lowed by decreases with preboiling time. Hence, furfural appeared t o react through an intermediate, possibly a ring opening. Such an open-ring structure was suggested by Kolfrom, Schuetz, and Cavalieri (9). Teunissen (8) investigated the scission of the furan ring under the influence of acidic reagents. H e suggested the intramoleculaI migration of certain atoms prior to a breakdown into levulinic and formic acids. One important qualitative feature of the reactions with OPD was that the fluorescent solutions obtained from numerous sugars possessed approximately the same excitation and fluorescence wavelength maxima (360 and 460 mp). This fact suggests the possibility that an intermediate common to pentose and hexose is fornied during the reaction. Different warelength maxima (333 and 435 mp) were obtained for the reaction of dihydroxyacetone and DLglyceraldehyde with OPD. 0ptimum Temperature. E xp eriments were performed to determine the temperature dependence of the reactions producing fluorescent carbohydrate moieties. I n the case of D-glucose, a stable plateau was reached in 3 hours a t 120" C. (At higher temperatures anomalous peaks appeared in the rate curves.) Satis-
factory results were obtained for pentoses and other reactive substances at temperatures near 125' C. The temperature dependence of the reaction of OPD with L-arabinose is shown in Figure 4. Synthetic Preparations. Attempts were made t o isolate solid products from reactions between O P D and D-glucose or D-fructose in 50% sulfuric acid. A small amount of a dark, amorphous powder was isolated. This substance showed a n intense, greenish fluorescence in joy0 sulfuric acid. However, the quinoxaline and benzimidazole derivatives of carbohydrates showed very little fluorescence. K e and 1.3 X obtained 2.5 X p a . per mpmole per ml. as fluorescent yields for 2-(~-lysotetraoxybutyl)quinoxaline and D-glucobenzimidazole, respectively, when these substances were dissolved in 50% H2SOd. Microreaction. By appropriate scaling down of the volunies used in the pilot reaction, i t was possible t o achieve the microdetermination of sugars in the range of 0.2 to 2.0 pg. of sugar per niilliliter of final dilution. For those sugars whose fluorescent yields in the pilot reaction were high, the range in the microreaction could be diminished accoidingly. The rate of reaction of carbohydrates with OPD
in the micioreaction for glucose and fructose m s similar to that of the pilot reaction. Three hours of heating a t 120" to 125' C. gave maximum fluorescence for these sugars. Calibration curves for some sugars in the microreaction are shown in Figure 1. The estimation of sugars was more easily made by the us? of these standard curves. Interfering fluorescent substances (as for a-keto acids) may be diminished by procedures outlined in our earlier work (7'). LITERATURE CITED
(1) Chaigaff, E., Levine, C., Green, C., J . Biol. Chem. 175, 67 (1948). ( 2 ) Moore, S., Link. K. P., J . Org. Chem. 5 , 637 (1940). (3) Moore, S., Link, IC. P., J . B i d . Chem.
159, 503 (1945). (4) Ohle, H., Kruyff, J. J., Chem. Rer. 77, 507 (1944). ( 5 ) Pigman, FT., "The Carbohydrates," p. 413, Academic Press. Xev York, 1957. (6) Pigman, W., Ibzd., p. 422. (7) Spikner, J. E., Towne, J. C., AYAL. CHEM.34. 146s i1962). (8) Teunisskn, H.' P., Rec. Traz. Chirn. 49, 784 (1930). (9) Wolfrom, M. L., Achuetz. R. 0.. Cavalieri, L. F., J . A m . C'hem. SOC. 71, 3518 (1949). RECEIVED for review August 27, 1962. Accepted December 11, 1962. Division of Biological Chemistry, 141st Meeting, ACS, Washington, D. C., Xarch 1S62.
Application and Theory of Unidimensional Multiple Chromatography JOHN A. THOMA Department of Chemistry, Indiana University, Bloornington, Ind., and Department o f Biochemistry, Indiana University School o f Medicine, Indianapolis, Ind.
b The theory of unidimensional mul(UMC) (retiple chromatography peated irrigation with solvents in the same direction) has been expanded and used as a basis for formulating guides for the practical application of this technique to the resolution of simple mixtures of compounds. Some important conclusions are: Solvents producing low R, values are capable of the best resolution using UMC. When two very similar solutes have been separated with the minimum number of passes, their average migration distance will b e 0.52 of the length of the support. There is no theoretical limit to the number of homologs which can b e resolved b y UMC if liquid-liquid partition is the only factor involved in resolution. Separation of two similar solutes passes through a maximum when the average e-l or distance migrated is 1
-
214 *
ANALYTICAL CHEMISTRY
0.632 of the length of the support. The number of irrigations producing this separation is
-1
Id1
, ,where
- R, 1
R,' is the average Rf of the two solutes. Some limitations as well as advantages and possible application of the method are discussed and demonstrations of its utility are presented.
chromatography entails any procedure involving repeated irrigation of a chromatographic support with one or more solvents (15). Although this method has gained substantial popularity as two-dimensional chromatography, the technique of unidimensional multiple chromatography (UMC) first proposed by Jeanes, Wise, and Dimler (19), has been almost completely neglected. The superb resolving power of U l I C is achieved by effectively ULTIPLE
increasing the length of the chromatographic support and the number of theoretical plates over hich the solutes migrate. Although U l I C is capable of excellent resolution of simple mixtures (10, 191, the excessive time required for multiple irrigation. has probably curtailed its use. In recent years, howel er, centrifugally accelerated chromatography (6, 18, 26, 27) and thin-layer chromatography, TLC [for recent reviews, see (33, 44) 1, have been introduced as analytical tools and both of these innovations have the advantage of decreasing solvent development time. For this reason. it is now feasible to employ a larger number of solvent passes when attempting t o resolve simple mixtures. Furthermore, a combination of TLC and UhlC should prove to be an ideal way to resolve mixtures, because many of the labors involved in column chroma-
tography a i t h arious supports-e.g., silica gel, alumina, etr-can be circumrented. These labors include packing the column, extruding, and streaking for band detection or analysis of a large number of tubes containing eluate, etc. Another great advantage of L X C is the ease of detection of compounds. While the theory presented here indicates that greater resolution can be achieved by continuous chromatography (see Discussion), the far greater simplicity of U l I C will often dictate its preference. The technique of USIC has also proved particularly effectil e for the chromatography of homologous compounds because the larger members of the series can be separated on the same support with the smaller homologs (10). A simple count from the fastest to a slower unknown spot reveals the chain length of the latter compound, for nhich a pure reference sample is often unaT ailablr. llecause of the increased practicality of t X C , mith the advent of TLC and centrifugally accelerated chromatography, it seemed desirable to elaborate the theory t o provide a guide for exploiting the potentialities and delineating the limitations of the method. The eupansion of the theorv of UMC based upon liquid-liquid partition chromatography under ideal conditions is the subject of this communication. Because of the simplifying assumption. made, it can be anticipated that the equations developed TT ill not always correspond exactly with experimental experience. It can be eupected, though, that the theory will serve suitahlv for formulating guides for a practitd approach for compound resolution. Although the theory developed applies directly t o liquid-liquid partition systems (6, 8, 28, 32), the suggested guide lineq for the selection of operating conditions will probably be suitable for other types of partitioning systems (14..@). Some of the advantages and limitations of I X C , both theoretical and practical, are discussed. Several practical applications of U X C with paper and silica gel as supports are also presented. For simplicity, throughout this manuQcript,R, is referred t o as R. THEORY
Spot Position at Maximum Separation. I n practice, only a n integral number of solvent passes, p , is given the solid support. Severtheless, in the theoretical devi3lopment below, the number of solvent passes is treated as a continuous rather than a discontinuous variable. Because the relationships between various R functions involved in partition chromatography are very complex, this treatment greatly simplifies the mathematical management of the equations.
Accordingly, the conclusions reached and the predictions made are strictly applicable only when p is a n integer and are approximate vhen p is not an integer. During ULIC as the number of solvent derelopments increase, the extent of separation of two compounds increases, reaches a maximum, and finally decreases as the solutes approach the end of the support. The reduced positions, distance from origin , occupied by the length of suuuort spots lvhen maximum separation is achieved are of fundamental importance because the difference between the reduced positions of the compounds under these conditions is the limit of resolution. To evaluate the average reduced position of two compounds a t maximum resolution, we begin with the equation relating R, the true or singlepass R value, to R,, the apparent R value, after p solvent irrigations ( I O , 19). When R is independent of paper position, (1 - R ) P = I - R, (1)
-
This equation was derived by Zetting R, equal to the sum of the solute migrations on the individual passes and noting that this sun1 is equal to one less the binomial. (1 - RIP, We then find Ap, the difference between the reduced positions of the tn-o compounds after p excursions using Equation 1, to be: A, = (1 -
R), - (1 - R -
6)’
(2)
where the R values of compounds I and J, respectively, are R and R 6 and 6 is the difference betn-een the true R values. Using Equation 2 in the limiting case as (6 -P 0), it is possible t o determine the reduced position of the solutes at maximum separation by first finding p,,, the number of passes producing maxiis then submum separation. p,,, stituted for p in Equation 1 and the equation simplifird, giving the reduced Equapositions. To determine p,,,, tion 2 is differentiated with respect to p after expansion and set equal to zero. Expanding Equation 2, we have: A, = (1 - R ) , - [(1 - E). p ( l - R).-lS + (PI3
+
2!
(1 -
. . . I (3)
x)p-?62+
and by neglecting higher order terms in 6, Equation 3 reduces to: Ap = p(1
- R).-1
6
(4) 4A’) dP
Then differentiating and setting __ = 0 and solving for p,,,, pm,,
=
yield:
-1 In, ( 1 - R )
and when R is small : 1 pmsx
(5)
By an independent derivation Jeanes el al. (19) were able to show:
and indicated that no advantage can be gained by employing more than p,.,, solvent irrigations. Equation 6 is a good approximation of Equation 7 especially for small values of E . Now substituting p,,,, for p in Equation 1 gives:
rhich on simplification yields: R,,,,
=
1-
($1)
Hence a t maximum resolution, the average position of the solutes is a constant, 0.632, and independent of R. Equation 9 relates to blie limiting case when the difference of t’he R values of two compounds apiroachcs zero, so that an infinitesimal separation is achieved even a t the reduced positions corresponding to maximum separation. But in a practical situation, \\-hen the difference in R values of the two compounds is finite, the average reduced position of the compounds is still 1 e-1, Hence the R,,,,axvalues will correspond to 1 ,-I
- e-l
+ A b2, t x and 1 __-
- %, for the quickly anti slon-ly ~
2 migrating spots, respectively. Here Apmaxis the maximum scpwation which can be achieved. Spot Position When Compounds Are Separated with Minimum Number of Passes, pmin, I n addition t o R,,,,, perhaps a more practical and particularly interding quantity which can be evaluated for U l I C is the minimum number of solvent passes, p ,,,,,,, requircd to resolvc two related compounds. Solution of this problem requires a knowledge of several relationships existing betneen various chromatographic paramc4ers and a knowledge of the average R, of when rrsolution the compounds, Rp:Ji8?) is achieved with the minimum number of passes. The possibility that the average reduced position of any tn-o closely related compounds which are just separated (two spots just apparent) might be a constant was suggested by the discovery that the average reduced position of two solutes a t msximum resolution was constant and independent of the migration rates. LIathematically an analytical demonstration of this expectation proved, in our hands, to be an unsolvable problem because of the extreme complexity of the equations involved and the fact that the equations are useful in regions where convergence of expanded forms is slow. VOL. 35, NO. 2, FEBRUARY 1963
21 5
Therefore, a n alternative procedure, the calculation of RElnof two substances as a function of various chromatographic parameters, was undertaken on the Indiana University IBhI 709 digital computer. Details of the computations are outlined below. The calculations demonstrated that the intuition mas correct, suggesting that RGln was independent of migration rates. For a very wide range of experimental conditions RZ,, was computed to be 0.52 with an average deviation of 0.02. Only solvents meeting certain requirements will be able to achieve the required resolution with p,,, irrigations. These requirements and the experimental selection of the appropriate solvent (if any exist) are detailed below: Selection of Solvent Producing p,,,. Attention is now turned t o the problem of selecting the molar proportions of a given set of solvent components which will produce pmin concomitant with a required separation, A. The value of 4 is preselected such that the spot centers are disengaged completely enough so that visual observation of the developed chromatogram mill allow the discernment of two spots. The value of A will vary with experimental conditions and depend upon the length of the paper, extent of loading, sharpness of the zones, etc. ( l a ,1 3 , d I ) . The actual preselection of A is left t o the judgment and previous experience of the investigator with similar systems. A theoretical approach to the selection of A is beyond the scope of this paper. However, on the second and subsequent passes, the solvent flows over the trailing edge of the spot before reaching the leading edge. This effect aids in sharpening the bands. During continuous chromatography , the magnitude of the spot constantly increases, since there are no sharpening forces a t play. Figure 2 graphically illustrates some of the relationships existing between various chromatographic parameters which are useful for selecting the desired solvent proportions. It indicates that the maximum separation, Apm,,, which can be achieved for two related compounds is a function of their average R, the average of the free energies of transport of the compounds from the stationary to the mobile phase, average A p , and the molar proportions of the irrigating solvent, N , . (Only two solvent components are allowed to vary.) It has been shown (3, 6, 7 , 29, 38, 39) that the migration rate and partition coefficient of a compound can be related to the molar proportions of the mobile solvent via the chemical potential of transport xhen the ratio of the cross-sectional areas of the phases is operationally constant. Hence, it seems reason216
ANALYTICAL CHEMISTRY
able that the problem of selecting the appropriate proportions can be solved by first assessing the chemical potential of transport, Apmin, which will satisfy the conditions imposed for separation with minimum effort. Then the correct molar proportions of solvent, N , (7, 58, S9), can be found by the graphical relation between N . and A pmin. We begin the evaluation of Apmin with a mathematical presentation of the simultaneous equations which demand solution: 1 - (0.52
+ A/2)
- (0.52 - A / 2 )
1
= (1
-
= (1 -
RC)Pmldi
(10)
Rd)Pmm
(11)
where R, and Rd are, respectively, the R values of compounds C and D. It is impossible t o solve for A p m i n (after appropriate substitution for R, and Rd in terms of Equation 13) by setting d(pmin)
=
0, since Equations 10 and 11
are discontinuous. rithm of Equations 10 by 11, expanding resulting equation, discarding second terms, we arrive at tion: 01
=
Taking the loga10 and 11, dividing the right side of the and collecting and and higher order the following equa-
In, (0.52 - A/2) Inc In, (0.52 A/2) >
(
+
=
R d
- Ro (12)
Using Martin’s equation (6,68):
where & is the gas constant in calories per mole and A is the ratio, AJA,, the ratio of the cross-sectional areas of the stationary and mobile phases. Solving for R in terms of the other parameters in Equation 13 and making the appropriate substitutions for R, and Rd in Equation 12 lead to: a =
1 1 1+ Aea@d/sT 1 + AeA@c/ET (14)
where ApC and Apd are the chemical potentials involved in the transport of compounds C and D from the stationary to the mobile phase. -4s an approximation to Equation 14, we have after rearrangement:
A,
= e-A@dR-T
- e-*@c/RT
(15)
which is excellent when AeA@/RT >> 1 or R is small (cf. Equation 13). When the compounds under investigation are similar in nature, it can be shown that the ratio of the free energy of transport of the t h o compounds is reasonably constant and essentially independent of the molar proportions of the irrigating liquid (58, 59). Hence, it is permissible t o substitute k ( A p d ) for A p C where k is equal to Apc/Apd t o
obtain Equation 16 containing a single unknown, Apd for evaluation. A and k are measured experimentally (38, 39). = e - A ~ d / g T = ,-k%,/sT
(16)
Apd then is equal to Ap,,, under these conditions. Although an analytical solution of Equation 16 for 4 p d is exceptionally difficult, the equation is in a form which allow us to reach several important conclusions. Inspection of the left side of Equation 16 shows that it is a positive constant, since Rd > R, (cf. Equation 12) while inspection of the right side shows that for positive or experimentally useful values of Apd, the range of variation is from zero t o plus infinity, since k > 1. Therefore, we conclude that there is some value for Apd corresponding to 4 p , , , which \ d l allow a solution t o the equation. Solution is accomplished by trial and error or by a method of successive approximation. JJ7hetheror not a solvent can be found which gives Apd is a matter for esperimentation. For each solvent, the range over which Ap can range will be limited by the molecular forces of the system in question. When A p d Q the maximum value of A p for the system, the molar proportions of solvent, Ks,giving 4 p d can be selected graphically if the relationship between A p and S, has been determined experimentally (38, ’99). Relationships for Homologs. It would be highly desirable t o establish chromatographic relationships between the smaller and larger homologs for UMC, since these polymers are of great interest for chemical and biological research. If the proper relationships could be ascertained, it should be possible to predict the conditions suitable for the resolution of the larger homologs and. furthermore, to ascertain the theoretical limits of fractionation, if any. A useful starting relationship from which important conclusions can be drawn is the correlation between the number of solvent passes required to 1-mer a migrate an n-mer and an n given distance on the support. Mathematically, this condition is met when:
+
(1 - Rm)P = (1
- R n + 1)Q
(17)
where p and q are the number of irrigations required to move the n-mer 1-mer to the same reduced and the n position on the support. R, and R,+I are, respectively, their true or singlepass R values. Taking the logarithm of Equation 17 gives: p l n , ( l - R,) = gln,(l - R n + l ) (18) Then substituting for R, and R, + in terms of Martin’s modified equation (IO) we have:
+
where A pr is the free energy of transport for the monomer, A p u is the free energy of transport for the added residue, and n is the chain length. Equation 19 simplifies when 1
