Prediction of partition coefficients in liquid-liquid systems and its

New Method for Prediction of Partition Coefficients in Liquid-Liquid Systems and Its Experimental Verification for Steroids by Static and Chromatographic Measurements J. F. K. Huber Laboratory of Analytical Chemistry, Unioersity of Amsterdam, The Netherlands

C. A. M. Meijers and J. A.

R. J. Hulsman

St. Anna Hospital, Geldroy, The Netherlands

A new method for the prediction of partition coefficients i s given in which the partition coefficients are described as a function of n parameters characterizing the solute and n parameters characterizing the liquidliquid system. A reference set of parameters had been determined by the correlation of a number of experimental partition coefficient data according to the least square method by a computer procedure. For the measurement of partition coefficients, a dynamic method had been elaborated in which standard data obtained by static measurements are used. The correlation method had been tested for 28 steroids in 6 ternary liquid-liquid systems composed by water, ethanol, and 2,2,4-trimethyl pentane. For n = 3, a precision of about 4% was obtained. SEVERAL SEPARATION PROCESSES are based on the distribution of the sample between two phases. The choice of the phase system is most critical for the result of such a separation. In general the ratio of the distribution coefficients is used as a guide line for the choice of the phase system, although the absolute value of the distribution coefficient has some significance too. The phase system for a particular separation is mostly chosen by trial and error. A second way is t o choose the phase system by means of a collection of empirical distribution coefficient data. A third way is the estimation of distribution coefficients from characteristic parameters. In the case of liquid-liquid distribution, the distribution coefficient is called the partition coefficient. A new method for its estimation is described in this paper. THEORY

Partition Coefficient and Retention Time. The limiting value of the partition coefficient Ki, at infinite dilution of a compound i between two liquid phases p and a is given (1) by the equation

where cti;

concentration of the solute i in the liquid phase k ( k = a or p) fio“ = limiting value of the activity coefficient of the solute i in the liquid phase k VB and V, = mol volumes of the solvents B and A . =

In chromatography the retention time t R , of a component i depends on its partition coefficient as follows: [ R i .=

tRo(1

+ Kioq)

(2)

(1) J. F. K. Huber in “Advances in Chromatography, 1970,” A. Zlatkis, Ed., Houston, 1970, p 348, and J. Chromatogr. Sci., 9, 72 (1971).

where

fRo

=

q

=

retention time of the mobile phase volume ratio of the stationary and mobile phase.

Estimation of Partition Coeflicients. A number of methods have been proposed for the estimation of partition coefficients. All of them trace back to the estimation of activity coefficients. These approaches assume binary solutions so that they can only be applied for the estimation of partition coefficients if the mutual solubility of the solvents is low. It is possible to correlate the limiting value of the activity coefficient in binary mirtures with the molecular structure of the solute and solvent molecules (2-5). These correlations are particularly successful for homologous series and have been verified also for partition coefficients (6-8). The estimation of activity coefficients in a theoretical way is only possible for the regular solution model (9, 10). The procedure can be extended also to other types of binary mixtures if empirical parameters are used (11-18). A new concept for the estimation of partition coefficients is presented here in which empirical partition coefficients are correlated in such a manner that the correlation factors allow a n optimal estimation of partition coefficients. Rohrschneider (13) has shown that the regular solution concept describes the logarithm of the partition coefficient ratio by a binomial which terms are composed by two factors from which one depends on the type of solute and the other on the nature of the solvent. An equation of this type is used for (2) G. J. Pierotti, C. H. Deal, and E. L. Derr, hid. Eiig. Chem., 51, 95 (1959). (3) G. J. Pierotti, C. H. Deal, and E. L. Derr, Amer. Doc. Zmt., Doc. No. 5782 (1958). (4) E. L. Derr, C. H. Deal, and G. J. Pierotti, Amer. SOC.Test. Muter., Spec. Tech. Pub/., 244, 111 (1957). (5) C. H. Deal, E. L. Derr, and M. N. Papadoupoulos, Itid. B i g . Chem., Furid., 1, 17 (1962). (6) A. J. P. Martin, Biochem. SOC.S y m p . , 3,4 (1949). (7) L. Alders, Appl. Sci. Res., A4, 171 (1954). (8) P. J. G. Kramer and H. van Duin, R e d . Trac. C/iirn. Pays-Bas, 73, 63 (1954). 19) ~, J. H. Hildebrand and R. L. Scott. ‘‘Regular Solutions.” Prentice-Hall, Englewood Cliffs, N.J., 1962. (10) J. H. Hildebrand and R. L. Scott, “Solubility of Nonelectrolytes,” Dover, New York, N.Y., 1964. (11) D. E. Matire, ANAL.CHEM.,33, 1143 (1961). (12) D. E. Matire, in “Gas Chromatography,” L. Fowler, Ed., Academic Press, New York, N.Y., 1963, p 33. (13) L. Rohrschneider, J . Gas Chromatogr., 6 , 5 (1968). (14) L. Rohrschneider, Forfschr. Chem. Forscli., 11, 146 (1968). (15) R. F. Blanks and J. M. Prausnitz, Znd. Eug. Clieni., Fur7dam., 3, 1 (1964). (16) J. L. Gordon, J. Pabit Techno/.,38, 43 (1966). (17) C. Hansen, bid. Eug. Clrem., Prod. Res. Dewlop., 8, 2 (1969). (18) R. A. Keller, B. L. Karger, and L. R. Snyder, in “Gas Chromatography 1970” N. Stock and S. G. Perry, Ed., The Institute of Petroleum, London, 1971.

ANALYTICAL CHEMISTRY, VOL. 44, NO. 1, JANUARY 1972

111

the correlation and estimation of partition coefficients. It reads : log Kt = at, x k p (3)

c P

in which atp = correlation factors which characterize the compound i x k p = correlation factors which characterize the liquid-liquid system k The determination of the correlation factors proceeds from the experimental partition coefficient data of a number of compounds in a number of phase systems. If n correlation coefficients are used, n solutes have to be chosen as standards and the following coefficient matrix is obtained:

. . . ai, a22 . . . a2,

all a12

a21

Arbitrary chosen values are given to the coefficients of the matrix so that with the experimental partition coefficients of the standards in the phase systems, the factors (xl,XZ. . . x n ) for the phase systems can be calculated (number of phase systems 3 n). The coefficients (al, a2 . . .a,) for the remaining solutes which were not chosen as standards can be calculated from the experimental values of the partition coefficients in n arbitrarily chosen phase systems from which the (xl,xz . . . x,) coefficients have been determined already. The coefficient matrix is adjusted by the least squares method according to

where Kir

=

experimental partition coefficient of compound i in phase system k .

In other words a t p and X k p are chosen in such a way that the relative difference between the calculated and measured value of K i r for all compounds and phase systems is minimal. The minimum value is determined by a digital computer using a known program (19) which has to be adapted by an additional part which reads in ALGOL:

;

S~RIRR~R

- -(THERMOSTAT

I

1-1

Figure 1. Thermostated vessel for static determination of partition coefficients For the estimation of the partition coefficients of a new compound which is not yet characterized, its partition coefficients in n phase systems have to be measured in order to obtain the (ax, a2, . .a,) values after which the partition coefficientscan be calculated in all the other phase systems from which the (xl,x2. , . x , ) values are known already. In an analogous manner, further phase systems can be characterized by measurement of the partition coefficients of n compounds with known (al, a2. . .a,) coefficients and calculation of the (xl,x 2 . . . x,) Coefficients. EXPERIMENTAL

Apparatus. The establishment of the distribution equilibrium was performed in a thermostated vessel (volume 50 ml) as shown in Figure 1. The content of the vessel was mixed by a magnetic stirrer. In order to eliminate the slightest differences in temperature, three thermostated vessels were used in parallel, two for duplicate determinations and one for the blank. The optical density of samples taken from the upper liquid layer was measured in a spectrophotometer (Zeiss PMQ 11) using quartz cuvets with a light path of 10 mm. The chromatographic apparatus is shown schematically in Figure 2. It consists of a number of building-blocks: RESERVOIR FOR THE STOCKOF MOBILEPHASE. In preparing the phase system, care must be taken that a complete equilibration between the mobile and the stationary phase is obtained at the same temperature as that at which the chromatographic process is carried out. After phase separation, the mobile phase is kept at this temperature in a vessel which is placed in a thermostated bath (HETO ultra-thermostate, type 01-623) that also thermostates the precolumn and the

real procedure INPROD (i,il ,i2,ai,bi,c) ; value ilj2.c; , , . integer - i,il,i2; real ai,bi,c; begin for i: = i l step 1 until i2 do c: = c+ai*bi; INPROD: = c end; boolean procedure minimum (n,y,f,g); value n; integer n;real f;array y,g; begin comment Steroids according to Fletcher Powell ; real a l ; integer c,i,j,k,l,m; array p(l+28(6+1)*28); m: = n s 3 4 ; c: =6*m; minimum: = true; f:=O; for i: = lstepl until 28 do for j := 1 step 1 until 6 do begin a l : =exp(INPROD(l,O,m-l,y(c+l*28+i),y(l*6+j),O))/K(i+28*j); f: = f+( 1 -a l ) 2;p(i+28*j) := (1 -al)*al ;end; for 1 : = 0 step 1 until m-1 do begin for i: = 1 step 1 until 28 do g(c+l*28+i): = -2*INPROD(j,l,6,p(i+j*28),y(1*6+j),O); for j : = 1 step 1 until 6 do g(1*6+j): = -2*INPROD(1,28,p(i+j*28),y(c+1*28+i),O); end ; end minimum; procedure FLETCHER POWELL (n,x,f,g,function,sugh,h,i max,i,eps,conv,stationary,calls); ~

(19) R. Fletcher and M. J. D. Powell, Computer J., 6 , 163 (1963). 112

I


effective light path of 10 mm. The measurements were carried out at a wavelength of 236 nm, the absorption maximum of most of the steroids under study. The output voltage of the amplifier, which is linearly related to the transmission amounts to 10 mV for 100% T. The relation between the concentration of a compound in the detector cell and the output signal is :

where ci

A T

+El

6

concentration of the compound specific absorbance d light path U = output signal in mV

iiii

Figure 2. Scheme of the liquid chromatograph 1. Thermostated vessel, containing the mobile phase (a) Pumping device 3. Thermostated precolumn 4. Sampling device 5. Thermostated separation column 6. Detector 7. Recorder 2.

separation column by pumping the bath liquid through jackets around the columns. PUMPINGDEVICE. Two types of pumps have been used. One is a pulseless piston pump (Labotron Type LDP-13A). The flow can be adjusted stepwise in the range of 2-80 ml/h. The maximum pressure is 15 kg/cm2. The other is a pulsating dual piston pump (Orlita, Type D.M.P. 1515/3). In order to eliminate the flow pulses, two Bourdon tube manometers and a capillary flow resistance were installed in series in the pumping circuit, which provided an efficient damping. The flow of this pump can be varied continuously in the range from 2-640 ml/h up to a maximum pressure level of 325 kg/cm2. PRECOLUMN. In order to eliminate slight variations in the temperature and the composition of the mobile phase, the latter is pumped through a precolumn where intensive contact with the stationary phase takes place. In order to increase the life time, the solid support in this column is highly loaded with stationary phase. SAMPLINGDEVICE. T o bring the sample directly on the column, two types of sampling devices have been used, a syringe (Hamilton, Type 701 N) together with a septum injection port and a sample valve. The sample injection by a syringe through a septum has two disadvantages: the septum has to be changed after a few injections, depending on the nature of the mobile phase, the quality of the septum material, and the pressure; and the injection of relative large sample volumes is difficult at high inlet pressure. To overcome these disadvantages a sample valve with interchangeable loops was constructed (20). The volume of the loop was chosen as 27 p1 in these experiments. SEPARATION COLUMN.The columns are made of straight thick-walled glass tubes with an internal diameter of 2.7 mm and a length of 25 cm. The tubes are filled by a packing of porous particles (diatomaceous earth, particle diameter 28-32 pm) which contain the more polar phase of the liquid-liquid system. The less polar phase is pumped through the column. The ends of the column are filled with small plugs of Teflon wool. The column is sealed by bored, tight fitting Teflon plungers, one of which is part of the injection system, the other one is connected with the detector by means of a Teflon tube with an internal diameter of 0.5 mm and a length of 20 mm. DETECTOR.The detector is a UV spectrophotometer (Zeiss PMQ 11) with a micro flow cell of 7.7-p1 volume and an (20) C . A. M. Meijers, Thesis, University of Amsterdam, 1971.

= = =

RECORDER.Because of the very low concentrations used in the study, the signal is fed to a linear recorder (Servogor, Type R E 511) and a scale expansion is applied to record the signal in the range 9 < U < 10 mV. In this way a deflection is obtained which is proportional to the concentration. The scale expansion is performed with the aid of a precision voltage supply (Knick, Type S-12). Materials. Spectroquality (Merck Uvasole) ethanol and 2,2,4-trimethyl pentane and double-distilled water were used as solvents. The solid support was prepared by grinding and sieving gas chromatographic grade kieselguhr (Merck). The steroids were specified for biochemical application (Merck LAB). Procedure. In the static measurement of partition coefficients a steroid is dissolved in the water-poor phase a until an absorbance of 0.5-0.8 at the wavelength of the absorption maximum in the UV range is obtained with a light path length of 10 mm. The absorbance E,, of this solution is measured against the (Y phase as a blank. A measured volume Va of the solution is stirred for 30 minutes with a certain volume V pof the water-rich phase p at constant temperature. After separation of the two phases the absorbance E, of the upper phase (Y is measured against a blank which was treated in the same way without addition of steroid. The partition coefficient is calculated according to

In order to assure that the measurement is carried out in the linear range of the solution isotherm the volume ratio Va/Vpis varied. Two methods have been used t o prepare the chromatographic column. In the first method measured amounts of the solid support and the water-rich liquid phase p are mixed together and filled in small portions into the column tube. Each portion is compressed by a plunger with a Teflon head fitted in the column bore. After the packing is placed, the interspace is filled by pumping through the mobile liquid phase a. In the second method the column is packed in the same way but dry solid support is used instead of support wetted with stationary liquid. In this case the stationary liquid is added by the injection of known amounts of the water-rich phase into the fluid stream at the beginning of the column. The dynamic measurement of partition coefficients is based on Equation 2 for the retention time. If fRi, fRo, and q are known, the partition coefficient can be calculated. For the measurement of t R a , a nonretarded solute ( K = 0 ) is needed. For many liquid-liquid systems, however, it is not possible to find a compound which has a partition coefficient near to zero. Furthermore it is often difficult to determine the phase ratio q accurately. Therefore two compounds with known partition coefficients are used to determine t~~ and q. By combining the equations for the retention time for the two reference compounds 1 and 2 the following expressions are derived :


113

K

20

'j

1.

!

\. .A

IO

,

,*/

0-0

10

.A

0

5

0

(7)

The partition coefficients of the test compounds can be calculated now after measurement of their retention times. In order to be sure that adsorption effects can be excluded, the retention times are also measured in a column packed with the unloaded solid support.

RESULTS AND DISCUSSION The distribution of 28 steroids in six ternary systems consisting of water-ethanol-2,2,4-trimethylpentane was studied at 25.0 i 0.1 "C. The equilibrium compositions of the phase systems were determined by gas chromatography. The data which are in good agreement with earlier results ( I ) are given in Table I. Static Measurements of Standard Partition Coefficients. The two steroids pregn-4-ene-3,20 dione and 17P-hydroxyandrost-4-ene-3-one were chosen as the standard compounds. A 20 cma solution of a steroid in the water-poor phase was used for each distribution experiment. First, the kinetics of the distribution process was investigated in order to be sure that equilibrium data are obtained. Figure 3, a and 6 show the progress of the distribution. A

mixing time of 5 minutes is sufficient to achieve equilibrium if the steroid is dissolved first in the water-poor phase. It appears however, that the mixing time must be much longer if the steroid is first dissolved in the water-rich phase. Although the irregular kinetics still ask for an explanation, the practical consequence is clear: the steroids must be dissolved first in the water-poor phase. Second, the linearity of the solution isotherm was confirmed for the standards and two other steroids in all six phase systems by variation of the phase ratio. According t o Equation 6, the ratio (Eao - E,)/Eol must be proportional to the phase ratio Vp/V, if the partition coefficient is constant. Figure 4 demonstrates the perfect linearity of the isotherms and confirms that the limiting value of the partition coefficient is measured. A compilation of data of the two steroids, which have been chosen as standard, is given in Table 11. The precision of the measurements was 1.8%. Each measurement was repeated five times. The precision of the mean partition coefficient data in Table I1 is therefore better than 1 %. Dynamic Measurements of Partition Coefficients by Chromatography. Solutions were made of each of 28 steroids in the 6 mobile a-phases given in Table I. Each steroid solution was injected on the top of the column and the retention time was measured. If possible, in the same chromatogram the retention times of the two standards, pregn-4-ene-3,20-

Table I. Equilibrium Composition in Mole Fractions of Six Liquid-Liquid Systems Composed of Water-Ethanol-2,2,4-Trimethylpentane at 25 "C Mole fractions Water-poor phase (a) Water-rich phase (0) __-. Phase system 2,2,4-Tri2,2,4-Tricode number Water Ethanol methylpentane Water Ethanol methylpentane 0.317 0.658 I 0.167 0.700 0.025 0.133 0.847 0.011 0.142 I1 0.278 0.671 0.051 0.865 111 0.378 0.009 0.126 0.601 0.021 0.093 0.900 IV 0.462 0.529 0.007 0.009 0.059 0.935 0.006 V 0.581 0.416 0.003 0.037 0.961 VI 0.702 0.296 0.002 0.002

114


Figure 4. Linearity of the distribution isotherms A = pregn-4-ene-3,20-dione; B = 17P-OH-androst-4C = 17P-OH-17a-methylandrost-4ene-3-one; ene-3-one; D = 17a-OH-androst-4-ene-3-one. Phase system I1 dione and 17P-OH-androst-4-ene-3-one, were measured by adding the standards t o the injection solution. In the cases that a sufficient separation could not be obtained, a mixture of the two standards was injected just before and immediately

after the chromatogram of the unknown compound was obtained in order to calculate the actual phase ratio. All measurements were performed five times. According to Equations 2, 7, and 8, the partition coefficients of the steroids could be calculated. The results are listed in Table 111. The precision of the dynamic chromatographic measurements of partition coefficients was found to be 1.6%. The precision of the mean values presented in Table I11 is better than 1 Control for Adsorption Effects. As mentioned earlier, stationary liquid can be added to the column by injection in order to load the solid support gradually. The phase ratio was determined after each addition of stationary liquid using Equation 7 by measuring the retention times of two steroids with known partition coefficients. The results of such a n experiment are shown in Figure 5. It proves that no proportionality but a linear relationship exists between the volume ratio q = V p / V ,of the stationary and mobile liquid and the total volume Va' of the stationary liquid, which had been injected. The linear relationship between q and V,' suggests that adsorption effects can be excluded. A possible explanation could be that a coating of the solid support with stationary liquid arises spontaneously because of a n initial water film. In order to support this conclusion, q was determined in a different manner. The retention times of a number of steroids on a column packed with dry solid support was measured together with the retention time of benzene. The composition of the eluent corresponded t o phase system V in which benzene has a very small paitition coefficient so that it can be used as the nonretarded solute. The phase ratio qo was calculated from Equation 2 assuming liquid-

Table 11. Compilation of Partition Coefficients of Two Standards in Six Phase Systems, Determined by Static Measurement at 25 "C Pregn-4-ene-3,20-dione 4.4310.07 9.0410.15 9.3110.15 9.45Zt0.16 7.80100.13 17P-OH-androst-4-ene-3-one 8.15 i 0.13 31.4 10.5 39.3 i 0.6 64.7 Zt 1 . 1 53.0 I0.9

5.41f0.09 40.8 10.7

Table 111. Partition Coefficients of 28 Steroids in 6 Liquid-Liquid Systems at 25 "C Code numbers of the phase systems refer to Table I I I1 I11 IV V 4.43 9.04 9.31 9.45 7.80 1. Pregn-4-ene-3,20-dione (progesterone) [standard] 5.61 17.7 19.0 26.1 15.6 2. 20P-Hydroxy pregn-4-ene-3-one (androstenedione) 5.82 16.4 19.1 25.7 17.1 3. Androst-4-ene-3,17-dione 4. Androstadiene-(4,9( 11))-3,17-dione 5.29 16.8 21 . o 26.3 21 .o (methyltestos5. 17p-Hydroxy-17a-methylandrost-4-ene-3-0ne terone) 5.60 22.1 26.1 36.1 29.6 5.62 24.4 29.4 40.7 29.3 6. 20a-Hydroxypregn-4-ene-3-one 8.08 25.2 28.0 50.0 40.6 7. 17a-Hydroxyandrost-4-ene-3-one(epitestosterone) 8. 3-Hydroxy estratri-( 1,3,5,(lO)-ene-17-one (estrone) 7.21 27.8 33.2 57.5 45.4 9. 17P-Hydroxyandrost-4-ene- 3-one (testosterone) [standard] 8.15 31.4 39.3 64.7 53.0 8.91 36.4 46.9 82 67.0 IO. 17a-Hydroxypregn-4-ene-3,20-dione (11 desoxycorticosterone) 11. 21-Hydroxypregn-4-ene-3,20-dione 9.94 45.0 61.3 88 69.0 10.57 48.6 70 122 104 12. Androst-4-ene-3,ll , I 7 trione (andrenosterone) 13. 11 P-Hydroxyandr ost-4-ene-3,17-dione 11.05 49.0 72 132 101 14. 17@-Hydroxyandrosta-1,4-diene-3-one 1 os 11.51 53.7 74 130 15. Estratri-(l,3,5,( 10))ene-3,17P-diol 11.63 71 96 170 114 16. 14a-Hydroxyandrost-4-ene-3,17-dione 11.79 89 143 347 326 17. 1 6 ~ H y doxypregn-4-ener 3,20-dione 11.54 92 154 300 340 18. 17a,21-Dihydroxypregn-4-ene-3,20-dione 14.0 112 220 384 385 19. 19-Hydroxyandrost-4-ene-3,17-dione 13.0 111 208 379 391 20. 11~,2l-Dihydroxypregn-4-ene-3,20-dione (corticosterone) 16.2 133 287 562 508 21. 3,16a,l7a-Trihydroxyestratri-(1,3,5,(10))-ene 17.1 169 290 630 538 (11 dehydrocorticos22. 21-Hydroxypregn-4-ene-3,11,2O-trjone terone) 16.3 160 302 700 573 23. 3,16/3,17/3,Trihydroxyestratri-(l,3,5,( 10))-ene 19.2 203 322 69 5 566 24. 1701~2 1-Dihydroxypregn-4-ene-3,11,20-trione (cortisone) 22.8 240 505 1250 1560 25. 17/3,21-Dihydroxypregn-4-ene-3,11,20-trione 26.0 253 490 1520 1840 (hydrocortisone, 26. 1lp,l7cu,21-Trihydroxypregn-4-ene-3,20-dione cortisol) 29.7 308 SO5 2850 3400 27. Estratri-(1,3,5,(lO))ene-3,16,17/3-triol(estriol) 30.2 340 790 3000 >4000 28. Estratri-( 1,3,5,(lO))ene-3,15,17/3-triol >4000 31.3 688 1580 >40W

VI

5.41 14.9 16.0 14.5 22.0 22.6 32.0 47.1 40.8

54.7 50.5 87 110 9s 101 275 272 372

408 526 590 542 620 860 1260 2400 >4WO >4000


115

Coefficients p = 2 x1

x2

Table IV. Characteristic Coefficients of Phase Systems Phase systems I1 111 IV

I

V

VI

+1.15 -0.98

+1.43 -1.16

+O. 787 -0.532

$0.235 +0.026

-0,908 +1.11

-1.34 +1.51

+1.65 -0.424 -1.14

$0.28 +2.15 -1.56

-0.055 +1.48 -0.731

$0.414 -0.613 +O. 036

fl.05 -3.18 +1.58

+ O . 819

p = 3 XI

x2 X8

Table V. Characteristic Coefficients of Steroids p = 2 p = 3 Steroid Steroid i aiz i ail ail ai2 ai3 1 8.91 9.01 1 7.11 5.22 7.07 2 12.3 12.6 2 9.72 7.24 9.87 3 12.3 12.7 3 7.27 9.78 9.95 4 12.5 12.8 4 9.88 7.30 10.0 5 13.7 14.2 5 10.9 11.1 8.05 6 14.0 14.5 6 11 .o 8.21 11.3 7 14.8 15.4 7 11.8 12.1 8.71 15.4 8 16.1 8 12.2 9.12 12.6 9 15.9 16.5 9 12.6 9.34 12.9 16.8 10 13.3 17.5 10 9.87 13.7 17.2 11 17.8 11 13.7 10.1 14.0 18.4 12 19.2 12 14.6 10.8 15.1 18.6 13 19.5 13 11.0 14.8 15.3 14 18.7 19.5 14 14.9 11.0 15.3 19.5 15 20.2 15 15.4 11.5 15.9 22.0 16 23.2 16 17.5 13.0 18.2 17 22.0 17.5 23.2 17 13.0 18.2 23.1 18 18.3 13.6 24.2 18 19.0 19 23.0 18.3 13.6 24.2 19 19.1 24.3 20 25.5 20 19.2 14.3 20.0 24.7 21 25.9 21 14.6 19.6 20.4 24.8 22 14.6 26.0 22 19.6 20.4 25.1 23 26.3 23 19.9 14.9 20.7 27.1 24 16.0 28.5 24 22.5 21.6 27.8 25 16.4 29.3 25 23.1 22.2 29.9 26 17.7 31.6 26 23.8 24.9 30.5 27 32.4 27 25.4 24.2 18.0 31.9 28 25.3 18.9 33.6 28 26.4

I

8.1 6.2

I1 4.1 2.9

111

5.6 5.5

IV 4.1 3.8

V

7.8 3.2

Kc,lc

I

/.

0.993Kcxp + 0.346

t

.

,$...:

Y :,

.i

a'

Id

,?/"

VI 6.6 3.6

liquid distribution in phase system V. With the partition coefficients of the steroids ranging from 64.7 to 1250, a fairly constant value of 4o = o.oo44 (precision of the measurement 12 '73 was found. Correlation of Partition Coefficients. The partition coefficients of 28 steroids in 6 phase systems as listed in Tables I and 111 were used for the correlation according to Equation 4 which means that 1 6 i 6 28 and 1 6 k 6 6. The correlation has been worked out by a digital computer (Electrologica X-8 with 48K memory) for p = 2 and p = 3. The results are presented in Tables I v and v. The partition coefficients can be calculated from these tables according to (10) The accuracy of the method can be judged from Table VI. As can be expected the accuracy of the correlation is higher for p = 3 than for p = 2. Figure 6 gives an impression of the excellent correlation which has been achieved with p = 3 for 116

$1.72

Figure 5. Linear dependence of volume ratio of stationary and mobile phases on injected volume Vo' of stationary phase

Table VI. Mean Relative Differences between Calculated and Measured Partition Coefficients, Phase system p = 2 p = 3

-2.08

I

10'

IO2

io3

K,,, -

r

Figure 6. Correlation between calculated and measured Partition coefficients of 28 steroids in six phase systems ( p = 3) the 168 data. The next step will be to apply the correlation approach to other types of compounds in order to test its general applicability. We hope to report in the near future on the results which have been achieved in column liquidliquid chromatography of steroids by the optimal choice of phase systems made possible by the correlation approach. ACKNOWLEDGMENT

The authors are grateful to T. de Neef, Technical University Eindhoven, who assisted with the elaboration of the computer program. RECEIVED for review July 15,1971. Accepted August 31,1971.


Prediction of partition coefficients in liquid-liquid systems and its

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