parallel (Figure 3a) and perpendicular (Figure 36) to the suture axis. The kIand function assumed to be a mixture of Cauchy and Gauss functions and special conditions were introduced which required that corresponding components in the two spectra had the same position and half band width. The spectra have been analyzed into five bands which are linear combination: of 40% Gauss/60% (lauchy functions. The curves lvere fitted at g5 equisIJaced with a standard deviation of 0.011.
LITERATURE CITED
( I ) Giese, A. T., French, c. S.,A p p l . Spectry. 9, 78 (1955). (2) Hart, R. R., J . Luol. spectry. 17, 368 (1965). ( 3 ) Jones, R. XI., Sechadri, K..S., Hopkins, (4) J. Levenberg, w . Can. ~ J . Chem. K., Quart. 409 334A p(1962). p l . Math.
164 (1944). ( 5 ) Marsh, R. E., Corey, R. B., Pauling, L., Biochim. Biophys. Acta 16, 1 (1955). (6) hfeison, J.7 J . Opt. SOC. Am. 5 5 , 1105 (1965). (7) Savitzky, 4.,Golay, h4. J. E., ASAL. CHEM.36, 1627 (1964). 2,
(8) Stone, H., J . Opt. SOC.Am. 5 2 , 998
(1962). (9) Tubom’Jra~ T . ~J . Chem. Ph?/s* 24, 927 (1956). (10) Vandenbelt, J. M., Heinrich, C., i l p p l . Spectry. 7, 171 (1953). (11) Longo, Yonda, Tu’. A., A.,Filmer, Hirs, C. D. H. H.,W., Pate, Anal. H., Biochem. 10,53 (1963).
R. D. B. FRASER
EIKICHISUZUKI
CSIRO Division of Protein Chemistry Parkville N. 2 Victoria, Australia
Simulation of Counter Double Current Distribution by Digital Computer SIR: Counter double current distribution (CDCD) differs from countercurrent distribution (CCD) and steadystate distribution (SSI)) in that both solvents move simultaneously in C D C D (S), whereas in CCD only one phase niovec (6) and in SSD the phases move independently (1). CCD has an adequate mathematical description ( 6 ) , but C D C D and SSD are not so easily described, and no general equations have been derived relating concentrations in the machine to partition coefficient, feed weight, feed position, transfer number, solvent ratio, and number of tubes in the fractionating train. Now a digital computer has been programmed to simulate the CDCD process. This discussion, however, is limited to the behavior observed when cperating in the preparative mode or “procedure 3” as deGignated by Post and Craig (3). EXPERIMENTAL
Assuming that a given mixture of qolute. is presented for separation and that an inimiscible solvent pair is available for which there are measured
partition coefficients, two parameters of the C D C D process are the solvent ratio ( R ) , which multiplied by the partition coefficient ( K ) gives the effective extraction coefficient ( E ) or RK = E , and the position of the feed tube. The number of tubes in an apparatus is also a parameter, and as used in this paper mill be 25, the number of tubes in our instrument. Rate of feed per transfer may, within limits, also be a parameter; however, the rate is assumed to be below an amount that would cause variations in partition coefficient and consequently may be ignored. I n the computer program written to simulate CDCD, the solute content of any given tube is calculated from the previous solute content in the two tubes directly to the right and left of it based on amounts specified by the extraction coefficient. Solutes leaving a particular tube do so as specified by the extraction coefficient, one fraction going to the right and one to the left. I n contrast to a more analytic approach to programming, this mathematical approach involves no cumulative constants, has no exponential terms, and will run indefinitely or as required. Input data consist of the partition co-
efficient, the solvent ratio, the amount of feed, the feed tube number, the number of tubes in the fractionating train, and the frequency of printout. The program may be stopped when either a specified number of transfers or any specified degree of steady state designated by a printed message is attained. This program written in Fortran I1 is available on cards from the authors upon request. RESULTS
The course of attainment of steady state for extraction coefficient E = 1.0, center feed, and 25 tubes is given in Figure 1. I n this and the following two figures, the ratio of sample weight per tube to the weight of feed per transfer ( T / F ) is the ordinate. An extraction coefficient of 1.0 with center feed constitutes the set of conditions resulting in the slowest possible attainment of steady state for 25 tubes, 665 transfers; all other variations with regard to position of feed and extraction coefficient reduce the transfers required. The parabolic-appearing curves of the initial transfers approach the straight
I
“I
Tube Number Figure 1. Rate of attainment of steady state for extraction coefficient 1.0 and center feed (tube 13) of a 25-tube extraction train for the given number of transfers ( T F ) The ratio of weight per tube to the weight of feed pertransfer is designated as
r/F
5
Tube Number Figure 2. Steady state calculations for extraction coefficient 1 .O and feed tubes 1, 3, 5,7,9, 1 1 , and 13 VOL. 38,
NO.
12, NOVEMBER 1966
1773
14 12 -
1 .ll
Feed
1.6 -
f
2.0
-’oh I
I I
r’
Figure 3.
Steady state calculations for extractive coeffi-
line sides of an isosceles triangle at steady state. Only steady stmatecondit,ions will be presented in figures and discussion following. Calculations in which the feed tube was varied are shown in Figure 2. Oddnumber tubes from 1 to 13 were chosen. Wit,h a partition coefficient of 1, the two legs are linear at steady state att.ainment, but the amounts eluting in raffinate and extract are affected as the feed position varies. The steady state straight lines for extraction coefficient 1.0 are reproduced in Figure 3 along with similar curves for extraction coefficient’s 0.1, 0.5, 0.6, 0.7, 0.8, and 0.9. The curves for the reciprocal values; namely, 10, 2.0, 1.667, 1.429, 1.25, and 1.1, are mirror images, respeclively, of the curves shown and are not reproduced here. =Is the extraction coefficient varies from 1, the curves become increasingly unsymmet’rical and nonlinear, one leg being bowed convexly
‘6
\
\
\
\ \ \
I I I
$0 :0
1
Tube Number
%
I I I
. I =
0.4 -
*0.
;
1.2 -
-20.8M
--e.*
\
0 0 0 0 00’
7.4
\
\
l-7.-O-@-@-@-
\ \
Figure 5. Simulation of published experimental data for the preparation of methyl linolenate from linseed oil esters (2) 0 Linolenate
and the other concavely while the maximum concentration decreases. Shown in Figure 4 is a plot of the percentage attainment of steady state for a 25-tube instrument as a function of the number of transfers with extraction coefficients ranging from 0.1 to 1.0 as the parameter. One may estimate the percentage attainment of steady state for any given number of transfers or may predict the number of transfers required to attain any designed degree of steady state corresponding to any specified extraction coefficient and its reciprocal value. Optimal combinations of feed tube and solvent ratio have been achieved empirically for the preparation of fatty
0 Linoleate
acids and reported in previous publications ( 2 , 4 ) . The experimental points reproduced in Figure 5 are for the published preparation of methyl linolenate from linseed oil methyl esters. The curves are theoretically calculated with the computer program by plugging in the constants for the partition coejficients, the solvent ratio, the feed tube, and the feed rate for each component. The calculations describe the analytical data adequately and probably within experimental error of the analysis. I n Figure 6 comparable data are shown for the isolaticn of methyl linoleate from corn oil (3). Again, the calculated lines adequately describe the experimental data. DISCUSSION
I Transfer Number Figure 4. Percentage attainment of steady state as a function of transfer number and extraction coefficient
1774
ANALYTICAL CHEMISTRY
Applicability of the digital computer program has been illustrated by simulating CDCD for a 25-tube instrument operated with variations of the extraction coefficients and the position of feed. Further, with specified combinations of these parameters, published experimental fractionations of esters from corn (4) and linseed oils (2) have also been simulated. These calculations not only provide confidence in the computer program, but also contribute to the understanding of the CDCD process. The present applications of the computer program have merely illustrated its utility; no account has been taken in these simulations of the variation in plate efficiency with feed rate (3). Moreover, the illustrations have been restricted to the steady state preparative mode designated by Post and Craig (3) as “procedure 3.” Remaining problems include simulating a t least two other modes of operation, studying the effect of varying numbers of tubes in the train,
LITERATURE CUED
1.0-
-
(1) Alderweireldt, F. C., ANAL.CHEM.
33, 1920 (1961).
\
w/x
(2) Butterfield, R. O., Dutton, H. J.,
Scholfield. C. R.. Ibid.. 38.86 (1966). (3) Post, O:, Cra
