Table 111. AH Values for Several C o m p o u n d s Compound
Propiophenone Benzophenone Benzaldehyde Acetophenone 9-Fluorenone f
=
IS-R 1% f”
k‘ (at 40 “C)
AH (kcallmole)
0.52 0.72
1.08
14.9
1.10
14.5
1.44 1.34
18.4 16.6
2.23
27.8
0.83
1.09 1.25
ratio of the volumesof the stationary to mobile phase.
tionary phase as did Knox and Vasvari (9). Consequently, we could not estimate AS. However, the trend seems to be the same as with AH. In general, AH seems to be rather small (being 2.23 kcal/mole for k’ of 1.25). The discrepancy in the benzaldehyde results might be attributed to the fact that it is not a phenone as are the rest of the compounds. This point should be further investigated. Nonetheless, following the argument of Knox (9), one can interpret the results in Table I11 to mean that AH determines the retention in our system.
SUMMARY viscosity of the mobile phase or t o changes in the kinetic processes which occur in the column. Knox and Vasvari (9) found, for their system, the reduced plate height h a t a constant reduced velocity to be temperature independent. This would indicate that the change in the diffusion coefficient of the solute is responsible for the change in H as the temperature is varied. We did not attempt to plot reduced plate height a t a constant reduced velocity as a function of T. However, the fact that the two H plots in Figure 5 seem to converge a t low velocity and t h a t they are not parallel a t high velocities might indicate that perhaps kinetic factors and the mobile phase viscosity are of importance in determining H. This speculation, however, must be studied in more detail since, as was discussed before, not all solutes show a large change in the plate height with temperature. From the relation log k’ us. 1/T (Van’t Hoff plots), one can obtain the heat of transfer from the stationary to the mobile phase. The intercept of such plots is related to the entropy of transfer. Table I11 shows AH‘S and a function related to the intercept, namely, AS-R log f, for several compounds as obtained on column 111. The factor f is the ratio of the volumes of the stationary to mobile phases. Except for benzaldehyde AH increases with k’, as was found by Knox and Vasvari (9) for Permophase ODS system. We did not try to approximate the ratio of the mobile to sta-
The results show that the retention behavior on bonded phases can be due to several contributions; among them, surface modification, and interaction with the bonded phase and with the mobile phase, as indicated by retention reversal of several solutes. Temperature studies indicate that the order of retention on the present bonded phase is determined mainly by the heat of transition from the stationary to the mobile phase. Studies of peak broadening indicate that stagnant pockets of mobile phase contribute significantly to the rate of mass transfer. I t still remains to be determined what the phrase “stationary phase” really means. Indications are that the bonded phase used here, and perhaps by other workers, can exist in patches of “brush” and polymeric areas. A study is needed in which the degree of polymerization on the support surface is carefully controlled. In addition, the effect of the chain length of the bonded phase on the chromatographic behavior of various solutes should be investigated. Such studies are now in progress in our laboratory. Varying the surface coverage of the bonded phase should be also be examined since, as was demonstrated here, it can modify the retention behavior in certain cases.
RECEIVEDfor review January 23, 1974. Accepted April 29, 1974.
Method for Prediction of Partition Coefficients in Liquid-Liquid Chromatography Paul Menheere, Claude Devillez, Claude Eon, and Georges Guiochon Laboratoire de Chirnie Analytique Physique, €cole Polytechnique. 7 7, rue Descartes, 75005-Paris
The potential value of ternary systems in liquid-liquid chromatography is explored and it is shown that in the absence of secondary effects, variations in selectivity due to changes in eluent composition can be determined from the changes in interfacial tension. Furthermore, the free energy of the partition process can be predicted with meaningful precision.
The interfacial tension between the two phases in a liquid-liquid chromatographic system is the master parameter for prediction of the potential selectivity, as the interfacial tension between the two liquids is dependent upon the differences in their physical nature ( I ) . A quasi linear relationship between the free energy of partition and the interfacial tension was established for (1) C Eon, B (1973)
Novosel, and G
Guiochon, J
Chromatogr. 8 3 , 77
those case where the two phases were mutually insoluble; however, such a relationship is fallible as soon as mutual solubility becomes a significant factor. The same arguments apply when two immiscible phases of a ternary mixture are the “eluents” phases and indeed Huber et al. (2-4) have already suggested the considerable potential of such systems. The investigation of these systems is therefore mandatory, and the present availability of reliable partition coefficients of numerous steroids in a series of ternary mixtures of water, ethanol, and isooctane ( 4 ) gave impetus to this work. Under defined conditions, it is possible to predict chromatographic behavior that is concomitant with the solu(2) J. F K . Huber, J. Chrornatogr. Sci.. 9, 72 (1971). (3) J. F. K . Huber, C. A. M . Meijers, and J. A. R J Hulsman, Anal. Chem., 44, 111 (1972). ( 4 ) J. F. K . Huber. E. T Alderlieste. H Harren, and H Pope, “Advances in Chromatography-1973,” A Zlatkis. Ed.. Department of Chemistry, University of Houston, Texas, 1973, p 327
ANALYTICAL CHEMISTRY, VOL. 46, NO. 11. SEPTEMBER 1974
1375
A
6- dZ
Ln Y
1
I
,
2
4
6
Figure 3. Variation of d r / d In tension of the system
K
6
dynexcm
*
I
8
10
as a function of the interfacial
6 [dyne x cm) I
0
4
2
t
0
6
10
Figure 1 . Variation of the logarithm of the partition coefficient of some representative steroids as a function of the interfacial tension of the system. The number for each curve refers to the compounds listed in Table I
Figure 4. Definition of A and 5 used in Equation 1
Table I. List of Steroids Studied
2
4
6
Figure 2. Variation of the slope of the tangents of the curves Figure 1 for u = 4.0 dyne per c m , vs. the logarithm of the partition coefficient (system I l l described in Table II. Solutes are numbered as in Table I )
bility parameter theory and such augurs well for future generalization. EXPERIMENTAL As the interfacial tensions of the systems studied are small, a Cahn electrobalance (Cahn-G) coupled to a Leconte Du Nouy tensiometer measures the force necessary to withdraw the platinum ring from an interface. Figure 1 shows a plot of the thermodynamic partition coefficients of certain steroids as reported by Huber et al. ( 4 ) us. interfacial tensions. Since the free energy of the partition process tends to zero as the two phases become completely miscible, and the partition coefficient becomes unity, the graph is a curvilinear. As indicated by Vignes ( 5 ) , at a given composition, the tangents to the curves corresponding to various solutes are concurrent, and this concurrency is a function of both surface tension and solute nature. Although the term “family” is not yet definable, in this context. the steroids so far studied “fit.” To verify this observation, the several curves were computer correlated and the slopes of tangents for the experimental interfacial tension values calculated. If the tangents are truly concurrent then the slopes vary linearly with In K for any value of surface tension: some scatter must be expected, however, due to the difficulties of the measurement of derivatives. Figure 2 shows such a plot and. although there is significant curvature, Figure 3 shows that the first derivative plotted us. interfacial tension, authenticates the hypothesis. Thus, in the first approximation, the concept has validity. provided that proper account be taken of secondary effects. The practical implications of the plot In K us. u are now discussed. ( 5 ) A Vignes, J Chim. Phys. Physicochim. Biol., 57, 966 (1960)
1376
9
1: Pregn-4-ene-3,20-dione (Progesterone) 2: 20p-Hydroxypregn-4-ene-3-one 3: Androst-4-ene-3,17-dione (Androstene dione) 4: Androstadiene-(4,9 (11))-3,17-dione. 5: 17p-Hydroxy-17a-methylandrost-4-ene-3-one 6: 20a-Hydroxypregn-4-ene-3-one 7: 17a-Hydroxyandrost-4-ene-3-one(Epitestosterone) 8: 3-Hydroxyestratri-(1,3,5, (10))-ene-lV-one- (Estrone) 9: 17P-Hydroxyandrost-4-ene-3-one(Testosterone) 10: 17a-Hydroxypregn-4-ene-3,20-dione 11: 21-Hydroxypregn-4-ene-3,20-dione 12: Androst-4-ene-3,11,17-trione (Androsterone) 13: ll~-Hydroxyandrost-4-ene-3,17-dione 14: 17p-Hydroxyandrosta-1,4-diene-3-one 15: Estratri-(1,3,5(10))-ene-3,17p-diol 16: 14a-Hydroxyandrost-4-ene-3,20-dione 17: 16a-Hydroxypregn-4-ene-3,20-dione
18: 17a-21-Dihydroxypregn-4-ene-3,20-dione 19: 19-Hydroxyandrost-4-ene-3,17-dione 20: llp,21-Dihydroxypregn-4-ene-3,20-dione(Corticoster-
one) 21: 3,16c~, 170-Trihydroxyestratri- (1,3,5, (10)) -ene (11-Dihydrocor22: 21-Hydroxypregn-4-ene-3,11,20-trione ticosterone) 23: 3,16p,17p Trihydroxyestratri-(1,3,5,(10)) -ene (Cortisone) 24: 17a,21-Dihydroxypregn-4-ene-3,11,2O-trione 25: 17p,21-Dihydroxypregn-4-ene-3,11,20-trione 26: llp,l7a,21-Trihydroxypregn-4-ene-3,20-dione (Hydrocortisone, cortisol) PREDICTION OF PARTITION COEFFICIENTS
Given the locus of the concurrencies of these tangents, it is possible to derive a curve for any new “familiar” solute, when K for a particular solvent composition is known, i.e., 1. e . ,
d In K - In K - B(u) ~da a - A(u) ( A and B being functions of a-cf.,
ANALYTICAL CHEMISTRY, VOL. 46, NO. 11, SEPTEMBER 1974
Figure 4 ) .
(1)
Table 11. Interfacial Tensions of the Two Phases of a Ternary Mixture Compositiona Less polar phase
Molar polar phase
a
System
u (25 " C ) dynes/cm
Water
Ethanol
Isooctane
I I1 I11 IV V VI
0.43 1.80 4.00 5.7 7.7 10.8
0.167 0.278 0.378 0.462 0.581 0.702
0.700 0.671 0.601 0,529 0.416 0.296
0.133 0.051 0.021 0.009 0.003 0.002
Water
Ethanol
Isooctane
0.025
0.317 0.142 0,126 0,093 0,059 0.037
0.658 0,847 0.865 0,900 0.935 0,961
0,011
0.009 0.007 0.006 0.002
From reference ( 4 ) .
Table 111. Parameters for the Prediction of Partition Coefficients (Equation 3) System couple"
1-2 1-3
1-4 1-5 1-6 2-3 2-4
System couplea
P
L
1.75 2.28 2.71 3.10 3.16 1.30 1.53
0.179 0.367 0,547 0.741 0.848 0.331 0.62
2-5 2-6 3-4 3-5 3-6 4-5 4-6 5-6
Table IV. Comparison between Measured and Predicted Values of the Partition Coefficients System 4 from system 3
P
L
1.76 1.80
0 .96 1. 1 6 0 .37 0 .82 1. 1 0 .53 0 .83 0 .32
1.18
1.35 1.38
1.15 1.17 1.01
Steroids'
1 2 3
4 5 6 7
The systems are characterized in Table 11.
8
9
In order to solve this equation, it is necessary to transform it by multiplying each side by:
10 11
12 13
14 15 16 17
and rearranging: In K i b ) = PJln
K ( a ) - LoJ
(2 1
18
where:
19 20 21 22 23 24 25 26
(3)
Equation 2 allows extraction of K for any new system provided Pab and Lab are known and these factors are independent of any solute parameter. The validity of this deduction may be tested using Equations 3 and 4 merely by interpolating the relevant experimental values of K ( 4 ) and the results of this exercise are listed in Table 111. Table IV shows the results of the progressive calculations for compositions 3 and 4 using the experimental data obtained from compositions 2 and 3, respectively. The fact t h a t agreement between the calculated and observed free energies of partition is generally better than *2?70 means that, thermodynamically, the predictive power is excellent, b u t in practice this can sometimes be reflected in a n error of u p to 25% in the value of K itself. Furthermore, the significance of Equation 2 lies in its usefulness in estimating changes in selectivity due to changes in eluent composition as, by definition:
S,,
=
K,IK,
(5)
and consequently: Thus, it can act as a n indicator for the most favorable condition for the separation of a pair of closely related compounds such as isomers. This does not involve any change in the chromatographic profile as it is no more
a
In K calcd
In K measured
2.33 3.13 3.15 3.25 3.50 3.64 3.58 3.80 3.97 4.18 4.49 4.64 4.68 4.71 5.01 5.48 5.56 5.98 5.91 6.29 6.30 6.35 6.42 6.95 6.91 7.49
2.33 3.19 3.18 3.20 3.49 3.60 3.80 3.93 4.04 4.27 4.33 4.65 4.74 4.72 4.98 5.69 5.55 5.79 5.77 6.17 6.28 6.39 6.38 6.97 7.16 7.79
Percentage oferror onK
System 3 from system 2
h K calcd
0
2.40
6 3 5
3.11
4 24 14 7 9 17 1
6 1 3 23 1
21 15 12 2 4 4 2 28 35
3.02 3.05 3.36 3.47 3.51 3.62 3.77 3.94 4.20 4.29 4.30 4.41 4.76 5.04 5.09 5.33 5.32 5.55 5.86 5.78 6.09 6.31 6.38 6.63
In K measured
2.36 3.05 3.06 3.15 3.36 3.48 3.43 3.60 3.77 3.94 4.21 4.34 4.37 4.39 4.65 5.05 5.12 5.48 5.42 5.75 5.76 5.80 5.86 6.31 6.28 6.78
Percentaee of error onK
4 6 4 10 0 1 8
2 0 0 1
5 7 2 12 1
3 16 10
22 10
2 26 0 10 16
The compounds names are liste in Table
than a "time dilating" effect, for, any change in eluent composition is reflected in the same variation of selectivit y for any solute pair. The advantages of this point of knowledge in the optimization of conditions for a specific separation are immediately obvious, b u t it must be realized t h a t where the selectivity is approximately unity for a given solute pair, there is no benefit in adding, for example, water to give a gross change in polarity. Typically system 1 has a selectivity of 1.025 which is barely improved by conversion to system 6 where it is 1.17. THEORETICAL CONSIDERATIONS
T h u s far, the empirical Equation 2, based on experimental fact, has not been considered from a theoretical point of view. It is therefore important to test its validity, and this is facilitated by involving the solubility parameter theory (6). Regrettably, this latter concept is not implicitly reliable, and this postulate requires it be used more as a mathematical model rather than an accomplished fact. (6) J. H. Hildebrand and R L Scott, "The Solubility of Non-Electrolytes." Dover Publishers, New York, N.Y., 1964, Chap X I and X I I .
ANALYTICAL CHEMISTRY, VOL. 46, NO. 11, SEPTEMBER 1974
1377
From the definition of K ( 1 ) :
K,
Log K j b= Pob X Log K j a -I- VjoMab where obviously:
= Y,”/Y,’
where y”, and y’, are the activity coefficients of a solute in each of two phases. Then for regular solutions of molecules of comparable dimension, the activity coefficient of solute j in the solvent p is:
where 6, is the solubility parameter function, but the volume fraction of the solute p, is sufficiently small to be neglected under normal analytical chromatographic conditions and therefore combining Equations 6 and 7 leads directly to:
Notice, Pub and Mub are dependent only on solvent compositions. Also Equation 2 and Equation 12 are identical provided the molar volume (V,O) remains constant. Such is certainly the case for the series of steroids studied and gives a primary condition to satisfy when another “family” of compounds is considered. In consequence, Equation 2 is of proper validity and thus may be applied in the general sense.
CONCLUSION Although interfacial tension is sufficient to characterize the polarity of liquid systems, it is not explicit in the equation for calculating selectivity. The variation of the partition coefficient of a solute with the composition of the liquid-liquid system can be predicted accurately enough to enable optimization of analytical conditions. If more accurate results are needed, it is better to use the Huber factorial analysis method ( 4 ) which requires more detailed analytical data than necessary for this approximative model.
I f a characterizes a certain solvent system, let:
and:
ACKNOWLEDGMENT Then Equation 8 may be transformed:
In K,“ = ZV,’6,f(a) + V,’’d(a)
(11)
Similarly, accepting that In K I b for solvent system b maintains, it can be seen that:
We are very grateful to C. E. Roland Jones for fruitful discussions.
RECEIVEDfor review November 12, 1973. Accepted February 26,1974.
Structure-Retention Relationships in the Gas Chromatography of Nucleosides S. E. Hattox and James A. McCloskey‘ lnstitute for Lipid Research and Marrs McLean Department of Biochemistry, Baylor College of Medicine, Houston, Texas 77025
Structure-retention time correlations have been studied for 32 nucleoside trimethylsilyl derivatives. Methylene unit (MU) values were measured with a precision of f 0 . 0 2 MU covering the range from 23 to >38 MU. Lower silyl derivatives [e.g., (TMS)3 vs. (TMS)4] exhibited longer retention times on OV-17 while the reverse was true using less polar SE-30 liquid phase. Higher MU values resulted from bet. . eroatom methylatlon ( e.g., 2’-O-methyl), or by replacement plots of MU values from ov-17 vs. ~ ~ - 3 of 0 by N or by yielded linear correlations having approximately the same slope but different intercepts for different groupsof structurally Similar compounds (e.g., purine pyrimidine nudeom sides). Perdeuteration Of the nucleoside skeletons Of the four major ribonucleosides decreased retention times by 0.01-0.08 MU, a change - which is insufficient to interfere with nucleoside characterization.
s.
Author t o whom inquiries should be addressed. 1378
ANALYTICAL CHEMISTRY, VOL.
Mainly because of their high polarity, nucleosides as a class represent one of the more difficult applications of gas chromatography. T h e earliest report is that of Miles and Fales ( I ) , who employed acetylation, methylation and 0isopropylidine formation for enhancement of volatility. As first demonstrated by Hancock ( 2 ) ,trimethylsilylation has subsequently found greatest use for nucleosides (3-18). Ex(1)H. T. Miles and H. M. Fales, Anal. Chem., 34,860(1962). 0(2) R. L. Hancock and D.L. Coleman, Anal. Biochem., I O , 365 (1965). (3) . . Y. Mizuno, N. Ikekawa, T. itoh, and K . Saito, J. erg. Chem., 30, 4066 ( 1965). (4)R. L. Hancock, J. Gas Chromatogr., 4, 363 (1966). (5)y. Sasaki and T. Hashizume, Anal. Biochem., 16, 1 (1966). (6)C. W. Gehrke, D. L. Stalling, and C. D. Ruyle. Biochem. Biophys. Res. Commun., 28,869 (1967). (7) M. Jacobson, J. F. O’Brien, and C. Hedgcoth, Anal. Biochem., 25, 363 11968) I
(8)B. H. Most, J. C. Williams, and K. J. Parker, J. Chromatogr. Scb, 38, 136 (1968). (9)R. L. Hancock. J. Gas ChrQmatogr.. 6, 431 (1968). (10)C. W. Gehrke and C. D. Ruyie, J. Chromatogr., 38,473 (1968). (11)R. L. Hancock. J. Cbromatogr. Scl.,7, 366(1969).
46, NO. 11, SEPTEMBER 1974
