Table VI. Analysis of Historical Creosote Oils by G C and Distillation Weight per cent per
Stasse No. 3
1
2
3
4
5
3.6 2.0 0.3
13.9 16.7 5.8
4.0 3.9 12.5
8.2 9.4 12.1
14.2 16.6 20.1
23.6 18.9 48.7
67.5 67.5
7.7 6.4
6.3 7.3 15.6
13.1 14.0 17.7
17.2 20.4 26.1
18.2 15.3 32.7
75.9 77.2 78.3 85.4
AWPA GC
AWPA
1.2
13.4 13.8 6.1
GC
4.8 5.6 0.6
17.3 18.6 7.8
7.9 8.7 21.7
14.9 16.8 21.3
18.0 21.5 30.2
15.4 14.2 18.0
12.0 10.6 4.8
11.2 11.9 8.1
11.4 9.9 18.7
14.9 19.1 22.9
11.0 13.8 24.8
7.4 13.0 19.6
Stasse 7
Stasse AWPA 9
6
Total Z (1-6)
Method
GC
Stasse 5
DFN
GC
Stasse AW PA
paring the three methods of analysis, clearly illustrate the above statements. The GC data agree very well with Stasse's. I t is to be expected that some volatile compounds were omitted from fraction 6 in his distillations when compared with the GC result, which includes additional compounds having boiling points to 450 "C. A much better fit to the curves of Stasse could have been obtained if the integration had been over narrower intervals of Tb, that is, of r1.2; however, the main intent would have been lost-namely, to determine the degree of correlation possible with the official standard distillation method (3). All of the GC data in Tables V and VI (last column) exhibit the large "on-column'' loss described earlier. While the nature of and mechanism for this loss can only be hypothesized a t this stage, it is nevertheless real, and reproducible. Its effect upon the GC data may also be observed as a consistent bias toward lower values for each of the fractions 2-5 when compared with those of Stasse by true distillation. In the latter case, the tar acids and bases, being volatile, would be expected to be found in the appropriate fraction. An examination of Roche's ( 1 1 ) list of 162 compounds reveals many such nonhydrocarbon aromatics which could be distributed through the first four fractions. Detector Correction Factors. This variable was used as defined previously ( 4 ) .Thus,
f\$,.,=
00
00
100 67.9 78.3
100
rwiil ~
r41i1
(2)
where rw(sl is the weight ratio of compounds to internal standard and rA(s) is the analogous peak area ratio. Factors were measured both for the n-alkanes, N = 16 through 2 2 , and for the 14 solutes comprising the MRS, Table IV. Included, also, are the appropriate values of f w c s , for each of the six distillation fractions, computed from chromatograms of the MRS. Graphically, the factors for the n-alkanes could be represented by a straight line as a function of carbon number, N , or equally, by the ratio of appropriate molecular . equation for this line is weights, r m i s lThe
(3) f,,,i,,[b'] = 0.274 f 0.368N Thus, any one of the n-alkanes was equally suitable as an internal standard for measuring the detector correction factors, with conversion from one to another by simple multiplication. Received for review April 9, 1973. Accepted July 26, 1973. The Forest Products Laboratory is maintained in cooperation with the University of Wisconsin. Mention of trade or company names is for purposes of identification only and does not imply endorsement by the U.S. Department of Agriculture.
Use of Multi le R, Values for Identification by Paper and Thin-Layer hromatography
8
Kenneth A. Connors School of Pharmacy, University of Wisconsin, Madison. Wis. 53706
Maximum information from chromatography for qualitative analysis is obtained when the R j x value for a compound in system X is independent of its value R f v in anOther system *' I t is found, for such systems, that the distribution of points in the R j x , R j v plane is close to a Poisson distribution. The number Of independent R j values required to identify a compound at a specified level of uncertainty can be calculated. Independence of Rf values is enhanced by using chromatographic systems that are qualitatively different from each other.
Chromatographic mc-ilities provide little usable information about a compound's identity, and so chromatographic techniques, though superlative for separating compounds and often effective for their quantitative determination, are not powerful means for qualitative analysis. Chromatography, when used qualitatively, is primarily a method of exclusion, the basic experiment being the comparison of mobilities of an unknown sample compound and an authentic specimen of a reference compound; if the mobilities in a common system are different
ANALYTICAL CHEMISTRY, VOL. 46, NO. 1 , JANUARY 1974
53
(granted appropriate attention to experimental uncertainty and possible artifacts), then it can be said that the sample compound is not identical with the reference compound. If the mobilities are not different, the only safe conclusion, in the absence of further information, is that the sample and the reference compounds may be identical. In order to reach a more definite conclusion, the chromatographic mobility is always combined with information from nonchromatographic techniques. This information may be obtained prior to chromatography (history and source of the sample, preliminary isolation, etc.), after chromatography (IR or MS examination, selective detectors in GC), or in some combination (chemical reaction, either before, during, or after separation). Still more information is often sought by measuring the mobility in more than one chromatographic system; the basis for this approach is the view that if the unknown and the reference compounds are actually different and yet exhibit identical mobilities in one system, such a coincidence will be very unlikely in all systems, so eventually it should be possible to find a chromatographic system in which these two compounds can be resolved. On the other hand, if their mobilities are identical in many chromatographic systems, the two samples are likely to be identical. This use of multiple chromatographic mobilities actually is fairly effective. In practice it can be applied by compiling a "library" of mobilities in several solvents, and then sequentially matching the mobility of the unknown sample in several systems to this library; it must be presumed that the library includes the unknown. This approach is exemplified by the study of Sunshine et al. ( I ) on the identification of 138 therapeutically active organic bases by thin-layer chromatography in seven solvent systems. Alternatively chromatographic "spectra" or profiles can be prepared, and the unknown profile matched to the catalog of known profiles (2-5). Systematic schemes have combined chromatography with classification by solvent extraction and selective color detection tests (6, 7 ) . Recently, Elgar (8) has noted that R f values for pesticides in one solvent system are often correlated with those in a different system, and he has concluded that measuring R f values in more than one system provides little information beyond that given in a single system. Drozen (9) has also pointed out that, if R f values in two systems are not independent, very little additional information is obtained from the second system. The analyst is therefore confronted with the extreme possibilities, in using R f values for identification, that either (a) a large (unspecified) number of chromatographic systems should be employed, or (b) the use of more than one system may be wasted effort. The present paper addresses these questions: (1) How many chromatograplxic systems should be used in seeking evidence of identity? (2) How should the chromatographic systems be selected? Attention is restricted to paper chromatography (PC) and thin-layer chromatography (TLC). (1) I . Sunshine, W. W. Fike, and H . Landesman, J . Forensic Sci., 11, 428 (1966). (2) "Some General Problems of Paper Chromatography,'' I. M. Hais and K . Macek. Ed., Czechoslovak Academy of Sciences, Prague. 1962. (3) V. Betina. J . Chromatogr., 15, 379 (1964). (4) A. Waksmundzki and J. Rozylo, J. Chromatogr., 38,90 (1968). (5) L. Reio, J. Chromatogr.. 48, 11 (1970). (6) K . Macek, J. VeEerkova. and J. Stanislavova, Pharmazie, 20, 605 (1965). (7) K. Macek, "Pharmaceutical Applications of Thin-Layer and Paper Chromatography,'' Elsevier, Amsterdam, 1972, Chap. 6. (8) K. E. Elgar. Advan. Chem. Ser.. 104. 151 (1971). (9) V. Drozen, p 199 in Ref. ( 2 ) .
54
THEORY Uncorrelated Systems. Each R f value has an experimental uncertainty that can be expressed in terms of zone standard deviation s (measured in R f units) in the direction of zone migration. I t will be assumed that s is independent of Rf and of the nature of the chromatographic system. Chromatographic resolution is defined Rs = ARf/ 45, and two zones are conventionally considered to be resolved when Rs = 1. The Rr scale of a single chromatographic system is then a line of unit length divided into (4s)-l distinguishable intervals each of length 4s. In this single system a maximum of (4s)-1 different Rr values (compounds) can be observed. Let R f , and R f , be R f values for a compound in chromatographic systems X and Y. Any such pair of values defines a point (Rfx,Rry)in the rectangular coordinate system generated by using the Rrx scale as abscissa and the R f , scale as ordinate. This Rf,,Rr, plane hassunit area and is divided into ( 4 ~ ) -distinguishable ~ squares, each of ~ . plane is conceptually, though not experiarea ( 4 ~ )(This mentally, equivalent to a 2-dimensional chromatogram.) The representation can be extended to m chromatographic systems, but it will usually be more convenient to deal with the Rfx,RfYplane; all of the mobility data obtained in rn systems can be presented in rn - 1such plots. We now calculate the probability that any two compounds may have the same Rr value. The probability that the first compound has an R f value in the first solvent system is obviously unity. The probability that the second compound has this same R f value is equal to the ratio of the interval corresponding to the first R f value, 4s, to the total length of the line, 1. Thus the probability is 4s that any two compounds have the same R f value in a single chromatographic system. The probability that two compounds will have the same R f value in two systems X and Y, provided that R f , is independent of Rrx for both compounds, is given, using a similar argument, by the ratio of the area of the square containing point (Rrxl,Rr,l) to the ~ . general, the probability that two total area, or ( 4 ~ ) In different compounds will have the same R f values in rn chromatographic systems, if the mobilities are independent in all systems, is ( 4 s ) m . This is the basis for the practice, described earlier, of using multiple R f values obtained in several solvent systems to aid in compound identification. Throughout this paper the quantity 4s will be given the value 0.1; though conservative, this estimate is reasonable (10, 11). We then calculate the probability of two compounds having identical Rf's in 1, 2, 3, . . . systems to be 10-1, 10-2, 10-3, . . ., respectively. Another way to interpret this calculation is that with m chromatographic systems a maximum of ( 4 s ) - m compounds can be resolved. This conclusion can be misleading, as will be shown later. It is important to ascertain if, in fact, Rr values in one system can be independent of those in another. This can be sought by making plots in the Rfx,RIYplane; lack of dependence for a set of compounds will be revealed by a lack of correlation between Rpx and Rr, values in such a plot. Figure 1 shows several examples of essentially uncorrelated systems. The actual identification problem is somewhat different from the situation described in arriving a t the probability that two compounds may possess identical R f values, in that the population of compounds of which the unknown substance is presumably a member is generally larger than two. Thus no gain has been made if the point (10) M . S. J. Dallas, J. Chromatogr.. 17, 267 (1965). (11) B. P. Lisb0a.J. Chromatogr.. 19, 81 (1965).
A N A L Y T I C A L CHEMISTRY, VOL. 46, N O . 1, J A N U A R Y 1974
Table I. Chromatographic Systems Symbol
Mode
A
TLC
B C D E
TLC PC PC T LC
F
TLC
G
PC PC PC PC
H I J
K
TLC
Description Benzene:dioxane:N H 4 0 H (60:35:5)/Silica gel G Methanol:n-butanol (60:40)/Silica gel G Isopropanol : N H 4 0 H :water (8: 1 : 1) Benzene:propionic acid:water ( 2 : 2 : 1 ) 2.5% Trisodium citrate:25% N H 4 O H (4:l)/Cellulose M N 300 n-Propano1:ethyl acetate:water ( 6 :1 : 3 ) / Cellulose M N 300 n-Butano1:acetic acid: water (4:1 : 5 ) M e t h y l ethyl ketone:2N N H d O H (2:l) Ethyl acetate:formic acid:water (70:20:10) Ethyl acetate:water:formic acid (60:35:5), u p p e r layer n-Butano1:acetic acid:water (4: 1 :2)/Silica gel G
L
TLC
M N
PC
0
PC
P
PC PC PC PC
Q R S
PC
n-Butanol: HCI (90:10), satd with water/Sil. ica gel G Isopropanol:25% N H 4 O H (4:1) Chloroform: methanol:25O/0 N H 4 0 H (80:45:15) n-Butano1:acetic acid:water ( 4 : 1 : 5 ) ,upper layer n-Butanol:ZN HCI ( 1 : l ) , upper layer 90% methano1:acetic acid:tetralin ( 1 0 : 2 :1 ) 80% ethano1:acetic acid:tetralin (10:2:1) Toluene:petroleum ether: methano1:water (5:5: 7: 3)
T
PC
U
TLC
V W
TLC PC PC TLC TLC
z A' B' C' D' E' F'
Benzene:petroleum ether: methanol:water (33.3:66.7:80: 20) Benzene/silica gel Chloroformisilica gel Methano1:HCI ( 1 : l ) Ethano1:HCI ( 1 : l ) Methanol/'Silica gel G Methano1:chloroform ( 1 : l)/Silica gel G Benzene:chloroform (3:1 )/formamide 95% ethanol/Silica gel G-0.1 N KHS04 Methanol/Silica gel G-0.1 N KHS04 Cyclohexane:benzene: diethylamine (75:15:10)/Silicagel G-0.1 N NaOH n-Butanol:5O/0citric acid (90:lO)/Chromedia-59io sodium dihydrogen citrate Water:methanol:methyIethyl ketone (i:5:5),ipolyamide+ 15% Cellulose M N 300 Water: methanol: methyl ethyl ketone (1:3:3)/polyamide+ 15% Cellulose M N 300 Light petroleum: methano1:methyl ethyl ketone (4:l:l)/polyamide+ 15% Cellulose M N 300 Light petroleum:methanol:methyl ethyl ketone ( 8 : l :l)/polyamide +- 15% Cellulose M N 300
G O L A
'
'
IO
1
R+x
Figure 1. Examples of uncorrelated systems. See Table I for descriptions of chromatographic systems A . Phenothiazines and related compounds; X = A , Y = 6 ( 1 2 ) . 6 . Hydroxyaromatic acids: X = C, Y = D ( 1 3 ) . C. Water-soluble dyes; X = E, Y = F ( 7 4 ) . D. Conjugated phenols; X = G , Y = H (15)
Table I I . Theoretical and Experimental Distributions for Some Uncorrelated Systems Figure l A ,
Figure 16,
T = 26
T = 37
__k
0 1
2 3
4
--
Figure lC,
Figure l D ,
T = 16
T = 22
Theory
Exptl
Theory
Exptl
Theory
Exptl
71 23
85.21 13.63 1.09
87 10 3
80.25 17.66 1.94
1
69.07 25.56 4.73 0.58
0.06
0
0.05
0 0
0.14 0.00
84 13 1 2 0
N ~ . T h e o r yExptl
77.11
81
20.05 2.61 0.23 0.01
13 5
4 2 0
0.00
sample space are Ri values, such as (R,+x~,Rf.ylj, ( R i x ~ , R f y 2and ) , so on for m = 2. We seek the probability p ( k ) that k points will be found in a cell. Let N be the TLC total number of cells, T the total number of points, and TLC TLC N A the number of cells containing k points. If the probability of occupancy of a cell by a point is independent of T LC .G ' t h e location of t h e cell (and is therefore l/N), the points will be distributed in the cells according to the Poisson H' TLC distribution, Equation 1, e-"' (1) p(k) = 7 I' TLC where X = TIN, X is therefore the average number of points per cell. Nk can then be found from NA= Np(kj. Table I1 gives the distributions of points for the plots J' T LC shown in Figure 1. The body of the table gives values of Nk calculated with Equation 1; since m = 2 for
