F,
=
V, = Vk
7
= =
volumetric flow rate of carrier gas a t 20’ C. and 1 atm. vol. of gas phase vol. of stationary phase carrier gas viscosity LITERATURE CITED
(1) Brennan, D., Kemball, C., J. Inst. Petrol. 44, 14 (1958). (2) Bruderreck, H., Schneider, W., Hal&, I., ASAL. CHEM.36, 461 (1964). (3) Desty, (D. H., Goldup, A., Swanton, K. T., Gas Chromatography 1961, Lansing,” p. 105, Academic Press, New York, 1962.
(4) Desty, D. H., Haresnape, J. N.,
Whyman, B. H. F., ANAL. CHEM. 32, 302 (1960). (5) Golay, hl. J. E., “Gas Chromatography 1958, Amsterdam,” p. 36, Butterworths, London, 1958. (6) Hal&, I., Hartmann, K., Heine, E., “Gas Chromatography 1964, Brighton,” The Institute of Petroleum, London. 1966. ~ - -, -in n r e - -m ( 7 ) HalBsz, I., Heine, E., Nature, 194, I
r
971 (1962)
( 8 , Heike,--E., Dissertation, Universitat
Frankfurt am Main, Germany, 1963. (9) Reisch, J. C.!, Robison, C. H., Wheelock, T. D., Gas Chromatography 1961, Lansing,” p. 91, Academic Press, New York, 1962.
(10) Schneider, W., Bruderreck, H., HalAsz, I., ANAL. CHEM. 36, 1533 (1964). (11) Wegner, E. E., Dissertation, Universitat Frankfurt am Main, Germany, 1961. RECEIVEDfor review August 17, 1964. Accepted December 24, 1964. Presented at the First International Symposium on Advances in Gas Chromatography, University of Houston, Houston, Texas, January 21-24, 1963. We express our gratitude to the Max Buchner Forschungsstifung for financial furtherance of this work.
Selection of a Chromatographic Solvent JOHN A.THOMA Department o f Chemistry, Indiana University, Bloomington, Ind., and Department of Biochemistry, Indiana University Medical School, Indianapolis, Ind.
b Two complementary quantitative indexes of the resolving power of a chromatographic system, the ratios of the chemical potentials of transfer of related compounds and the ratio of the cross-sectional areas of the liquid phases, are proposed and evaluated. Graphical procedures are developed for determination of these chromatographic parameters for systems of homologous polymers and structurally related solutes. Criteria for the use of these parameters are outlined and when experimentally tested held for polar solutes and solvents. The theory of regular solutions is applied to the problem of selecting solvent components and leads to the conclusion that for polar systems it will often be more profitable to study variations in solvent proportions than to study alterations of the sglvent components. Additional guide lines and practical suggestions for the selection of chromotogrqphic conditions based upon theory and accumulated experience are proposed.
0
major objectives of the theory of partition chromatography is to identify the various factors which govern the rate of compound migration during chromatography and to establish quantitative relationships If, in addition, the among them. dependency of these factors on the physical properties of the solute and solvent can be assessed, the theory of solution and principles of physical chemistry should be of. considerable aid in the selection of suitable chromatographic solvents and environments for separation of both known and unknown mixtures. 1-nfortunately, the complexity of the chromatographic pheNE OF THE
9
ANALYTICAL CHEMlSTRY
nomena (2, 9, 10, 20) precludes a rigorous theoretical approach to the selection of an appropriate solvent, partly because of the uncertainty of the nature of the phases (1, 16, 17, 26, 30) involved in paper partition chromatography. However, even if the phases could be precisely defined, solution theory has not been developed to the point where it could consistently furnish useful quantitative predictions about the effect of solvent alterations on solute migration rates (18, 29). I n addition, chromatography is basically a dynamic rather than an equilibrium phenomenon and solvent concentration gradients both along and across the support ( 4 , 8 , 1 0 , 1 1 , 3 4 )complicate the theoretical picture even further. However, a general quantitative correlation of R, data might be made for some systems in terms of certain empirical relationships which are analogous to those theoretical relationships that would be expected to apply to partition processes in certain limiting cases. The need for such quantitative correlations is obvious if the use of paper chromatography is to advance beyond the state of a completely empirical art. Thus while many studies have been concerned with the quantitative relationships of R, and chemical constitution, analysis of the quantitative variations of migration rates with changes in solvent have only rarely been attempted (1, 5 , 38, 49). The present approach is based on a quantitative index oi the resolving capacity of a particular system which can be semi-empirically correlated to environmental changes and performance characteristics of the system. The results are interpreted in terms of general principles already established. I n addition, the use of solution theory to relate these physical
parameters to molecular parameters of the solute is described. The systems employed to test the ideas developed here involved ascending and descending chromatography on paper supports, with and without prior exposure to solvents, with carbohydrates as solutes and polar solvents as irrigating liquids. The polar solvents and solutes were selected for the present investigation because Martin’s equation seems to be obeyed closely. On the basis of theory and our experience four guide lines for the selection of appropriate chromatographic conditions are detailed below. THEORETICAL
To evaluate graphically the chromatographic functions involved in paper chromatography, the relationship between these functions and Rf or other suitable Rr functions is necessary. The theory developed by Martin and his coworkers (4,26-28) relating chemical constitution to Rf provides the appropriate starting relationship (See Appendix for definition of symbols) :
It should be noted here that considerable experimental evidence has been amassed to verify Martin’s postulates (22, 20, 21) and that Green, Marcinkiewicz and coworkers (11-15, 22-25) have presented especially convincing evidence supporting these pcstulates using a new technique, flat-bed chromatography. For a homologous series ( 6 , 27, 41) since n = chain length in terms of re
peat units, ni will be designated as sa, and Equation 1 transforms to:
The parameters A . ~ / 9 sand Ap,/Apb, the cross-sectional area ratio and the chemical potential of transfer ratio, are the two parameters which will be used as resolving indexes. Under certain conditions both A . ~ / i l s and A p a / A p b may remain constant while both A p a and Apb are varying as solvent proportions are changed (see below). In such cases Equation 2 becomes parametric and plots of R.wn us. n - 1 generate families of lines intersecting a t the coordinate ( - Ap.,/Apb, log,A.w/As). Furthermore, the slopes of the lines of the plot will be - A p b / R T and the intercepts a t n - 1 = 0 will be logeA.~~/--Is- A p L , , / R T . Thus under the stated conditions, graphical analysis of R , data allows evaluation of all of the chromatographic parameters for various solvent systems which vary only in the relative proportions of the solvent. I t should be emphasized, however, that an intersecting pattern of straight lines for plots of RM,, us. n - 1, is not in itself convincing evidence that A,w/24s and Apa/Apb are necessarily constants. For example, even though the reasonable assumption is made (see below) that the logarithm of the crosssectional area ratio is linearly related to the chemical potential of transfer as in Equation 3, Equation 2 remains parametric.
may be used as parameters in equations derived from theoretical considerations-e.g., Equations 2 and 4-to provide quantitative correlations of chromatographic data. Our comments to this point have been restricted to homologous polymers, but a more general treatment for the evaluation of the chromatographic parameters of two related compounds can also be carried out. The equations for the evaluation of the chromatographic parameters for similar compounds are different from those used for homologous saccharides because the parameter n is no longer available for use. For any two solutes the chemical potential of transfer and cross-sectional area ratio are related to the R.w value through Equation 1. Hence using this Equation, two simultaneous equations describing the relationship between R.w= and R M and ~ the corresponding chromatographic functions can be written for any solutes, X and Y , by substituting Apz and Apu (total energy of transfer of the whole molecules, X and Y ) for the summed energies of transfer of the functional groups into Equation 1. These simultaneous equations can be combined and rearranged to give the useful result:
significance of the slopes and the intercepts of those plots which are actually linear remains obscure and only apparent cross-sectional area ratios and apparent chemical potentials of transfer can be evaluated. Thus, although the physical interpretation of the constants estimated graphically may be obscured by the complexity of the chromatograhpic system, these constants are nevertheless useful for establishing the intrinsic resolving power of a particular set of solvent components. Before turning our attention to the conditions under which the ratio of chemical potentials of transfer between the stationary and mobile phase for two related compounds-Le., A p v / A p z --are independent of the molar proportions of irrigating solvent, it is first convenient to consider how the free energy of transfer of a single compound between any two binary mixtures depends upon the molar proportions of the two solvents. A common procedure for calculating the free energy of transfer (or the distribution coefficient) of a compound from one phase to another is to measure the relative solubilities of the compound, in the two phases.
M’ -R.M= = log, A-
ApZ =
RT log, N ,
As’
J
where
r
In M
(5)
When the log of the solubility of a solute in a binary mixture is linearly related to NHzo-i.e., by Equation &and when NH,OI n M - N%,o s is the same for both solutes, then A p , / A p , is a constant and equal to flu/&.
RT log, N , Since the range of variation of for useful solvents is generally limited to about 0.3 it is approximately true (from Equation 3) that &/As is linearly related to NHzO.I n such situations a plot of Rw, us. n - 1 will again lead to intersecting lines but with an intersection coordinate of [ ( Ap./Apb C b R T ) , D b ] . However, the identity of both the slopes of the lines and the intercepts at n - 1 = 0 remain unchanged. In cases such as this where a relationship between A w/As and the ratio of the chemical potential of transfer exists, the physical interpretation of the coordinates of intersection becomes uncertain and it is no longer possible to identify the chromatographic parameters with simple physical processes. However, from a practical point of view, ambiguous identity of the resolution indexes is not of serious concern here since apparent cross-sectional area ratios and apparent chemical potentials of transfer may be empirically evaluated, a t least in some cases (see Results), and
s
RT log, N .
r l i L
In
1
and ARM = R M ~ RM,
When [AM/ABI,, [AMMIAsI,,and A p , / A p , are constant, a plot of R M , us. ARM will yield a straight line whose intercept is log, A’M/A’s and whose slope is 1/(1 - A p u / A p u , ) . From this slope the ratio of the chemical potentials of transfer can be evaluated. When [ & / A s ] , and [AM/As], are equal, A’.w/A’s becomes equal to [ A M / A s ] =and under these circumstances the value of [ A M / A B ]can , be substituted into the two original simultaneous equations and the parameters A p z and Apu can be calculated for each solvent mixture. As in the derivation for homologous polymers, the above conditions leading to linearity in AR,,, us. R M plots are not unique. Hence, the precise physical
= a=
+ P.NE,o
(6)
Since Equation 6 is general, it follows that A p g / A p z is independent of the proportions of solvent follows whenever A p , for any two solutes, is linearly related t o a common variable of the solvent mixture-e.g., volume fraction-and the solutes “see” the same phases. One case in which this relationship holds over a wide range of is shown in the Results section. Others have been reported (35,36). One further step remains; that is, to relate N B , O I n M and N H ~,nO s to the mole fraction of water in the solvent reservoir, NH20. To do this it is necessary to make the following assumptions. Provided the solutes are not migrating too close to the solvent front, (R, 5 0.8), it is reasonable to assume that the composition of the mobile phase is approximated by that of the developing solvent. (Assuming a linear relation between the composition of the mobile phase and developing phase will lead to the same conclusions, see below.) Since concentration gradients of solvents must certainly exist across the paper VOL. 37, NO. 4, APRIL 1965
501
for the water miscible solvents under consideration, it is difficult, if not impossible, to suggest a precise mathematical model which describes the effects of these solvent gradients on the distribution of the solutes across the paper. To obtain a workable model it is suggested that the mole fraction of water in the effective stationary phase is linearly related to the mole fraction of water in the mobile phase. Thus where N R a 0is the mole fraction of water in the irrigating solvent:
(It is anticipated that ( and e may be sensitive to both solvent components and the solutes being resolved. I n other words, the cross-sectional area ratio may depend in part on the nature of the solute.) When log,N, is a linear function of N H z O (as in the case shown in the Results section) and in addition when the mole fraction of water in both mobile and stationary phases are linear functions of N H , o , the free energy of transfer, Ap, must also be a linear function of NHrO.Thus, substitution of 7 into 6 in conjunction with Equation 5 establishes the following linear relationship : Apz =
&(NH,o [1
- (=I
f
62')
(8)
Since Ap is directly proportional to R M (Equation 1) when the apparent cross-sectional area function, . 4 ~ / A s , is constant, plots of R M us. mole fraction of water (or in some cases volume fraction) will be straight lines. Using Equation 8, the ratios of the chemical potentials of transfer can now be written in terms of constants and the mole fraction of water in the irrigating solvent.
been found that the logarithm of the solubility of lactose is linearly related to the mole fraction of water in solution over a rather wide range of solvent compositions, the constant, b, (see Equation 6) for polar molecules will be given to a first approximation by the difference in the free energy of solution of the solute in water and its free energy of solution in the organic liquid (see Results). Suggestions relative to those physical properties of the organic solvent which are most likely to affect this free energy difference and hence p can be derived from the following treatment of solution theory. The dependence of the solubility on the physical constants of the solvent and solute for restricted types of solutions has been developed by Hildebrand and his coworkers (18). Implicit in their development was the assumption that in the solutions under consideration the entropy of mixing was the same as that for an ideal solution (in other words there is no preferential ordering of the molecules of the solution) but that solution was accompanied by a change in enthalpy. They proposed the name ['regular solution" for such a system. The free energy of transfer of a solute between two regular solutions can be equated to the difference in the enthalpy of mixing in the two solvents. Although it is recognized that the solutions with which we have been dealing are not regular, the theory of regular solutions is introduced because it is instructive in indicating what factors may influence solubility and may be useful for making qualitative predictions. By considering the total interaction forces between all molecules in solution, the following equation relating the partial heat of mixing to the cohesive properties of the solvent and solute was developed :
=
The conditions under which the ratios
of the chemical potentials of transfer of two related compounds remain constant are somewhat restrictive. I t is required that the slope, (, and the intercept, E , of Equation 7 must be approximately the same for the solutes. Only when the two solutes are closely related in structure and in solubility characteristics and when resolution is most difficult-i.e., under conditions of interest in this paper-is this possibility likely to be realized. If the constants pz and 0, in Equation 9 could be evaluated with the aid of solution theory (18, 99), it should then be possible to predict the effect of changes of solvent components in binary mixtures on the ratio, Apu/Apz, assuming Cz = t u and c1 = eu-i.e.. that Apu/Ap2 = &/pL. Since it has 502
0
ANALYTICAL CHEMISTRY
RT
(&
- 6.)'
(10)
I t immediately follows that the free energy of transfer from one dilute solution-i.e., water-to another is then given by the following equation : Bz
= ALL,, Vz[(61
- A U ~ . H , O= 8.)' -
-
(6&0
6z)']
(11)
Thus, the ratio of chemical potentials of transfer of the two solvents can be equated to the physical properties of the molecules comprising the solution :
%! = APZ
Since only the constant 61 in Equation 12 can be varied by changing the identity of the organic component, two interesting conclusions follow. First, when the nature of the organic component of the mixture is altered, the ratio Apu/Apz will vary if the cohesive properties (a1) of the solvent are varied. Second, since the cohesive properties of the solvents most frequently employed for chromatography of polar molecules are approximately the same (see Results), the change in the numerator and the denominator with a change in solvent will usually be of the same magnitude and in the same direction. I t is thus likely that the ratio of the chemical potentials of transfer ail1 only be slightly influenced by most component changes. Hence we would predict that the ratio of the chemical potentials of transfer \yould remain approximately constant even though changes were made in the organic coniponent of the system. This suggests that the chromatographic characteristics of one system could be closely duplicated by another if suitable solvent porportions were selected. For polar solvents, additional terms accounting for specific solute-solvent interactions and orientation effects will have to be introduced into Equations 10 and 12 to account for changes in the activity coefficients of the solutes. Again, however, these factors generally will alter the numerator and denominator [or .alternatively the activity coefficients (39)]in the same direction and by the same magnitude thus leaving the ratio of the chemical potentials of transfer relatively unaltered for different sets of solvent components. It should be emphasized that their approximation will be valid only for closely related compounds which are difficult to separate. It is only in cases where very specific interactions between solute and solvent occur that significant changes can be introduced into the ratio of the chemical potentials of transfer. It should also be pointed out here that solutes with the same cohesive properties can be resolved if their molecular volumes are different. For example, the difference in molecular volume is probably the important factor in the resolution of homologous mixtures. EXPERIMENTAL
Solubility of Lactose. The solubility of lactose (lactose.HzO, Fisher reagent grade) in mixtures containing various proportions of water and tertbutanol (reagent grade) were determined by approaching equilibrium from subsaturation and supersaturation a t 25' i 0.1" C. The approach to equilibrium was studied by the procedure described below.
suspended in the vapors 1 hour before irrigation was begun. The papers were spotted 2 cm. from the bottom. When the solvent reached the top of the papers, they were removed from the chamber, air-dried, and the sugars were located as described above. The 3 X 8 inch plates for thin layer chromatography were prepared as described elsewhere (40). The dextrins were spotted 2 cm. above the bottom of the plate which was then placed in 5 (diameter) x 10 (height) inch cylinders. Chromatography was performed by the ascending technique at room temperature, 25" f 1' C. When the solvent reached the top of the plate, it was withdrawn, air-dried, and the sugars were located by the procedure of Stahl (57). RESULTS
.2
.4
.6
.e
1.0
MOLE FRACTION WATER
Figure 1 . Saturating solubility of lactose in various solutions of water and t-butanol a t 25" =k 0.1 " C. Equilibrium was approached from both directions
Because small amounts of tertbutanol were found to interfere with the development of the anthrone test for lactose, the standard procedure (19) was modified. I n a typical assay, a 4 ml. sample was withdrawn from the jacketed tubes, centrifuged and dried over anhydrous sodium hydroxide pellets under vacuum, and the last traces of tert-butanol driven off by a gentle flame. The sugar was then diluted and analyzed by the anthrone method. Equilibrium was assumed to have been obtained when the concentration of lactose in the water-tert-butanol mixture remained constant for a period of 5 to 7 days. The duration of the experiments was 3 to 4 weeks. Paper Chromatography of Carbohydrates. For these experiments, all mono- and disaccharides a n d solvents were of reagent grade a n d employed without further purification. The preparation of t h e maltodextrin a n d dextran oligosaccharide mixtures by acid hydrolysis of amylodextrin and dextran has been described elsewhere (45). All chromatography experiments with the dextrins and mono- and disaccharides were conducted in 6 x 36 cm. glass tubes at 25" f 0.1" C. with various exposure times to the solvent vapors and the spots located by the silver nitrate-sodium hydroxide reagents by the dip technique (44). For ascending chromatography the papers were spotted 1 cm. from the solvent and descending chromatography the papers were spotted 4 cm. from the solvent. The dextran oligosaccharides were chromatographed a t room temperature (25" rt 1" C.) on 8 X 8 inch sheets of Eaton and Dikeman 613 paper in 10 (diameter) X 10 (height) inch jars. Fifty milliliters of solvent were added to the jars and the paper cylinder was
IO
I
0.01
Verification of Assumptions. The validity of most of t h e conclusions reached in t h e Theory section requires t h e following assumptions: (1) a linear relationship exists between the , the irmole fraction of water, N E I O in rigating solvent and the free energy of transfer of solute, X, between stationary and mobile phases or, equivalently, between Nalo and the logarithm of the solubility of the solute; (2) the ratio of the chemical potentials of transfer of closely related compounds is independent of the molar proportions of irrigating solvent; (3) the cross-sectional area ratio, is operationally constant and independent of the molar proportions of the developing solvent;
8
.2 .4 .e .e 1.0 MOLL FRACTION WATER
Figure 2. Illustration of linear dependence of R, function or free energy of transport on mole fraction of water in water-n-propanol mixtures Plotted from dato in ( I ) . Ascending chromatography and no preexporure to solvent vapors before irrigotion; bars indicate variation introduced into ordinate by variation of 0.01 in R/ value
CHAIB
LENG\H-I
'
Figure 3. Plot illustrating procedure for evaluation of partition parameters for homologous polymers Solutes, dextran oligorocchorides; solvents, water-ethanol-nitromethone mixtures; paper, Eoton and Dikemon No. 613; temperature; 25' f 1 C. Papers were exposed to solvent vapors 1 hour prior to irrigation
% bv
volume
water
ethanol
nitromethone
A
20
6 C
23 19 15
35 40 45 50
37 37 36 35
curve
D
and (4) A M I A Bis not related to the solute migration rate provided the solute origin is not too far from the solvent reservoir. Assumption 1 can be tested by measuring the dependence of the solubility of the solute in question on the mole fraction of water in a binary mixture. For the systems under study the assumption was verified by showing that the logarithm of the solubility of lactose and hence the standard free energy of solution is a linear function of the concentration of water between 0.2 and 1 mole fraction (Figure 1). Hence, it is reasonable to assume that the free energy of solution for other polar solutes will vary linearly with NE*,,. The points on the curve (Figure 1) are averages of the saturating solubility determined by approaching equilibrium from subsaturation and supersaturation. The linear dependence of the free energy of solution or, alternatively, the free energy of transport of a solute, on NarO and the constancy of A,w/As can be simultaneously demonstrated from chromatographic data if plots of Rw us. N H , O are linear. Equivalent plots can more readily be constructed by plotting R j / ( l-Rf) us. the mole fraction of water on semilogarithmic paper. I t should be noted that conditions 1, 3, and 4 are all simultaneously satisfied when RM varies linearly with N,,,o. If they VOL. 37,
NO. 4,
APRIL 1 9 6 5
503
are not, then a curved relationship between R U and ' Y H 2 0 would be found. The linearity of Figures 2-5 is offered as
r
-021
.o I
experimental evidence that conditions 1, 3, and 4 are fulfilled by the types of systems under investigation. The linearity of these curves also complies with restriction 2 which requires that the ratio of the chemical potentials of transfer of two related compounds be independent of the molar proportions of the irrigating solvent. The discovery that R f is fairly insensitive to distance from the solvent reservoir (39) on the lower half of the paper is also obvious support for requirement 4. Although the individual effects of A M / A and ~ A p on the RM values have not been sorted out in Figures 3-5, the procedures for doing so are described in the Theory section. When these quantities are evaluated and plotted us. NHtO it was found, as anticipated, that A u / A s was independent of N H ,while ~ AI was linearly related to ",O. A more complete discussion of these findings will be the topic of another communication. A typical graph of R , / ( l - R f ) vs. N H 2 0 plotted on semilogarithmic paper for various amino acids is shown in Figure 2 ; the data were gleaned from a publication of Burma and Banerjee ( I ) . Although the data in Figure 2 and similar graphs are curved above 0.8
1
, 0
1
, \m\ 2
4
6
CHAIN LENGTH -I
Figure 4. Dependence of R f function of maltodextrin oligosaccharides on chain length for descending chromatography at 25' f 0.1 ' C. Paper, Eaton and Dikeman No. 61 3 ; descending chromatography; solvent, water-f-butanol (numbers in figure correspond to male froction water n solvent); no preexposure to solvent vapors before beginning irrigation
mole fraction water, this large concentration of water is beyond the useful chromatographic range. Since linearity between NH,o and R y has also been established for other systems, this is now the expected relationship for chromatography of polar solutes with polar solvents. The abnormal curve exhibited by lysine (Figure 2) is probably associated with the excessive streaking noted by the authors due to adsorption on the paper. Undoubtedly further anomalies will be encountered so that extensive testing of the equations and assumptions under diverse conditions will be required to establish their general usefulness and limitations. The possibility that solvent gradients existing along the paper may influence the value of d w : A , ? was tested by assessing this function as the spotting distance from the solvent reservoir was changed. The maltodextrin oligosaccharides were employed as solutes and chromatography was performed by the ascending technique for various solvent mixtures on three different types of papers. The results of these experiments are portrayed in Figure 6 where it is seen that the area ratio can increase, decrease, or remain essentially constant as the spotting distance from the solvent mixture is changed. Even though the area ratio varies with paper position, the graphs for these systems were all composed of families of intersecting lines similar to those in Figures 3 and 4. Although this experiment supports the requirement that is constant, its value depends upon the distance of the starting point from the solvent reservoir. There seems little doubt that compensating factors must be involved in the migration rates. Measurement of Chromatographic Parameters. There are several equivalent ways (see Theory) in which
0.5
RM
).5
lI
0
- 1 00
I
I
-0.60 -0.20
I
I
I
'020 '0.60 '1.00
1.0
R~b-R~, Figure 5. Plot illustrating procedure for evaluation of partition parameters for structurally related compounds Paper, Eaton and Dikeman No. 6 1 3 ; temperature, 25' z!z 0.1' C.; solvents, various proportions of water and 1-BuOH. Papers were exposed to solvent vapors 10 hours prior to irrigation; ascending chromatography plat characteristic of good data Plotting symbol
0
A 0
c 3 E 0
504
0
galactose galactose xylose monnose mannose mannose
ANALYTICAL CHEMISTRY
b lactase xylose lactase xylose lactose galactose
2t 4 6 8 IO Distonce above Solvent ( C m )
12
Figure 6. Variation of cross-sectional area ratio as function of starting position for various systems at 25' f 0.1 ' C., for ascending chromatography of maltodextrin oligosaccharides X ; water-1-BuOH, Eaton and Dikeman No. 048 paper
0;water-acetone, A; water-1-BuOH,
Eaton and Dikeman No. 6 2 9 paper Eaton and Dikeman No. 6 2 9 paper Popers were not exposed to solvent vapors before irrigation
Rl functions can be plotted for graphical assessment of the chromatographic parameters. One procedure for determining the parameters involves plots of RM values us. an appropriate v a r i a b l e e.g., Figure 5. The alternate procedure involves transposing RI values to R,/(l-R,j values and graphing these on semilogarithmic paper on the ordinate us. an appropriate variable-e.g., Figures 2-4. Figures 3 and 4 are examples of plots used for evaluating the chromatographic parameters of homologous compounds. A n e ~ n r n n of l ~II nlnt, n q d .-. fnr evalnatino ._..___I___,_____ ,____ _.I.llI___~ the chromatographic parameters for a series of structurally related compounds is illustrated in Figure 5. Although the data in Figure 5 were collected for unionized carbohydrate molecules, the data of nurma and Banerjee (I) for amino acids in the water-propanol Esystem also lead to linear lines intersect inrr ..., at a common point (S8). The only exception (S8)occurred when methionine was used as one of a pair of amino acids. Although the ordinate intersection of lines constructed using methionine as one of a pair of amino acids did not agree with the intersection common to the other amino acids, the lines were linear. In the Theory section it was shown that a situation of this type could arise if A u / A s was a function of the solute (but constant) and if Ap,/Ap. was independent of Na,o. These results have been very encouraging and it appears that the chromatographic parameters can he evaluated for both ionized as well as unionized molecules on paper by both ascending and descending chromatography for both binary and ternary solvent mixtures. The data which are displayed in Figures 3-5 are typical of good data which exhibit a minimum of experimental scatter. While the experimental scatter of the data was considerably greater than that depicted in Figures 3-5 for other systems, it was apparent that families of straight lines were still
intersect at a common point, A detailed analysis of the results of these extensive investigations will be the subject of a forthcoming communication. An extensive application of these techniques to carbohydrates has r e vealed that the ratio of the crosssectional area is independent of the molar proportions of solvents for most binary and ternary systems, that the ratio may be influenced by the papersolvent combination, that the ratio may be influenced by the spotting distance from the solvent reservoir, that the ratio chromatography, and that the ratio i's critically ~.dependent upon the clliss of solute and upon the supporting media
~
(SS). The sensitivity of the ratio, A M / A s , combinations was measured by employing the malto-
to paper-solvent
....
-
1 f'igure 7.
Popergram and thin layer illustroting effect of lorge change in rotio of AH/As on resolution of moltodedrin oligosaccharides
".._. Lhromatogrom
rlorttinr h r t r a t m naino " ns tmt m l"""".l"l "I...~tho
ascending technique on unmodified papers. Surprisingly it was found that the area function was almost invariably 3 f 1 if the irrigating solvents were binary or ternary systems miscible with water (3.9). While most of the values clustered closely around 3, occasionally some paper-solvent systems gave values as low as 2 and as high as 4-a 10070 fluctuation. Although this variation may he considered to he rather large, the actual effect on zone separation is quite small. Even this 100% change is quite small compared to the change on going from paper to Kieselguhr where the ratio increased to 40 i 4 (46), a change of at least an order of magnitude. We interpret this result to mean that the steepness of the solvent gradients is set up by the stationary support and only slightly modified hy the organic component of the developing liquid. Therefore, the most obvious way to attempt to change the crosssectional area ratio would he by selecting the proper support rather than the varying solventpaper combinations. Effect of A D ( / A Bon Resolution.
Since the theory predicts that to a
I
Left: Keiselguhr G wppoI1; waterethanokl butonol, 20-30-50 by volme. Right: Eaton ond Dikeman No. 613 paper. 2535-40y0 b y woterelhanol-I-butonol. volume. Rolio of transport potenliols for both systems was 1.6 x) that only difference In ~ros-sectiond area ,alios can 0CCO""t for *.ariation in re.01". lion
yo
first approximation the chemical potentials of transfer will he independent of solvent composition for closely related compounds, the most obvious way to increase resolution is to differentially change the nature of the solutes and to find a chromatographic system where the cross-sectional area ratio is markedly increased. An example of the profound effect that changing the cross-sectional area ratio can produce on the degree of resolution is dramatically illustrated in Figure 7. This figure shows several photoreproductions of the maltodextrin oligosaccharide chromatograms on paper and on thin layer plates of Kieseleuhr.
For both chromatograms, the ratio of the chemical potentials of transfer was 1.6 but the effective cross-sectional area ratio on the plates is 20 times greater than that on the paper. The difference in spot size on the two chromatograms is also striking and demonstrates another important advantage of thin layer chromatography over paper chromatography. Solubility Parameters. The solubility parameters (a measure of molecular cohesion) of a number of solvents frequently employed for chromatography of polar solutes are given in Table I. The values for some miscellaneous solvents are also included for comparison. It is interesting to note that the solubility parameter is rather constant even though the polar characteristics of the compounds are markedly different. DISCUSSION
Cross-Sectional Area Ratio, A MAs. At least two different attempt? have been made to measure this ratio, but the unverified assumptions used in the calculations lead to questionable results ( 3 , 4 ) . Since the “true” value of the area ratio will depend upon the distribution of the solute in the local solvent gradients, it will be necessary to evaluate A,,,-/As directly from R, data collected under operating conditions. The general belief that A M / & was not constant along the paper no doubt discouraged attempts to measure this quantity. At the same time the fact was overlooked that the success of Martin’s theory relating RV values to molecular structure demanded that A ni/.4s be operationally constant. This observation has been partly responsible for our efforts to formulate a method for graphical determination of the chromaand tographic parameters &/& Apy/ApZ involved in paper chromatography described above. The details of the method and its limitations are presented in the Results section. Even though A 4 w / r lmay ~ be related to A p (see Theoretical) substitution of reasonable relationships between A.w/As and Ap into Martin’s equation gave, after rearrangement, an equation unaltered in form but with chromatographic parameters whose interpretation was changed. Whether or not the interrelationships suggested are the proper ones is not as important as the fact that many interrelationships may be hidden in Xartin’s final equation. Hence it is doubtful that any definite conclusions about the nature of the phases can be made from chromatographic data alone. Even though the precise significance of the experimentally-measurable parameter is obscure, it is important to remember that this ratio is one objective index of the resolving potential of a chromatographic 506
ANALYTICAL CHEMISTRY
system and will be useful in selecting a superior solvent. Free Energy of Transfer. The extent to which two structurally related compounds can be separated by paper chromatography is directly proportional to a n experimentally accessible function, the ratio of the chemical potentials of transfer of the two solutes between the mobile and stationary phases. This function serves as a n objective and quantitative index (at constant A M / . 4 s ) for the resolving efficiency of a given paper-solvent system. Because this ratio is related to the resolving potential of the solvent components, it is important to establish those factors which maximize this index. One approach to this goal was made by applying the theory of solution to the choice of solvent components (4, S d ) , even though this approach is presently impractical at the quantitative level. Qualitatively, however, the theory of solution does shed illumination in several areas (see Theoretical) and leads to useful guidelines substantiated experimentally and detailed below for the selection of optimum chromatographic mixtures. Varying the organic component of the mixture will change Apu, the numerator, and Ape, the denominator, of Equation 12 but in the same direction and by approximately the same magnitude since the cohesive forces of the different organic components are relatively constant (cf. Table I). This simultaneous alteration of numerator and denominator will leave the ratio of the chemical potentials of transfer hardly affected, so that no great advantage is predicted for a change in a component of the irrigating mixture if A,M/As is not greatly altered. It is not unlikely that the widely different claims made for similar chromatographic liquids is much more a reflection of differences in molar proportions than in components. The optimum choice of solvent proportions, after all, can only actualize the separating potential characteristic of a given set of components. These conclusions have all been amply supported by a rather extensive analysis of the chromatographic separation of various carbohydrates which indicates that changes in solvent components introduce very small changes in the ratio of chemical potentials of transfer. Criteria based on the least squares analysis are being designed to test how much experimental error contributes to the deviations (32). Guides for Selection of Chromatographic Environments. The guide lines set out below are practical suggestions designed to meet, with minimum effort, the requirements sufficient to expect a chromatographic separation and are based on the ideas developed above. I n principle, at
least, the separation of two compounds can be accomplished by moving them over a sufficient number of theoretical plates with any solvent mixture that can differentiate between them. The obvious approach to the chromatographic problem, then, is to select a discriminating solvent which can give rise a t the same time to adequate migration rates. I t is, however, unfortunate that one of these goals can generally be achieved only a t the expense of the other. For this reason and because of interconnected and opposing factors in chromatography, it is often necessary to make practical compromises in the design of an acceptable chromatographic system. The guide lines below represent an attempt to meet these practical compromises in the most expedient matter. It will often be more profitable to study variations in solvent proportions than in solvent components. This rule is based on the theoretical prediction that when a change in solvent composition does not differentially alter the structure of one of the solutes, the resolving potential of the new system will be minimally improved only if A M / d s increases. A decrease in d ,,-/AS, which is just as probable as an increase, would diminish the resolving potential. Because of the very small changes in the resolution indexes for most shifts in solvent components, the separation achieved by one system can often be very closely approximated by another system simply by choosing the correct proportions. Hence, a logical approach to the choice of a chromatographic liquid is to alter solvent proportions to maximize the resolving potential of the solvent components. Obviously, before the solvent proportions can be varied, it is necessary to decide upon a set of solvent components, a problem discussed elsewhere (31, 38, 40). The selection of solvent proportions has been somewhat simplified by a computer analysis of the influence of the variation of the chromatographic ratios on R, values (42). The results of this investigation revealed that regardless of the value of A w / A S and A p v / A p z , the maximum separation between two similar solutes is achieved when the zones have migrated approximately the length of the support. Obviously, then, solvent proportions should be selected which give average R, values of about 0.25. A similar suggestion was also made by Jermyn and Isherwood a number of years ago ( 7 ) . This mixture represents the best compromise between solvent discrimination and migration rate. If changes in solvent components are made, they should be designed to selectively alter the structure of the solutes. Since the chemical potential of transfer depends critically upon the
molecular constitution of chromatoIf with reasonable effort a chromagraphed molecules in related solvents, tographic system cannot be found which AkJApz can be increased if only one of will resolve the compounds in a single the molecules can be structurally alpass, recourse should be made to unitered. This can most easily be accomdimensional multiple chromatography plished by modificat.ion of functional or to continuous chromatography. The groups. For example, the degree of principal advantages of these techniques ionization of structurally related acids is that without sacrificing solvent diswith different pK values may be difcrimination the number of theoretical ferentially shifted by manipulation of plates over which the zones pass is inthe p H of buffered chromatographic creased. Some guide lines for the selecsolvents (20). By the judicious choice tion of operating conditions for these of an organic component or other addiprocedures have been outlined elsetive it may be possible to change where (58,45). Apu/Akz by promoting selective solvent It is clear that the guide lines proposed above will not be a panacea for equilibria. Aromatic molecules imall chromatographic difficulties because mediately suggest themselves for this of the complexity of chromatography. purpose because of t’heir notorious Hence it will be necessary to apply the ability to form specific molecular comideas developed here under a wide plexes. The popularity of mixtures variety of conditions to test their gencontaining aromatic molecules is no eral utility. I t is anticipated, though, doubt related to selective solvent that the systematic application of equilibria. The importance of giving theoretical principles can significantly serious consideration to the chemistry reduce the effort and frustration inof the solute mixture before a haphazard volved in the choice of chromatographic select,ion of solvent components is conditions. begun cannot be underrated. FurtherThe fact that chromatographic inmore, for pilot studies, it should be dexes for some systems are independent emphasized that if solvent components of the molar proportions of the irare changed the dissimilarities of their rigating solvent is of exceptional conproperties should be as great as can be t,olerated while retaining a miscible sequence. For the first time it allows solvent. Keep in mind that only the individual effects of variations in the chromatographic environment on miscible systems offer the degree of migration rates to be quantitatively and flexibility which will permit the use of objectively sorted out and in the second these guide lines. place it provides a needed approach for Select those combinations of supports and solvents which give the largest the systematization and correlation of chromatographic data for these sysvalue of a4,u,’-4s. As t,he molar proportems. The benefit of these correlations of water in the irrigating liquid tions ought to be the selection of better decreases, the R, values of the polar solutes show a parallel decrease while solvents with less effort. the chemical potentials of transfer and I n addition to offering more efthe ratio of Rf values increase (58). fective ways of selecting developing conditions, knowledge of the environI t then follows that a pair of solutes mental effects on the chromatographic moved over an approximately equal indexes should increase our insight into number of theoretical plates will be the chromatographic process. For exseparated to a larger degree by solvent ample evaluation of the chromatomixtures producing the smallest R, graphic indexes ( A M / A Sand Apv/Apz) values. This situation forces a comreveals that the superior performpromise between large migration rates ance characteristic of Kieselguhr and large R, ratios. The handicap imis related to the large effective crossposed by this restriction can be circumvented by increasing the ratio of sectional area (46). Detailed studies at a quantitative level of such environthe cross-sectional area. The increase mental effects as temperature, paper in L4,,ft’Aspermits the use of solvent modification, and solvent composition proportions giving high chemical pomay lead directly to optimum conditentials of transfer and good separating tions by allowing the opposing factors power by ensuring that the solutes pass governing resolution to be minimized. over the required number of theoretical plates. The advantage of a large d,t,j.ls is dramat’ically illustrated in Figure i. The increase in resolution APPENDIX cannot be ascribed to a change in disSymbols crimination potential on Kieselguhr because the ratio 4 ~ ~ l u c 0 s y l / A ~ g l uiso 0 B e A = Cross-sectional area C = An empirical constant 1.6 for the maltodextrin oligosaccharides D = An empirical constant on TLC and on paper. Since it has N = Mole fraction been found that A u / d s is often inR = Gas constant aen$itivt> t o the paper-solvent system, T = Absolute temperature mow extensive experimentation with a = An empirical constant variety of supports is recommended. c = An empirical constant
An empirical constant An empirical constant AE The latent heat of vaporization AH The latent heat of fusion To = The temperature of fusion AU = The heat of mixing V = The molecular volume = The volume fraction b = dAE,..,/V and is referred to as the cohesive property of a liquid = = = =
e’
{
Subscripts = Property of monomer unit, A b = Property of residue B , added to polymer to increase chain length one unit i = Type of functional group 1 = Organic component of solvent M = Property of mobile phase n = Chain length or number of functional groups of a specified type S = Property of stationary phase z = Property of molecule, X = Property of molecule, Y y a
ACKNOWLEDGMENT
Able technical assistance was provided by Anita Rohrer and Dwight Davis. LITERATURE CITED
(1) Burma, D. P., Banerjee, B., J . Indian Chem. SOC.28, 135 (1951). (2) Cassidy, H. C., “Techniaues in Organic Chemistry,” A. Weiiberger, ed.,
Interscience, New York, 1957. (3) Consden, R., Gordon, A. H., Martin, A. J. P., Biochem. J . 38,224 (1944). (4) Djkstein, S., J. Chromatog. 2 , 204 (1939). (5) Durso, D. E., Mueller, W. A., ANAL. CHEM.28, 1366 (1956). (6) French, D., Wild, G. M., J. Am. Chem. SOC.75, 2612 (1953). (7) Jermyn, &I. A., Isherwood, F. A,, Biochem. J. 44, 402 (1949). (8) Giddings, J. C., J . Chem. Educ. 35,588 (1958). (9) Giddings, J. C., “Chromatography,” E. Heftman, ed., p. 20, Reinhold, New York, 1961. (10) Giddings, J. C., Keller, R. A., “Chromatography,” E . Heftmann, ed., p. 92, Reinhold, New York, 1961. (11) Giddings, .J. C., Stewart, G., Ruoff, A., J. Chromatog. 3, 239 (1960). (12) Green, J., Marcinkiewicz, S., Ibid., 10,35 (1963). (13) Ibid., p. 354. (14) Ibid., p. 389. (15) Green, J., Marcinkiewicz, S., McHale, D., Ibid., 10, 158 (1963). (16) Hanes, C. S.,Can. J . Biochem. Phys. 39, 119 (1961). (17) Hanes, C. S., Isherwood, F. A , , Nature 164, 1107 (1949). (18) Hildebrand, J. H., Scott, R. L., “Solubility of Nonelectrolytes,” 34th ed., Reinhold, Nyw York, 1950. Hofreiter, B. T., p. 389, Academic Press, New York; 1962. (20) Lederer, E., Lederer, M., “Comprehensive Biochemistry,” XI. Florkin and E. H . Stotz, eds., p. 151, Elsevier, New York, 1962. (21) Lederer, M., Proceedings of the Second International Congress of Surface Activity, p . 506 (1957). 1,
VOL. 37, NO. 4, APRIL 1965
0
507
(22) Marcinkiewicz, S., Green, J., J . Chromatog. 10, 184 (1963). (23) Ibzd., p. 366. (24) Ibzd., p. 372. (25) Xarcinkiewicz, S.,Green, J., MeHale, D., Ibid., 10, 42 (1963). (26) llartin, A. J. P., Ann. Rev. Biochem. 19, 517 (1950). (27) >\Iartin, A. J. P., Biochem. Soc. Symp. 3 , 4 (1949). (28) Martin, A. J. P., Synge, R. L. ?*I., Bzochem. J. 35, 1358 (1941). 129) XIartire. D. E.. ANAL. CHEM.33. 1143 (1961'). 130) hIoore. S.. Stein. W. H..' Ann. Rev. ' Biochem. 21, 517 (1952). (31) Aluller, R. H., Clem, D. L., ANAL. CHEM.23,408 (1951). { 32) Perisho, C., Department of Chemis~
try, Mankato College, Minnesota, unpublished data, 1964. (33) Rohrer, A,, Davis, D., Thoma, J., unpublished data, 1964. (34) Ruoff, A. L., Prince, L., Giddings, J., Stewart, G. H., Kolloid-2. 166, 144 (1959). (35) Soczewinski, E., J . Chromatog. 8, 119 (1962). (36) Soczewinski, E., Wachtmeister, C. A., Zbid., 7,311 (1962). (37) Stahl, E., Kaltenbach, U., Zbid., 5, 351 (1961). (38) Thoma, J. A., ANAL.CHEM.35, 214 (1963). (39) Thoma, J. A,, J . Chromatog. 12, 441 (1963). (40) Thoma, J. A., 'Wethods in Carbo-
hydrate Chemistry," R. L. Whistler,
ed., 4, p. 221, Academic Press, New York, 1964. (41) Thoma, J. A., Talanta 8, 829 (1961). (42) Thoma, J. A., unpublished data, 1964. (43) Thoma, J. A., French, D., API'AL. CHEM.29,1645 (1957). (44) Trevylan, W. E., Procter, D. P., Harrison, J. S., Nature 166, 444 (1950). (45) Weill, E. E., Department of Chemis-
try, Rutgers University, Tu'ewark, New Jersey, personal communication, 1964. RECEIVEDfor review JUIY 20, 1964. Accepted February 10, 1965. This research was supported in part by a grant from the General Medical Division of the U. S. Public Health Service GM 08500-04, and in part by a grant from Corn Industries Research Foundation.
Gas Liquid Chromatography at Low Temperatures Resolution of Some Deuterated Ethanes W. ALEXANDER VAN HOOK and MARGARET E. KELLY Department of Chemistry, University o f Tennessee, Knoxville, Tenn.
C4H8-cyclo CrH7T mixtures. The first b A technique for the gas chromatoof these represents the only member of graphic resolution of some of the the saturated hydrocarbon series in deuterated ethanes is described. which complete resolution on packed Chromatograms for the systems C 2 H r CnD6; C2H6-C2H4D2, 1,l d ; and C Z H ~ liquid partition columns has been reported, although Gant and Yang have C2HsDare shown at various temperasucceeded in partially resolving all of the tures between 158°K. and 273°K. intermediate deuterated methanes on The separation factors, S, are calcuGSC columns packed with activated lated from the chromatograms and charcoal. Using a capillary column compared with the vapor pressure Falconer and Cvetanovic (3) have ratios, R. It is observed that InS is conobtained complete separation of a sistently a factor of about 1.3 times saturated hydrocarbon system differing InR over that temperature range where by only four deuterium atoms. Separaa direct comparison can b e made and tions of saturated hydrocarbons from it is pointed out that this result is in their deuterated isomers have in the accord with the statistical theory of isopast been performed a t 0' C. or above. tope effects in condensed systems.
G
LIQUID (GLC) or gas solid chromatographic (GSC) separations of isotopically substituted hydrocarbons are of interest both as a practical analytical tool and as a method for investigating isotope effects in solution (GLC) or during adsorption processes (GSC). Hopefully the latter two phenomena can be ultimately employed to gain a fuller understanding of the intermolecular forces in solution or in the adsorbed state. There are several reports in the literature of the successful separation of various deuterated compounds from their protiated analogs. These have been summarized recently by Gant and Yang (4) and Root, Lee, and Rowland ( 7 ) . [An additional interesting separation of benzene and perdeutero benzene has been reported by Cartoni (.%')I. Root et al. reported the development of a recycle technique employed to separate : CH4-CD4; and cyclo nC4Hla-nC4Dlo AS
508
ANALYTICAL CHEMISTRY
tion times and grossly broadened unresolved peaks were observed. For these reasons the technique of gas liquid chromatography was adopted. EXPERIMENTAL
The gas chromatograph, built in this laboratory, was of conventional design. Helium carrier gas flowed from a liquid nitrogen cooled charcoal trap through the reference side of a Gow-Mac four filament Pretzel thermal conductivity cell, past a rubber septum type injection port, and into the copper column which was coiled and contained in a one-gallon dewar flask. A short section of capillary tubing connected the column exit with the detector and flowmeter. The first separations were performed Vapor pressure measurements on the using molecular sieve supported methylentire series of the deuterated ethanes cyclopentane (MCP) packing a t -78" C. (8) indicated that these isotopic isomers The resolution was a function of the hismight be separable by gas chromatogtory of the packing and appeared to be raphy. The isotope effects are inverse particularly sensitive t o poisoning. Simand all of the vapor pressure ratios, R , ilar results were found for acetone and [defined as R = ( P C ~ H ~ & , / P C ~ H2,3,4-trimethyl ~)] pentane coated molecushow maxima in the temperature range lar sieve columns. I n this respect it 125' to 140' K. It is accordingly most might be noted that molecular sieves carefully dried a t 200' C. under vacuum practical to attempt the separations at and then coated in the absence of water low temperatures. A second advantage vapor and protected from poisoning are of low temperature operation is that ineffective. They give long retention reasonable flow rates can be maintained times and broad unresolved peaks. with smaller pressure drops than are Thoroughly poisoned columns give qhort required a t room temperature and retention times and sharp unresolved above. These advantages are to some peaks while intermediate ones do give extent offset by low sample vapor pressome separation. Our best separations have been persures which increase the retention times formed with columns using MCP supenormously. We have found it imported on firebrick. We have to date practical to work below -115' C. restricted our studies on firebrick colPreliminary experiments were perumns to XICP packings since in the formed at -78" C. using gas solid chromolecular sieve experiments we obmatography with charcoal, alumina, served the best separations with this and molecular sieve columns. I n all substance. MCP is convenient for low cases adsorption on the solid surface was temperature liquid columns because of so strong that inordinately long retenits very wide liquid range and low vapor
