Static and Chromatographic Measurement and Correlation of Liquid-Liquid Partition Coefficients J. F. K. H u b e r ,
E. T. Alderlieste, H. H a r r e n , a n d H. Poppe
Laboratory of Analytical Chemistry, University of Amsterdam, Amsterdam, The Netherlands
A new method for the determination of liquid-liquid partition coefficients is presented. In this method static and dynamic measurements are combined in order to achieve both high precision and rapid measurement. A favorable feature is the fact, that the compounds need not be pure to enable the determination of their partition coefficients. The precision of the measurement is better than 2 % and the time needed for the dynamic measurements is only a few minutes. The partition coefficients of several compounds, which are used as standards in the dynamic measurements, are determined by a static method. The correlation of data by means of factor analysis can be improved significantly because of the improved precision of the data. Pesticides, steroids, alkyl benzenes, and nitrobenzene derivatives were used as samples and ternary mixtures consisting of water, ethanol, and 2,2,4-trimethyl pentane as liquid-liquid systems.
The partition between two liquid phases is used for the separation of mixtures in various processes. The most important separation method based on liquid-liquid distribution in chemical analysis is liquid-liquid chromatography. In order to obtain the most favorable conditions, chromatography has to be carried out in the linear range of the distribution isotherm. On this premise the chromatographic resolution of two components is determined mainly by the ratio of their distribution coefficients in the stationary and the moving liquids. The choice of the optimal phase system for the separation of a given mixture by chromatography follows from the consideration of the equation for the resolution of the successive components (1). In liquid-liquid chromatography, the choice of the phase system is especially difficult because of the enormous assortment of liquid-liquid systems. To help choose the phase system, methods for the prediction of liquid-liquid partition coefficients have to be developed. Such a procedure can be derived from the correlation of experimental data (2). The practical benefit of the prediction of partition coefficients depends on the accuracy of the data correlation, which is determined to a large extent by the precision of the data set used. Compounds separated by liquid-liquid chromatography can be characterized by their partition coefficients. These values can be used for the identification of the compounds. The efficiency of the identification by means of liquid-liquid partition coefficients is determined by the precision of these data. From the requirements for the systematic choice of a liquid-liquid system as well as for the identification by retention data, it follows that a precise and accurate method for the measurement of liquid-liquid partition coefficients is needed. Such a method. which in addition should ( 1 ) J. F . K. Huber, J. Chrornatogr. Sci.. 9, 72 (1971). ( 2 ) J. F . K . Huber. C. A . M . Meijers, and J. A . R . J. Chem.. 44, 111 ( 1 9 7 1 ) .
be rapid, can be developed by the combination of static and dynamic measurements. The static measurements are carried out in order to obtain precise and accurate standard data for the dynamic chromatographic measurements, which allow a rapid determination of further liquid-liquid partition coefficients from retention time measurements using the standard data for the calculation.
EXPERIMENTAL Procedure. The static determination of liquid-liquid partition coefficients is carried out according to the following scheme: 1. The liquid-liquid system is prepared by mixing the components in a given ratio a t constant temperature. The composition of both liquid phases is determined by gas chromatography. Whether equilibrium exists is checked by means of a repeated gas chromatographic analysis of the phases after a significantly longer time of mixing. 2. The two liquid phases being in equilibrium are separated. A given mass of the solute is dissolved in a given volume of one of the phases in order to obtain a known concentration. Some quantity proportional to the solute concentration in the solution is measured. In this work, the absorbance of light of suitable wave length or the gas chromatographic peak area was used. 3 . A known volume of the prepared solution of the compound in the one liquid phase is mixed at constant temperature with a known volume of the other liquid phase until equilibrium is a t tained, whereupon the two phases are separated. The same quantity which was measured in step 2 for the initial solution is measured again for the solution in equilibrium with the other solvent. The partition coefficient is calculated according to the equation
in which K , = partition coefficient of the component i in the phase p and a , c , k = concentration in the phase k ( k = 0 or 3 ) ,A , = quantity proportional to the concentration in phase a (Alo = initial value); V, = volume of the phase k ( k = a or p). 4. The determination of the partition coefficient is repeated at different concentrations in order to assure that the linear range of the distribution isotherm is not exceeded. This is the precondition for a constant value of the partition coefficient. In the dynamic determination of partition coefficients, a linear relationship is assumed between the retention time and the liquid-liquid partition coefficient:
where t R l = retention time, measured from the moment of the sample injection until the indication of the peak maximum by the detector, t H o = average residence time of the mobile phase, q = V,/V, = volume ratio of the stationary and the mobile phase. The retention time may only be expected to be a linear function of the liquid-liquid partition coefficient according to Equation 2 13) if adsorption effects are negligible; if the liquid in the pores of the solid support behaves like the free liquid; and if the distribution isotherm is linear. In principle the unknown partition coefficient of a compound can be calculated by means of Equation 2 from its retention time and the retention times of a t least two other compounds with known partition coefficients (21. The retention time measurements have to be carried out under exactly the same conditions. Applying Equation 2 for the three compounds and combining the
Hulsman, Anal. ( 3 ) J. F. K. Huber, J. Chrornatogr. S o . , 7 , 85 (19691
ANALYTICAL CHEMISTRY, VOL. 45, NO. 8, JULY 1973
1337
I
a
c-
10%
Figure 1. Relative standard deviation U K X (in percentage) defined by Equation 4 with Kx and K Z as variables and K 1 as constant parameter having the values 5 ( a ) , 10(b), 20(c), and 40(d)
0
three resulting equations give the expression for the calculation of the unknown partition coefficient:
KX
b
2C
i,'
'
5 10 2'0
I I&
I
I
200
300
I
--
-
in which the indices 1, 2 , and X mark the two standard compounds of which the partition coefficients are known and the compound of which the partition coefficient has to be determined. The error propagation in Equation 3 can become significant depending on the relative magnitude of the particular values of the partition coefficients and retention times. This effect can be calculated with different assumptions on the errors of the individual parameters. For the case of a constant relative error of the partition coefficients K1 and Kz and a negligible error of the retention times, the following equation for the relative standard deviation of K x can be derived after substitution of the corresponding expressions for the retention times according to Equation 2 :
7 \ L
5 0 0
400
(4)
C
t
10%
with c K x = relative standard deviation of the unknown partition coefficient and cKs = ~ ' =~ L '1K Z = relative standard deviation of the known partition coefficients. The computation of the relative standard deviation has been carried out by means of a digital computer for a set of partition coefficients and assuming a value of 3% for L ' ~ The ~ . results are plotted in Figures l a - d . From Equation 4, it follows t h a t the error has a minimum at K x = 2K1Kz/(K1 K 2 ) . From the figures it can be seen, that the error becomes considerable if K x differs strongly from Kz as well as from K1, and exceedingly large if K x is much smaller than K1 and Kz. Because of the possibly large error propagation in Equation 3, it is preferable to determine first t~~ and q in Equation 2 by linear regression from a number of data points. The unknown partition coefficient is then calculated from the corresponding retention time tRx and the parameters t R o and q using Equation 2 . This procedure allows one to control the significance of nonlinearity effects of the distribution isotherm, additional adsorption effects on the liquid-liquid or liquid-solid interface, and the constancy of t R oand q during the measurements. The more the correlation coefficient T~~ of the retention time and the partition coefficient approach one, the less significant are nonlinearity and adsorption effects and the more constant have been t~~ and q during the series of measurements. The correlation of experimental data can be performed by using methods of factor analysis. In order to apply these methods, liquidliquid partition coefficient data are described by the equation
+
5
J " 1626
I
1 0 ;
I
200
, I 300
I 400
d
1
10%
with u i p = factor depending on the nature of the solute i, a k p = factor depending on the nature of the liquid-liquid system, and p = index of the factors. According to the rules of linear algebra and Equation 5 , partition coefficient data are represented by a matrix, the factors of which have to be determined by numerical procedures. In earlier work (2) a rapid optimization procedure 14) was applied in order to find a n approximation with a given number of factors. The procedure allows finding of a minimum for the errors according to the least squares method. It can happen, however, t h a t a secondary minimum is found instead of the absolute minimum. For this reason, another method of factor analysis, known as "principal components" method ( 5 j , was used in the present study. This (4) R. Fletcher and M . J. D . Powell, ComputerJ.. 6, 163 (1963) ( 5 ) P. Whittle, Skand. Aktuarietidskrift, 35, 223 (1952).
1338
ANALYTICAL CHEMISTRY, VOL. 45, NO. 8, JULY 1973
Table I . Equilibrium Composition of Ternary Liquid-Liquid Systems Consisting of the Same Components [the Data at 25 "C Had Been Published Already in Another Paper (211 less polar phase
more polar phase
-
mole fraction
mole fraction 2,2,4-Tri-
Tern p,e r at u r e C
Water
Ethanol
20.0"
0.856 0.391 0.167 0.278 0.378 0.462 0.581 0.702
0.144 0.590 0.700 0.671 0.601 0.529 0.416 0.296
25.0"
2.2.4 Tri-
methyl pentane 0.000
Density, gIcm3
Water 0.000
0.952 0.829
0.019 0.133 0.051 0.021 0.009 0.003 0.002
Ethanol
methyl pentane
Density, !3/cm3
0.01 5 0.072 0.31 7 0.142 0.126 0.093 0.059 0.037
0.985 0.916 0.658 0.847 0.865 0.900 0.935 0.961
0.689 0.689
0.012 0.025 0.01 1 0.009 0.007 0.006 0.002
Table I I . Partition Coefficients of Standard Compounds at 20.0 "C in Ternary Liquid-Liquid Systems Described in Table I
Phase system characterized
-
Dynamic values
Static values
VK,' % Solute KLb 0.857 p-Nitroanisol 1.9 4.26 2.2 o-Chloronitrobenzene 10.41 0.7 15.81 p-Nitrotoluol 1.6 p-Chloronitrobenzene 20.96 2.7 25.40 m-Chloronitrobenzene 0.391 n-Propylbenzene 1.3 4.62 n-Butyl benzene 0.6 5.45 n-Pentyl benzene 0.9 7.70 0.7 n-Hexylbenzene 9.57 1.1 n-Heptylbenzene 10.97 1.9 n-Decylbenzene 25.21 a x t a t e r = mole fraction of water in the more polar liquid phase ( = mobile phase) b K L = average value of the partition coefficient. C vK = coefficient of variation (percentage) for the measurement of K,. d n = number of measurements.
by x",,ter
Q
method can be applied if the data matrix is complete and the statistical error of the data is constant. As a result, a n exact solution is obtained with n factors a k l . . . akn for each phase system k , and n factors a,l , , . u r nfor each solute i. The number n of the factors is determined by the size of the matrix. By reducing the number of factors to r < n the data matrix is reproduced with decreasing precision using Equation 5. The sum of the squares of the differences between the calculated and the experimental values of log K,k equals the sum of the eigenvalues of the neglected factors. When taking the set of r factors having the largest eigenvalue, the sum of the squares of the differences corresponds to the minimum obtainable with r factors. Apparatus. The analysis of the liquid phases was carried out by means of a gas chromatograph with thermal conductivity detector (Becker Unigraph TC 406). The column was constructed from a copper tube of 1200-mm length and 4-mm internal diameter. It was packed by a porous polymer adsorbent (Porapak Q, Waters) 150-180 Km and operated a t 230 "C. The carrier gas was helium. The apparatus for the liquid chromatographic experiments consisted of the thermostated reservoir (custom made), the diaphragm pump (OTlita D M P 1515) with damping unit (custom made), the thermostated separation column (custom made), the thermostated refractometric detector (Waters R4) and the potentiometric recorder (Goertz, Servogor RE 511). Reservoir, column, and detector were thermostated in series by the same water bath (Haake F T ) . The columns were constructed from thick-walled glass tubes of 250-mm length and 2.7 mm internal diameter. They were packed with a hydrophobic or hydrophilic porous solid which
-
VK,' %
nd
K,*
9 9 9 9 9 9 6 5 6 9 12
4.26 10.32 16.09 21 .oo 25.16 4.51 5.73 7.52 9.62 12.40 25.26
1
0.2 0.9 0.4 0.5 0.9 2.7 1.9 2.8 1 .o 0.7 1.3
nd
9 6 6 3 6 7 6 8 7 10 10
-
Ki,stat)/ %,dyn.%yo
0.0 -0.9 -4-1.7 +0.2 -1.0 -2.4 f4.9 -2.4 +0.5 +11.5 +0.2
I
"I
0
-
(Ki.dvn.
__t
Xpolar
'0.5
1
Ha0
Figure 2. Logarithm of the partition coefficient a s function of the
mole fraction of water in the more polar phase for ternary liquid-liquid systems consisting of the s a m e components described in Table l and for four steroids selected a s standard compounds Present data: 0 ; previous data: V progesterone, 0 androstenedion. 0 methyl testosterone, A testosterone: 0 critical mixing point ANALYTICAL CHEMISTRY, VOL. 45, NO. 8, JULY 1973
1339
Table Ill. Regression Data for the Linear Relationship between Retention Time and Partition Coefficient ( t R i = a -k b K i ) in the Ternary Liquid-Liquid Systems Described in Table I Phase system characterized by XLatera
a (s)
0.856
169 167 169 176 174 174 175 175 175 192 194 186 191
0.391
v,.
%b
6.8 3.4 4.6 1.7 0.8 2.2
1.5 0.1 0.4 5.2
3.8 0.9 3.7
205
2.0
194 199 207
7.1
200
206
2.2
4.3 3.9 1.9
b(s)
12.0 12.4 12.5 12.7 12.7 12.6 12.1 12.2 12.3 19.8 18.8 19.1 16.8 18.9 24.8 18.7 18.1 17.0 20.1
1'bl
YQb
5.5 2.7 3.6 I .4 0.7 1.9 1.7 0.1 0.4 2.3 1.8 0.4 1.8 0.9 2.3 1 .o 2.1 1.9 0.8
nc
r t Kd
3 3 3 4 4 4 3 3 3 4 4 3 4 4 4 4 4 4 4
0.9993 0.9997 0.9995 0.9998 0.9999 0.9996 0.9999 1 .oooo 1 .oooo 0.9995 0.9997 1 .oooo 0.9997 0.9999 0.9995 0.9999 0.9996 0.9996 0.9999
= mole fraction of water in the more poiar liquid phase ( = mobile phase). b v,, v b = reiative standard deviation (percentage) of the measurements of a or b. c n = number of data. r t K = correlation coefax&ater
ficient.
*
The static experiments were carried out in glass vessels of about 90-ml volume. The construction was similar to the vessel described earlier (2) except that a stopcock had been added at the bottom. The vessel had a water jacket thermostated by a water bath, and its content could be stirred by means of a magnetic stirrer. A number of distribution experiments can be performed a t the same time connecting the mixing vessels in series with the water bath. The separation of the phases can be speeded up by centrifugation. Extended computations were performed on digital computers (Electrologica X-8 and Digital Equipment PDP9) with core memories of 40 K and 420 K. Figures 1, a-d were made by means of a plotter (Houston Instruments, Complot DP-1-M1) connected to the computer. Chemicals. Four groups of compounds were used for the distribution experiments: nitrobenzene derivatives (Merck ORG), alkyl benzenes (Polyscience or Baker), steroids (Merck, for biochemical applications), and pesticides (Polyscience). Although some of the compounds proved to be impure, no purification was carried out, since the usefulness of the method for the determination of partition coefficients for the components of mixtures could be proved in this manner.
RESULTS AND DISCUSSION A number of ternary liquid-liquid systems were prepared from water, ethanol, and 2,2,4-trimethyl pentane. At 25 "C, the particular phases were prepared separately according to the known phase diagram (3). At 20 " C , where the phase diagram was not known, the components were mixed for 6 hours in a thermostated container by shaking. After that, the phases were separated and analyzed by gas chromatography. The composition of the ter-
Table I V . Partition Coefficients of Pesticides Measured by the Dynamic Method at 20.0 "C in the Ternary Liquid-Liquid System Described in Table I by the Mole Fraction of 0.857 for Water in the More Polar Phase Relative standard deviation Purity indicated Partition by supplier, coefficient, for 3 measureCompound Yo w / w mean value ments, % 100 0.60 1. y-l,2,3,4,5,6-hexachlorocyclohexane (Lindane) 6.7 95 0.79 7.6 2. Dimethyl 2,3,5,6-tetrachloroterephthalate (Dacthal) 98 0.80 2.5 3. 2-Chloroallyl diethyldithiocarbamate (Vegadex) 4. 1 , l -Dichloro-Z,Z-bis(b-chlorophenyl)ethane(TDE. D D D ) 70 1.04 2.9 5. 1 , 1 , 1-Trichloro-2,2-bis(p-methoxyphenyl)ethane, (Methoxychlor, DMDT) 90 1.10 0.0 6. 1,2,3,4,10,1 O-Hexachloro-6,7-epoxy-l,4,4a,5,6,7,8,8a-octahydro-l,4-endo,exo100 1.51 3.3 5,8-dirnethanonaphthalene (Dieldrin, HEOD) 7. 1,2,3,4,10,1 O-Hexachloro-6,7-epoxy-l,4,4a,5,6,7,8,8a-octahydro-l,4-endo,endo99 1.96 2.0 5,8-dimethanonaphthalene (Endrine) 8. l,l,l-Trichloro-2,2-bis(p-chIorophenyl)ethane (DDT) 99 3.24 0.6 9. 4,7-Methano-3a,4,7,7a-tetrahydroindene (Heptachlor) 72 4.21 1.2 10. cu,a,cu-Trifluoro-2,6-dinitro-N,N-dipropyl-~-toluidine(Trifluralin) 5.65 95 0.5 1 1 . 1,2,3,4,10,1O-Hexachloro-l,4,4a,5.8,8a-hexahydro-l,4-endo,exo-5,85.77 90 1.4 dimethanonaphthalene (Aldrin, H H D N ) 99 12. 2,2-Bis-(p-chlorophenyl)-l, I -dichloroethylene ( D D E ) 5.90 0.8 11.77 98 0.9 13. Dodecachloroctahydro-1,3.4-methano-2H-cyclobuta[c.d]pentalene (Mirex) was supposed to serve as inert support for the corresponding stationary liquid. The hydrophobic solid support was prepared from diatomite material (Hyflo Super-Cel. Johns Manville) by grinding and classifying in an air classifier (Alpine 100 MZR) to a particle size range of 15-25 pm. I t was silanized by means of trimethychlorosilane. The hydrophilic solid support was prepared from diatomite material (Kieselgur, Merck) by grinding and classifying to a particle size range of 5-10 @m.Distilled water, absolute ethanol (Merck) and 2,2,4-trimethylpentane (British Drug Houses), boiling range 98-99.5 "C, purified by percolation through a silica column were used for the liquid-liquid systems. Depending on the sample the water-rich phase or the water-poor phase was used as stationary phase in combination with the hydrophilic or the hydrophobic solid support, the other liquid phase being used as mobile phase. The support was loaded with the stationary liquid by injecting 5 times 50 p1 into the eluent stream. 1340
ANALYTICAL CHEMISTRY, VOL. 45, NO. 8, J U L Y 1973
nary liquid-liquid systems prepared is given in Table I together with the density measured by means of a pycnometer. In the chromatographic experiments, one of the coexistent phases was chosen as stationary phase, the other being used as the mobile phase. Static Determination. A mixing time of 6 hours guarantees the settling of the equilibrium state. The precision of the static determination of liquid-liquid partition coefficients was found to be influenced strongly by the manner in which the liquid phase to be measured is withdrawn from the mixing vessel. Low precision was obtained with a syringe. This is ascribed to the demixing of the liquid phase which was observed when the needle was dipped into the liquid, probably because of the cooling of
~~
~
Table V . Partition Coefficient of Steroids at 25.0 "C in Ternary Liquid-Liquid Systems Consisting of the Same Components Described in Table I [Improvement of Recently Published Data (2)] Mole fraction of water in the more polar phase used for the characterization of the phase system 0.167 Compound
1. 2. 3. 4. 5.
Pregn-4-ene-3,20-dione(progesterone) (standard) 20P-Hydroxypregn-4-ene-3-one Androst-4-ene-3,17-dione (androstenedione) (standard) Androstadiene-(4,9(1 1 ))-3,17-dione 17P-Hydroxy-17a-rnethyIandrost-4-ene-3-one(methyltestosterone)
4.4
5.6 5.8 5.3 5.6
0.278 0.378 0.462 0.581 Average value K i of the partition coefficient
8.8 15.2
14.2 14.5 18.4
10.6 21.1 21.3 23.3 28.9
10.3 24.4 24.0 24.5 32.8
0.702
4.1
7.5 16.9 18.6
14.6 15.8 14.2 22.5
23.3 33.6
(standard) 6. 7. 8. 9. 10. 11. 12.
13. 14. 15. 16. 17. 18. 19.
20. 21. 22.
5.6
20a-Hydroxypregn-4-ene-3-one 170-Hydroxyandrost-4-ene-3-one (epitestosterone) 3-Hydroxyestratri-(1,3,5,(1 0 ) )-ene-l7-one(estrone) 1 7~-Hydroxyandrost-4-ene-3-one(testosterone)jstandard) 1 70-Hydroxypregn-4-ene-3,20-dione 21 -Hydroxypregn-4-ene-3,20-dione( 1 1 desoxycorticosterone) Androst-4-ene-3,11,17-trione(andrenosterone) 1 lp-Hydroxyandrost-4-ene-3,17-dione 17p-Hydroxyandrosta-l,4-diene-3-one Estratri-(l,3,5,(1 O))ene-3,17P-diol 140-Hydroxyandrost-4-ene-3,17-dione 1 6a-Hydroxypregn-4-ene-3,20-dione 1 7 a .2 1- Di hyd roxypregn-4-ene-3,20-dione 19-Hydroxyandrost-4-ene-3,17-dione 1 l/3,21-Dihydroxypregn-4-ene-3,20-dione (corticosterone) 3,160, 170-Trihydroxyestratri-(1,3,5,(10))-ene 21 -Hydroxypregn-4-ene-3,11,2O-trione(ll-dehydro-
8.1 7.2 8.2
20.1 20.7
32.5
36.7
30.9
44.5
22.6 25.3
36.6 43.2 51.5
50.9
11.5
28.9 35.2 37.8 38.1 41.5
11.6 11.8 11.5 14.0
67.4 69.6 84.2
13.0
83.5
8.9 9.9 10.6 11.1
17.1
126
16.3
119
67.1 76.6 78.8 80.9 105 156 168 240 227 31 3 31 6 329
19.2 22.8 26.0 29.7
151
351
178 188 228
550
16.2
54.2
99.6
56.9
326 322 477
534
641
593
682
589 1060 1290 241 0
674 1860 2200 4060
295 256
33.6 50.3
52.4 61.5 78.2 80.6 122 119 127 134 387 404 458 465 605
71.5 76.6 105 114 112 146
23.1
33.2 46.7
43.3 58.7 54.1
94.5 120 107 110 303 300 410 450 58 1 652 599
corticosterone) 23. 3.1 6fl,17P-Trihydroxyestratri-(l,3.5, (1 0))-ene 24. 1 7 a , 2 1-Dihydroxypregn-4-ene-3,11.20-trione(cortisone) 25. 17@,21-Dihydroxypregn-4-ene-3,11,2O-trione 26. 11~,170,21-Trihydroxypregn-4-ene-3,20-dione(hydrocortisone, cortisol)
the liquid by the needle. Much better results were obtained by withdrawing the liquid from the mixing vessel by means of a stopcock. The results obtained a t 20 "C for nitrobenzene derivatives in a ternary system with a very large difference in the composition of the two liquid phases and for alkyl benzenes in a system with smaller difference are represented in Table 11. The partition coefficient was defined by choosing in Equation 1 the water-poor phase as p and the water-rich phase as cy. The compounds were selected to be suitable as standards in the dynamic measurements on the corresponding phase systems. The relative standard deviation of the measurements is smaller than 2% even a t low values of the partition coefficient. The accuracy of the static determination depends mainly on the purity of the sample. Significant systematic errors can arise in using Equation 1 if impurities are present which have a comparable or larger molar absorbance and distribute differently between the phases compared to the main compound. Dynamic Determination. The main sources of error in the dynamic determination of liquid-liquid partition coefficients are adsorption effects, nonlinearity of the liquidliquid distribution isotherm, nonconstancy of the operating conditions, and errors in the partition coefficients of the standard compounds. The total error caused by these effects can be recognized and eliminated to a large extent by using a t least three standard compounds and plotting their retention times in the chromatographic column as a function of their partition coefficients measured by the static method. The value of the correlation coefficient expresses the degree of approximation to the linear relationship described by Equation 2 . True liquid-liquid distribu-
533 876
685 951 1390 2660
tion in the linear range of the isotherm and constant operating conditions are ensured if the correlation coefficient has a value near to one. In this case the parameters a = t R o and b = tRoq of Equation 2 can be calculated by linear regression of the data of standard compounds with known partition coefficients. In order to test the dynamic method, measurements were carried out with the compounds and phase systems investigated already by the static method. Mixtures of these standard compounds were injected in series into liquid chromatographic columns a t 20 "C containing the water-poor phase as stationary phase and the water-rich phase as mobile phase. The partition coefficient of each compound was determined from Equation 2 using the other compounds for the determination of the regression parameters a and b. In order to simulate realistic conditions, the samples injected immediately before and after the test sample were considered to be the standard samples. The stationary phase corresponding to a water content of 0.012 was found to strip off significantly. A few minutes after loading the column by injecting stationary liquid, a nearly linear decrease of the phase ratio was observed in the next hours which amounted to 7% per hour for a value of q N 0.1. For this reason, the retention times of the standard compounds were interpolated from the values measured before and after the test sample. In the first evaluation of the data, good agreement between dynamic and static data was found with the exception of heptyl benzene. The evaluation was repeated after eliminating heptyl benzene as standard, assuming a significant systematic error in the static measurement of this compound. The results are shown in Tables I1 and 111. It can ANALYTICAL CHEMISTRY, VOL. 45, NO. 8, J U L Y 1973
1341
Table V I .
Factors of the Equation log K i =
aipakp
Determined by the "Principal Components" Method of Factor
P
Analysis for Steroids in Ternary Liquid-Liquid Systems of Table I at 25 "C Phase system characterized by xk,~,,
ak1
ak2
ah3
ah4
ah5
ah6
0.167 0.278 0.378 0.462 0.581 0.702
4-2.417 4-3.939 4-4.716 4-5.132 4-5.309 4-5.075
4-0.186 4-0.208 4-0.140 4-0.033 -0.147 -0.260
-0.016 4-0.032 4-0.029 -0.026 -0.094 4-0.081
4-0.081 -0.016 -0.047 4-0.004 -0.012 4-0.026
-0.015 -0.018 4-0.048 -0.020 -0.004
-0.008 4-0.035 -0.027 -0.009 4-0.009 4-0.002
Solutes
all
a12
a13
a14
ai5
a16
4-0.429 4-0.599 4-0.605 4-0.614 4-0.677 4-0.690 4-0.734 4-0.768 4-0.785 4-0.830 4-0.850 4-0.912 4-0.926 4-0.928 4-0.961 4-1.099 4-1.098 4-1.150 4-1.150 4-1.210 4-1.231 4-1.233 4-1.251 4-1.358 4-1.392 4-1.498
4-2.531 4-1.639 4-1.414 4-1.394 4-0.999 4-1.174 4-0.781 4-0.265 4-0.735 4-0.535 4-1.164 4-0.357 4-0.139 4-0.402 4-0.863 -0.694 -0.668 -0.489 -0.758 -0.594 -0.457 -0.447 -0.155 -0.614 -1.073 -1.619
-1.256 4-0.841 4-0.556 -0.855 -0.407 -0.049 -0.785 4-0.744
-0.431 4-0.116 4-0.578 -1.239 -1.268 -1.814 4-2.007 4-1.123 4-0.601 4-0.888 -0.042 4-0.838 4-1.754 4-1.411 -0.051 -0.477 -1.198 -0.842 -0.939 -0.440 -0.148 -0.906 +0.112 -1.011 4-1.025 4-0.670
4-0.329 4-1.735 4-0.630 -0.372 -0.279 4-0.719 -0.309 4-0.088 -0.566 -0.396 -1.491 -0.971 -0.286 -1.138 4-0.866 4-1.448 -1.255 -1.659 -1.385 -0.331 4-0.566 4-1.815 4-0.516 -0.714 4-0.315 4-1.715
-0.196 -0.253 -0.958 -0.743 4-0.872 4-0.291 4-0.975 4-0.916 4-0.238 4-0.171 -0.592 -0.475 -1.118 4-0.058 4-0.194 +0.834 4-1.297 - 1.042 -0.024 -2.387 4-0.955 -0.533 4-1 993 4-0.324 4-1.243 - 1.965
1. Pregn-4-ene-3,20-dione(progesterone) (standard) 2. 20P-Hydroxypregn-4-ene-3-one 3. Androst-4-ene-3,17-dione (androstenedione) 4. Androstadiene-(4,9( 11 ))-3,17-dione 5. 17~-Hydroxy-l7a-methylandrost-4-ene-3-one(methyltestosterone) 6. 20a-Hydroxypregn-4-ene-3-one 7. 17a-Hydroxyandrost-4-ene-3-one (epitestosterone) 8. 3-Hydroxyestratri-(l,3,5, (1O))-ene-l7-one(estrone) 9. 17P-Hydroxyandrost-4-ene-3-0ne (testosterone) (standard) 10. 17a-Hydroxypregn-4-ene-3.20-dione 11. 21 -Hydroxypregn-4-ene-3,20-dione (11 desoxycorticosterone) 12. Androst-4-ene-3,11,17-trione(andrenosterone) 13. 1 I@-Hydroxyandro'st-4-ene-3,17-dione 14. 17P-Hydroxyandrosta-l,4-diene-3-one 15. Estratri-(l,3,5, (1O))-ene-3,17P-diol 16. 14a-Hydroxyandrost-4-ene-3,17-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. 1 1P,21 -Dihydroxypregn-4-ene-3,20-dione(corticosterone) 21. 3,16a,17a-Trihydroxyestratri-(1,3.5, (10))-ene 22. 2l-Hydroxypregn-4-ene-3,11,20-trione( 11 dehydrocorticosterone) 23. 3 , l 6@,17@-Trihydroxyestratri-(1,3,5, (1 0 ) ) - e n e 24. 17a,21 -Dihydroxypregn-4-ene-3,11,20-trione(cortisone) 25. 17P,21-Dihydroxypregn-4-ene-3,11 ,20-trione (hydrocortisone, 26. 11~,17~,21-Trihydroxypregn-4-ene-3,20-dione cortisol)
be seen that the values for the correlation coefficient are excellent and that the accuracy, indicated by the relative difference between dynamic and static data, is good as well as the precision. It may be assumed in general that the dynamic data will be more accurate, if a linear relationship between retention time and partition coefficient is confirmed, since several static data are used for the determination of each dynamic value. The dynamic method was applied to determine the partition coefficients at 20 "C for a number of pesticides in the same phase system used in the experiments with alkyl benzenes. Three of the alkyl benzenes were used as the standard compounds taking their dynamic partition coefficients as reference data for the linear regression. The results are given in Table IV. The precision is good again at higher values of the partition coefficient and still satisfying for pretty low values. In a recent paper (2), liquid-liquid partition coefficients of steroids were presented, which had been determined with Equation 3. The calculations on the error propagation described by Equation 4 have shown that relatively small errors in the reference data can cause large errors in the results if Equation 3 is used. As was pointed out for heptyl benzene in Table 111, the error in the static determination of partition coefficients can be significant due to the impurity of the sample. In order to achieve high precision and accuracy, the static measured partition coefficients of the standard compounds must be controlled by dynamic measurements using a t least three standard compounds, which allows the calculation by linear regres1342
ANALYTICAL CHEMISTRY, VOL. 45, NO. 8, JULY 1973
-0.555 -0.339 -0.275 -0.140 4-0.982 4-0.289 4-0.636 -0.375 -0.244 4-0.898 4-1.203 4-1.043 4-1.475 4-0.633 +1.679 -2.105 -1.626 -1.833
4-0.000
sion as was demonstrated in Tables I1 and 111. In order to improve the former data, the static determination of partition coefficients in six ternary systems consisting of water, ethanol, and 2,2,4-trimethyl pentane a t 25 "C was repeated with four steroids instead of two, controlling the results by dynamic measurements. The new static data are shown together with the older data in Figure 2. The logarithm of the partition coefficient changes smoothly with the composition of the ternary systems, having a maximum a t different compositions for different compounds. The new static data were used as reference data for the calculation of the partition coefficients of the other steroids reported in the previous paper (2). The results are shown in Table V. The improvement due to the use of corrected reference data was up to 20%. Data Correlation. In order to find a systematic approach for the selection of phase systems, methods for factor analysis had been used in the past for the correlation of retention or partition data in gas-liquid (6-11) and liquid-liquid chromatography (2). In this work, a correlation ( 6 ) L. Rohrschneider, J. Chromatogr., 17, 1 ( 1 9 6 5 ) ; 22, 6 ( 1 9 6 6 ) ; 39, 383 ... (1969) ---, P. T . Funke, E. R . Malinowski, D. E. Matire, and L. Z. Pollara, Separ. Sci.. 1, 661 ( 1 9 6 6 ) . W. 0. McReynoids. J. Chromatogr. Sci., 8, 685 (1970) P. H. Weiner and D . G. Howery, Car? J . Chem., 50, 448 ( 1 9 7 2 ) ; Ana/. Chem., 44, 1 189 (1 972) P. H. Weiner and J. F. Parcher, J. Chromatogr. Sci.. 10, 612 ( 19 7 2 ) . P. H. Weiner, C. J. D a c k , and D. G . Howery. J. Chromatogr., 69, 249 ( 19 7 2 ) . \
Table V I I . Precision of the Factor Analysis Depending on the Number of Factors Used Number of factors 6 5 4 3 2 1
Average value of the relative standard deviation in the partition coefficient, %
0
5.1
5.6
7.6
9.5
21.4
was carried out with the 156 partition coefficients of 26 steroids in 6 ternary liquid-liquid systems given in Table V. According to Equation 5 , the logarithm of the partition coefficient is assumed to be described by the sum of a certain number of terms which are products of two factors, one depending on the nature of the solute, the other depending on the nature of the solvent system. A matrix of 6 columns and 26 rows can be formed from the 156 elements given by the logarithm of the partition coefficients in Table V. The values of the factors which determine the elements of the matrix were calculated by using the principal components method of factor analysis. This method can be applied since the data matrix is complete and the absolute error of the logarithm is constant if a constant relative error is assumed for the partition coefficients themselves. The results of the calculation confirm that the data can be reproduced exactly if the solutes as well as the solvent systems are characterized by 6 factors each, which are given in Table VI. The importance of each factor is measured by the eigenvalue belonging to it and, in this way, the factors can be arranged according to the relative contributions to the logarithms of the partition coefficients. In Table VI1 is shown how the precision decreases due to the reduction of the number of factors used. A very satisfying precision of 7% is obtained already with three factors. In comparison with the optimization method used formerly (2), the factors are better arranged according to their importance. This is shown in Figure 3 where the first three factors of the phase systems are given as a function of the composition of the phase systems. The first factor is dominating strongly. A difference in the importance of the factors may not be expected for the steroids, because their factors are normalized in the calculation procedure.
Figure 3. Factors of Table V I as function of the mole fraction of water in the more polar phase for ternary liquid-liquid systems consisting of the same components described in Table I 0 first factor, 0 second factor, A third factor ( X 10)
CONCLUSION The use of partition coefficients as identification parameters is promising but needs further increase of precision of their measurement. This seems to be possible by applying linear regression with sufficient static and dynamic data to reduce the statistical and especially the systematic error which is caused mainly by the impurity of the samples. From the results obtained so far in the correlation of partition coefficients, it can be concluded that the prediction of partition coefficients can be performed with sufficient accuracy to enable the systematic selection of suitable liquid-liquid systems for the separation of a given mixture.
ACKNOWLEDGMENT The authors wish to acknowledge the assistance of L. F. M. de Haan, Mathematical Center and of H. R. de Jongh, Wilhelmina Hospital, with the elaboration of the computer programs. Received for review January 2, ,1973. Accepted January 29, 1973.
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