ANALYTICAL CHEMISTRY, VOL. 51, NO. 6 , MAY 1979 (1 1) D. J. Eatough, T. Major, J. Ryder, M. Hill, N. F. Mangelson, N. L. Eatough, L. D. Hansen, R. G. Meisenheimer, and J. W. Fischer, Atmos. Environ., 12, 263 (1978).
RECEIVED for review December 11, 1978. Accepted January
637
29, 1979. We gratefully acknowledge support from the U.S. D~~~~~~~~~of E ~contract ~ ~ ~ -~7 6 - ~ ~ - 0 2 - 2~ 9 8 8 . and ~,0 0 2 the Electric Power Research Institute, Contract RP1154-1. Contribution No. 156 from the Thermochemical Institute, Brigham Young University.
Theory of Concentration Effects in Gel Permeation Chromatography Josef JanEa Institute of Macromolecular Chemistry, Czechoslovak Academy of Sciences, 162 06 Prague 6, Czechoslovakia
The change in elution volume following a change in the concentration of injected polymer solution in GPC is due to many contributing processes. In the theoretical model, three basic contributions are taken into account, namely, a change in the effective size of permeating molecules, and thus a change in the distribution coefficient according to the respective Calibration curve; viscosity phenomena in the interstltlal volume; and, finally, secondary exclusion. The first two contributions lead to an increase in elution volumes, while the last, secondary exclusion, causes reduction in elution volumes with increasing concentration. Changes in the concentratlon of Injected polymer solution were also considered which occur directly at the beginning of the column due to the distribution between the mobile and the stationary phase, and also due to the longitudinal spreading. Mutual proportions between the individual contributions to the overall concentration effect were calculated. The relationshipsderived uslng dimensionless quantities may be interpreted as a calibration function explicitly involving the effect of concentration.
Concentration effects, i.e., the dependence of the elution volume and of the width of the elution curve on concentration and overall amount of injected polymer solution in gel permeation chromatography (GPC) have been observed in many works. Waters ( 1 ) supposed the increase in elution volume with increasing concentration to be due to the higher viscosity of injected solution, Boni et al. ( 2 , 3 )observed that the change in elution volume with a change in concentration was a linear function of the logarithm of molecular weight or of intrinsic viscosity. In the latter case, they obtained a single linear dependence for various polymers. Similar results were obtained by Lambert ( 4 ) . The hypothesis of viscosity phenomena was supported by Goetze et al. ( 5 ) ,who injected a polymer solution in a solvent whose relative viscosity was higher than that of the solvent used as the mobile phase. According to them, viscosity phenomena cause a change in the elution volume, but not the whole change can be assigned to these phenomena. Moore (6) explained the viscosity phenomena as “viscous fingering”. Ouano ( 7 ) stressed the effect of overloading of the column in the injection of solutions of mixtures of standard polymers having different molecular weights and high concentrations. Rudin (8-10) showed that the effective hydrodynamic volume of macromolecules in solution decreased with increasing concentration and that this effect must be taken into consideration in constructing a universal calibration graph. This hypothesis concerning the 0003-2700/79/035 1-0637$0 1.OO/O
effect of concentration on the elution volume was supported also by other authors (11-13), who observed that the effect of concentration on the elution volume in a thermodynamically poor solvent (under the 9 conditions, when the effective dimensions of the macromolecular coil do not vary with concentration) was weaker. Using the latter observations, it was suggested that the thermodynamic quality of the solvent should be estimated from concentration effects ( 1 4 ) . I t was also observed that the mutual arrangement of the individual columns affected the concentration dependence of the elution volume (15),and that, with increasing flow of the solvent, the concentration dependence of the elution volume decreased (16,17). An increase in the width of the elution curve with increasing concentration and volume of the injected polymer solution was observed by several authors (18-20). Hazel1 et al. (21) assumed (but did not prove) an increase in concentration effects with decreasing efficiency of the columns, which is at variance with further results, as is shown below. Hellsing (22) investigated the effect of concentration of the polymer present in the mobile phase on the elution volume of natural macromolecules. Bartick and Johnson (23) outlined the possibility of using differential GPC in the study of concentration effects, while BakoB et al. (24) utilized the same method in the study of incompatibility of various polymers and concentration effects under such conditions. In some papers (25-29), concentration effects were interpreted as a consequence of the osmotic pressure a t the boundary of the mobile and stationary phase, leading to shrinkage of the gel in the eluting zone (27) and/or redistribution of macromolecules of various sizes in the polydisperse sample (28,29). Cantow et al. (30) observed exceptionally a stronger effect of concentration with samples having a broad distribution compared to those with a narrow distribution. Altgelt (31) assigns concentration effects a t particularly high concentrations to secondary exclusion. The review just outlined shows that up to now no paper has been published in which the likely causes of concentration effects would be treated in a complex manner. In our earlier papers (32-36), concentration effects were studied both theoretically and experimentally as complex processes from various viewpoints and in various experimental arrangements. In this paper, we would like to offer a complete and unifying theory of concentration effects under conditions where the gel structure remains unchanged and where interactions such as adsorption, incompatibility, and others do not operate.
THEORY Let us investigate the change in the distribution coefficient of a monodisperse polymer with a change in concentration. C 1979 American Chemical Society
638
ANALYTICAL CHEMISTRY, VOL. 51, NO. 6, MAY 1979
T h e formal equilibrium distribution coefficient in GPC is defined by
For an arbitrary, Le., maximum, average etc. yA, if the maximum of the concentration profile is in the coordinate A, it holds
Yx = where V , is the elution volume of the respective polymer at zero concentration, Vois the interstitial volume, Vi is the pore volume. At a real concentration, K ~ p is c changed by AKGPC. With rigid gels, such as those used in most of the packings, changes in the structure and pore sizes need not be considered. Changes in the structure of soft gels have already been quantitatively formulated (27). Under these conditions, factors contributing to the change in A K G p C are (a) AKs caused by a change in the effective dimensions of permeating macromolecular coils with varying concentrations, and thus by a change in KGpC according to the respective calibration function, (b) A K V due to viscosity phenomena in the mobile phase, (c) AKE due to secondary exclusion. I t holds, then, U G p C
=
S f U
U
V f U
E
x = u/L,
1
= x/L,5 =
U/Vi,
y = g/g,
(3)
where u is the coordinate of the position of the maximum of the concentration profile in the direction of the column axis, x i s t h e axial coordinate along the column, u is the standard deviation of the Gaussian concentration profile expressed in this case in units of the elution volume, L is the column length, g is concentration (w/v), g, is the critical concentration corresponding to the critical volume fraction @x of the polymer in solution, when the sizes of solvated macromolecules are identical with those observed in the 6 conditions. Dimensionless quantities can, of course, be defined on the basis of retention times instead of elution volumes, but it is necessary that all dimensionless quantities be mutually consistent. The concentration profile on the column (Le., distribution of polymer concentrations along the column axis) may be described by the Gaussian function
F(1) = -e-(1/2)[(1-x)2/E21
5
(4)
6
The overall variance of the concentration profile at the column end ET2
=
E? + ED2
=
[I2
x ( h 2 - 51')
(10)
u = U/UES
where urn is the volume of the just excluded coil (on the given column system) in the standard state (in the 0 solvent), where t = 1. Let the calibration function of the given column system be defined by the polynomial
KGPC= P, [In ( 4 1
(11)
The calibration function thus defined by means of dimensionless quantities makes possible a simple comparison of experimental results obtained on various separation systems. In an infinitesimal interval, the calibration function is approximated by a straight line with the slope q , i.e., by
--aK
(12)
a In (ut) - 4
The just excluded coil is then defined as a minimum um value for which q = 0. The dependence of e on concentration is given by Equation 13, according to Rudin and Wagner ( I O )
-1 = 1+ to
6
where
and
t
E
=
to
.( $)
at y = 0, if ( I O )
= I , a t y = 1, if [VI0
=K N 5
(15)
and
(5)
is equal to the sum of variances of contributions of the injected volume E12 and of the dispersion caused by the column ED*. For the variance of the concentration profile with a maximum in the coordinate A it holds, then, EA2
Ex
Effect of Coil Expansion. The hydrodynamic volume of the solvated polymer is defined by the product u t , where u is the volume of unswollen coil and t is a dimensionless swelling factor. Let the dimensionless quantity be defined as
(2)
Let us first define some dimensionless quantities
E1
-7'1
(6)
Immediately after the injection on the column, the sample solution will penetrate not only the interstitial volume, but also the accessible volume of the pores; the original 71corresponding to the concentration of the injected sample is changed to y'I according to
(7) yIvo = ?"I(vo + RGPCVi) According to large experience with rigid porous packings such as silica gels or porous glasses, one may assume, with good approximation, that Vi = V,; thus it holds
where the intrinsic viscosity [ q ] and molecular weight M under given conditions are determined by the Mark-Houwink equation with the constant K and exponent a [q]=
KM"
(17)
which under the theta conditions is reduced in Equation 15. In preceding equations, M , is half the molecular weight of the repeating monomer unit in a vinyl polymer, 0 (in A) is the effective bond length (IO). It also holds that g, = @xM/NoU
(18)
u = 4dVI$M/3@'
(19)
and
where No is the Avogadro constant and the Flow constant (37) is @ ' =3.1 X The above may be summarized as KGpc is the average formal distribution coefficient along the column. We also assume that all processes in the column proceed sufficiently quickly in the state of equilibrium.
AKs = q
s,'
In (ut)dX - qln
(ut,)
ANALYTICAL CHEMISTRY, VOL. 5 1 , NO. 6, MAY 1979
639
and after rearrangement
as= -q
In
to
+ q J’In t dX
(21)
Integrals in Equations 20 and 21 reflect the fact that the concentration in the zone moving in the column varies owing to the longitudinal spreading. Their values de facto equal the average values of integrated variables. Let Equation 13 be transformed into e
= 1/(A
+ yB)
(22)
where A = l / t , and B = ( t o - l ) / t o . By substituting from Equations 6,9, and 22 into Equation 21 and rearrangement, one obtains the equation
AKs = -q In
to r
the solution to which is
[
A K S = -q In
to
+ (ETA + BY’It1) - By’I E1 + ErA + BY’IEI A(ET + EI)
B2?’21t? A * ( ~ -T(I2) ~
The solution to Equation 30 is
Details of Calculation, cf. Appendix. The starting Equations 25 and 29 are of empirical character, since so far the nature of processes operating in the mobile phase and leading to the concentration dependence of the elution volume has not been explained in detail. What obviously operates here are frictional forces (29),trans-column velocity profiles (38),stagnant spaces in the column packing (39) and, with respect to the dependence of concentration, effects on the flow rate of the mobile phase (33, 36), also possibly effects of the non-Newtonian flow (33, 40) or turbulence (41). These problems are still being studied. Secondary Exclusion. The distribution coefficient at zero concentration is given by the accessible pore volume, determined predominantly by the difference between the average pore size and the size of permeating macromolecules, while the effect of pore size distribution may be neglected ( 4 2 ) . KGpC =
Details of Calculation, cf. Appendix. It would be possible, of course, t o use another theory of the dependence of the effective sizes of macromolecules in solution on concentration, but the model used (10) is in good agreement with the experiment; neither would any other model cause any principal change in the suggested conception of concentration effects. Viscosity Phenomena. I t has been postulated (31) and experimentally proved (32) that
(1 -
4)’
r is the radius of a cylindrical pore, R is the radius of the macromolecular hydrodynamical equivalent sphere. Equation 32 expresses the fact that the migration of a sphere in the cylindrical space occurs in a limited volume of concentric cylinder, the radius of which is given by the difference between the radii of the sphere and of the cylindrical space. At a given concentration, the volume occupied by macromolecules must be deducted from the accessible pore volume g
p = -N,V~
(33)
M
where vspecis the specific viscosity of polymer solution related to pure solvent, the constant K is defined by Equation 29. The dependence qspec on y may be expressed in terms of virial expansion
p is the volume fraction of macromolecules in solution. For a given concentration, it holds, then,
KIGPC= ( 1 - $)‘(l
K
l1 (al 0
yx
(34)
(35) In the integral form, i.e., with respect to the change in p along the column = -KGPC‘F
AKE = - L I K G P C d h
(36)
By using the average value of RGPC and substituting from Equations 6, 9, 22, and 33 into Equation 36, one obtains KGPcNougxEIY’I
with the Huggins constant k H . Equations 25 and 26 thus yield
AKv =
p)
whence =E
where a, are virial coefficients. Usually, expansion to i = 2 is sufficient with good approximation; a special case here is the Huggins equation
-
S E = -
+ a2yx2)dX
M
(37)
where constant K may be ascertained from the concentration dependence of KGpC of totally excluded macromolecules (29)
By substituting from Equations 6 and 9 into Equation 28, one obtains
(38)
840
ANALYTICAL CHEMISTRY, VOL. 51, NO. 6 , MAY 1979
For details of calculation, cf. Appendix DISCUSSION In a preceding paper (35), we discussed in detail the contribution to the concentration effect due to a change in the effective dimensions of permeating macromolecular coils and the contribution of viscosity phenomena. Now some consequences are examined which follow from Equations 24, 31, and 38 with respect to the absolute values of AKs, AKv, and A K E . The equations show (and it can be readily demonstrated by, e.g., numerical calculation) that the absolute values of AK become higher with the increasing injected volume of the polymer solution expressed in the parameter (1. The concentration effects are even more pronounced with increasing column efficiency, that is, with decreasing difference between the parameters, lT - EI. Both conclusions are in agreement with experimental results (32-34). It has been found already in an earlier paper ( 3 5 ) ,by substituting experimental values into derived relationships, that under concrete experimental conditions AKs:AKv in the central part of the calibration curve was approximately 1:4, and that consequently the contribution of viscosity phenomena in tne interstitial volume greatly prevails over that due to the change in the effective dimensions of permeating macromolecules. This ratio is virtually independent of the overall concentration, of the overall injected amount and of column efficiency (35). It varies of course with the varying value of q / K , until for q = 0 in both extreme regions of the calibration curve, AKs = 0. T h e ratio AKE:AK~is best illustrated by the following reasoning. For the viscosity of spherical particles, Einstein’s equation (43) qrel = 1
+2.5~
functions; in other words, if AKcPc from Equations 2, 24, 31, and 38 is added to the calibration function defined, e.g., by Equation 11, a relationship is obtained which allows one to calibrate the given separation system by using standard samples of various concentrations. There is no need to extrapolate to zero concentration, because the effect of concentration in the calibration function thus defined is expressed explicitly. Some applications of the above equations were published previously (32-36).
APPENDIX A. Effect of the Expansion of the Permeating Coil. In Equation 23 we substitute the expression
tr2 + and
2mdm =
tt) dX .$I
(A-2) and
ET.
By rear-
( t T 2 - [I2)
I
BylItI)mdm
-
SET m In mdm] (A-3) E1
The second integral in square brackets has a direct analytical solution, while the first integral is solved by further substitution.
Am
+ ByrItI= n
(A-4)
and (40)
With respect to Equation 36, it holds
Under such conditions, AKE:AKv depends only on K for the given system, and on the respective distribution coefficient of the polymer in question. According to Equation 41, neither column efficiency, nor injected volume, nor concentration can affect this ratio, which varies only with KcPC. If experimental data from earlier papers (32,34)are used for the purposes of illustration, K = 0.5 and the relationship
AKv
-
[ &“I In ( A m +
2
dm = d n / A
1
HE-
((T2
The integration boundaries then are rangement,
(39)
is valid. Hence, Equation 25 may be rewritten to
A K V = 2 . 5 K L CpdX
64-11
- [I2) = m2
KGPC
1.25 is obtained. This means, that at R G p C = 1 the viscosity phenomenon is almost compensated for by the effect of secondary exclusion, while at lower R G ~values, C AKv prevails over ME,according to Equation 42. Since in real polymer solutions,,v,, depends on concentration according to Equation 26, used in the relationship 28, a t higher concentrations the second quadratic term of the virial expansion becomes more operative, and AKE:AKv becomes also concentration-dependent, decreasing with increasing concentration. Similarly, this ratio depends on column efficiency and on the overall injected volume, which ensues from the fact that the integrals are not reduced as in Equation 41, but the effect of AKv is stronger. nKE:nKvdecreases with increasing column efficiency and with increasing injected volume. These findings have been verified and corroborated numerically. In conclusion, the fact should be stressed that Equations 2, 24, 31, and 38 may be employed to express calibration
(A-5)
with the integration boundaries (At1 + BT’IEI)and (AFT + BN’~.$~). The first integral in square brackets on the right-hand side of Equation A-3 then becomes
s
WT+ BY’&;)
(AEr +
Wit;)
~
-
A2
s
~
l
~
t
~
In n dn =
W E T + BY’IEI)
(A& + B~’r€i)
- In
A2
n dn -
Both integrals on the right-hand side of Equation A-6 have direct analytical solution. The indicated procedure used in solving them gives the final relationship 24. B. Viscosity Phenomena. In Equation 30, a substitution identical with that used in A-1 is performed for both integrals, which thus have direct analytical solution. C. Effect of Secondary Exclusion. In Equation 37 again, substitution identical with that in A-1 is performed, after which the integral obtained has direct analytical solution.
LITERATURE CITED (1) J. L. Waters, A m . Chem. SOC., Div. folym. Chem., Prepr., 6 , 1061 (1965). (2) ~, K. A. Eoni. F. A. Sliemers. and P. E. Sticknev. J . folvm. Sci.. Part A - 2 . 6, 1567 (1968). (3) K. A. Eoni and F. A. Sliemers, Appl. folym. Symp., 8, 65 (1969). ( 4 ) A. Lambert, Polymer 1 0 , 213 (1969). (5) K. P. Goetze. R. S . Porter, and J. F. Johnson, J . Polym. Sci., Part A - 2 , g , 2255 (1971). (6) J. C. Moore, Sep. Sci., 5, 723 (1970). (7) A. C. Ouano, J . folym. Sci., Part A-7, 9, 2179 (1971). (8) A. Rudin, J . folym. Sci., fart A-7, 9, 2587 (1971). (9) A. Rudin and H. W. Hoegy, J . folym. Sci.. Part A- 7 , 10, 217 (1972). (10) A. Rudin and R . A . Wagner, J . Appl. folym. Sci.. 20, 1483 (1976).
ANALYTICAL CHEMISTRY, VOL. 51, NO. 6, MAY 1979 (11) Y. Kat0 and T. Hashimgto, J. Polym. Sci., Part A - 2 , 12, 813 (1974). (12) D. Berek, D. BakoH, L. Soh&, and T. Bleha, J. Polym. Sci., Polym. Lett Ed., 12, 277 (1974). (13) D. Berek, D. BakoH, T. Bieha, and L. Soltes, Makromol. Chem., 178, 391 (1975). (14) T. Bieha, D. BakoS, and D. Berek, Polymer. 18, 897 (1977). (15) P. M. James and A. C. Ouano, J. Appl. Polym. Sci., 17, 1455 (1973). (16) J. N. Little, J. L. Waters, K. J. Bombaugh, and W. J. Pauplis, J. Polym. Sci.. Part A - 2 , 7, 1775 (1969). 117) . . J. N. UMe. J. L. Waters. K. J. h b a w -h . and W. J. PauDiis. J , Chromatwr. Sei., 9, 341 (1971). (18) D. Braun and G. Heufer, J. Polym. Sci., Pari 6.3, 495 (1965). (19) T. A. Maidacker and L. B. Rogers, Sep. Sci., 8, 747 (1971). (20) J. Y. Chuang and J. F. Johnson, Sep. Sci., 10, 161 (1975). 121) . . J. E. Hazell. L. A. Prince. and H. E. StaDelfeldt. J. Poivm. Sci.. Part C. 21, 43 (1967). (22) K. Heiising, J. Chromatogr., 36, 170 (1968). (23) E. G. Bartick and J. F. Johnson, Polymer, 17, 455 (1976). (24) D. BakoS, D. Berek, and T. Bleha, Eur. Polym. J., 12, 801 (1976). (25) L. W. Nichol, M. Janado, and D. J. Winzor, Biochem. J., 133, 15 (1973). (26) H. Vink, Eur. Polym. J., 9. 887 (1973). (27) P. A. Baghurst, L. W. Nichol, A. G. Ogston, and D. J. Winzor. Biochem. J., 147, 575 (1975). (28) M. Schweiger and G. Langhammer, Plaste Kautsch., 24, 101 (1977).
641
(29) B. G. Belenkii and L. Z. Vilenchik, "Chromatography of Polymers" (in Russian), Chimia Edition, Moscow, 1978. (30) M. Cantow, R. S. Porter, and J. F. Johnson, J. Polym. Sci., Part 8, 4, 707 (1966). (31) K. H. Aitgelt, Sep. Sci., 5, 777 (1970). (32) J. JanEa, J. Chromatogr., 134, 263 (1977). (33) J. JanEa and S.Pokorng, J. Chromatogr., 148, 31 (1978). (34) J. JanEa and S.Pokorng, J. Chromatogr., 156, 27 (1978). (35) J. JanEa, J. Chromatogr., in press. (36) J. JanEa and S.Pokornq, J. Chromatogr., in press. (37) P. J. Fiory, "Principles of Polymer Chemistry", Cornell University Press, Ithaca, N.Y., 1953. (38) J. C. Giddings, J. Gas Chromatogr., 1, 38 (1963). (39) C. Horvath and H. J. Lin, J. Chromatogr., 128, 401 (1976). (40) J. W. Daily and G. Bugliareilo, Ind. Eng. Chem., 51, 887 (1959) (41) J. H. Knox, Anal. Chem., 38, 253 (1966). (42) M. Kubh and S. Vozka, J. Polym. Sci., Part C , in press. (43) H. Morawetz, "Macromolecules in Solution", John Wiiey and Sons, Inc., New York, 1965.
RECEIVED for review October 23, 1978. Accepted January 5 , 1979.
Simultaneous Determination of Vitamin A Acetate, Vitamin D, and Vitamin E Acetate in Multivitamin Mineral Tablets by High Performance Liquid Chromatography with Coupled Columns Stephen A. Barnett" and Leroy W. Frick Mead Johnson & Company, 2404 Pennsylvania Avenue, Evansville, Indiana 4772 1
A reverse phase high performance liquid chromatographic method for the simultaneous determination of vltamin A acetate (retinol acetate), vitamin D, (ergocalciferol) and vitamin E acetate (d,/-a-tocopherol acetate) in multivitamin mineral tablets has been developed. The method requires dissolution of the sample in water-ethanol-pyridine solution (50:46:4), extraction of the vitamins into warm hexane, addition of cholesterol benzoate internal standard, and separation with a methanol-water gradient elution on coupled pBondapak Phenyl-pBondapak C,( columns. Detection of the vitamins and internal standard is monitored at 280 nm with separation accomplished in approximately 50 min. The assay is specific for each vltamln, and typical relative standard deviations for analysis of dosage forms are 0.059, 0.065, and 0.023 for vltamin A acetate, vitamin D,, and vitamin E acetate, respectively.
Compendia1 procedures for the analysis of vitamins A, D, and E lack specificity, are time-consuming, and are not amenable to simultaneous determination from a single sample preparation. In general, analysis of each of these vitamins by compendial methodology requires saponification, solvent extraction, and may require sample cleanup by open column adsorption chromatography. Quantitation is accomplished by spectrophotometric or colorimetric analysis of column eluent. Results using compendial methods are dependent upon the manipulative skills of the individual analyst, and generally lack precision within and between laboratories. Recent growth of reverse-phase high performance liquid chromatography has enhanced the analytical capability of the vitamin chemist. Procedures for the separation of mixed 0003-2700/79/0351-0641$01 .OO/O
vitamin standards (A, DP,E, and K) by high performance liquid chromatography are found throughout the literature ( 1 ) . Thompkins and Tscherne have described the determination of vitamin D, in gelatin-protected vitamin A and D, beadlets using adsorption chromatography after sample dissolution in dimethyl sulfoxide ( 2 ) . Osadca and Araujo have separated vitamin Dz from vitamin D3 on reverse phase packings in the presence of other vitamins in dosage forms ( 3 ) . Vitamins A, D, and E, were separated quantitatively by interfacing high performance liquid chromatography with continuous flow analysis ( 4 ) . T o date, the other forms of separation analysis, such as gas-liquid chromatography and thin-layer chromatography, do not possess the combination of sensitivity and flexibility required for simultaneous determination of these compounds. This paper describes a procedure for the simultaneous determination of vitamins A acetate, D,, and E acetate from a single sample extract using high performance reverse phase liquid chromatography and internal standard techniques. The procedure eliminates saponification, lengthy extractions, and sample cleanup, is specific for the compounds of interest in the presence of interference, and has very good internal precision compared to current compendial methods. This technique provides the high degree of resolution, reproducibility, and ease of quantitation required in the industrial quality assurance laboratory. Increased use of such new ill greatly reduce the imprecision and inaccuracies technology w associated with vitamin analysis.
EXPERIMENTAL Reagents and Solvents. Hexane, methanol,tetrahydrofuran, and pyridine were obtained from Burdick and Jackson, Muskegon, Mich. Retinol acetate d,l-a-tocopherylacetate and cholesterol benzoate were obtained from Sigma Chemical Company, St. Louis, 0 1979 American
Chemical Society
