(22) Gilliland, E. R., I n d . E n g . Chem. 26, 681 (1934). (23) Gordon, S. Xl., Krige, G. J., Pretoriotis, V., ANAL. CHEM. 36, 750 (1964). (24) Harper, J. hI., Hammond, E. G., I h i d . , 37,486 (1965). (25) Jones, W. L., I h i d . , 33, 829 (1961). (26) Kieselbach, R., I b i d . , 35,1342 (1963).
(27) Knox, J. H., SIcLaren, L., I h i d . , 36, 1477 (1964). (28) Ottenstein, D. AI.) J . Gas U m m a b g . 1 , N o . 4, 1 1 (1963). (29) perreti, R.H,, purnell, J , H., A ~ CHEM.34, 1336 (1962). (30) I h i d . , 35, 430 (1963). (31) Sawyer, 11. T., Barr, J. K., I b i d . , 34, 1518 (1962).
RECEIVEDfor review August 24, 1964. Accepted January 25, 1965. Work submitted by J. XI. Harper in partial fulfillment of the requirements for the degree of ~doctor ~ of philosophy . to the faculty of Iowa State University of Science and Technology, Ames, Xovember 1963. Journal Paper No. 5-4932 of the Iowa Agricultural and Home Economics Experiment Station, Ames, Project KO.1517.
Packed Capillary Columns in Gas Chromatography ISTVAN HALASZ and ERWIN HEINE' lnstitut fGr Physikalische Chemie der Universitut, Frankfurt am Main, Germany
b Packed capillary columns were produced by drawing out glass tubes which were loosely filled with a granular solid of narrow mesh range. Properties of these packed capillary columns are compared with those of classical packed columns. Small phase ratio, high specific gas permeability, low hmi, values, and the flat minimum and flat ascending branch of the h vs. 6 curve for packed capillary columns all allow short times of analysis. The packed capillary columns are especially advantageous if the stationary phase is a liquid coated, or uncoated, active solid, but it can b e used with inactive support too.
A
still contained 2 to 3% of water and had a surface area of 130 sq. meters per gram (11). The Chromosorb P (JohnsNanville, New York, N. Y.) used was acid washed. A thick-walled glass tube, 1 to 1.5 meters long (with 2.2-mm. i.d. and 6-mm. 0.d.) was filled with the support.
BRIEF C O L I ~ J N I C A T I O N ( 7 ) reported
the use of packed capillary columns in gas chromatography. The columns should have an inner diameter of less than 1 mm. (preferably between 0.3 and 0 . 4 mm.) with the chosen value not being greater than about 3 to 5 times the diameter of the solid granular packing. Figure 1 illustrates such a packed capillary column. PREPARATION OF PACKED CAPILLARY COLUMNS
Support. Any granular solid possessing high mechanical strength as well as great thermal stability (during the glass-drawing operation) can be used as support for packed capillary columns. Alumina and Chromosorb P were used in this study. hliiniina was prepared by thermal treatment of hydrargillite [r-hl(OH)s], which contains 0.23% NaO and has a total loss a t red heat of 35% (according to the producer, C;lllrlG Chemie Erzeugnisse und Adsorptionsmittel ii.G., hluttenz, Switzerland). The particle diameter ranged between 0.10 and 0.15 mm. The act,ive oxide was formed by glowing at 500' C. for 10 hours; it
Present address, Department of Chemistry, University of California, Riverside, Calif.
0.3 mm. Figure 1 . column
Sketch of packed capillary
Column Preparation. I n filling the glass tube with support, a moderately loose packing has to be achieved. If the packing is too dense, the diameter of the capillary is extended during the drawing process, leading to a n irregular, fragile capillary with bad separating qualities. If the packing is too loose, it will not be stable mechanically and the particles will be shifted by the carrier gas stream. The correct packing density depends on the solidity and the diameter of the solid particles, as well as the diameter of the capillary. The most favorable packing density with alumina particles was achieved by introducing a 1-mm. diameter glass rod, freshly drawn out on the glass-drawing apparatus, into the glass tube. The remaining space was filled with the solid with slight tapping. The rod was carefully pulled out of the glass tube, which was fastened horizontally in the glass-drawing apparatus (4). The tube was drawn out a t a ratio of 1:50. The packed capillary column thus obtained had an inner diameter of 0.32 mm. and an outer diameter of about 0.9 mm. Variations of the inner diameter within 1k0.02 mm. occur due to the influence of the packing. I n filling the glass tube with Chromosorb P packing, it was possible to obtain a properly loose packing by careful filling without use of a glass rod. The drawn capillary had an inner diameter of about 0.43 mm.; this relatively large inner diameter obviously is due to the packing having widened the capillary during the drawing process. Experiments have shown (8) that a temperature of 700" to 800' C. is reached in the glass tube for more than 1 minute during the drawing process, although the glass used has a softening point of about 550' C. Therefore it is possible that the alumina glowed a t 500' C. might be modified during the drawing process. Because of the high temperatures, the packed capillary columns cannot be coated with a liquid stationary phase before the drawing process. Coating is VOL. 37, NO. 4, APRIL 1965
495
the column were connected with the gas chromatographic apparatus by means of metal capillaries which were 150 mm. long with 0.25-mm. i.d.
5
f
6
w
ul
B
CHROMATOGRAPHIC APPARATUS
in
The gas chromatographic apparatus was similar to that already described ( 2 , 6). The flame ionization detector (FID) was combined with a recorder (full-scale time, 0.3 second) or with a high speed ultraviolet galvanometer recorder. The short time of response of both the electrometer amplifier and the mirror galvanometer allows an undistorted recording of peaks as narrow as 0.2 second. The outlet pressure, p , , of columns was atmospheric in all experiments.
W
cc cc W
D
8 W
COMPARISON OF PACKED CAPILLARY AND CONVENTIONAL PACKED COLUMNS
carrier gas: hydrogen molstened over NazSOd IO H 2 0 a t 20' C. Ap = 1.0 atrn. p = 1 atm. u = 4 1 cm. per second K = 8 X l O - ' s q . cm. I = 0.5 pl. gas FID h for C Z ' = 0.060 cm. h for CJ = 0.062 cm. h far nC4 = 0 . 0 6 3 cm.
8
The packed capillary column is to be regarded as a type of packed column. In order to compare the separating qualities of packed capillary and classical packed columns, one column of each type was prepared. Both columns had the same length, were packed with the same alumina, and were operated a t the same inlet pressure, p , , and a t the same temperature. Only the inner diameter of the columns and the sample sizes differed. Both columns were scavenged with hydrogen a t 80" C. for several days. The hydrogen was moistened over Sa2SO4.10H20 at room temperature. Retention. Figures 2 and 3 show the separation of identical mixtures on the two columns. T h e retention time of the inert gas was determined separately in Figure 2. I n both columns the coincidence of the relative retentions of the components is satisfactory j t 2 7 3 , indicating that the alumina in the packed capillary column had not been modified by the drawing
-
carried out in the drawn column (IO). Alumina coated with B,p'axydipropionitrile (ODPN) yields a new stationary phase, which is only slightly hygroscopic. The glass-drawing apparatus produced the columns in the form of spirals having a diameter of 120 mm. The packed capillary column was placed between two concentric metal rings of about the same diameter. Both ends of
I
1
20
I
60
I
60
1
1
80
I
I
100
1
b
o
Rmisccl
I AP I 1 I 1 2 [at Figure 4. HETP (for ethylene, propane, and n-butane) vs. 6 curves for a packed capillary column
1
I
I
Parameters are same as in Figure 2
496
ANALYTICAL CHEMISTRY
f
H
Bm
3
W
a cr W
0
cr
0
V W
K
360
-
t
240
120
0
SECONDS
Figure 3. Separation of C1-C4 hydrocarbons on a classical packed column. Composition of sample and parameters a r e same as in Figure 2, except: ( I ) Air, (2) k' = 0.29, (3) 1.00,(4) 1.31, ( 5 2.78, ( 6 ) 4.33, ( 7 ) 6.63, (8) 7 . 5 4 1.d. of column: 4 mm. 13.4 grams alumino per meter of column length 17 = 5.1 cm. per second K = 1 X 1 O-? rq. cm. s = 0.2 ml. gas catherameter h for Co' = 0.190 cm. h far Ct = 0.161 cm. h for nC1 = 0.093 cm.
process. The quantity of alumina in the packed capillary column was calculated from the ratio of net retention volumns, assuming that the state of the alumina was the same in both columns. The classical packed column contained 13.4 grams, while the packed capillary column contained 26 mg. of alumina per meter of the column length, corresponding to packing densities of 1.06 grams per milliliter in the classical packed column and about 0.28 gram per milliliter in the packed capillary column. Since 60% of the space in a classical packed column is occupied by the packing particles, onIy about 15YG of the packed capillary column is occupied. The four-fold smaller packing density in the packed capillary columns leads to the very closely spaced sequence of peaks shown in Figure 2. I n order to examine the reproducibility of the properties of the stationary phase, both columns were scavenged with dry nitrogen a t 120" C. for one week. The relative retentions a t 80" C. before and after heating and scavenging were reproducible within +C 1%, \Then moistened carrier gas mas employed. Permeability. Specific gas permeability ( K ) of the packed capillary column in Figure 2 is 8 X lo-' sq. cm. and that of the classical packed column in Figure 3 is 1 X lO-'sq. em. (particle size: 0.10 to 0.15 mm.). Reproducibility of permeability is not as good in packed capillary columns as in classical
Table I. Coefficients of the HETP Equation 1 for the Packed Capillary Column at 60" C. (graphically detd. from Figure 6)
B' (cm.2/
A (cm.) Ethylene C z ' 0 017 Propane Cs 0.024 n-Butane C4 0.030 I
b i i
5 I
15
10
Ccm/ucf
+ AP
1
1
2
3
fat
I
Figure 5. HETP (for ethylene, propane, and n-butane) vs. u curves for a classical packed column Parameters a r e same as in Figure 3
parked columns. Thus permeabilities between 6 and 11 X lo-' sq. cm. were determined for packed capillary columns, all of which had been prepared in the same manner. The permeability is known to depend on the packing density (9). While the overall packing density was maintained constant, variation in local packing density apparently caused the variation in specific permeability. Permeabilities are higher for packed capillary columns than for classical packrd columns, but lower than for open-tube columns of the diameters usually employed in gas chroniatography. Plate Height and van Deemter Coefficients. The height equivalent
h to a theoretical plate ( h = L i n = L u . 2 '16tE2)depends on t'he length averaged column pressure ( I , 4 ) :
value is only 13 em. per second (hmin.about 0.6 mm.) for the classical packed column. The minima of the h us. fi curves of the packed capillary columns lie at higher a values, the minima are flatter, and the ascending branch of the curves is flatter than that of classical packed columns. A 10-meter-long packed capillary column was prepared having the same stationary phase, inner diameter, and phase ratio ( V g / V k as ) the packed capillary column which gave the results shown in Figures 2 and 4. The h vs. zi curve of the 10-meter-long column at 60' C. curved upward a t higher values. In Figure 6, where h is plotted against ziij, the curve has a linear ascending branch, which suggests that the peak broadening t'akes place mainly in the gas phase (co'>> ck). On this basis, the coefficients ( A , B', and Co') in Equation l were determined graphically from Figure 6 and are listed in Table I.
fi
sec.)
C,' (see.)
0 96 1 1 X lo-' 0 52 2 1 X 0 28 2 8 X
Effect of Column Length on h u s . curves. By elongation of a
column-with the other parameters remaining constant-the hydrodynamic resistance of the column rises. To achieve the same a values, a higher pressure drop, A p , is necessary. The corresponding pressure correcting factor, j, becomes smaller a t constant outlet pressure-e .g., atmospheric pressure. If C k can be neglected compared with C,' the minimum of the h us. ti curve will be found a t ti = j d B T , Assuming that the other coefficients in Equation 1 remain unchanged, the minimum of the h us. fi curve for the longer column will thus lie at smaller fi values. I t follows that the descending branch of the curve is flatter and the ascending branch is steeper for the longer column than for the shorter one (Figures 4 and 6). The experimental comparison made here is not quite correct, however, since the column temperature was 80' C. in Figure 4 and 60" C. in Figure 6. REQUIREMENTS FOR SEPARATION
The h and K values in Figure 2 for the packed capillary column are more favorable than the corresponding values in Figure 3 for the classical packed colum. Kevertheless, separation is better in Figure 3. Because of its low
Where j is hfllartin's pressure correcting factor of the volume flow velocity ( j = po:'p); A , B ' , CQ',and C k are coefficients independent of pressure. In Figures 4 and 5 the height equivalents t,o a t,heoretical plate are given for ethylene, propane, and n-butane as functions of the mean linear flow velocit,y (a)for both column t,ypes. The capacity ratios (k' = k V k / V Qfor ) each of the curves are also shown. Parallel to t,he horizont'al axis, the pressure drop on the column ( A p ) is plotted for moistened hydrogen uspd as the carrier gas. The parameters belonging to the minimum of the h vs. a curve are in this paper designated as hmin, and amln. L Figures 4 and 5 show that the h m i , 1 I I I I ) values for n-butane a t different capacity 50 100 150 200 250 Ccm/soQ ratios, k', in the two columns are coinciFigure 6. HETP (for ethylene, propane, and n-butane) vs. G / j curves for a packed dentally almost the same for both colca pilla ry column umn types. Comparison shows that a,,,, for n-butane lies above 30 em. per Parameters a r e same as in Figure 2, except: serond for the packed capillary column = 10 meters (h,,,, about 0.7 mm.), whereas the = 60' C. VOL. 37, NO. 4, APRIL 1965
b
497
t ,
5
C SECONDS
I
I
I
lo0
50
1
150
Figure 8. Packed capillary column under optimum conditions at 80°C.
I
200
250 [SKI tm
Figure 7. Necessary pressure drop vs. necessary time of analysis at a resolution of R = 1.5 for:
Composition of sample and parameters a r e same as in Figure 2, except: 1 = 5 meters Ap = 2 atm.
(a) a packed capillary column (calcd. from Figure 4) and ( b ) a classical packed column (calcd. from Figure 5 )
packing density (hence low k') the 2-meter packed capillary column is not able to separate the substances completely. From this example it is evident that the knowledge of the specific permeability ( K ) and of the theoretical plate number [n = 16 ( ~ R / w alone ) ~ ] does not suffice to estimate the quality of a column. This can also be seen in the extreme example of an uncoated empty column, which has an optimum permeaability and plate number, but no separating power a t all. Necessary Length, Pressure Drop, Analysis Time, and Plates. An attempt has been made (6, 8) to characterize the different column types by using magnitudes necessary for a separation problem, the necessary column length L,,, the necessary pressure drop Ap,., the necessary analysis time t,,, and the necessary number of effective plates Arne, ~~
Table II. 6 and HEETP Values for n-Butane, and I,,, Apns and t,, Values for Separation ( R = 1.5) of iso- and n-Butane at 80" C. on Alumina Activated at 500" C.
(Calcd. from Figures 2 and 3 ; N,,
=
2450)
a ) Packed capillary column
Q
(cm./ sec.) 7 5 16 4 24 7 32 ___ 41 48 58 65
H
Lne
Apns
tm
(cm.) (m.) (atm.) (sec.) 0 26 6 4 0 64 218 1 15 90 0 23 5 6 1.6 56 0.22 5.4 38 1.9 0.19 4.8 4.7 2.3 28 0.18 3.4 30 5.6 0.23 7.8 0.32 5.5 35 7.1 8.8 0.36 35 b ) Classical packed column 1000 13 3 8 0 172 4 3 15 510 5 1 0 119 3 0 267 17 7 5 0 092 2 3 2 1 183 9 8 0 082 2 0 2 2 128 12 1 0 070 1 8 108 2 6 14 0 0 069 1 8 30 113 16 3 0 083 2 0 ~ 17 8 0 087 2 3 4 4 110
498
ANALYTICAL CHEMISTRY
The effective number of plates, X , is defined (3) as N = 16 ((t8 - t,)/w)2and the height equivalent to an effective plate as H = L / N . Using H and insteadof h and n the equations can be written in the following simple form :
A comparison between the two column types shows that the packed capillary column has to be twice to three times longer than the classical packed column to have the same number of effective plates, although the h values are in our case practically the same, as has been shown in Figures 4 and 5. This results from the fact that (I ~
(3)
H
t", = - (1 ii
+ k')N",
(4)
where
H=h(,)
1+k'
(6)
For isobutane-n-butane as the pair of substances 1 and 2, the relative retention is r12 = 1.138 a t 80" C., with alumina activated at 500" C. as the support. Assuming a resolution R = 1.5 to be sufficient for the separation, then Xn6will be 2450 (Equation 5). If N,, for a wanted resolution has been calculated from tabulated relative retention values, Ap,,, t,", and L,, can be calculated using Equations 2, 3, 4, and 6, provided the h (or H ) us. ii curve is known for the components with the larger retention time. I n Table IIa and IIb, these necessary values were calculated for the separation problem isobutane-n-butane based on the h us. ii curves for n-butane presented in Figures 4 and 5. To make possible the comparison of the two types of columns, some data from Table I1 were plotted in Figure 7 . This Figure shows Apn*as a function of ins. It must, however, be kept in mind when evaluating this plot that any a parpoint ~ in the curve corresponds to ticular column length, a fact which may be seen from Table IIa and IIb.
")' is more
than twice as large for the packed capillary as for the classical packed column. When both column types have the same pressure drop, A p , the H/zi values will be lower for the packed capillary columns, though the H values are higher than for the other column type. But Equation 4 shows that the H/zi values help to determine tn6. Thus, a t a given pressure drop, the analysis times t,, will be shorter for the packed capillary columns than for the classical packed columns. The smaller k' for packed capillaries also shortens tne. Figure 7 and Table IIa and I I b also show that the most favorable analysis time for the packed capillary column is shorter than for the classical packed column despite the greater column length L,, required of the former type. I n spite of the fact that the packed capillary column is longer than the classical packed column, a smaller Apne is necessary for the former because of its better permeability, K . This may be most important, if quick analysis is wanted, but Ap is limited by the equipment. Experimental Verification. If the h (or H ) us. zi curve is known for a n arbitrary column length, the most favorable column length, along with the other optimum parameters, can be calculated from Equations 2 t o 6. The calculated values in Tables IIa and I I b have been verified experimentally (Figures 8 and 9). For both columns nearly the optimum conditions were selected a t 80" C. (the underlined values in Table IIa and IIb). The measured analysis times were 32 and 120 seconds, respectively, for R = 1.5. The Performance Index ( 5 ) determined at the
120
60
0
t SECONDS
Figure 9. Classical packed column under optimum conditions at 80" C.
column length). Much smaller samples must therefore be used in packed capillary than in the classical packed columns (a ratio of about 1:400; see Figures 2 and 3). Shorter analysis times can be obtained with the packed capillary columns than with the classical packed columns giving the same resolution. This advantage is of particular importance when the inlet pressure of the column is limited because of instrumental reasons, and where the column performance is controlled by gas phase mass transfer. The packed capillary columns are useful in GAC and GLC as well as in GSC.
Composition of sample and parameters a r e same as in Figure 3, except: AD = 3.1 atm.
LIST OF SYMBOLS
w CK
PACKED CAPILLARY COLUMNS I N GLC A N D G A C
The applicability of packed capillary columns in gas liquid (GLC) and gas adsorption layer chromatography (GAC) is illustrated by separations made on two additional packed capillary columns. Figure 10 shows the analysis of halogenated hydrocarbons on alumina coated with ODPN (GAC). The peaks are symmetrical. Figure 11 demonstrates the separation of saturated hexanes and heptanes in GLC.
J"
=
pressure
correcting
from the Equation
factor
u
=
(1) methane (2) 1,1,24rifluor- 1,2,2-trichlorethane ( 3 ) chlorethane ( 4 ) 2-chlorpropane ( 5 ) 1,2-dichIorethane (6)carbontetrachloride (7) methylene chloride ( 8 ) chloroform particle size: 0.1 0-0.1 5 mm. I = 5 meters i.d. of column: 0.32 mm. fc = 70' C. carrier gas: hydrogen Ap = 2 atm. F, = 2.5 ml. per minute s = 0.7 pg. FID; full scale deflection 5 X 1 0-lo amp.
(6)
KP ' I $1
partition coefficient k , / k , relative retention size of sample entering column temp. of column retention time of inert gas tR = retention time of a peak measured from the start U = -. mean linear velocity of the
'
ta'
carrier gas peak width at base line
t
0
C- MINUTES
= r12= s = t, = to =
=
2
4
Figure 10. Analysis of halogenated hydrocarbons on a packed capillary column (alumina activated at 500" C. and coated with 20% by wt. ODPN in methylene chloride)
k
w
,
I
1
6
at = 1 k p per sq. em.
n-butane peak was 30 poise for the packed capillary column and about 90 poise for the classical packed column.
II
7
5 ,
CONCLUSIONS
The free gas cross section of a packed capillary column varies within wide limits (Figure 1). Because in our case there is, side by side, only space for three granules a t the most,, the packed capillary column resembles a capillary with strongly varying radius. I n the packed capillary column there are virtually no dead spaces which are not continuously scavenged. The contribution of the dead spaces to peak broadening thus can practically be neglected. The continuously strong change of the local linear carrier gas velocity effects mechanical mixing of the moving phase. Mass transfer in the gas phase of packed capillary columns is thus not only determined by diffusion, but is also accelerated by convection. Because of the loose packing, the phase rat,io ( V , Vk)of the packed capillary columns is large and the capacity ratio ( k ' ) is small compared with the respective values of classical packed columns. Since the packed capillary columns have a smaller inner diamet,er, they contain, moreover, less stationary phase for the separation than the classical packed columns (0.026 gram 2's. 13.4 grams of alumina, respectively, per meter of the
L
2 f-
I
1
1
0
MINUTES
Figure 1 1 . Separation of saturated hexanes and heptanes on a packed capillary column (Chromosorb P coated with 10% by wt. squalane in n-pentane) (1 1 methane ( 2 ) neopentane ( 3 ) n-pentane (4) 2,2-dimethyl butane ( 5 ) 2-methyl pentane and 2,3-dimethyl pentane (6)3-methyl pentane (7)n-hexane (8) 2,2-dimethyl pentane (9) 2,2,3-trimethyl butane (1 0) 3,3-dimethyl pentane and 2-methyl hexane ( 1 1) 2,3-dimethyl pentane and 3-methyl hexane ( 1 2 ) 3-ethyl pentane ( 1 3 ) n-heptane particle size: 0.1 05-0.1 25 mm. 1 = 5 meters i.d. of column: 0.42 mm. f, = 90' C. carrier gas: hydrogen p. = 2.5 atm. p,, = 1 otm. F, = 2.5 mi. per minute s = 0.3 pg. FlD; full scale deflection 1 O W 8 amp: VOL. 37, NO. 4, APRIL 1 9 6 5
499
F,
=
V, = Vk
7
= =
volumetric flow rate of carrier gas a t 20’ C. and 1 atm. vol. of gas phase vol. of stationary phase carrier gas viscosity LITERATURE CITED
(1) Brennan, D., Kemball, C., J. Inst. Petrol. 44, 14 (1958). (2) Bruderreck, H., Schneider, W., Hal&, I., ASAL. CHEM.36, 461 (1964). (3) Desty, (D. H., Goldup, A., Swanton, K. T., Gas Chromatography 1961, Lansing,” p. 105, Academic Press, New York, 1962.
(4) Desty, D. H., Haresnape, J. N.,
Whyman, B. H. F., ANAL. CHEM. 32, 302 (1960). (5) Golay, hl. J. E., “Gas Chromatography 1958, Amsterdam,” p. 36, Butterworths, London, 1958. (6) Hal&, I., Hartmann, K., Heine, E., “Gas Chromatography 1964, Brighton,” The Institute of Petroleum, London. 1966. ~ - -, -in n r e - -m ( 7 ) HalBsz, I., Heine, E., Nature, 194, I
r
971 (1962)
( 8 , Heike,--E., Dissertation, Universitat
Frankfurt am Main, Germany, 1963. (9) Reisch, J. C.!, Robison, C. H., Wheelock, T. D., Gas Chromatography 1961, Lansing,” p. 91, Academic Press, New York, 1962.
(10) Schneider, W., Bruderreck, H., HalAsz, I., ANAL. CHEM. 36, 1533 (1964). (11) Wegner, E. E., Dissertation, Universitat Frankfurt am Main, Germany, 1961. RECEIVEDfor review August 17, 1964. Accepted December 24, 1964. Presented at the First International Symposium on Advances in Gas Chromatography, University of Houston, Houston, Texas, January 21-24, 1963. We express our gratitude to the Max Buchner Forschungsstifung for financial furtherance of this work.
Selection of a Chromatographic Solvent JOHN A.THOMA Department o f Chemistry, Indiana University, Bloomington, Ind., and Department of Biochemistry, Indiana University Medical School, Indianapolis, Ind.
b Two complementary quantitative indexes of the resolving power of a chromatographic system, the ratios of the chemical potentials of transfer of related compounds and the ratio of the cross-sectional areas of the liquid phases, are proposed and evaluated. Graphical procedures are developed for determination of these chromatographic parameters for systems of homologous polymers and structurally related solutes. Criteria for the use of these parameters are outlined and when experimentally tested held for polar solutes and solvents. The theory of regular solutions is applied to the problem of selecting solvent components and leads to the conclusion that for polar systems it will often be more profitable to study variations in solvent proportions than to study alterations of the sglvent components. Additional guide lines and practical suggestions for the selection of chromotogrqphic conditions based upon theory and accumulated experience are proposed.
0
major objectives of the theory of partition chromatography is to identify the various factors which govern the rate of compound migration during chromatography and to establish quantitative relationships If, in addition, the among them. dependency of these factors on the physical properties of the solute and solvent can be assessed, the theory of solution and principles of physical chemistry should be of. considerable aid in the selection of suitable chromatographic solvents and environments for separation of both known and unknown mixtures. 1-nfortunately, the complexity of the chromatographic pheNE OF THE
9
ANALYTICAL CHEMlSTRY
nomena (2, 9, 10, 20) precludes a rigorous theoretical approach to the selection of an appropriate solvent, partly because of the uncertainty of the nature of the phases (1, 16, 17, 26, 30) involved in paper partition chromatography. However, even if the phases could be precisely defined, solution theory has not been developed to the point where it could consistently furnish useful quantitative predictions about the effect of solvent alterations on solute migration rates (18, 29). I n addition, chromatography is basically a dynamic rather than an equilibrium phenomenon and solvent concentration gradients both along and across the support ( 4 , 8 , 1 0 , 1 1 , 3 4 )complicate the theoretical picture even further. However, a general quantitative correlation of R, data might be made for some systems in terms of certain empirical relationships which are analogous to those theoretical relationships that would be expected to apply to partition processes in certain limiting cases. The need for such quantitative correlations is obvious if the use of paper chromatography is to advance beyond the state of a completely empirical art. Thus while many studies have been concerned with the quantitative relationships of R, and chemical constitution, analysis of the quantitative variations of migration rates with changes in solvent have only rarely been attempted (1, 5 , 38, 49). The present approach is based on a quantitative index oi the resolving capacity of a particular system which can be semi-empirically correlated to environmental changes and performance characteristics of the system. The results are interpreted in terms of general principles already established. I n addition, the use of solution theory to relate these physical
parameters to molecular parameters of the solute is described. The systems employed to test the ideas developed here involved ascending and descending chromatography on paper supports, with and without prior exposure to solvents, with carbohydrates as solutes and polar solvents as irrigating liquids. The polar solvents and solutes were selected for the present investigation because Martin’s equation seems to be obeyed closely. On the basis of theory and our experience four guide lines for the selection of appropriate chromatographic conditions are detailed below. THEORETICAL
To evaluate graphically the chromatographic functions involved in paper chromatography, the relationship between these functions and Rf or other suitable Rr functions is necessary. T h e theory developed by Martin and his coworkers (4,26-28) relating chemical constitution to Rf provides the appropriate starting relationship (See Appendix for definition of symbols) :
It should be noted here that considerable experimental evidence has been amassed to verify Martin’s postulates (22, 20, 21) and that Green, Marcinkiewicz and coworkers (11-15, 22-25) have presented especially convincing evidence supporting these pcstulates using a new technique, flat-bed chromatography. For a homologous series ( 6 , 27, 41) since n = chain length in terms of re
