Equations for the Average Solvent Composition and the Interstitial Column Volume in Column Fractional Precipitation Methods Wolfgang W. Schulz' and William C. Purdy, Department o f Chemistry, University of Maryland, College Park, hid. HE SEPARATION Of Substances with 'similar physical and chemical properties, such as the fractionation of polymers into homogeneous molecularweight fractions, remains a challenging problem. One method that has proved successful in the fractionation of industrial polymers is the column fractional precipitation technique of Baker and Williams ( 2 ) . This is an equilibrium method in which the polymer, contained in a column and supported by an inert material such as glass beads, is subjected to simultaneous temperature and solvent gradients. A linear temperature gradient along the length of the column is achieved by jacketing the column u i t h an aluminum block, heating the upper end of the block with Xichrome wire, circulating a cooling liquid through the lower part of the block, and insulating the entire column well. .Iconstant-volume miving vessel delivers solvent to the column at a rate of approximately 6 ml. per hour and contains initially a high percentage of nonsolvent, in which the polymer is only very slightly soluble. The percentage of a second solvent of higher elution power or "good" solvent increases exponentially with the total volume delivered to the column. At a particular solvent composition, the most soluble molecular-weight species of the polymer, which is precipitated nonselectively on the column support. dissolves and moves down the column to a lower temperature region, where it is again precipitated. It is redissolved by solvent of a higher elution power and is carried down the column in a series of precipitation and extraction steps. The fractions emerge from the column as saturated solutions and are generally collected n ith a constant-volume fraction collector. I t , therefore, becomes necessary to knom the a1 erage solvent composition of each collected fraction. Equations are developed to predict the average solvent composition of these fractions on the basis of the exponential miving function (1, S) and to determine the interstitial column volume.
the one described by Baker and Williams (2) The mode of solvent addition to the mixing vessel differed in many respects from that previously described (9). While the nonsolvent which was placed initially in the mixing vessel was either t'he pure solvent or a solvent mixture, the good solvent in every case constituted a single solvent which was distilled directly into the mixing vessel. -4 250-m1. boiling flask and a 35 em. long, water-cooled, Friedrichs condenser were used. The drip-tip joint of the condenser allowed the solvent to flow into the funnel of the distillate collector, which vias placed between the boiling fla5k and the condenser. The outward-
-
Figure 1. paratus A. B. C. D.
E. EXPERIMENTAL
Apparatus. T h e fractional precipitation apparatus, shown in Figure 1, was built in this laboratory and was similar in design and dimensions to 2222
ANALYTICAL CHEMISTRY
F. G.
H. 1. J.
K. 1.
Fractional precipitation apCondenser Distillate collector Boiling flask Heating mantle Mixing vessel head Mixing vessel Magnetic stirrer Heating wire Insulation Aluminum Block Micro glass bead packing Cooling coils
leading funnel vas connected to the head of the mising vessel by Teflon tubing, 5/16-inch i.d. The solvent was distilled a t such a rate that the funnel was kept constantly full, the excess solvent returning to the boiling flask. The head of the mixing vessel consisted of a 27 male joint, the upper end of which was fused to a short section of capillary tubing. The solvent flow was controlled by a stopcock, which was insert,ed between the capillary tubing and the Teflon connector. During the early experiments the mixing vessel had to be filled through its loner outlet by applying suction to the top of the distillate collector. The filling process \vas facilitated when a microstopcock was added to the head to provide an outlet to the atmosphere. In addition, this microstopcock permitted gas to be removed from the head where it may have collected during an experiment'al run. Ten-milliliter fractions were collected in test tubes with a Rinco Automatic Fraction Collector. Procedure. The solvent composition of the emerging fractions was measured using a cyclohexane-chloroform solvent system. T h e column was washed with 250 ml. of Spectroanalyzed cyclohexane (Fisher Scientific Co.). T h e same solvent was placed in t h e 250-ml. mixing vessel. Purified chloroform (4) was distilled into the mixing vessel. The column was kept at room temperature without a temperature gradient, and about 20 ml. of the solvent were left above the packing. Thirty-fiye fractions were collected with a 10-ml. siphon at a rate of approximately one fraction per hour. The tubes vere stoppered with rubber stoppers. Aliquot portions were transferred to volumet'ric flasks immediately after completion of the run and diluted with Spectrograde cyclohexane. Spectrophotometric absorption curves Jvere recorded with a Beckman IR 4 spectrophotometer. The path length w.s 0.15 mm., and the reference medium was air. Per cent transmittance values a t 13.1 microns were read off the chart, converted first to absorbance values, and then to volume per cent of chloroform in cyclohexane. A volume per cent of chloroform in cyclohexane calibration curve was prepared under identical conditions from chloroformcvcloherane solutions of known comIyositions. The 10-ml. siDhon was calibrated bv employing condhions of an actual run. 1 Present address, Esso Reeearch and Engineering Co., Linden, N. J.
‘l‘he siphon was wetted with p-dioxane and then filled with the same solvent from a 50-ml. buret. Near the point n here the siphon began to operate, the solvent flow from the buret was lowered to an approximate rate of 10 ml. per hour and the flow was not interrupted until the siphon was almost empty. The volume of t h e siphon was read from the buret. The 250-ml. mixing vessel was calibrated by delivering fiv: 50-ml. portions of p-dioxane with a pipet to the mixing vessel. After closing t h e vessel with the mixing head, i t was completely filled from a 50-ml. bLret through the upper connecting head allowing air to escape through the micr ostopcock.
70
60 n,
GI V Y
0
50
c w z
Figure 2. gradient
Solvent f
40
w
Curve I: Theoretical curve Curve I / : Experimenial curve Curve 111: Corrected experimental curve
5 0’ Z
30
20
CALCULATIONS IO
The mixing function for the case of a constant-volume mixing vessel has been demonstrated to be (1, 3) : In
c 2
-c
cz-c
lo
v
here C2 = volume per ceni of good solvent added to mixing vessel C , = volume per cenl of good solvent initially in mir ing vessel C = volume per cenl of good solvent in effluent u = total volume of offluent V = volume of mixin; vessel. The concentration of good solvent in the effluent at any particular effluent volume is 11
where a = ln(C2 - Cl), a con3tant. The average eoncentration of good solvent, C, for an effluent fraction, v.! - vl, is
(3)
‘I‘he effluent volume, v, should he measured from the point Khere the first infinitesimally small change in solvent composition occurs in the effluent (breakthrough point) The effluent volume from the beginr ing of the run to this point corresponds t o the interstitial column volume. Sincc this interstitial volume is generally not knoivn, some means has to be found to determine the breakthrough point. Theoretically, v can be calculated from Equation 3 by measuring the average concentration, C, of any fraction over a known rarge, - ul. If t’, is then expressed as
50
ever, the firbt fraction which indicates the presence of good solvent already represents the average concentration over a small range in solvent composition. The breakthrough point, vo, can be calculated by measuring the volume per cent of good solvent, To,in the fir.bt fraction
where C = the average concentration of good solvent over the volume range, ut)
- 00.
If v,
=
0, then
For the case that the mixing vessel contains initially only nonsolvent (C,= 0), vzf from Equation 6 becomes infinite. A more reasonable expression is obtained for the limiting case of C1 = 0, if the exponential terms in Equation 5 are expanded to the quadratic terms.
I
zl2
v1
=
02
,
I
=
- (uz
-
01)
ziL can be obtained directly.
If the column is iniiially filled with pure nonsolvent, thc breakthrough point corresponds to the point where the first infinitesimally sniall fraction of good solvent leaves the cdumn. How-
100
VOLUME
~
!5 0
I
I
200
250
,
retical values, although the general shape of the exponential curve was folloived (Figure 2 ) . This indicated that mking occurred not only in the mixing vessel but also in the column, the mixing volume being much larger than the measured volume of 270 nil. By arbitrarily selecting a point on the experimental curve, such as the point corresponding to fraction S o . 31 with 53.5 volume per cent of chloroform, and recalculating the theoretical mixing volume, a corrected volume of 310 ml. was obtained Using this new volume to recalculate all theoretical values, a new curve was obtained, which coincided much more closely with the experimental curve. The fact that the two curves were not parallel indicated that the additional mixing volume could not simply be added to the measured mixing volume. The difference between the measured and calculated mixing volumes watS much larger than could be explained by assuming mixing to have occurred in t h r liquid above the packing. 3Iiuing must also have occurred within the packing and \vas probably caused l x diffusion, especially in view of the qhn solvent flow.
DISCUSSION LITERATURE CITED
The cyclohexane-chloroform systcni was used to compare theoretical solvent composition values of fractions with observed values. l h e amount of chloroform in a fraction was determined from infrared absorption measurements, using the C-C1 stretvhing band at 13.1 microns. Cyclohexane was completely transparent a t this wavelength. The calibration curve follon ed Beer’s law. The interstitial column volume wac calculated to be 81.40 ml. The observed chloroform concentrations were low compared t o the theo.
Alm, R. S., Williams, R. J., Tisellus, A . , A c t a C”hPm.Scand. 6 , 826 (1952). ( 2 ) BakeI, C. A., Williams, R. J., J Chrm. Soc. 1956, 2352. C3) Kingbaurn, W. R., Kurz, J. E., J Polymer Scz. 41, 275 (1959). (4) Yollman, H., Becker, H., Corell, AI., Streeck, H., Ann. 531, 1 (1937). (1)
Presented at Division of Analytical Chemistry, 144th Meeting, ACS, Los Sngeles, Calif., April 1963. The authors are indebted to the United States Air Force (Contract AF33(616)-5063) and to the National Science Foundation for support of this work. VOL. 35, NO. 13: DECEMBER 1963
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