was needed. Separation of each component was complete (Table I). Some pairs of derivatives, heptamethylenediamine cs. A-amino-rz-lauric acid, P-alanine us. adipic acid, and yamino-n-butyric acid C J . suberic acid, were close to one another. Careful adjustment of initial column temperature and temperature program rate effected best resolution of these same pairs of derivatives. The calibration curves for determination of nylon 6,66 were constructed in the usual manner with octamethylenediamine (C& glutaric acid (C5),and y-amino-n-butyric acid (C,) as the internal standards. The slopes of the curves were 12.8 for the e-aminocaproic acid and 8.48 for the hexamethylenediamine, and yield milligrams of the amino acid and the diamine per unit area ratio. The internal standards for other copolyamides could be selected from Table I. The gas chromatograms for the determination of nylon 6,66 are shown in Figure 2. The glutaric, adipic, y-amino-n-butyric, and e-amino-n-caproic acids, and hexamethylene- and octamethylenediamines were weighed (6 to 10 mg), esterified, and dried; 0.7 nil of the trifluoroacetyl anhydride and 0.5 ml of the mcthylene chloride were added and gas-chromatographed.
The data presented in Table I1 indicate that the method has a n average relative error of about +2%. Gas chromatography of the reaction mixtures proved the trifluoroacetylation of diamines to be quantitative. Application of the homologs to the internal standards reduced the error caused by esterification and acetylation to a minimum. The complete acid hydrolysis of nylon 6 was accomplished in 2 hours, nylon 66 in 4 hours, and nylon 11 and nylon 12 in 8 hours. Twice the time of hydrolysis was satisfactory. The degree of acid hydrolysis of the polyamides was examined by gas and thin-layer chromatography (TLC). For TLC, glass plates were coated with silica gel G. The plates were developed with 1-butanol-25 ammonia-watcr (70 : 25 : 5). Staining was effected with ninhydrin. ACKNOWLEDGMENT
The authors are indebted to the Toyo Rayon Co., Ltd., for supplying polyamide samples and to K. Kobayashi for her technical assistance. RECEIVED for
review August 28, 1969. Accepted October 21,
1969.
I AIDS FOR ANALYTICAL CHEMISTS Graph for Attaining Maximum Separation in Unidimensional Multiple Chromatography Gilbert Goldstein Dicision of Laboratories, Beth Israel Medical Center, 10 Nathan D. Perlnzun Place, New York, N . Y. 10003
INTHE TECHNIQUE of unidimensional multiple chromatography (UMC), employed with paper and thin layers, an alternating sequence of development and drying takes place repeatedly with the same solvent in the same direction. This method was devised to gain the advantages of a greater effective distance of travel of the solvent front while retaining a shorter length for the support medium itself. The theory of U M C has been documented in a series of publications (1-8). The treatment by Thoma (5, 6) is especially exhaustive. R values are reproducible only under rigidly uniform conditions. They depend upon layer activity and thickness, chamber saturation, development distance, distance of starting point from solvent surface, quantity of test substance applied and solvent in which it is applied, as well as other factors (9). (1) A. Jeanes, C. S. Wise, and R. J. Dimler, ANAL.CHEM., 23, 415 (1951). (2) . , H. C. Chakrabortty and D. P. Burma, Anal. Clzim. Acta, 15, 451 (1956). (3) H. P. Lenk, Z . Anal. C/iem., 184, 107 (1961). (4) N. Zollner and G. Wolfram, Klin. Wochendzr.,40,1098 (1962). ( 5 ) J. A. Thoma, ANAL.CHEM., 35,214 (1963). (6) J. A. Thoma, J . Cliromatog., 12, 441 (1963). ( 7 ) H. Halpaap, C/iem.-6ig.-Tec/z., 35, 488 (1963). (8) R. Riidiger and H. Rfidiger, J . C/ii.ornaiog., 17, 186 (1965).
(9) G. Pataki, “Techniques of Thin-Layer Chromatography in Amino Acid and peptide Chemistry (Revised Edition),” Alln Arbor Science Publishers, Inc., Ann Arbor, Mich., 1968, PP 40-6. 140
Nevertheless, the theoretical and the observed values generally agree well enough to permit use of the theory in determining approximate behavior ( I , 2). A fundamental equation of UMC, due to Jeanes et al. ( I ) is nRf= 1 - (1 - R,)n, where nRf is the relative distance travelled by a substance after n solvent passes. As it increases, the distance separating two substances with differing R, values increases to a maximum and then decreases ( I , 3-5, 7, 8). Also due to Jeanes et al. ( 1 ) is an equation which may be written
N =
log ( a b ) log (1 - b/1 - a )
where N is the number of passes producing maximum separation, and a and b represent the Rfvalues. We may express Equation 1 in exponential form, and set it equal to y , giving y = a (1
- a)N = b (1 - b)”
(2)
Only those N values that are positive and integral, and those a (or b) values that lie between 0 and f l are physically meaningful in the context of UMC. If, subject to these restrictions, we now plot y cs. a for various values of N , those regions where > > we Obtain a series of Curves as in Figure 1. (For higher N values, the ordinate can be constructed on an expanded scale).
ANALYTICAL CHEMISTRY, VOL. 42, NO. 1, J A N U A R Y 1970
+
‘3
Inspection reveals that there are two points, u,-Le., two R,’s-on each curve for every value of y . Accordingly, each curve represents the optimum number of passes, N, for any two Rl’s situated at the same height, y , on the curve. If two R, values do not lie precisely on any curve at a given height, the closest N is used. Differentiating Equation 2 yields
(3) Setting Equation 3 equal to zero and solving for a gives a=-
1 N+1
(4)
as the maximum point for each curve. (Except when N = 1, the other solution is a = 1, representing a minimum or a point of inflection; but this solution is irrelevant to the present discussion). As the difference between two R,’s at the same height on a given curve diminishes, they approach one another from opposite sides of the curve and coincide with the maximum point in the limiting case. A rearranged form of Equation 4, N = l / a - 1, was derived empirically from Equation 1 by Jeanes el al. ( I ) . These authors did not interpret a graphically, but only as the aforementioned case of two R,’s nearing the same limit. When the percentage difference between two R,’s is small enough, the average R , may be substituted for a in the rearranged Equation 4, giving a prompt solution for N. It is true that the curves are rendered superfluous in such instances. For example, alanine (R1 0.22) and glycine (R, 0.18) in butanol/glacial acetic acid/water 4: 1 :1 ( I O ) show N = 4 whether the curve or the equation is used. But when the
Figure 1. Plots of y = a (1-aa)”, showing relation between Rf values, a, and optimum number of passes, N percentage difference is high, introducing the average R , into the equation will provide incorrect values for N, and it is here that the utility of the curves becomes manifest. In the case of asparagine ( R , 0.07) and histidine (R,0.31) in phenol/water 4 :1 (IO), the equation gives N = 4 as the closest integral value, while the best value, as the curve shows, is actually N = 5. An even wider discrepancy is evident with the pair aspartic acid (Rf 0.17) and lysine (Rf 0.03) in butanol/glacial acetic acid/water 4 :1 :1 (IO), for which N = 9 (equation) and N = 11 (curve), the latter being the correct value.
RECEIVED for review May 22, 1969. Accepted September 11, 1969. (10) G . Pataki, “Techniques of Thin-Layer Chromatography in
Amino Acid and Peptide Chemistry (Revised Edition),” Ann Arbor Science Publishers, Inc., Ann Arbor, Mich., 1968, pp 6770.
ANALYTICAL CHEMISTRY, VOL. 42, NO. 1, JANUARY 1970
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