Figure 5. Chromatogram of kerosine, 1 20-foot, 0.1 0-inch i.d., 0.1 25-inch o.d., SF 5-microliter sample, thermistor detector
off the tops of the first two peaks indicated that the control-grid voltage had exceeded the linear response rangebut direct vapor analyses possibilities are illustrated. Figure 5 shows a chromatogram of kerosine with a 120-foot low-pressure drop packed column, programmed temperature. The temperature of the column and time of elution of terpenes and terpenoids from this 120-foot lowpressure drop packed column is comparable with a 75-footJ 0.01-inch i.d. capillary column. HETP curves were obtained with the low-pressure-drop packed column, and the optimum column efficiency was established a t approximately 5 cm. per second. S o appreciable loss in efficiency was observed with several tenths of milligram loads. Data are sum-
marized and compared in Table 11. Because of the efficiency and capacity of the low-pressure drop packed column, highly efficient columns can now be built to prepare milligram quantities of pure material heretofore very difficult to obtain. ACKNOWLEDGMENT
The authors thank H. S. McDonald for his suggestions, D. C. Patterson for his help, and R. S. Souza for assistance in construction and assembly of the equipment. LITERATURE CITED
(1) Ettre, L. S., Cieplinski, E. W., Averill, W., J . Gas Chromatog. 1, 7 (1963). (2) Halasz, I., Horvath, C., ANAL.CHEM. 35, 499 (1963).
96-50 low-pressure drop packed column,
(3) Jentzach, D., Hoverman, IT., J . Chromatog. 11, 440 (1963). (4) McEwen, D. J., ANAL. CHEM.35, 1636 (1963). ( 5 ) Quiram, E. R., Ibid., p. 593. (6) Schwartz, R. D., Brasaeaux, D. J., Shoemake, G. R., J . Gas Chromatog. 1, 32 (1963). ( 7 ) Sternberg, J. C., Poulson, R. E., ANAL. CHEM.36, 58 (1964). (8) Teranishi, R., Buttery, R. G., McFadden, W.H., Mon. T. R.,Wasaerman, J.,Ibid., p. 1509. (9) Zlatkis, A., Kaufman. H. R.. S u t u r e 184, 2010 (1959). RECEIVEDfor review March 26, 1964. Accepted April 29, 1964. 2nd International Symposium on advances in Gas Chromatography, University of Houston, Houston, Texas, March 23-26, 1964. Reference t o a company or product name does not imply approval or recommendation of the product by the L-. S. Department of Agriculture to the exclusion of others that may be suitable.
Partic le-to-Co Iumn Diameter Ratio Effect on Band Spreading J. C. STERNBERG and R. E. POULSON' Beckman Instruments, lnc., Fullerton, Calif.
b Packed columns conventionally in use employ particlesfrom '/8 to ' / b o of the column diameter. Recent studies have suggested a departure from the generally accepted proportionality between observed plate height and particle diameter in columns packed with particles larger than '/8 the column diameter; plate heights smaller than a particle diameter have even been reported in one instance. A systematic study of the effect of column-toparticle diameter ratio on the spreading of unretained component peaks has been carried out and has revealed some heretofore unrecognized relationships. Special experimental methods employed are described and their 1492
ANALYTICAL CHEMISTRY
validity demonstrated. The possibility of obtaining plate heights for unretained components smaller than the particle diameter has been verified, and the performance expressed in terms of the product of plates per unit pressure drop and plates per unit time has been found to b e optimal for particles l/* to '/3 of the column diameter. The performance of packed columns over the entire range of particle-to-column diameter ratios i s compared with open tubular columns. New data are also presented on the effects of pressure drop and of very high linear velocities on column performance, and a suggested effect of incipient turbulence i s indicated.
T
in packed columns have been obtained using very small packing particles, and it is generally accepted t'hat a direct proportionality exists between plate height and particle diameter (4,8). For retained components the plate height is about 3 to 5 times the particle diameter, while for unretained components the plate height is 2 to 3 times the particle diameter (3) ; in every case plate heights greater than the particle diameter are expected. -1recent' paper by Giddings and Robison ( I I ) , however, reported HE BEST PLATE VALUES
1 Present address, C . S.Department of Interior, Bureau of Mines, Petroleum Research Center, Laramie, Wyo.
a case in which an experimentally observed plate height was less than one iiarticle diamet'er for a column packed with fairly large diameter beads; this result has been considered further in a subsequent paper by Giddings (10). 'The recent work of Halasz and Heine (16) suggests further that performance is surprisingly good when particles having diameters to of the column diameter are used; normal packed columns employ particles having diameters 1l or less of the column diameter. Thiy study of unretained component spreading in columns of various part'icleto-column diameter ratio was undertaken in a n attempt to gain a better understanding of these apparent anomalies in terms of the fundamental gas phase processes occurring. Several interesting conclusions and suggestions for further work have arisen from this study. Work with unretained components presents experimental difficulties which have been cited by earlier investigators (17, 18, 20). Accordingly, it was first necessary to devise a n experimental system capable of rapid response and free of extraneous peak broadening influences. As a test of the performance of this system, the behavior of an unretained peak in a small open tube was studied. These results provided experiment'al confirmation of the ~ireshureeffect, as treated by Giddings (!i>13) and re-examined by Sternberg and Poulson (22). EXPERIMENTAL
Ai general scheme of the apparatus used in this study is shown in Figure 1. Samples were injected rapidly and reproducibly by means of a pneumat,ically actuated Teflon slider valve, V , (Beckman LG-6 process gas chromatograph valve, introducing 5-pl. gas samples) which triggered a micro-switch, N S to indicate injection time. The valve \vas close-coupled to the column, e, bz- using hypodermic needle stock through fittings containing silicone rubber inserts; needle stock coupling also permitted pressure measurement a t the head, p,, and tail, P L , of the column. Ilownstreani pressure was adjustable by means of a low dead volume variable restrictor, R , consisting of a nylon capillary tube mounted through a hole in a rnetal block; the tube could be compressed as desired by a ball bearing pushed by a screw entering the block a t a right angle to the length of the tube. The column was close-coupled to a neiv type of very low dead volume hydrogen flame burner, H F [Heckman GC-4 burner ( 2 1 ) ] . The response fidelity of this burner is illustrated in Figure 2 , where the effect on peak halfwidth of additional hydrogen to sweep out the burner base is compared for the GC-4 burner and a standard burner with a carrier flow of only 10 cc. per minute and with sample introduced ~
ELECTROMETER
RECORDER
+ I-
-
c '
SAMPLE
VENT
iy
(SLIDER SHOWN
N
DOWN POSITION1
Figure 1 .
Schematic diagram of apparatus used
through a 0.027-inch i d . open tube, 80 cm. long. Output signals were read on a Sanborn fast writing galvanometric recorder with preamplifier (Model 151-1800), with the signal developed across a 22megohm load resistor in series with the flame electrodes. A Beckman GC-4 high-speed electrometer (21) was used when it became available during the latter stages of this study. Seither load resistor nor preamplifier was required with the electrometer, and a broader dynamic range was available; in some of the runs the electrometer output was fed into the ax.-d.c. coupler (Type 9806 A) of a Beckman Offner (Model RS) Dynograph recorder. Both systems were found to be capable of handling peaks of 10-msecond half-width without distortion.
Pressures were read both directly and differentially; depending upon the pressure range measured, a differential water or mercury manometer or an Ashcroft Duragauge pressure gauge was used. The system was leak-checked under pressure to ensure no leakage in excess of 0.3 ml. per minute. RESULTS
Performance Check-Open Tubular Columri. The performance of the system was evaluated p w g open tubular columns, for M hich plate height could be calculated directl) from theory (f4. 20). A 190-foot long 0.02-inch i d . stainleqs steel tube (Superior Tube, Korristown, Pa.) \+ai used
Q 0.IJ
010
'L G C - 4
BURNER
"t (SEC j
e
a05
5yl MElHANE (VNREIb"bl RETENTION TIME I 8 0 SEC
0 a 3 B o w . 0027
CIRR1ER
I D ORN
HELIUM, 01s C C / S C
< n m o m
Figure 2.
3
2
I
FLOW TO WRNER ICC./SEC
4
>
Performance of the low d e a d volume burner used VOL. 36, NO. 8, JULY 1964
1493
~~
in this study, and methane samples were introduced. The column was connected to t,he inlet and detector with butt seals to 0.010-inch i d . nylon capillaries. Extra-column effects were shown to be negligible using a short correction column ( I I ) , connect'ed in the same manner as the actual column, and with identical pressure and flow in the inlet and outlet port'ions of the system achieved by adjusting the low dead volume variable restrictor described earlier. Performance data for the open tubular column are shown in Table I. The last row in the table contains the minimum plate height from the Golay theory of capillary column performance ( I 4 ) , which gives, for an unretained component,
with Do. the gaseous diffusion coefficient and uua the linear velocity of an unretained component, both a t atmospheric pressure. r is the radius of the tube. I t follows from Equation 1 that
H
~ = r~ / d~3 ,
(2)
and
The observed minimum plate height, however, was found to depend on inletto-outlet pressure ratio, P, in agreement with the expressions derived by Giddings ( I S ) and Sternberg (28). These lead to the modification of Equations 1 and 2 to give
and
where denotes the apparent plate height, obtained from the emergent peak width and retention time, and
Conditions at optimum p o , p.s.1.a. p ~ p.8.i.a. ,
P = PO/PL F a , (corrected), cc./sec. to,,, sec. (~d cm./sec. ,,~, wIJ2,sec. tlwm O m i , , , cm. 9 (P4 - 1) ( P- 1) fl = g (P3 - 1)s cm.
ZImhn. from theory, & , cm.
1494
ANALYTICAL CHEMISTRY
Variation of H with uu.-
0.020-inch i.d. column, D,, Only after making this correction are the data brought into satisfactory agreement, as shown by the excellent agreefrom ment between P/fl and theory. The calculated values of (uyo)opl differ by a relatively larger amount, although theory predicts that they should be equal. However, the minima in the H us. u,. curves are so broad that there is considerable latitude in the selection of the time or velocity which truly represents the minimum, although the value of I?,,,,, is well-defined by the data. Because of this latitude, values of the diffusion coefficient obtained in this way are not highly precise. The difficulty is illustrated by the calcuiated data in Table 11, which shows H v s . u,, for a 0.020-inch i.d. column if em D,, = 0.7 sec. Packed Column Studies. Since the system was proved capable of yielding true band widths free from extra column effects, i t became feasible to proceed with the originally planned study of packed columns and the relationship of particle size, shape, and tube diameter to column efficiency and pressure drop. Measurements were made on column packed with glass beads and with Chromosorb-P, covering a range of particle-to-column ratios from 1: 20 to about 1 : 1.5. Column lengths and diameters and particle diameters were measured for each column. The glass beads (Minnesota Mining and Manufacturing Co.) were selected for roundness by rolling them down a slightly inclined glass plate, then were degreased with perchloroethylene and dried. Chromosorb-P (Johns-Manville Corp.) was used in preference to the white ma-
Performance Data on Open-Tubular Column, 0.020-inch i.d., 190 foot long, T = 2 2 " C., He carrier, 5 PI., CH4 sample
Table l.
(f?m,D/fl),
Table II.
~
.Without restrictor 42.8 18.3 2.34 0.433 60.0 211.4 0.230 261 0.0153 1.06
With restrictor 49.9 39.1 1.28 0.347 102.0 173.0 0.375 272 0.0141 1 .oo
0.0144
0.0141 0.01466
= 0.7 cm 2 sec.
uuO,cm./sec.
8,cm.
140
0.01538 0.01469 0.01466 0.01468 0.01481 0,01520
180
191 200 220 250
terial because of its greater mechanical strength. Packing materials were sieved before using, and particle sizes were taken from the dimension of the average sieve size. Glass beads were also measured by micrometer. Data were obtained on retention time, peak width, and inlet and outlet pressures for passage of an unretained component (methane) through each column. Xlso for each column, data on volume flow rate as a function of inlet and outlet pressures were obtained. From these data it was possible to determine minimum plate height and optimum linear velocity, specific permeability, inter- and intra-particle porosity, and the .4, B , and C, coefficients of the van Deemter equation for plkte height, expressed in the form
Gif,= '4
+B + UU,
CgU,.
(7)
The symbols are defined as for Equation 1, with A , B , and C,,, having their usual meanings as eddy diffusion, longitudinal diffusion, and gas phase mass transfer coefficients, respectively. The data obtained on the glass bead and Chromosorb-P packed columns are presented in Table 111 and Figures 3 thr-ugh 9. Complete data are presented in t,he Appendix Various aspects of the data will be treated in the discussion which follows. Discussion of Results. Perhaps the most immediately striking feature of the results is the obtaining, in several cases, of plate heights smaller than the particle diameter (Figure 3). The optimum plate height attainable appears to increase with increasing particle diameter, as had been generally accepted previously ( 3 ) . but yith the proportionality constant, a = H,>,,,jd,, dependent upon the ratio, d,,/dc, of particle to tube diameter and upon the intra-particle porosity, as well as u1)on the partition ratio, k ; only the k dependence has been noted in previous1~published work ( 3 ) . Plate heights smaller than a particle diameter have been reported previously hy Gidtlings (11) in the earlier cited espcriinent~ using large glass bends. More rerently, the results presented by Heinc 11'6) also show plate heights smaller than the
CDMdOCD
????? 31110
particle diameter in the drawn-glass packed capillary columns of the type invented by Halasz and Heine ( l j ) , although attention was not drawn to the fact by these authors. Apparently for normal ratios of d,jd, ('18 to '150), for firebrick and other porous packings, the ratio of plate height to particle diameter is reasonably constant and clearly greater than unity. The value of H,n3,,/dp = 2.0 for unretained components as reported by Dal Kogare and Chiu (3) is in essential agreement with the value of 1.9 obtained in this study for normal columns with porous packing materials. For glass beads, changes in HminJdP are discernible pver a wider range of d,;d, ratio. H m L n , / disp clearly appreciably smaller for the beads than for porous particles suggesting that the time required for diffusion of components into and out of intra-particle pores definitely contributes to peak spreading. The sharp improvement of I?,in,/dp with increasing particle-to-column diameter ratio verifies the claim of Halasz and Heine (16) and of Knox and RIcLaren (18) that gas phase mass transfer is aided by the forced crossing of flow lines due to the irregular structure of the packing. This point will be considered in more detail in the subsequent discussion of the C, term: The decreasing value of H,.i,./dp with increasing particle size in a fixed diameter column (thus with increasing d J d , ratio), indicates that the price paid in plate height for using larger particles to diminish pressure drop is not as severe under these conditions as would-be expected from the assumption that H m J d p stays constant. Furthermore, as can be seen from the specific permeability data (Table 111) the improvement in permeability (calculated as Eo = qLF,p,/:I,App,, where q is the viscosity, L is the length and A , the area of the column, F a is the volume f l o ~rate, and p a , p,, and Lip are atmospheric pressure, mean column pressures and column pressure drop, respectively) resulting from increased particle size tends to become even greater than the anticipated proportionality to square of particle diameter, because the particles pack with greater void as the part,icle size increase moves into the range where d,,'d, becomes greater than Thus, if an upper limit esists on the practical inlet pressure available, a far greater total number of plates can be obtained for a given column diameter by using a longer column packed with particles of larger diameter; as the plate height increases, honeirer, the analysis time required for the same number of plates also increases. The specific permeability of a packed column is a function of particle diamVOL. 36, NO. 0, JULY 1964
1495
0
0
EFFECTIV?
D +
CHROHMORB
-. -
CHROHOSCW. USING C H R W X I R B , USlNO GLASS BEAOS. USING GLASS B U D S , USING
EFFECTIVE dp SIEVE A m dp EFFECTIVE dp SIEVE rYQ y
-P
P
'\* {,
i
.i
.4
;
6
7
8
9
I O
-__~_ Figure 4. Dependence of porosity upon particle-to-column diameter ratio PARTICLE-TO-CCCL"
1
2 PARTICLE
- TO-
4
5
7
6
COLUMN D I A M E T E R RATIO.
dp /dC
Figure 3. Dependence of plate height upon particle-tocolumn diameter ratio
eter, d,,, and inter-particle porosity, 6 , according to the Kozeny-Carman equation.
where Fa, is the volume flow rate at atmospheric pressure and column temperature, and since
V, = A,L, Sphwical particles of diameter less than l'lo the tribe diameter pack with a porosity of essentially 0.40. Thus the effective particle diameter can be evaluated from the measurements of flow rate and inlet and outlet pressures, from which specific permeability is evaluated, using a column diameter such that e = 0.40. Once the effective particle diameter is known, it can be used to evaluate e from permeability data for columns having other values of d,/d,. The porosity obtained in this way is the dynamic porosity, eo, which does not necessarily correspond to the interparticle fractional void volume or static porosity, e a . The difference can readily be seen by taking an open tubular column and introducing just one particle having a diameter equal to that of the tube; an interparticle fractional void volume (e,) of 0.99 or higher may result, but there will be no flow if the particle completely blocks the tube, leading to a dynamic porosity ( e d ) of zcro. The total static porosity of the colunin, e l = V,,/V, = er;ifm is also obtained from the data. Here V, is the gas phase volume, Vc is the total column volume, and f,,,is the mobile fraction of the gas phase volume (the fraction in inter-particle pores). Sinre the time of transit, t u , of an unretained component is
1496
ANALYTICAL CHEMISTRY
(10)
where A, and L, are the cross-sectional areas and the length of the column, it follows that
_ -- LF,, ~ . pa _ Ed
fM
A,L,
p
(11)
For the glass beads, f . is~ equal to unity, since there is no intra-particle void (non-porous particles). The individual Chroniosorb-P particles, however, are themselves about 76% void, leading to lower values of ft{, given by €8
fM
= e,
+ (1 -
e&
(12)
where 4 is the fractional void volume within a particle. (The value of 0.76 for 4 was obtained by assuming e, = 0.4 for large ratios of d,/d, and calculating fl{ and 4 from the known e,/fv). The static porosity, e,/fv, is therefore higher for porous than nonporous particles. 130th static and dynamic porosity depend upon the particle-to-column diameter ratio, d,/d,, as is shown by Figure 4 and by the data in Table 111. A dynamic porosity of greater than 0.5 appears to be virtually unattainable with spherical particles packed directly into a column such that they support one another, because there is a tendency for the packing to assume a geometry uhich obstructs the flou a t d,,'d, ratios greater than 0.3 or 0.4. A major advantage of the drawn glass capillary technique of Halasz and Heine lies in the fact that in their technique some particles are supported by sticking to
DimETm R m o ,
dp/dc
the walls, and may be spaced from one another, making the porosity higher than attainable by direct self-supporting packing. The greater irregularity of shape and range of particle size with porous particles causes the dynamic porosity to be lower for Chromsorb-P than for glass beads in the range of large d,/d,; this is also apparent from Figure 4, and is due to the way that some of the irregular particles can pack snugly together. The product of the number of plates per unit time and the number of plates per unit pressure drop for an unretained component is a convenient measure of column performance, since one generally seeks the greatest number of plates per unit time, but is practically limited by the inlet pressure which may be used. This performance factor is closely akin to the performance index, P.1; of Golay ( 1 4 ) . I t can readily be qhown
_ . _s 1 '
ti A p
B o / e l ~-___ p,,,, - ~. p(1 f k,)q
(13)
Since p,,.,/p ranges only between 0.75 a t p o l p ~= and 1.0when palp,, = 1, for components of comparable retention ratio, k,, and with a carrier gas of given viscosity, vr the dimensionless ratio Bolel,H 2 is a direct measure of the product of the plates per unit time and the plates per unit pressure drop. This ratio is conveniently compared at the minimum plate height, H,,,for an unretained component to get a single number which is a useful indey of column performance. This number is shown to be a function of particle-tocolumn diameter ratio in Table 111 and Figure 5 . The figure shows hon strikingly this performance factor increases in the range of large particle-to-column diameter ratio. Comparison with Plate Height Theory-The Van Deemter Coefficients. The data obtained on inlet and outlet pressures, retention times, and peak widths, for an unretained component (methane) in the various glass bead and Chromosorb-P packed columns have been employed to
ever, see Knos and 1IcLaren ( ~ g ) ] ; it has been interpreted ( I ) as a correction on the appropriate \relocity to be used, or as a correction factor niodifying the diffusion coefficient ( 5 ) . I3ohenien and Purnell ( I ) have suggested that y is approsimately unity when the carrier gas velority, u,,, c o ~ n puted as the ratio of the volume flonrate to the inter-particle cross-sectional area, is used instead of the velocity. u,,, of an unretained component. The longitudinal diffusion term would then be
MRMAL
RANGE
2 D,, - 2 .f.vL)ga u,,
0
I
2
.3
4
5
6
6
7
and y is seen to be equal to f . l f j which is the fractional inter-particle pore volume. Uohemen and Purnell {)resent data of unretained peak spreading in glass bead and Chromsorb columns which alqiear to support this sugge5tion; however, their proof rests upon a somewhat questionable interpretation of the data presented, with the value of the B coefficient for glass bead columns evaluated from the slope of a small segment of an H us. l / u curve in a region in which the curve apparently deviates from the larger linear portion found a t lower velocities. If the brst overall curve is drawn, it i R found that the results no longer sulqiort the contention of the authors. DeFord, Loyd, and Ayws (.T) ha\.? obtained data on the B coefficient for a wries of columns with vai,\~ingliquid
1.0
9
PARTICLE O - COLUMN RATIO, _ dp/d, _ _ - T_ _ _DIAMETER ~ ~ _ _ ~
Figure 5. Dependence of column performance upon particle-to-column diameter ratio. Upper curve: glass beads; lower curve: chromosorb-P
compute for each column the values of
d ?B , and C, in the modified van Deemter equation, (24) Equation 7 . Computations were performed on the If311 1410 computer, and also furnished statistical information on the standard deviations of each coefficient. I n carrying out the calculations it was found that certain data points taken a t high velocity had to be neglected in fitting the other data to the modified van Deerliter equation-all points a t greater than twice the optimum velocity were discarded. This feature will be discussed a t some length later in the paper. The results of the calculations are presented in Table IV and Figures 6 through 8. The significance of the values found for each of the van Deemter coefficients will now be individually discussed. ~ I U L T I PPATH L E TERM,A . I n each of the columns studied, the d value found is negligible, within experimental error. This is as to be expected for small diameter columns, especially when great care has been taken to eliminate extra-column dead volume effects. Because the .1 term is negligible, the equation can be rewritten as
and f?u../fi is a linear function of u,'... The computer program furnishes Hu,,,/jl and uZun values so that the linear relationship can be verified graphically. Graphs of this relationship for a few of the columns are presented in Figure 6; the fall-off of plate heiqht a t hiqh linear velocity, mentioned above, is particularly evident from these data.
(IS)
The alternative coupling theory approach to be discussed shortly affords another view of the .1 term. LONGITUDISAL DIFFUSIONTERM,B. The contribution of longitudinal diffusion to plate height is 2 y Duo/u,,, and this is probably the most thoroughly understood term in the plate height eapression. The tortuosity factor, y, however, is not readily calculable [how-
1
ut, Figure 6.
L).oob
20.000
(CM4SEC.P
Representative plots of
Hu,,/h
vs. uii02
VOL. 36, NO. 8, JULY 1964
1497
Table IV.
Column number
Particle Column diameter diameter (sieve av.) B = 2yD,, d,, p d,, p cm.2/sec.
25005 25002 25001 12502 12501 06302 08301
4700 4700 4700 1930 1930 99 1 1600
86 210 420 210 420 420 1150
0,8743 1.0161 0.9038 1,0025 1.0809 1.0377 1.0303
25003 25004 12503 12505 12504 80001
4700
210 387 210 210 387 1500
n .8xw
4700 1930 1930 1930 3230
fO B c0 -- -d=- 2 Std. dev. wD,, cm.Z/sec. sec. X lo4 Glass Beads f0.0078 0.674 f O ,0055 2.160 10.0116 5.722 f0.0058 1.105 f0,0070 1.439 f0,0220 1,393 f O . 0211 6.996
Chromosorb 4.438 ~ 0,071 15.74 0,0068 4.819 0.0283 4.536 0,0090 8,056 0.03 69.2
n . on38
0,8693 0.8284 0.8503 0.8882 0.85
loading and found that the c,oefficient tends to decrease with increasing loading. This observation cannot be reconciled with the assumption that f4[ is the controlling factor, since f.11 should increase and tend to increase B with increasing liquid loading. DeE’ord concludes that the effective diffusion coefficient, y D g n , includes both diffusion in the inter-particle volume and diffusion through the particles; increased liquid loading decreases the diffusion through the particles, which would decrease the B term, as observed. DeFord et al. did not compare glass bead with Chromosorb packing particles. The work of Sorern (LO), when recalculated, gives a ratio of B values for bead and Chromosorb columns which is also inconsistent with the suggestion of Bohenirn and I’urnell, in that reasonable values of the f.,f term cannot account for the observed ratio. Since, however, a sizable . I term esists in his results, it is difficult to assign the B value with certainty. The more recent work of Kieselbach (8, 17) a t first appears inconsistent with
van Deemter Constants for Columns Studied
~
fQC,
Std. dev. sec. x i o 4 f O . 067
f0.182 320,449 f0.099 f O . 153 10,224 f1.028
. _
n 240 0.68 0.337 1,579 0.250 2.0
all previous results, and with the present work, in finding essentially identical B values for beads and Chromosorb. However, graphical esaminaJion of the Kieselbach data on an IY7k us. uo2 plot suggests that a small systematic difference may exist between the B values obtained with porous and, nonporous supports, and in a direction consistent with the results of this study, particularly if less weight is given to the highly scattered values obtained a t very low velocity. The values of B and related quantities obtained in this study are compared in Table V with those previously found by other investigators and described above. The value of D,, reported for methane in helium was measured in this study, using an open tube, following the method of Giddings and Seager (12 ) . Our findings (Table IV) indicate an average of about 15% greater B value for glass bead than for Chromosorb columns over the range of particleto-column diameter ratios included in this study. However, closer scrutiny of the present data reveals that in the
‘+,y Figure 7.
1498
Effect of particle diameter on gas phase mass transfer coefficient ANALYTICAL CHEMISTRY
A
2Xd, cm.
Y
W
0 f 0.0018 0 f 0.0032 0 f 0.0064 0 i 0.0027 0 f 0.0044 0 i 0.0056 0 f 0,0099
0.64 0.74 0.66 0.73 0.79 0.76 0.75
0.62 0.34 0.22 0.17 0.056 0.054 0.037
n in
nM
nt x
0.63
0.72
0.60 0.62 0.65 0.62
0.75 0 .i o 0.37 0.21
=
nn2.i
0 zi 0:003a
0 i 0.0050 0 f 0.0153 0 f 0.0030 0
‘/(-inch 0.d. (4700-micron i.d.) columns, particularly with the smaller beads, the value of B obtained for the glass bead columns approaches very closely to that obtained for the Chromosorb columns. Kieselbach used columns of essentially this diameter, with small glass beads (100 to 120 mesh), in the same range as those giving the low B values in the present study. Sorem used relatively coarse beads, which would fall more in the range of the higher B values found here. Hence, apparently there is no clear contradiction in the experimental results on columns without liquid; it is apparently essential to make comparisons only where column and particle diameters are comparable, and the theory must take into account the effects of these parameters. The effect of liquid loading cannot be evaluated on the basis of available data; information on the influence of liquid loading on the value of B for an unretained component under otherwise equivalent conditions is required, and such data are not yet available. In any event, the range of values of the longitudinal diffusion term is very small, so that interest in these questions is largely academic. G a s PHASE MASS TRANSFER TERM, C,. With the van Deemter -4 coefficient shown to be negligible and the B coefficient covering a range of only 15% in these studies, the variations between columns are almost entirely attributable to gas phase mass transfer effects embodied in the C, term. C, itself is shown as a function of glass bead particle diameter for two column diameters in Figure 7 . The nearly quadratic rise characteristic of the larger column is present, if a t all, only for very small particles in the smaller column, with the C, term tending to level off for larger particles in that column. Theoretical treatments ( 7 , I O ) predict in Equation 7 a quadratic
I 02
oe
0 1
0 1
dP ' d c
Figure 8. Effect of particle-to-column gas phase mass transfer.
diameter ratio on
"""
dependcnce of C , uIion the particle diameter. d,
where w is a characteristic of the packing geometry. If omega is assumed constant for various particle-to-column diameter ratios, then this leads to the already cited essential linear relationship between the minimum plate height, H,i, , and d,. Data for the two diameters of column shown in Figure 7 , as well as for other diameter columns, fall on a single smooth curve for glass beads (and a separate curve for Chromosorb-P) when the ratio of C , to d P 2is plott'ed as a function of particle-to-column diameter ratio in Figure 8. The values of the proportionality constant w are strongly dependent upon the particle-to-column diameter ratio: for glass beads, t'his dependence estends well into the range of particle and column diameters normally employed, while for the porous Chromosorb packing the value of w appears nearly constant-as has been generally accepted heretofore-in the normal range of particle-to-column diameter ratio below 0.1, but drops off steeply for higher values of this ratio. For glass beads, with particles relatively
Table V.
Figure
9.
large for the column, w becomes as small as of its value for normal particleto-column diameter ratios. For Chromosorb, the fall in w is about three-fold as larger particles are used relative to the column. The residual w value for large values of d,/d, is sisfold smaller for the beads than for the Chromosorb, although the w values differ by only 50% for very small d J d , ratios. This residual w value for Chromosorb particles is probably associated with the diffusion time into and out of the pores of the particles themselves. The relatively small magnitude of this residual w term compared with the normal w value substantiates Giddings' ( 7 , IO) conclusion that diffusion into and out of the pores of the particles themselves is only a minor contributor to gas phase mass transfer under normal conditions. The values of w in the normal range of d,/dc are in good agreement with the theoretical predictions of Giddings ( 7 ) , but the residual value for porous particles is still tenfold greater than his calculated contribution of intra-particle pores.
E
If lf
R c m 2/sec (using u u o )
Sample Carrier
D,,,ern 2/sec !J
WYC
Performance at High VelocityTurbulence and Coupling Theory. One remaining new conclusion from these studies deals with the high floir departure from the van Deemter equation, as shown by the low values of Hu,,/fl a t high uZQa in Figure 6. The recent paper by Kieselbach (17') also shows lower plate heights a t high velocities than can be accounted for by the normal modified van Deemter equation, and this has been cited by Giddings (8) in support of his coupling theory ( I I ) , in which the multipath and gas phase mass transfer terms effectively combine in parallel instead of in series. Giddings has drawn on the logical extension from gas to liquid chromatographic columns to find the effectively high velocity data which clearly support the coupling theory, gas chromatographic data have tended to show too much scatter to afford a definitive test of coupling theor>, and high velocity data for unretained components have been lacking. Since the present data seem to show somewhat less fluctuation than those of Kieselbach, it was attempted to fit
Comparison of Measured Parameters in Longitudinal Diffusion Term for Unretained Components
Sil-0-Cel and Chromosorb
flf
I*
Evidence for turbulence from flow data
Bohemen and Purnell ( 1) 4 7 0 10-0 32 0 :39-0 46 0 76-0 78 0 51-0 59 0 90-1 07
Norem
Kieselbach (17)
(20)
4 7 0 42 0 40
0 95 (recalculated) Air H? He s* 0 71 0 91 0 50-0 59 0 67
4 0 0 0 0
7 137 38-0 39 82-0 98 39-0 47
Glass beads Sternberg and Poulson (this study) 19-47 0 21-0 39 0 40 0 86 0 46
0 85
0 86
Air He 0 71 0 60
CH, He 0 69 0 62
Bohemen and Purnell ( 1 ) 4 7
0 0 0 1
08-0 38 36-0 38 36-0 38 0
1 21 (recalculated) Hz N2
0 91 0 67
Norem (20)
4 0 0 0 1
7 38 40 40
0
1 40 (recalculated) Air He 0 71 0 99
Sternberg Kieselbach and Poulson (17) (this study) 4 7 4 7 0 137 0 09-0 42 0 40 0 40 0 40 0 40 1 0 1 0 0 83
0 93
Air He 0 71 0 58
CH, He 0 69. 0 67
VOL. 3 6 , NO. 8, JULY 1964
1499
them to the coupling theory. The coupling theory equation was expressed as
W r -
g&g 02, and the constants BCJA', B, C,, and C , / A ' were found by the method of least squares (23)with the four constants treated as independent parameters. The consta_nts found were then used to calculate H/fl values, which were compared with the observed values. Inconclusive results were obtained in these calculations employing the approximate single term expression of coupling theory instead of the more exact summation form. It was found that the high velocity points can be brought nearly into line by adding to Equation 14 a term Eu2, with E negative, as found by Giddings (S),but such a term merely shows the direction of the correction needed, and does not really support or refute coupling theory. The consistent high velocity fall-off of plate height, is also subject to an alternative interpretation based on turbulence. If turbulence exists, it would be expected to increase with velocity and to cause the gas phase mass transfer term, C,/D,,, to become velocity dependent; this may be regarded as an increase with velocity of the effective lateral diffusion coefficient. I n a first order approximation, the effect of turbulence would be to cause a linear increase in the effective lateral diffusion coefficient, so that D,, becomes replaced in the gas phase mass transfer term by Do,(1 au,,).
+
A _ fl
- A
c,
BD,, +
+
D , (1
+ a~,,)
uu,
(18)
If the A term can be neglected, this equatim can be cast into a form which is identical to the functional dependence resulting ivom the coupling theory, shown in Equation 17, and with
Of course, the effect of turbulence on plate height may well be different from that given by this simple approximation. While the possibility of turbulence at first consideration seems remote a t the low Reynolds numbers existing in these columns, the pressure drop-flow data clearly show that some turbulence is present. h flow equation which has been found applicable over a wide range of velocities has been developed by Carman ( 2 ) . This equation can be expressed in the form shown below: 1500
ANALYTICAL CHEMISTRY
The b coefficient determines the contribution due to turbulence. If the b term were zero, this expression would reduce to the Kozeny-Carman equation for
laminar flow, with p; ' A' constan't. U",
It has, however, been found in this study that p,.Ap/u,, is not constant b u t varies linearly with linear velociby in t h e columns used in the range of linear velocities employed, as shown in Figure 9. The turbulence contribution increases as the particle diameter decreases (at constant column diameter), vihile the turbulence contribution incrf:ases as the column diameter increases a t fixed particle diameter. At present these observation:; can only be presented and the alternative explanation suggested. The d a t a obtained thus far do not seem to show any systematic re1at)ionship between the degree of turbulence, expressed b y the fractional departure of the observed
!?d! from ? its intercept, and 'die
mag-
UU,
njtude of the dep,srture from linearity of
Hu,,us. uUa2 data,. ~
fl
It would be helpful
to have data obtained with several carrier gases in :x particuhr column, since the .I' term of coupling theory would be expected to be independent of which carrier gas is used, while the effective A' based o n turbulence (A' = Co/aDoo) would be expected to vary with carrier. .4n experimental result was obtained in a very different application in the process of measuring: t h e flow rate of natural gas in a 20-ir.tch diameter pipeline (6). A pulse of nitrous oxide injected a t an upstream point was sen.sed by an infrared detection system :At a point 22 miles downstream. Aft,er a transit time of 4l/'2 hours, the nitrous oxide appeared as a discrete peak .with a base width of about one rninute. This corresponds to over one millioin theoretical plates for a plate h
