The work reported here is coneistent with, b u t not conclusive proof for, the coupling theory of eddy diffusion. The proof of this theory would be greatly advanced if i t were possible to shorn the actual variation of A with flow velocity. This would be enormously difficult using the ordinary gas chromatographic methods. Glueckauf (17’) has shown this kind of variation in a liquid system but i t is difficult to judge the reliability of his data. The fact that the classical eddy diffusion picture seems t o work in chemical engineering studies, many in the proper range of Reynolds numbers, indicates that the predicted transistion mith velocity occurs a t some point. The authors are not familiar with any evperimental work which is in significant disagreement with the coupling theory. LITERATURE CITED
(1) Ayers, B. O., Loyd, R. J., DeFord, . 33, 987 (1961). D . D., A N ~ LCHEM.
(2) Bohemen, J., Purnell, J. H., . “Gas Chromatography, 1958,” p. 6., D. H. Desty, ed., -4cademic Press, New York, 1958. (3) Bohemen, J., Purnell, J. H.. J . Chem. Soc. 1961, 360.
(4) Brennan, D., Kemball, e., J. Inst. Petrol. 44, 14 (1958). (5) Carberry, J. J., Bretton, R. H., A.I.Ch.E. Journal 4, 367 (1958). (6) Collins, R. E., “Flow of Fluids through Porous Materials,” p. 51, Reinhold, New York, 1961. ( 7 ) Deemter, van, J. J., Zuiderweg, F. J., Klinkenberg, A., Chem. Eng. Sei. 5 , 271 (1956). (8) Desty, D. H., Godfrey, F. M., Harbourn, C. L. A., “Gas Chromatography, 1958,” p. 200, D. H. Desty, ed., Academic Press, New York, 1958. (9) Giddings, J. C., J . Chem. Educ. 35, 588 (1958). (10) Giddings, J. C., J . Chromatog. 5 , 61 (1961). (11) Giddings, J. C., Nature 184, 357 (19.59) \ _ _ _ _
(12) Ib[d., 187, 1023 (1960). (13) Giddings, J. C., Seager. S. L., J . Chem. Phis. 33, 1579 (1c60). (14) Giddings, J. C., Seager, S. L., Stucki, L. R., Stewart, G. H., ANAL. CHEM.32, 867 (1960). (15) Glueckauf, E., -4nn. AT. Y . Acad. Sei. 72, 614 (1959). (16) Glueckauf, E., “Gas Chromatography, 1958,” p. 33, D. H. Desty, ed., Bcademic Press, New York, 1958. (17) Glueckauf, E., “Vapor Phase Chromatography,” p. 29, D. H. Desty, ed., Academic Press, New York, 1957. (18) Golay, M. J. E., “Gas Chromatog-
raphy, 1960,” R. P. W. Scott, ed., Butterworth, Washington, 1960. (19) Jones, W. L., ANAL. CHEM.33, 829 (1961). (20) Keulemans, A. I., Kwantes,,, A., “Vapor Phase Chromatography, p. 15, D. H. Desty, ed., Academic Press, New York, 1957. (21) Kieselbach, R., ANAL. CHEM. 33, 23 (1961). (22) Ibid., p. 806. (23) Klinkenberg, A., Sjenitzer, F., Chem. Eng. Scz. 5 , 258 (1956). (24) Klinkenberg, A , , Sjenitzer, F., Nature 187, 1023 (1960). (25) Kramers, H., Alberda, G.; Chem. Eng. Sei. 2 , 173 (1953). (26) Littlewood, A. B., “Gas Chromatography, 1958,” p. 23, D. H. Desty, ed., Academic Press, Xew York, 1958. (27) Ibid., p. 35. (28) Korem. S. D., AYAL. CHEY. 34, 40 (1962): (29) Purnell. J. H.. Ann. il;. Y . Acad. Sci. 72, 592 (1959). ’ (30) Rijnders, G. K. A,, “Gas Chromatography, 1958,” p. 18, D. H. Desty, ed., Academic Press, Kew York, 1958. (31) Scheidegger, A. E., “The Physics of Flow Through Porous Media,” p. 137, Macmillan, Yew York, 1957. RECEIVEDfor review January 18, 1962. Accepted April 23, 1962. Work supported by the U. S.Atomic Energy Commission under Contract AT-(11-1)-748. ’
~
A Study of the Performance of Packed Gas Chromatog r a phy Columns S. DAL NOGARE and JEN CHlU Plastics Deparfrnent, E . 1. du Pont de Nemours and Co., Wilrningfon, Del. The van Deemter-Jones plate height equation was used to evaluate the performance of small packed columns. Three well defined limiting efficiencies a t optimum carrier gas velocity can b e derived for specific values of the partition ratio, k . The plate height i s shown to b e proportional to the support particle diameter. The existence of the postulated gas phase mass transfer and velocity distribution terms i s established, and an estimate of the gas phase correlation term and gas diffusion distance in terms of particle diameter i s made. The relation between fl (the ratio of free gas space to liquid phase volume in the packing) and resolution is derived. A criterion i s established for p consistent with best resolution and efficiency.
I
is generally accepted that the efficiency of chromatographic columns expressed as H.E.T.P. or number of theoretical plates is a good measure of column performance r i t h respect to T
890
ANALYTICAL CHEMISTRY
a particular set of operating parameters. Efficiency is derived from dimensions taken from a single chromatographic peak, TI hereas resolution, or separation, involves two peaks. Consequently, the parameters of retention and relative retention, as n-ell as the manner in v hich these are affected by temperature, liquid phase loading, support particle size, and carrier gas velocity, must be considered in applying gas-liquid chromatography to difficult problems. I n this study, the efficiency of small diameter packed columns was evaluated as a function of particle diameter and the column characteristic, p , related to liquid phase loading, for a series of nparaffins. A linear relationship was observed between efficiency and particle diameter and limiting ratios ryere established. The significance of these results and the implications with regard to resolution are discussed. THEORETICAL
Jones ( I S ) has recently reported an expanded H.E.T.P. rate equation for
packed columns n-hich contains, in addition to the familiar van Deemter terms, several terms describing peak spreading in the gas phase. This equation is formally related to Golay’s capillary column treatment ( I O ) and may be considered an equivalent expression applied to the more complex geometry of packed columns I n this Jyork m-e will base our discussion of experimental results on this equation. If care is taken to eliminate experimental contributions to the d term, Jones’s equation is H = B/u
+ Ciu + (Cl
+ cz + C3)u
(1)
where B and C1 are the van Deemter molecular diffusion and liquid phase mass transfer terms. The C1 term represents resistance to mass transfer in the gas phase, C, is the velocity distribution term, and C3is a correlation term accounting for interaction between C1 and CI. Because the correlation term is extremely difficult to evaluate, i t will not be considered in this discussion. This introduces the reservation
that a significant C3 term will accumulate i n the C1 term, as noted later. Differentiation of Equation 1 gives the optimum velocity Uopt
=
[B/(Cl
+ + Cz)I”*
SAMPLE PORT ,?EATER
F. I. D. I
(2)
c 1
from which the minimum theoretical plate height is obtained H m , n = 2[B(C1
+ C: + C Z ) ~ “ ~(3)
COLUMN
On substituting into Equation 3, the correct functions for the various terms as given by Jones I
I
OVEN
Figure 1 .
I
Gas chromatography ap-
from about 100 t o 1000 for the usual capillary columns. Since the solutesolvent-temperature parameters, K and CY, are independent of p, more theoretical plates will always be required for the same separation from a large p column under otherwise identical conditions (18, 19). The experimental part of this work was concerned mith the effect of varying p on limiting efficiencies, the variation of p with liquid phase loading, and t h e dependence of efficiency on support particle size. A discussion of the results in terms of Equations 10 and 11 suggests the best practical conditions for resolutions.
paratus where y is a tortuosity factor; k is the partition ratio; cI and cz are numerical coefficients for the corresponding terms; d l , do, and d, are the liquid film, gas film. and particle thickness, respectively; and D,and D Lare the gas phase (at p o ) and liquid phase diffusivities, respectively. Equation 4 s h o w t h a t the C L term n 4 l be zero in two cases when the m, partition ratios are k = 0 and k and that the C, term is zero only when k = 0, i.e.,
-
HL,,( k Wk,n ( k ‘-f
= 0) = 2 ( 2 - / ~ 2 ) ” ’ d p
m)
=
(5)
+
~ [ ~ ? ( c I ~z z ~) l ” ~ d p(6)
A proportionality factor, z = d,/d,, is introduced in Equation 6 to permit evaluation of differences in do between supports. The two equations represent limiting values of H,,,, which can be readily obtained experimentally n i t h solutes of very small or very large retention (partition ratios). These two limiting efficiencies are independent of the pressure or temperature of the system providing the optimum gas velocities are observed. It is seen from the strong dependence and D 1t h a t each of Equation 4 on k , D,, solute in a mixture will evhibit a specific H,,,. Solutes with partition ratios intermediate between those required by Equations 5 and 6 will usually show larger H,,,, values reflecting the degree to nhich the column is liquid pha,.e controlled ( C J # 0 ) . This is demonstrated by ren-riting Equation 4 for k = I where the Ci term is maximum Hd:,(k = 1) = 2 [ 2 7 (61 . Do li; . di2
+ c1 . $ + c:>ll”d,
EXPERIMENTAL
ratio of free space to liquid phase volume in the column, V.V/VL. The assumption of liquid film uniformity is implied b u t probably never realized in practice beyond 1 to 2% liquid phase loading on Chromosorb supports ( 1 ) . p is shown belovi to be an important column characteristic in resolution considerations, and Scott’s study of capillary columns (20) includes an evaluation of this parameter ( a in his terminology). Following the suggestion of Golay ( 1 1 ) , the resolution of two closely spaced, equal-area peaks may be expressed as a sigma separation
where x i s the retention value for the two solutes and c is the standard deviation of the peaks; assuming u1 = uz = U . Resolution is 97.77G complete when R = 4 and 99.97, complete when R = 6. On substituting c for the eecond peak from the standard equation for theoretical plate number, N = L / H = 16 ( Z / Y ) ~= ( Z / O ) ~and , the partition ratio and coefficient from the general expressions 5 = x ~ ( l X-) and pk = K
+
R =
dV
(1
- B +FK?)
(9)
Further substitution of the relative retention, a! = K 2 / K I ,gives
and for R = 4, the number of theoretical plates required is
dP2
(7) The C, term in this equation shows the dependence of efficiency on liquid phase loading, d?, and on the diffusivity ratio for the solute-solvent-carrier gas system. Liquid film thickness can be roughly related to column packing parameters by dl = V M / S ~ where ~ , V Mis the free space in the packed column, S is the total surface area of the support, and p is the
(11)
This equation is identical to Purnell’s general equation (18) if the factor in K Z is expanded and the appropriate net retention volumes are inserted. The column characteristic, p, is explicit in the above resolution equations. For conventional packed columns, p ranges from about 3 to 100 and
The apparatus used in this work (Figure 1) consisted of a small volume sample port, column, and flame ionization detector (F.I.D.). An effort was made to reduce extra-column dead volume to a minimum. The elimination of dead volume was essential in obtaining theoretical column performance. The dead space in the flame ionization detector ilas calculated as 0.05 cc., that in the injection channel of the sample port is 0.02 cc. These volumes represent about 2 and 1% of the moving gas volume in the column, respectively. All experiments were carried out with pure C1 and Cs to C9 n-paraffins as solutes, Nujol as the liquid phase, and helium as carrier gas. The column oven was maintained at 60” A I” C. for most experiments. Columns. All columns n-ere 8 feet by 1,’16-inchi.d. copper tubing arranged in coils of 5-inch diameter. This gave n coil-to-column diameter ratio of about 80 and a negligible contribution t o plate height (8). Standard tubing connections n ere used to attacli columns t o the sample port and F.I.D. Columns were packed in straight lengths n i t h slov addition of the packing and continuous tapping. A length of 3,’8-inch tubing n-as placed around the column to serve as n guide and to minimize flexing during this operation. The columns were considered filled n hen n o further settling of the packing was observed after 5 minutes’ tapping. The amount of packing \vas determined by difference weighing. Column ends were capped flush with 200-mesh copper screen (RCA electron microscope grids) to eliminate the dead volume introduced by glass woo1 plugs. Along with the use of small diameter columns and narrow mesh size of solid support, this should reduce the A-term contribution to plate height t o a minimuni ( 1 5 ) . Column Packing. Carefully sievesized fractions of Chromosorb-R (JohnsR’lanville) with a specific surface of 4 sq. meters per gram 13-ere used as solid supports. To eliminate possible adsorption effects, the material n as silanized with Siliclad (Clay-Adams, N. Y.) which was shown in the authors’ laboratory t o reduce substantially tailing of polar solutes. Silanizing reduced the specific surface to about 2 sq. meters VOL. 34, NO. 8, JULY 1962
891
J
30r
0.4
I
I t
0.5 -
-
RECORD E R S 0 BROWN
MOSELEY SANBORN
0
N
A
0.3-
0.2lot
E 0.
I=
0.1
IO I
0.2
I
I
0.4
I
0.6
I
0.8
I
1.0
Figure 2. size A,
0.21
H vs. sample
4
6,
Flame ionization detector
/ ! &
pZEROI
I
I
I
0.08 0.12 0.16 SAMPLE S I Z E , p l
per gram and the liquid-holding capacity of the support to about 20y0 Nujol. The absence of detectable adsorption of the C5 to CS n-paraffins was established by plots of k us. per cent liquid phase (1 to 16y0) which, in all cases, linearly extrapolated to the origin. Packings were prepared by the volumetric addition of a standard Nujolhexane solution to a weighed amount of silanized Chromosorb-R in excess methylene chloride. The solvent was removed by spontaneous evaporation with gentle agitation to apparent dryness. Final drying was carried out a t 100" C. in a vacuum oven. All transfers were quantitative and the weight of the packing was checked to obtain the exact composition. Before filling columns, the preparations were resieved t o eliminate fines. A glass bead column was prepared with 80- to 100-mesh silvered beads (Potters Bros., Carlstadt, IT. J.) in the same manner. Microscopic examination of the wetted beads showed Nujol dispersed in patches on the surface; and at liquid phase loadings of >0.03%, liquid accumulation a t contact points was visible. Sample Port. The small sample port shown in Figure 1 was a brass block 11/4X 1 X 3/g inches with inch channels. Velocity of the carrier gas in the channels was approximately equal to that of moving gas a t the packed column inlet. Liquid samples of 0.1 to 1 pl. and vapor samples of 1 t o 10 p1. were injected with Hamilton syringes of 1- and 10-pl. capacity. Care was taken to expel the sample near the column inlet, point A in Figure 1, to minimize transport time and mixing with the carrier gas. A large sample port with an estimated volume of 0.3 cc. with a Gow-Mac micro thermal conductivity detector was initially used in this work. Column
892
ANALYTICAL CHEMISTRY
Figure
3.
30 t R , sac
Fidelity
of
40
50
recorders
Thermal conductivity detec-
tor
0.04
20
4
I
0.20
efficiency determined with this apparatus showed an optimum sample size which decreased with increasing molecular weight (retention) as shown in Figure 2,A. The large sample port with the F.I.D. gave the results shown in Figure 2,B, in i+-hich a smaller optimum sample size was observed (note sample size scale change). A combination of the small sample port and F.I.D. gave efficiencies shown for zero sample size. The latter corresponds to 1 to 2 pg. of each solute and was obtained by injecting 1 to 5 pl. of vapor sample obtained by complete vaporization of the n-paraffin mixture in a heated vacuum chamber. These experiments suggest that an optimum sample size as observed by several workers (8, 3) is an artifact arising from an extra-column dead volume which is significant relative to the moving gas volume in the column. The combination of small sample port, F.I.D., and zero sample size gave the highest efficiency observed in this work and was used in obtaining all subsequent data. Detector. A conventional F.I.D. was constructed with a 1-cm. length of 18-gage hypodermic needle attached to a Teflon TFE-resin plug as the jet. The dead volume between the jet tip and column was 0.05 cc. Two identical 4-mm. platinum wire loops served as electrodes. The cathode was placed in the plane of the jet tip and the anode superposed about 1 cm. above the tip. Elimination of direct contact between the jet and cathode reduced the noise level in this detector. A polarizing voltage of 600 volts d.c. was applied t o the electrodes. The high impedance electrode signal was converted through an E and H electrometer amplifier Model 201C (E and H Research Labs., Oakland, Calif.) and applied to one of the recorders discussed below. A sen-
sitivity of s = 35 pa. per mg. per second and a linear range extending to a t least 200 pg. was obtained for n-hexane. The noise band, R,, rarely exceeded 5 X 10-7 pa. indicating a limit of detection for n-Ce of Qo = 2R,/s = 3 X 10-8 mg. per second. These values are in good agreement with the F.I.D. data reported by Condon, Scholly, and Averill ( 7 ) . Three different recorders mere used in this work: a Sanborn Model 150 with 5-msec. response, a Moseley Model 8Od with 0.25-second response, and a Brown 1-mv. recorder with 1-second response. The fidelity with which these instruments followed experimental detector signals mas determined by plotting retention timepeak width ratio (2 u ) us. retention time as shown in Figure 3. A comparison with the Sanborn response (assumed correct) shows the Lloseley correctly followed the detector output for retention times greater than 11 seconds, while the Brown recorder showed fidelity for peaks of retention time greater than 30 seconds. A11 three recorders were equipped with variable chart speeds which mere adjusted to increase peak width and improve the accuracy of peak measurements. The Brown recorder was used except in experiments where its response limitation required the smaller response time of the Moseley or Sanborn recorders.
Apparatus Evaluation. I n the absence of adsorption and sample introduction effects, extra-column volumes, and detector time constant limitations, chromatographic peaks theoretically approach a symmetrical Gaussian distribution for the large number of theoretical plates usually found in gas chromatography columns. The asymmetry of experimental peaks, therefore, is a good measure of the degree to which apparatus limits the realization of good column performance. il simple measure of asymmetry was adopted in which the back and front half-widths a t the base line, b and f,are defined by the tangents t o the inflection points and a perpendicular line drawn through the peak maximum. The difference, I b - f = A W , and asym-
I
Table I. Peak Asymmetry Measurements" tR,
0
10
20
40
30
As Solute Sec. k ( - ) 1.01 c1 20 0 28 0.23 ( - ) 1.03 n-Cs 40 1.01 1.00 n-C7 n-Cs 72 2.69 ( + ) l . O l n-Cb 161 11.1 ( - ) 1.05 a Zero sample, 60" C. column perature, 8 inch/min. chart speed.
50
SECONDS
Figure 4.
Gas chromatograms of n-paraffins
+
+
nietry is given by As = ( b f ) / ( b f - A W ) with (+) to indicate tailing and (-1 to indicate leading. Values of As > 1 indicate peak distortion due to apparatus limitations and/or nonideal solution behavior. Since H.E.T.P. is proportional to the square of the peak width, As2 is the factor by which the theoretical plate height is exceeded in a particular apparatus. The asymmetry contribution of any chromatograph is most apparent in fast peaks. Consequently, the above apparatus was tested with a fast column: 0.05% Sujol on silvered glass beads. The r t w l t s are presented in Table I. These riisults show that asymmetry contributions from this apparatus were negligible, even for methane whose retention time corresponds to the passage time of the carrier gas. The negative asymmetry for n-C9 was also observed in other experiments for n-Cla and preslimably arises from nonideal solution behavior often observed with solutes having large partition coefficients on lean columns. All efficiency data presented in this report m-ere obtained from peaks with As2 < 1.10, representing less than 10% divergence from theory. The chromatogram in Figure 4 is typical of the performance obtained with this apparatus. Column Characteristics. Particle size, packing uniformity, and pressure drop are readily determined by measurement of the gas flow characteristics of the column. Four columns packed only with solid supports of various sieve size were prepared and their porosity and permeability calculated by the procedure of Bohemen and Purnell ( 5 ) . The values for interp:trticle porosity, E, permeability, Bo, average particle diameter (from mesh size range), and the calculated effective particle diameter are given in Table 11. The effective particle diameter corresponds to that of spherical particles offering the same resistance to gas flow. The porosity is uniform for all columns in close agreement n-ith the theoretical figure of 0.42 for randorn close packing of spheres with a small diameter range ( 4 ) . Electron microscope examination of thin sections of Chromosorb-R showed that interconnected large voids are randomly distributed in this material. The increased bulk and packing densities for the small particle supports suggest that communition occurs by preferential fracture through these struc-
tures. The ratios of average to effective particle diameter show that the support particles offer about 2070 greater resistance to flow than spheres of the same average diameter. I n the Kozeny-Carman model ( 6 ) , the permeability to gas flow is proportional to the square of the effective particle diameter. This relationship is seen to hold well from the ratios presented in the last column of Table 11. I n general, the data in Table I1 shorn the
5.
p
vs.
per
cent
liquid
degree of uniformity achieved in the preparation of packed columns for this work. RESULTS AND DISCUSSION
The different columns prepared for this work are identified by mesh size range and p. The latter was calculated from p = V,/VL, where V M is the retention volume for a n inert gas (methane) corrected to column temperature and pressure by the compressibility factor of James and Martin (la). Values of V.M for all columns agreed to within 4% of the free space ~~
Table II.
~
Mesh
Size 30/35 40/45
1.02 1.10
tem-
~
Gas Flow Characteristics of Silanized Chromosorb-R Columns"
u. s.
Standard
1.00
value independently calculated from absolute and packing densities of the dry supports after correction for liquid phase volume. V L was obtained from the known weight and density of liquid phase present in the packing. A plot of p vs. per cent liquid phase, Figure 5, is applicable to all Chromosorb-R columns containing liquid phases of density close to Nujol. This curve shows t h a t p decreases very slowly with per cent liquid phase greater than about 20%. Typical H,,, results obtained with 80- to 100-mesh columns of different /3 values are plotted against k in Figure 6. These experimental curves exhibit the limiting efficiencies a t k = 0 and k + predicted by Equations 5 and 6 for all p values and the maximum a t k = 1 expected for columns of low p by Equation 7 . -411 Hmi, values were obtained a t optimum gas velocities experimentally determined for each solute and column from R us. Q plot. For methane R showed a definite minimum a t a Q almost twice as high as that for 12octane. Curves similar to the 80- to 100-mesh results in Figure 6 were obtained for each solid support listed in Table I1 for a t least two values. The temperature independence of the limiting efficiencies is demonstrated by the dashed curved for p = 11 in Figure 6 obtained a t 76' C. The higher temperature resulted in a significant reduction of the maximum a t k = 1 but gave the same limiting efficiencies. These curves confirm the presence of the gas mass transfer term, C,, and the velocity distribution term, CB. The data a t high k values were sufficient for all columns to permit a good extrapolation to the -horizontal asymptote. Estimates of H & made
7. LIQUID P H A S E
Figure phase
As2 1.02 1.06
Density Packing Bulk 0.73 0.432 0.74 0.440
B, e
0,413 0,404
x 107,
Sq. Cm.
21.4 9.54 3.45
dPJ
Av. 545 385
214 0.77 0,413 60/80 0.452 163 1.96 0.80 0,412 80/100 0.474 a Columns! 8 feet by l/ls-inch i.d.; helium, 25' c.
Eff. 434 304 174 132
.4v./eff. 1.20 1.21 1.19 1.19
VOL. 34, NO. 8, JULY 1962
B"/dP; x 10 (eff.)
1.14 1.03 1.14 1.11
893
Table 111.
yo Liquid Phase
Mesh Size 80/100
correlation coefficient, p , was assumed zero in obtaining the above values of c19. A positive correlation term would result in an exaggerated value of c1z2 since this term is added as c3 to the bracketted sum in Equation 6 where c3 = 2 p ~ ( c ~ c ~ Introducing )~'~. c3 and assuming p = 1, Equation 6 may be factored to give
Limiting Plate Heights for Chrornosorb-R Columns
1
10
11 11 (76' C.)
16 5 16 5 10
60/80 40/45 30/35
a
0.034
11 11
0 : 036
7.4 34 7.4 34 13 34 13
5
10
&,
EA,,, Cm.
205 13
Cm. 0.048 0.048 0.049 0.049 0.050 0.069
...
...
:
0 050
0.061
0.070
0.116 0.112 0.159 0.159
o:iio
0.110
Table IV. Limiting Plate Height to Particle Diameter Ratios
H&
2
4%(zcll'* +
~2'12)
dp
from which c1z2 = 0.3 for the effective d, as compared to 1.5 for a zero correlation. The latter value is probably too
80/100 MESH SUPPORT
-
=
%
COLUMN TEMP. ,OC
NUJOL
CHROMOSORB
205
59
I
13 I1
2.0 1.8
30/35
40)45 60/80
2.3
8O/lOO
2.1
Av.2.1
2.6
2.9
2.3 2.9 2.6 2.6
30 3 0 3.0 3.0
II
3.7 3.8
GLASS BEADS
3.7 3.7 3.7
0.05
7 417
60
at,
on this basis and values obtained directly from methane are listed in Table 111. The direct proportionality between limiting plate heights and particle diameter implied by Equations 5 and 6 is demonstrated by the constancy of ratios for the different supports in Table IT.'. Ratios for both average and effective diameters are given. These results represent the best possible performance obtainable Ivith columns similar to those used here. This work also confirms the proportionality between efficiency and cl, postulated by Glueckauf ( 9 ) . Note t h a t these values are independent of p and temperature of the columns. The maximum a t k = 1 is gradually reduced with increasing p, presumably because of decreasing d l , and increasing p , and aoptrequired for optimum performance of high p columns. Pressure would be expected to affect the Cl term by a factor 2 p 0 / ( p z p o ) if uo is used (14, 17'). With increasing p, both pressure drop and were found to increase. Unfortunately, values of H:',n could not be measured accurately because of the experimental difficulty
O.O2t
0;
Ib
io
io
40
do
-
Figure 6.
H,,, vs. k
io
do
for various
810
p's
n/d,
+
Table V. Optimum p and Per Cent Liquid Phase for Chromosorb-R Columns
%
hlesh Size 30/35 40/45 60/80 80/100 5
d, (eff.), Cm. 4.3 X
3.0
1.7
1.3 Taken from Figure 5 .
894
*
Liquid pop$ Phase" 6 25 8 15 15 9 19 8
ANALYTICAL CHEMISTRY
of obtaining solutes with the precise value of k = 1. The curve for the glass bead column in Figure 6, however, shows this maximum point. Figure 7 is a plot of the values of E n i n , curve A, and Rg,,,curve B, against particle diameter. Extrapolation of these data to zero shows that essentially all contributions to plate height from the various gas terms can be related to particle diameter. The pressure independence of these terms is also confirmed. The slopes of these plots correspond to the values for R,,,/d, in Table IT', and the magnitude of the gas term constants in Equations 5 and 6 can be obtained. From estensive experimental data, Kieselbach (16) has determined that the value for the tortuosity, y, is close to 0.6. If this value is introduced into Equation 5, the slope of curve -4 gives a value of c2 = 1.4 for the effective particle diameter and c2 = 0.9 for the average particle diameter. An estimate of the quantity c1z2 also can be made from curve B and Equation 6, giving c1z2 = 1.5 and 1.0 for effective and average particle diameter, respectively. However, Jones's original equation contains a correlation term, C3 in Equation 1, which reflects the interaction between the C1 and Cz terms. The correlation term is Ca = 2p(C1C2)1/2 and becomes zero when k (and C,) is zero. The
o'161 0.14
Figure
7.
dp(EFFECTIVE1, p
HmiU
-
A, for 6, for "',in
vs. d,
(effective)
( k = 0)
(k +
a)
large, corresponding to z = 2.5 and 1.5 if c1 assumes the theoretical values of and 2//3 for gas f l o ~in tubes of cylindrical and rectangular cross section, respectively ( I S ) . For c1z2 = 0.3, the corresponding values for z are 1.1 and 0.45, which are reasonable if gas is considered to flow only around, and not through, the support particles as proposed by Bohemen and Purnell(5). As i t is highly improbable that d, > d,, these values for z indicate that the cor-
relation coefficient has a value of about one for these packings. In terms of resolution, i t is desirable t o employ the most efficient column possible since efficiency enters into resolution as W 2 = ( L / H ) l @ . Increasing the column length by a factor of 4 or decreasing H by a factor of 1/4 is required to double resolution. Also, according to Equation 9, the smallest possible p consistent with efficiency leads to the best resolution in any case. An idea of the effect of p on resolution can be gotten from Figure 8 shob-ing the number of theoretical plates required for a 4 u scyaration ( R == 4) for various partition Coefficients and levels of p assuming A K = 10. These curves are dwivcd from Equstion 9 o nhich is rewrittm t o c.rcymnd t o rquation 11 as
Such curl-es Thaw the necessity of employing small p packings if Y (or column length) is to be kept to a practically attainable value in any separation situation. Packed columns have a practical pressure-drop limitation to column length but present the advantage of low p. Capillary columns usually have longer length and offer the advantage of large N . This distinction has been n-ell emphasized by Purnell (18)
I
From the dependence of minimum plate height on k and p, as in Figure 6l i t is evident t h a t a suitable column would have a p characteristic that is the smallest possible consistent with the least variation of H,,, with k . This efficiency-resolution criterion is realized when HCln = Hg,ln; Le., from Equations 6 and 7 in iyhich the correlation term ( p = 1) and the pressure correction factor have been introduced,
41
+
c ~ ” * z ( ~ c I ” * z 4 ~ 2 ~ ” )(13)
This equation may be simplified by introducing the values c1 = 2 / 3 1 c2 = 1.4, x = 0.5, D,’Di IO6> and d l = a v . ~ / S p ,n.here a is a proportionality constant b e h e e n the ideally uniform distribution of liquid phase on the support surface and the actual surface coverage. - i n approximation for a is obtained from Equation 13 by inserting the value of V-W/S which is close to lop4 for all supports studied in this work. p = 20 which by extrapolation from the data in Figure 6 meets the criterion HZ:n = H$in for the 80- to 100-mesh packing, and the corresponding particle diameter. The result is a = ‘v 6, which on substitution into Equation 13 and rearrangement leads to
1
’
I
I
I
I
I
ance t o mass transfer in liquid phase coefficient reflecting resistance to mass tranefer in gas phase coefficient reflecting velocity distribution in gas phase coefficient reflecting the interaction between C, and Ce numerical coefficient in C1 numerical coefficient in Cz tortuosity factor in B diffusivity of sample into gas phase diffusivity of sample into liquid phase liquid film thickness gas film thickness particle diameter of solid support interparticle porosity of solid support front half-width of a peak H.E.T.P. at point along column length avera e H.E.T.P. = L / N H or gt uopt H,,, or for k = 0
J
P = 1000
-1
8 :500
P
:
IO0‘
200
K2
‘k a,,,for k or
Figure 8. Number of theoretical plates required vs. partition coefficients showing effect of p on resolution
Column inlet pressure, p,, is a function of the optimum velocity which, in turn, varies n i t h d,, p, and the particular solute being considered. The pressure factor in brackets, however, varies from 1.7 to 2.5 for p J p o ratios of 2 to 5 , the range required by the optimum relocities obsened in this vcork. Setting p J p o = 3, values of p may be estimated which correspond to the liquid phase loadings meeting the efficiency-resolution criterion. These values are given in Table V. The evperimental &,, us. k curve for 16% liquid phase on 60- to 80-mesh Chromosorb-R shon s a tendency to maximize, but the 575 curve is essentially flat over the range k = 3 to k = 40. Curves for 5 and lOy0liquid phase on the 40- to 45- and 30- to 35mesh supports were flat in this range. Unfortunately, the high loading predicted for the 30- to 35-mesh support vas not tested experimentally. Different carrier gases, liquid phases, and temperatures would be expected to alter the constant in Equation 14, primarily through their influence on D,and D I in Equation 13. NOMENCLATURE
As
velocity-independent constant in van Deemter equation = proportionality constant between ideal and actual distribution of liquid phase on support surface = ratio = K z / K l = asymmetric value = ( b +
B
=
9 a
(Y
B O
b
P CZ
=
f)/(b + f -
Aw)
coefficient reflecting molecular diffusion in gas phase = permeability = back half-width of a peak = ratio of free gas space to liquid phase volume in the column = V M / V L = coefficient reflecting resist-
H,,, H,,, or
ami,, Hmin k
-+
m
for = 1 partition coefficient partition ratio = ( t
~-
l,)/to
column length number of theoretical plates
Po P
S ta
tR
U
ti
uupt,7 i o p l uo
VM VL
W
z
column inlet absolute pressure = column outlet absolute pressure = correlation coefficient for C1 and CZ = total surface area of solid support = elution time of air or methane = elution time of sample component = carrier gas velocity at point along column length = average carrier gas velocity = L/t, = optimum u or 11 for minimum H = u at column outlet = volume of free space in the column = volume of liquid phase in the column = peak width a t 0.368 (peak height) = proportionality factor = =
Pi
do/&
LITERATURE CITED
(1) Baker, W.J., Lee, E. H., Wall, R. F., “Gas Chromatography,” p. 21, H. J. Xobels et al., eds., Academic Press, New York. 1961. (2) Bethea, ’R,hl., Smutz, M., -4NAL. CHEM.31, 1211 (1959). (3) Bethea, R. M., St7heelock, T. D., “Gas Chromatography,” p. 1, H. J. Noebels et a!., eds., Academic Press, New York, 1961. (4)Bohemen, J., Purnell, J. H., “Gas Chromatography, p. 6, D. H. Desty, ed., Academic Press, New York, 1958. (5) . . Bohemen, J., Purnell. J. H., J. Chem. Soc. 1961, 360. (6) Carman, P. C., “The Flow of Gases Through Porous Media,” p. 8, Butterworths, London, 1956. (7) Condon, R. D., Scholly, P. R. Averill, W., “Gas Chromatography,” VOL 34, NO. 8, JULY 1962
895
p. 30, R. P. W.Scott, ed., Butterworths, 1960. (8) Giddings, J . C., J . Chromatog. 3, 520 (1960). (9) Glueckauf, E., Analyst 77, 931 (1952). (10) Golay, M. J. E., “Gas Chromatography,” p. 36, D. H. Desty, ed., ileademic Press, Sew Tork, 1958. (11) Golay, M. J. E.. “Gas Chromatography,” p. 315, V. J. Coates et al., eds., Academic Press, Sew York, 1958.
(12) James, .4. T., Martin, a. J. P., Analyst 77, 915 (1952). (13) Jones, W. L., .;ira~.CHEM. 33, 829 (1961). (14) Kieaelbach, R.,Zbid.. 33, 23 (1961). (15) Ibid., p. 806. (16) Kieselbach, R., private communication. (17) Litt,lmood, A. B., “Gas Chromatography, p. 22, D. H. Desty, ed., Academic Press, Sew York, 1958.
(18) Purnell, J. H., J . Chem. SOC.1960, 1268. (19) Safranski, L. W., Dal Nogare. S.. Chem. Eng. Xews 39, 102 (1961). 120) Scott, R. P. W., Hazeldean, G. S. F., “Gas Chromatography,” p. 144, R. P. W. Scott, ed.. Butteraorthe. London, 1960. RECEIVED for review February 19, 1962. Accepted -4pril 24, 1962.
Determination of Hydrocarbon Types in Gasoline by Gas Chromatography RONALD L. MARTIN Research and Development Department, American Oil Co., Whiting, lnd.
b Gas chromatography provides a new approach to hydrocarbon-type analysis. Two separation steps, combined in a single 30-minute gas chromatographic run, resolve gasolines into aromatics, olefins, and saturates. In the first step, aromatics are separated from saturates plus olefins with a P,fl’-thiodipropionitrile column, and saturates plus olefins are measured as they emerge; the column is then backflushed to remove and measure the aromatics. In the second step, olefins are separated from saturates in the column effluent by reaction with mercuric perchlorate. The saturates pass unaltered through the mercuric perchlorate, are collected in a liquid nitrogen trap, sent back through the column, and measured again. Olefins are determined b y difference between the chart areas for saturates plus olefins and for saturates alone. Analyses of gasolines and naphthas by the new method check well with those by liquid chromatography and mass spectrometry. High accuracy was attained on known synthetics. The new method does not require removal of components with five or less carbon atoms, as do the conventional methods. Elimination of the depentanization step permits direct analysis of full range gasolines.
A
of gasolines for three major hydrocarbon types-aromatics, olefins, and saturates-is often required in petroleum laboratories. Such analyses are used to determine product quality and to guide refining processes. Three methods are commonly used: the fluorescent indicator adsorption (FIA) method (2, 6 ) , mass spectrometry (3, 4, IO), and chemical methods, typified by ASThI method D-875 ( 1 ) . I n the FIA method, the sample is chromatographed into the three hydroKALYSIS
896
ANALYTICAL CHEMISTRY
FLOW P d T T E R N I
Figure 1.
1
FLOW P I T T E R N 2
1
Analysis scheme
carbon types on silica gel; two fluorescent dyes make the three hydrocarbon zones distinguishable under ultraviolet light. This method is simple to perform and has been applied directly to samples boiling as high as 600’ F. Accuracy usually is satisfactory, but rests on the assumption that the unavoidable overlap a t the color boundaries is equal for each type. Mass spectrometric methods are of two kinds. K i t h the older method (a, 4,two runs and a treatment n i t h acid for removal of olefins are required. I n a recent method ( I O ) , parent-ion and fragment-ion spectra are combined to give a faster analysis. Mass spectrornetry can give more information than the other methods; saturates and olefins can be divided into subgroups, and aromatics and olefins determined by carbon number. Disadvantages are espensive equipment and tedious calibrations. Bccuracy usually is good but depends heavily on calibrations with the type of sample to be analyzed. In chemical method D-875 (I), aromatics and olefins are determined together by reaction with sulfuric acid, and olefins are determined separately by reaction with bromine. The method is less popular than the others because it is long and the olefin determination is often in error.
A11 three methods suffer from the same disadvantage in the analysis of gasolines; for reliable results, components through four or five carbon atoms must be removed before analysis. With the FIA method, the sample should be depentanized and the lower boiling fraction analyzed separately for saturates and olefins. K i t h the mass spectrometric methods and the chemical method, debutanization is needed. =1 gas chromatographic method that would not be subject to the disadvantages of the other methods has been developed. The low boiling components need not he removed, and the analysis is fast and easily performed. PRINCIPLE OF METHOD
Gasolines are separated into aromatics, olefins, and saturates using two separate steps combined in a single run. Aromatics are separated from saturates and olefins with a &?’-thiodipropjonitrjle column; olefins are then separated from saturates by reaction 17ith mercuric perchlorate (5, 8, 1 4 ) . iichieving both separations in a single run requires a liquid nitrogen trap for storage and a system for changing the direction of carrier gas flow. The scheme is illustrated in Figure 1. This figure shows the apparatus components and the order in which they are arranged in each of two flow patterns. The sample is added with the apparatus in flow pattern 1. A11 saturates and olefins are eluted from the column together in one large unsymmetrical peak before the Ion-est boiling aromatic, benzene. The saturates and olefins are detected as they emerge from the column. After passing through the detector, the olefins are caught by the mercuric-perchlorate absorber; the saturateq pass through the absorber and are collected in the liquid nitrogen trap.
