indices for the purpose of showing the similarity in the behavior of many liquids and thus to help reduce the number of stationary phases in use. Along these lines, Weiner and Howery ( 7 ) applied a least squares rotational scheme in a factor analysis and tested an 8-factor system. They recognized the limitations of their approach and admitted that a complete solution to the problem would probably require a knowledge of new interaction terms. When combined with the multiplicity of factors already employed, this presents a formidable task.
THEORY Molecules can be described unequivocally when their constitution and geometry are established. The constitution is given by the reduced formula reporting the kind and number of atoms that are the building blocks of the structure. In the chromatographic process where the molecules transfer repeatedly between the gaseous and liquid phases and no chemical reactions occur, the only geometrical changes that need to be considered are those caused by rotation about the axis of the bond and any consequent modification of bond angles. This results in a conformational change or change in the distribution of the conformers if there is more than one preferred conformation. For given classes of substances containing particular functional groups such as alkanes, alkenes, cycloalkanes, alkadienes, etc., the following equation is proposed for the isothermal retention time t on any stationary phase: log t
=
a
+ bn
(1)
Here a is a variable dependent upon the geometry of the particular molecule, b is a constant dependent upon the (4) L. J. Rohrschneider, J. Chromatogr., 17, 1 (1965). (5) L. J. Rohrschneider. J. Chromatogr., 22,6 (1966). (6)W. 0. McReynolds,J. Chromatogr, Sci.. 8,685 (1970). (7) P. H. Weiner and D. G .Howery. Anal. Chem.. 44,1189 (1972)
ANALYTICAL CHEMISTRY, VOL. 45, NO. 6 , MAY 1973
921
If t h e r e t e n t i o n t i m e s o f a given substance o n three stat i o n a r y phases (subscripts 1 , 2 , 3 ) are considered, t h e n
Table I. Regression Characteristics for Octadecene-1, Dimethylsulfolane, and Squalane
No.
Class of substances
No. of substances
Square of the multiple correlation coefficient
1 2 3 4 5
Alkanes Cycloalkanes Alkenes Cycloalkenes Alkadienes
38 18 58 5 8
0.9931 0.9826 0.9728 0.9998 0.9854
Residual std dev
Maximum dev
0.14 0.12 0.17 0.02 0.09
0.33 0.28 0.47 0.01 0.12
Alkanes Cycloalkanes Alkenes Cycloalkenes Alkadienes
CO
c1
c2
= a,
+
b1n
(2 )
log
t,
= a2
+ b2n
(3)
log
t3
= a3
+
b3n
(4)
+ K,u, + KZU~ +K
3 ~ = 3
0
(5)
i s f u l f i l l e d . Since t h e values o f ai depend u p o n conformat i o n a l changes, t h i s c r i t e r i o n corresponds t o a l i n e a r relat i o n s h i p between average energy levels of t h e various conformers. E q u a t i o n s 2 , 3 , a n d 4 c a n b e rearranged t o give:
c3
47.098 71.808 -33.163 -11.841 2.004 6.381 -7.747 8.507 6.095 7.737 17.906 -0.530 5.197 14.406 1.642 -5.663 -27.155 29.198 5.586 -23.981
a , = l o g t , - b,n
a n d E q u a t i o n s 6,
ber o f carbon atoms. In t h e c o n t e x t o f a m u l t i p l i c i t y o f s t a t i o n a r y phases, b o t h o f t h e parameters a a n d b depend upon t h e structure o f t h e liquid phase a n d therefore c a n b e i n t e r d e p e n d e n t t o some extent.
(6)
b2n
(7)
a3 = l o g t3 - b3n
(8)
a2 = l o g t2 -
kind a n d n u m b e r o f f u n c t i o n a l groups, a n d n i s t h e num-
7, 8 s u b s t i t u t e d i n t o 5 t o give:
K O + K,(log t , - b , ~ )+ K,(lOg
t2
- b2n) +
&(log
t3
- b3n) = 0 (9)
Table 1 1 1 . Retention Data and Carbon Numbers for Alkanes Logarithms of relative retention
No
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38
922
Name of alkane
Ethane Propane 2-methyl propane Butane 2,2-Dimethylpropane 2-Methylbutane Pentane 2,2-Dimethylbutane 2,3-Dimethylbutane 2-Methylpentane 3-Methylpentane Hexane 2,2-Dimethylpentane 2,4-Dimethylpentane 2,2,3-Tri methylbutane 3,3-Dimethylpentane 2,3-Dimethylpentane 2-Methylhexane 3-Methylhexane 3-Ethylpentane Heptane 2,2,4-Trimethylpentane 2,2-Dimethylhexane 2,5-Dirnethylhexane 2,4-Dimethylhexane 2,2,3-Trimethylpentane 3,3-Dimethylhexane 2,3,4-Trimethylpentane 2,3,3-Trimethylpentane 2,3-Dimethylhexane 2-Methyl-3-ethylpentane 2-Methylheptane 4-Methylheptane 3,4-Dimethylhexane 3-Methyl-3-ethylpentane 3-Ethylhexane 3-Methylheptane Octane
OD-1, 25 "C
DMS, 25 "C
-
2.1938 -1.6162 - 1.2441 - 1.0458 0.9872 -0.6536 -0.5129 -0.3439 0.1878 -0.161 2 -0.0947 0.0000 0.1156 0.1414 0.1649 0.2643 0.3381 0.3310 0.3731 0.4133 0.5052 0.4313 0.5866 0.6365 0.6493 0.6551 0.6972 0.7332 0.7551 0.7853 0.7818 0.8254 0.8331 0.8338 0.8331 0.8525 0.8555 1.0073
- 2.0458
- 1.5376 - 1.2441
- 1.0506
-
-
KO,K1,
Kz, K3 exists such t h a t t h e criterion:
Table II. Regression Coefficients for Octadecene-I, Dimethylsulfolane and Squalane Class of substances
t,
It i s assumed, furthermore, t h a t a set o f n u m b e r s
K O
No. 1 2 3 4 5
log
- 1.0655
-0.7399 -0.6162 -0.4921 -0.3382 -0.3382 -0.2588 0.1979 0.121 5 -0.1068 -0.0362 0.0445 0.1092 0.0603 0.1139 0.1761 0.2117 0.1219 0.2586 0.2956 0.3214 0.3720 0.3844 0.4428 0.4814 0.4670 0.4804 0.4591 0.4823 0.5236 0.541 1 0.5184 0.5038 0.6284
-
ANALYTICAL CHEMISTRY, VOL. 45, NO. 6, MAY 1973
Squalane, 27 "C
-3.5346 -2.9867 -2.6300 -2.4401 -2.3840 -2.0670 - 1.9359 - 1.7642 -1.6146 1.5964 - 1.5286 1.4464 1.3298 - 1.3063 1.2692 1.1759 -1,1090 1.1273 1.0814 1.0376 -0.9650 -1.0227 -0.8768 0.8336 -0.8159 -0.8044 -0.7724 -0.7291 -0,7042 -0.681 1 -0.6828 -0.6580 -0.6463 -0.6371 -0.6326 -0.6260 -0.6187 -0.4824
-
Carbon no.
Calcd carbon no
2 3 4 4 5 5 5 6 6 6 6 6 7 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8
2.31 2.94 3.93 4.00 4.88 4.89 4.93 5.95 6.00 5.97 6.02 6.03 6.78 6.86 6.99 7.13 7.07 7.02 7.15 7.15 7.10 7.89 8.00 7.94 8.04 7.79 7.76 7.91 7.90 8.16 8.04 8.01 8.03 7.95 7.98 7.92 8.33 8.24
Table IV. Retention Data and Carbon Atoms for Cycloalkanes Logarithms of relative retention Carbon No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Name of cycloalkane
OD-1, 25 "C
DMS, 25 "C
Cyclopentane Methylcyclopentane Cyclohexane 1,l-Dimethylcyclopentane 1-cis-3-Dimethylcyclopentane 1-trans-3-Dimethylcyclopentane 1-trans-2-Dimethylcyclopentane 1-cis-2-Dimethylcyclopentane Methylcyclohexane Ethylcyclopentane l11,3-Trimethylcyclopentane 1-trans-2-cis-3-Trimethylcyclopentane 1-trans-2-cis-3-Trimethylcyclopentane 1-cis-2-trans-4-Trimethylcyclopentane Cycloheptane Isopropylcyclopentane Propylcyclopentane Ethylcyclohexane
-0.2197 0.0973 0.2514 0.3206 0.3775 0.3969 0.4065 0.5515 0.5729 0.6263 0.5809 0.6749 0.7033 0.8209 0.8932 1.0111 1.1126 1.1109
- 0.1469
Squalane, 27 "C
- 1.6284 - 1.3288
0.0565 0.2106 0.2063 0.2143 0.2405 0.2601 0.4354 0.4257 0.4878 0.3400 0.4071 0.4586 0.5799 0.800G 0.7896 0.8808 0.8831
-1.1649 -1.1129 - 1.0640 -1.0448 - 1.0339 -0.8854 -0.8658 -0.8228 -0.8703 -0.7833 -0.7503 0.6336 -0.5499 -0.4504 -0.3565 0.3468
-
no.
Calcd carbon no
5 6 6 7 7 7 7 7 7 7 8 8 8 8 7 8 8 8
4.98 6.03 6.15 6.72 7.12 7.08 7.01 6.88 7.13 7.08 7.84 8.09 7.94 7.98 6.91 7.94 8.07 8.06
Table V. Retention Data and Carbon Numbers for Alkenes Logarithms of relative retention No
Name of alkene
OD-1, 25 "C
DMS. 25 "C
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44
Propene 2-Methylpropene Butene-1 trans- Butene-2 cis-Butene-2 3-Methylbutene-1 Pentene-1 2-Methylbutene-1 trans- Pentene-2 cis-Pentene-2 2-Methylbutene-2 3,3-Dimethylbutene-1 4-Methylpentene-1 2,3-Dimethyl butene-1 4-Methyl-cis-pentene-2 4-Methyl-trans-pentene-2 2-Methylpentene-1 Hexene-1 2-Ethylbutene-1 cis- Hexene-3 trans- Hexene-3 2-Methylpentene-2 3-Methyl-trans-pentene-2 trans-Hexene-2 cis-Hexene-2 3-Methyl-cis-pentene-2 4.4-Dimethylpentene-1 2,3-Dimethylbutene-2 4,4-Dimethyl-trans-pentene-2 3.3-Dimethylpentene-1 2,3,3-Trimethylbutene-1 4,4-Dimethyl-cis-pentene-2 3,4-Dimethylpentene-l 2,4-Dimethylpentene-l 2,4-Dimethylpentene-2 3-Methylhexene-1 3-Ethylpentene-1 2,3-Dimethylpentene-l 5-Methylhexene-1 2-Methyl-trans- hexene-3 3-Methyl-2-ethylbutene-1 4-Methylhexene-1 4-Methyl-cis- hexene-2 4-Methyl-trans- hexene-2
-1.6696 -1.1232 - 1.1163 0.9914 -0.9431 -0.7670 -0.5986 -0.5654 -0.4962 -0.4789 -0.4306 -0.4763 -0.2557 -0.2104 -0.2190 - 0.1878 -0.0937 -0.0804 -0.0343 -0.0329 -0.0320 -0.0044 0.0663 -0.0057 0.0199 0.0166 0.0191 0.1274 0.0755 0.1202 0.1303 0.1688 0.1761 0.1889 0.2146 0.2276 0.2307 0.2472 0.2582 0.2418 0.2945 0.2905 0.2753 0.2847
-0.8041 -0.8386 -0.7190 -0.6459 -0.5918 -0.4237 - 0.3507 -0.3279 - 0.2899 -0.2233 -0.3872 - 0.1 739 - 0.0984 -0.1379 -0.1 238 0.0166 0.0000 0.0741 0.0445 0.0220 0.0986 0.1 729 0.0535 0.1092 0.1358 0.0162 0.2610 0.0561 0.1176 0.1 764 0.1772 0.1664 0.2087 0.2079 0.2055 0.1940 0.2615 0.2646 0.1875 0.3047 0.2891 0.2499 0.2420
-
- 1.2757
Squalane, 27 "C
Carbon no.
Calcd carbon no.
-3.0595 -2.5321 -2.5230 -2.4056 -2.3565 -2.1918 -2.0315 - 1.9965 - 1.9303 -1.9111 - 1.8681 - 1.9090 - 1.6977 - 1.6538 - 1.6629 -1.6319 -1.5450 - 1.5346 - 1.4856 - 1.4828 - 1.4785 - 1.4561 - 1.3841 - 1.4592 - 1.4295 - 1.4355 - 1.4309 - 1.3261 - 1.3716 - 1.3307 - 1.3224 -1.2857 - 1.2782 -1.2716 - 1.2472 - 1.2388 - 1.2277 - 1.21 18 1.2090 -1.2147 -1.1643 -1.1713 - 1.1864 - 1.1759
3 4 4 4 4 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 7 6 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7
2.90 3.81 4.09 4.20 4.11 4.96 5.09 4.90 5.23 5.14 5.04 5.75 5.97 5.77 6.00 6.13 5.90 6.08 5.98 6.18 6.35 6.04 6.11 6.29 6.17 5.96 6.73 5.99 6.91 6.83 6.53 6.79 6.91 6.70 6.88 6.95 7.10 6.81 6.80 7.24 6.88 6.93 7.06 7.18
-
ANALYTICAL CHEMISTRY, VOL. 45, NO. 6, MAY 1973
923
Table V. Continued Logarithms of relative retention No
Name of alkene
45 46 47 48 49 50 51 52 53 54
5-Methyl-trans-hexene-2 3,4-Dimethyl-trans-pentene-2
2-Methylhexene-1 3-Methyl-trans-hexene-3
Heptene-1 2-Ethylpentene-1 3-Methyl-cis-hexene-2 3-Methyl-trans-hexene-2 3-Methyl-cis-hexene-3 2-Methylhexene-2 trans-Heptene-3 cis-Heptene-3 3-Ethylpentene-2 2,3-Dimethylpentene-2
55
56 57 58 ~~~~~~~~
~
~
~
~
OD-1, 25 "C
DMS, 25 "C
0.3045 0.3881 0.4014 0.4298 0.4232 0.4166 0.5052 0.4669 0.4624 0.4639 0.4472 0.4564 0.4871 0.5145
0.2676 0.3959 0.4198 0.4445 0.4077 0.4195 0.5039 0.4859 0.4559 0.4625 0.3941 0.4366 0.5072 0.5564
Squalane, 27 "C
Carbon no.
Calcd carbon no.
7 7 7 7 7 7 7 7 7 7 7 7 7 7
7.15 7.02 6.84 6.94 7.05 7.00 7.13 6.96 7.10 7.07 7.36 7.17 6.99 6.87
-1.1586
- 1.0691 - 1.0721 - 1.0376 - 1.0535 - 1.0501
-0.9618 -0.9996 - 1.0052 - 1.0039 -1.0218 -1,0119 -0.9784 -0.9531
~
Table VI. Retention Data and Carbon Numbers for Cycloalkenes Logarithms of relative retention No.
Name
OD-1, 25 "C
DMS, 25 "C
Squalane, 27 "C
Carbon no.
Calcd carbon no
1 2 3 4 5
Cyclopentene Cyclohexene 3-Ethylcyclopentene 1-Methylcyclohexene 1-Methylcyclopentene
-0.2815 0.3139 0.5378 0.7694 0.2033
0.0149 0.5415 0.6203 0.9016 0.401 1
-1.7069 -1.1244 -0.9190 -0.6882 - 1.2426
5 6 7 7 6
4.99 6.01 7.00 6.99 6.01
Table V I I . Retention Data and Carbon Numbers for Alkadienes Logarithms of relative retention
No.
Name
Butadiene-I ,3 2-Methylbutadiene-l,3 3-Methylbutadiene-l,2 Pentadiene-1 -trans-3 Pentadiene-1-cis-3 Pentadiene-1,2 Pentadiene-2,3 Hexadiene-l,5
1 2 3 4 5 6 7 8
OD-1, 25 "C
DMS, 25 "C
Squalane, 27 "C
Carbon no.
Calcd carbon no
- 1.0915
-0.4724 -0.0070 0.0095 0.1252 0.1752 0.0966 0.1072 0.1838
-2.5176 - 1.9539 - 1.8788 1.8620 -1.8187 - 1.8091 1.7788 1.6260
4 5 5 5 5 5 5 6
3.99 4.97 5.03 5.12 4.90 5.02
-0.5058 -0.4389 -0.4001 -0.3625 -0.3655 -0.3382 - 0.1662
Table V I I I. Regression Coefficients for Hexatriaconlane, p-Phenyldiphenylmethane, and Paraffin Wax Class of substances
Alkanes
CO 5.147
c1
cz
c3
6.933
-11.262
6.421
-
5.02 5.96
Table IX. Regression Characteristics for Hexatriacontane, p-Phenyldiphenylmethane, and Paraffin Wax Class of substances
No. of substances
Square of the multiple correiation coefficient
Alkanes
32
0.9773
Residual std dev
Maximum dev
0.16
0.32
~~
In terms of n, Equation 9 becomes n
=
c, + c, log t , + c2 log t 2 + c, log t,
(10)
where CO, CL C2, C3 are constants with the following values: C, = K , / ( K l b l K2b2 K3b3), where i varies from 0 to 3. When relative rather than adjusted retention time is used, an equation of the same form as Equation 10 can be
+
+
applied.
Multiple-Retention Rule. Criterion 5 can be p u t into a general form employing m retentions: rn
KO -t iC= 1K , a ,
5
O
(11)
Consequently the formula for carbon number can be ex-
tended as well: n = 924
co +
cc, m
log t ,
I-1
(12)
ANALYTICAL CHEMISTRY, VOL. 45, NO. 6, MAY 1973
The number m = 3 was selected for this work since it gave better predictions than either of m = 1 or m = 2. On the other hand, m = 4 seemed t o improve the accuracy of the carbon number determination somewhat, but at the expense of requiring one third more measurements than m = 3.
Computation. Multiple regression analysis was used in assessing the values of the coefficients in Equation 10. The quality of the fit can be judged by the square of the multiple correlation coefficient, the residual standard de-
viation, and the maximum deviation. It must be stated here that because of the "non-calculability principle" (8) some positive or negative deviation of the calculated carbon number from the actual one must always be expected. For practical purposes, this should be as small as possible. If by "maximum deviation" is meant the highest absolute value of the difference between the carbon number and the calculated value, this should not (8) A. W. Ladon, Chrornatographm 4, 171 (1971).
Table X. Retention Data and Carbon Numbers for Alkanes Logarithms of relative retention No
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
22 23 24 25 26 27 28 29 30 31 32
Name of alkane Pentane Hexane Heptane Octane Nonane 2-Methylbutane 2-Methylpentane 3-Methylpentane 3-Methylhexane 2-Methylhexane 2-Methylheptane 2,2-Dimethylbutane 4-Methylheptane 2,3-Dimethylbutane 2,2-Dimethylpentane 2,4-Dimethylpentane 3,B-dimethyl pentane 2,3-Dimet h yl pen tane 2,2-Dimethylhexane 2,Fi-Dimethylhexane 2,4-Dimethylhexane 3,3-Dimethylhexane 2,3-Dimethylhexane 3,4-Dimethylhexane 2,2,4-Trimethylpentane 2,2,3-Trimethylpentane 2,3,4-Trimethylpentane 2,3,3-Trimethylpentane 3-Ethylpentane 2-Methyl-3-ethylpentane 3-Methyl-3-ethylpentane 3-Ethylhexane
BDP, 78.5 'C
PW, 78.6 'C
0.0000 0.3838 0.7582 1.1278 1.4908 -0.1135 0.2625 0.3263 0.6702 0.6304 0.9926 0.1271 1.0052 0.2625 0.4771 0.4886 0.6160 0.6580 0.8176 0.8531 0.8722 0.9289 0.9836 1.0306 0.7226 0.9085 0.9642 1 .oooo 0.7143 0.9930 1.0141 1.0290
0.0000 0.3636 0.7210 1.0792 1.4336 -0.1192 0.2529 0.31 18 0..6170 0.5729 0.9315 0.1004 0.9460 0.2405 0.4099 0.4200 0.5843 0.6053 0.7396 0.7738 0.7945 0.8555 0.9299 0.9854 0.6294 0.8382 0.9047 0.9400 0.6656 0.9460 1.0039 0.9850
0.0000 0.3909 0.7672 1.1399 1.5105 -0.1367 0.2718 0.3365 0.6812 0.6385 1.0043 0.1271 1.0212 0.2788 0.4914 0.51 19 0.6294 0.6693 0.8463 0.8756 0.8921 0.9420 0.9956 1.0414 0.7324 0.9106 0.9782 1.0026 0.7210 1.0374 1.0607 1.0755
be bigger than 0.5 for a set of compounds belonging to a given class. If this is so, then it will be quite safe to round the calculated number to the nearest integer t o obtain the actual carbon number. From this point of view, the fit would become perfect. Three Stationary Phases. Relative retention data of a series of alkanes, cycloalkanes, alkenes, cycloalkenes, and alkadienes on octadecene-1 (OD-1) and dimethylsulfolane (DMS) were taken from the work of Cramers (9) and combined with values on squalane as measured by Hively and Hinton (IO). A regression analysis based upon Equation 10 was then performed. The quality of the fit is shown in Table I. The corresponding regression coefficients are reported in Table 11. The detailed list of retention values, corresponding carbon numbers of the compounds, a n d those calculated from the regression equations for alkanes, cycloalkanes, alkenes, cycloalkenes, and alkadienes are provided in Tables 111, IV, V, VI, and VII. By inspection of Tables I and III it is evident that, on the basis of the statistical measures, alkanes fit the regression model excellently. For the population of 38 compounds, the square of the multiple correlation coefficient is 0.9931, t h e residual standard deviation is 0.14 and the maximum observed deviation is 0.33. Cycloalkanes, as it appears from Tables I and IV conform to the regression equation equally well. A similarly good fit is exhibited by the alkenes and alkadienes, according to Tables I, V, and VII. The best correlation is shown by the cycloalkenes (Tables I, VI), albeit on a limited population of only 5 compounds, with the square of the multiple correlation coefficient being 0.9998, the residual standard deviation being 0.02, and the maxi(9) C A Cramers, Ph D Thesis Eindhoven University, Netherlands, 1967 (10) R A
Carbon
HTK, 78.5 "C
Calcd carbon no
5.15 6.22 7.21 8.13 9.04 4.83 5.87 6.06 7.22 7.17 7.99 5.71 8.02 6.05 6.99 7.09 6.88 7.19 7.92 7.97 7.98 8.00 7.89 7.88 7.77 7.85 7.93 7.93 7.23 8.04 7.68 8.10
mum deviation being 0.01. It is readily apparent from these observations, that the combination of the results on the three stationary phases, octadecene-1, dimethylsulfolane, and squalane provides a very useful tool for the determination of the carbon number of all of the available hydrocarbons in the classes considered. It is, however, essential that the class of hydrocarbon be predetermined. This is, therefore, a n advance over the previous procedures where the determination of a carbon number was based upon a knowledge of the homologous series relationship. The data, so far considered, were obtained by using high resolution open tubular columns operated at room temperature. In other trials, packed column data obtained by Bayer (11) at an elevated temperature were used. These were the relative retentions of 32 alkanes on hexatriacontane (HTK), p-phenyldiphenylmethane (BDP), and paraffin wax (PW). Tables VIII, IX, and X present, respectively, the regression equation, the quality of the fit, and the detailed list of retention values, carbon numbers, and calculated carbon numbers. Again the fit is very good. The square of the multiple correlation coefficient is 0.9773, the residual standard deviation 0.16, and the maximum deviation 0.32. Many other groups of three stationary phases have been analyzed by this method using data for 21 alkanes with equally satisfactory results. In addition, an experimental research program has now been completed involving another extension of the James-Martin rule.
Received for review November 30, 1972. Accepted January 23, 1973. (11) E.
Hively and R E Hinton, J Gas Chromatogr, 6, 203 (1968)
no. 5 6 7 8 9 5 6 6 7 7 8 6 8 6 7 7 7 7 8 8 8 8 8 8 8 8 8 8 7 8 8 8
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