Measurement and Interpretation of the C Terms of Gas Chromatography J. CALVIN GlDDlNGS and PAUL D. SCHETTLER Department o f Chemistry, University of Utah, Salt lake City, Utah This work deals with the significance
of the nonequilibrium or C terms in It i s shown, gas chromatography. first, that the C terms have an important role in column resolution. Two new methods are then proposed for the experimental isolation of liquid and gas contributions, Ci and C,. These methods are applied to a conventional GLC column, a glass b e a d column, a preparative column and a gas solid column. The experimental results are combined with theoretical interpretations to evaluate the chang-, ing role of the C terms in different kinds of columns. The experimental characteristics and problems of each of these systems are discussed and cornpared.
T
C TERMS of gas chromatography reflect the role of nonequilibrium or mass transfer in peak broadening and overlap. These terms may originate with mass-transfer processes in the gas phase, in the liquid phase, or with the kinetics of surface adsorption. The relative importance of these contributing processes depends upon the experimental system and its conditions. The situation is obviously different in gas liquid chromatography than in gas solid chromatography, in columns with diatomaceous earth supports compared to glass bead columns, and in small diameter analytical columns as compared to preparative scale columns. I t is one of the primary objectives of this paper to study the changing role of the C terms in going from one technique to another. Both esperimental and theoretical evidence bear on the problem. As part of the experimental study, two new techniques have been evolved for isolating the C terms from fully pressure corrected experimental data. The C terms are, by definition, velocity coefficients in a plate height esl)ression. We may think of a given !)late height contribution as HE
where C, is the relevant C term for the Iirocess in question. The various H , and C , terms may be additive, as with itationary phase processes, or coupled, ab n i t h mobile phase processes. The flon velocity, 21 is the velocity of an
inert peak (usually approximated by an air peak) being carried through the column. This corresponds with the usual definition for flow velocity and is such that it can easily be measured experimentally by reference to the inert peak. Since the C terms and the plate height are intimately related, it is necessary to justify (in view of a recent tide of criticisms) the importance of the plate height as a column characteristic. A plate height value does not specify column resolution, but it is a n essential component of resolution. Quite obviously resolution is composed of a selectivity or differential velocity term which indicates the separation of peak centers, and a spreading or overlap term which indicates the degree of crosscontamination. The plate height is a direct measure of the latter (this conclusion in no way suggests that the theoretical plate model is adequate as a fundamental theory of column processes; it merely indicates the utility of the plate height as a useful parameter). The plate height, then, is a measure of resolution for any particular pair providing the selectivity or differential velocity is known. I t can be shown, in fact, that 4 ? / 4 (where X = Xo. of plates) is equal to the resolution per unit of relative velocity difference or, alternately, to the resolution per unit of relative retention time difference for neighboring peaks ( 5 ) . Thus plate height is a basic part of column resolution. I n some cases it is desirable to characterize a column by the effective (4) plate height, H , , and the associated quantity, the number of effective theoretical plates, Ne (resolution per unit of relative selectivity is given by However H can be converted to H , by the simple relationship, H = H e (1-R)2, so that any theory valid for one is automatically applicable to the other. (The quantity R is the component-peak velocity divided by that of the inert peak.) A prerequisite to the study of C terms is the experimental isolation of each C contribution. In gas liquid chromatography this usually reduces to the problem of separating C l (liquid phase nonequilibrium term) from C, (gas phase nonequilibrium term). This separation cannot be achieved by
dAK/4).
looking solely a t the peak width. Additional information must be obtained, a fact which probably esplains why only a handful of workers have isolated the separate terms. Several techniques have been used for discriminating between C, and C,, terms. The first such isolation of tern-s was reported by Giddings, Seager, Stucki, and Stewart (10). These authors observed the selective effect of a changing column pressure, the latter obtained by the different flow resistance of a long parent column and the shorter lengths into which it was subsequently divided. Kieselbach (11, 12) and Dal Kogare and Chiu (1) effected the isolation of C, and C l terms by observing the change in plate height with changing retentive capacity. Perrett and Purnell (13) used a method in which the gas phase term was canceled out by the proper choice of flow velocity using two different carrier gases or outlet pressures. DeFord, Loyd, and Ayers ( 2 ) evaluated C,, and C L using a computer program and data acquired with a variable outlet pressure. Experimental programs similar to these have also been used in the study of capillary columns (3, 15). METHODS FOR ISOLATING C TERMS WITH FULL PRESSURE CORRECTION
While several approaches have been used in separating the esperimental C terms from one another, as indicated above, few of these have been based on the fully pressure-corrected plate height. I n particular the f , term (see below) has been ignored, without full justification, in most treatmmts. Whilefl does not vary from unity by more than 12.5y0, it can nonetheless have a significant effect in accurate work ( 2 ) . The present methods should make it more convenient to determine the necessity for thefl term. Aside from the early efforts in this laboratory to account for full pressure correction, the only conqdete esperimental study with f, accounted for has been made by DeFord, Loyd, and .\yers ( 2 ) . These authors also verified the nature off, exl)erimentally. The apparent (or measured) Illate height, 8.of a gas liquid chromatographic column may be exilressed a3 ( 9 ) VOL. 36, NO. 8, JULY 1964
1483
0.15
”hi. e \ l ) r e 4 o n may also be written in the form ahere H , is the total gas phase contribution found locally within the c.olumn (including eddy diffusion, longitudinal diffuion, and gas phase mass tranifer), v, is the outlet velocity and fi andf, are the pressure correction terms given by fl
-
1) ( P 2 - 1) (P3 - 1 1 2
9
(P4
f2
= -~
=
(6)
(7)
when the diffusion coefficient at unit is allowed to vary (perpressure, D“’, haps through a change in carrier gases) ; by @ = Po
(8)
when the outlet pressure, p,, is allowed to vary; and by
when simultaneous changes are permitted in both D,‘ and p,. When z is considered as the variable in place of the outlet velocity, u,, Equation 3 is found to be
where the espression H , (z) reminds us that for any given column H , is a function of z only. 130th of the methods discussed below are based on making several series of runs with 6 held constant within a series but purposely vaGed from one series to the nest. If H/f1 is plotted against 5 = v,, +, a different curve is obtained for each value of the parameter +. This is illustrated for a hypothetical case in Figure 1. As will be shown later the spacing between curves is proportional to the magnitude of the stationary phase term, C i (gas liquid chromatography) or C, (gas solid chromatography). This plot has the advantage that member curves 1484
ANALYTICAL CHEMISTRY
f, 0.0:
I
0.
\\here P is the inlet/outlet pressure ratio, pl:p,. The latter correction term, f L j is by chance identical to that obtained by James and Martin for correcting the retention time and retention volume for pressure gradients. All theories of chromatography now estant agree that H , is a function of, first, the structural properties of the column and its support, and second, the parameter
6 = l/D,,’
A
(4)
3 (P2 - 1) 2 (P3 - 1)
x = V,@ where @ is given by
0.10
I
I
20
40
I
I
I
60
I
ao
X
Figure 1 .
A typical plot of
will never cross if the experimental data are valid and conform to Equation 10. However, spurious contributions arising from equipment time lags or errors in the Do’values used will often force the curves to cross. An instrumental system may, in fact, be checked for these difficulties by plotting two or more such curves using inert (nonsorbing) columns. The curves should coincide if the system is working properly and if correct diffusion and pressure parameters have been used. Much of the value of the specific methods discussed below is a result of the useful properties of this method of plotting data. Method A. Least Squares Computer Program. DeFord, Loyd, and Ayers (9)have pointed out that several alternative methods could be used in the analysis of gas chromatographic data by computer. The method proposed here is particularly direct and simple, and appears to work well in practice. The experimental data is written in terms of the Sam: quantities as used in Figure l-i.e., H / f l is tabulated in terms of the corresponding x = u, 6 value. Some equation is then chosen to represent H,. Since the latter is a function of z only, it is necessary to write the equation as a func. tion of x. Although nearly any series with sufficient terms to represent H , can be used to separate out the Cl term, it is preferable to use a meaningful expression for H , so that the other resultant least squares parameters will have significance. Perhaps the two best choices are
h/fl vs. x
= v, 4
DeFord et al. (9). The second contains an eddy diffusion term, .4. Use of the latter in no way implies that the classical eddy diffusion concept is correct. Even with the coupling theory of eddy diffusion a small “apparent” A term will arise ( 8 ) , and since the coupling equations themselves are esceedingly difficult to use in a least squares analysis the simple form of the last equation is preferable for the sake of simplicity. Previous worh has shown that the inclusion of has little effect on the measured valne of
c,.
(12)
Once the form of H , is chosen, a least squares fit of Equation 10 is made to all the esperimental data. The C L term is automatically differentiated from the C, term by virtue of the different dependence of these terms on the parameter 4 (this is illustrated in This differentiation Equation IO). occurs as long as @ is varied over a sufficient range to effect a measurable change in H l j , a t a given value of z. The procedure outlined above does not require that @ be constant for a series of runs (and thus varied only from series to series). The value of @ could, in fact, be varied randomly from run to run. Hoyever this would prevent the use of H / f l plots as shown in Figure 1. The latter are valuable in showing experimental anomalies and, in general, indicating the overall precision of the data and the significance of the results. Method B. Measurement of E?/jl Increment of _Constant z. The increment in H/fl a t constant z is indicaJed by the vertical gap between the H / f i curves in Figure 1. This increment can be obtained directly from Equation 10 in the form
where, when @ = p , , B’ and C,’ are the usual B and C, parameters evaluated at unit pressure. The first is the simple form recommended by
The gas phase term drops out because at constant x it remains unchanged.
H, H,
=
+ C,’x A + B’/x + C,’X =
B’/x
(11)
Hence the C1term may be obtained as
-i.e., as the increment in €hfldivided by z times the increment in the quantity f2,fl~. The use of this method requires a separate plot for the series of curves representing f2, lfl$. Once the C Lterm is so obtained, the parameters connected with the gas phase can be deduced from the H, curve. The latter is obtained simply as
H , = f l i f 1 -C,xfz/'flQ (15) as indicated by Equation 10. The use of an increment method in which the gas phase contribution cancels on two runs was first suggested by Perrett and Purnell ( I S ) . The correction factor, f l , was not incorporated into their analysis. Two points with identical z values were located on a plate height-flow velocity plot. The "tie line" between these points is a diagopal line of varying slope. Using the H f l us. z plot, as suggested here, any vertical line becomes an appropriate line. This will be illustrated shortly. There are several possible variations on the present method of plotting and interpreting data, but each loses the advantage of the vertical tie line. For instance, H,fl may be plotted against v,jz;fl. The tie lines, once located, should all be parallel. The value of C L then equals the increment (along the tie line) in H,fi divided by the increment in u,f2, fi. Another possible method is analogous to the procedure used by Perrett and Purnell except that fi is accounted for. I n this case H/f1is plotted against voL The value of C L is obtained as A(H/flfllA(u,fil fi). The value of P must be determined a t each end of the tie line in order to evaluate f l andf2. Comparison of the Two Methods. There are advantages a n d disadvantages in each of the two methods proposed above. At this point there is no clear-cut advantage for either method, so we will confine ourselves to some of the considerations which are involved in choosing between them. First, it is obvious that method X requires the availability of a computer. If this requirement is satisfied, it will ordinarily require no more than a few minutes computer tinie to analyze very extensive data. Preparation of the data for computer analysis is more time consuming, however, and when this is considered the two methods are about equally demanding on time. 'This conclusion may be modified to some extent since method X probably requires less data. Method 13 yields more information than method A. One gets all the gas phase parameters (A, B and C,, de-
pending on the equation chosen) as well as CL. Method B yields the underlying H , curve, but further work must then be done in its interpretation. Method -1forces one to choose an equation for H , (for example, Equation 11 or 12) even though there is some uncertainty in the form which should be used. This disadvantage is slight, however, because the final C l value depends only on having some form for H , (completely empirical if desired) which will conform well to the data. I t has long been known that Equations 11 and 12 are adequate in this regard. Method I3 provides the most direct check for data consistency because C L should be the same for all tie linesLe., the same for each value of 2. This advantage was pointed out by Perrett and Purnell in connection with their earlier method. Method A is not without this desirable feature, however, since the computed curves will not fit the data unless the data are consistent with a constant C L . This lack of fit is easily detected for any gross inconsistencies. EXPERIMENTAL
This study deals with a wide range of chromatographic systems, and thus involves the use of a number of separate experimental set ups. These will be described briefly belou . Conventional GLC Columns. This work was done using a modified Burrell Kromotog Model K-7 with a flame ionization detector. T h e dead volume of the original instrument, to flame detector
t
sampling capillary
column
Figure 2. Device used to minimize dead volume a t outlet and to give variable outlet pressure
about 1 ml., produced peak asymmetry (notably tailing) and a n uncertainty in t h e true retention time of the column. T h e take-off block was thus dismantled and the flame detection device within it modified by cutting out the original connection to the column and silver soldering the appropriate Swagelok fitting directly to the unit. This allowed the column to be fastened directly to the detector or, alternately, used in the modification shown in Figure 2. The latter involved a capillary soldered into a copper tube (to permit standard Smagelok connections) and extending from the flame unit down into the column packing. The bulk of column effluent was bled out through the T at a pressure in e x e s of 1 atmosphere. A small stream passed through the short capillary to the flame. Since the inner capillary diameter was 0.004 inches, a negligible dead volume was involved. This system largely eliminated peak distortion due to column end effects a t the outlet. I n addition the outlet pressure can be readily arid accurately varied over a considerable range for a given capillary by adjustments in the bleed-off valve. I t can be varied over a wide range by interchanging the capillary with one of different dimensions. T o reduce dead volume a t the inlet, the injection block was replaced by a n injection unit in which the needle of the syringe extended to the head of the column. The above modifications reduced the dead volume to a few hundredths of a cc. and eliminated the tailing observed with the original instrument. Temperature control was achieved with an oil bath using a mercury thermoregulator control in which everything except the flame unit is immersed. This replaced the original air bath. Because of the flame the detector equilibrated a t a temperature higher than that of the bath and thus eliminated the possibility of condensation. The column employed with this apparatus was constructed from a 395-em. length of 3/1e-in~hcopper tubing. This was filled with 60- t o 80-mesh Chromosorb W containing 20%, by weight, of dinonyl phthalate (DNP) deposited with acetone as a solvent. Isobutylene vapor was injected in amounts of 1-5 pl. using helium and nitrogen as carrier gases. The column was held a t 50' C. Evaporation of the liquid phase was minimized by presaturating the gas with D S P prior to its entrance into the column. Glass Bead Columns. A PerkinElmer Model 154 was used for the glass bead studies. KO modification was necessary in the case because the CCterm was unusually large a n d t h u s not easily affected by dead volumes. The column material was prepared by mixing a weighed amount of squalane, solvent, and 0.98-mm. glass beads followed by evaporation of the solvent. This was packed into a 200-em. length of l/l-inch copper tubing. Syringe injection was used. The carrier gases, presaturated before the column, were helium and n trogen. The temperature was about 50" C. VOL. 36, NO. 8, JULY 1964
1485
0
0-b
40
'
sb
I20
a
I60 '
260
' 240
'
280
Plate height d a t a for Chromosorb W column
Ci is determined from the ratio of the two heavy lines which a r e directly above and below one another
Preparative Scale Columns. ;i96 cubic-foot constant-temperature ( h0.5' C.) oven was constructed for preparative work. This accommodat,ed large diameter columns up to 3 meters in length. The oven contained, in addition to the column, a pre-heator, injection port, and the detector. The latt'er was a Gow Mac t \ y e W thermal conductivity cell used in conjunction with a 5-mv. recorder. Injection was accomplished by syringe directly into a vaporization chamber filled with lead shot. The column used in this study was a 1-meter length of 2-inch diameter copper tubing. The packing was 30- to 60-mesh Johns Nanville Chromosorb P loaded with 25% Dow Corning 200 Fluid (dimethyl polysiloxane). Data were taken at' 100' C. using benzene as the solute and with both helium and nitrogen as carrier gases. The sample size was kept, as small as possible consistent with detectability in order to separat,e out the purely column effects. G a s Solid Columns. T h e apparatus was the same as t h a t described for the conventional GLC studies. .Ilumina of 30- to 40-mesh was modified by SaOH as described by Scott (f4). The column was 1 meter long and with 3! ,e-inch diameter. h helium carrier gas was used with n-heptane as the solute. Outlet' pressures were chosen a? 30 and 60 1i.s.i. above atmospheric. RESULTS
This study is intended to demonstrate some of the relationships existing between the esperimtntal apljroaches to column 1)aranieters in different column 1486
ANALYTICAL CHEMISTRY
I
'
X
Figure 3.
I
systems. The wide scope of this work prevents a detailed discussion of individual systems. Emphasis is placed on the distinctive features of each system and the particular problems that may arise in the analysis of C terms. Conventional GLC Columns. The usual column of gas liquid chroniatography, packed with a porous solid support and its entrained liquid, is the standard of comparison for all column studies. This column has received a n overwhelming fraction of the attention so far devoted to this subject. Except for work done in this laboratory, none of the other types of columns have ever been related to their constituent C terms. A large majority of conventional columns will apparently eshibit a Ci term in the range from 3 x 1 0 - ~to 3 X second, with 10-3-10-2 second being most common. The precise value may be expected to depend strongly on the pore structure of the solid support. The C , term may be approximated by the universal espression
C, = odP2/D, (16) where w is a constant of order unity. In a typical situation the particle diameter, d,, and the gaseous diffusion coefficient, D,, might equal 0.02 em. ( A 60-80 mesh) and 0.4 cni.Z/second, respectively. Thus C , is of the order of 10-3 second. This is in the same approximate range as the Ci terms. Such columns are
thus quite well balanced with respect to the C terms. ?;either term is ordinarily of sufficient magnitude to completely mask the effects of the other, and thus the system is a convenient one for experimental study. Figure 3 shows the re with the Chromosorb IT in all subsequent figures, J is here taken ~ ' . support has rather as t ~ ~ p ~ ; DThis large pores and the C f value is quite large-i.e., Cl = 1.64 i< lo-*. This value was obtained using method B . The figure shoys that a wide gap esists between the H /flcurves. a fact which reflects the large C iterm. (The value of Cf, as shown by Equation 11, is equal to 1 J times the ratio of the gap in H / f , curves and the gap in f 2 / f , p at the same z value. h vertical tie line connecting two such g a p is sh Figure 3.) The w value for this is 3.6. This is larger then usual for reasons not yet clear. I n any case there is a good balance between the two dominant C terms, even though each is somewhat larger than average. Glass Bead Columns. The only detailed work on the C terms of glass bead columns has suggested that C I may totally dominate C, under all but unusual circumstances ( 7 ) . The esperimental basis of this conclusion rests on a study of beads > 0.5 mm, in diameter. There is no reason to expect a departure from this situation with smaller beads, howel-er, in uniformly packed columns of .small bore. This matter will not be entirelj- clear until it has been studied more estensively. The small size of glass beads normally required for analytical columns is generally responsible for large pressure
(i), we would expect a value several times larger than lop2 second for 60- to 80-mesh beads and a value somewhat greater than second for a very fine packing of 230-270 mesh. The C, term is espected to follow Equafor 60- to 80tion 16-e.g., C , mesh beads. While the dominance of Cl in glass bsad columns will be responsible for H / j l us. x curves with wide spacing between, a plot of H us. mean velocitju,f2, yields a different kind of result. As seen by Equation 2, a system in wtich C I dominates will yield the same H l j , us. mean velocity plot irrespective of the carrier gas or outlet pressure. The coincidence of these plots may be taken as direct evidence that gas phase effects are negligible. The exact 01)posite is observed when the gas phase terms domi9ate the liquid phase term; plots of H,Yl us. x with different values of 6 mill be coincident while H ,ji us. mean velocity will be noncoincident. This will be discussed further in connection with gas solid chromatography. The above conclusions are borne out by Figures 4 and 5 . These results were obtained from the system described in the esperimental section (There is no data shown in the ex
-
-
Nitrogen Helium
01
1
I
I
I
I
2
4
6
8
IO
VO f
I
I
12
14
16
,
Figure 5. The coincidence in this plot of i / f 1 vs. mean velocity shows that the C, term is negligible for the glass bead column
able assumption that C I and C, will be changed in the same ratios by changes in bead size. Esceptions to this will likely be found only with extremely small beads. Providing that glass bead columns perform consistently throughout a wide range of bead sizes, we may expect both C l and C, to vary roughly in proportion to bead size squared. Since a Ct value of 0.2 second has been obtained for a 0.1 70loading of tri-o-tolyl phosphate as 0.054 em. diameter beads
gradients. The fully pressure corrected methods proposed here should therefore be very well suited to the study of such columns. Based on present knowledge, one expects to obtain a fairly large Cl term and a rather small C , Lerm. Thus the separation between H’jl plots (proportional to the magnitude of C l ) should be large and easily discernible. However the dominance of C1 will ordinarily make it very difficult to measure a C, value. Thi. conclusion is based on the reason-
8.0 A
H , cm.
1
Helium Nitrogen
0
6.0
c
2.o 0
F
0
I
1
I
I
2
4
6
8
0.2 0
I
~,*o~o-o
I
1
1
IO
o
I
I
I
14
~
1
I
4
12
O
16
~
I
o
I
1
I
18
20
~
o
I
~
I
o
I
I
22
l
24
o
I
VOL. 36, NO. 8, JULY 1964
l
ot
1
1487
~
o
C
2.c
-Fi f,
1.0
01
I
I
I
1
-015
1
200 Figure 7.
1
I
600
800
X , cm.-'
Plate height data for gas solid column.
tremely low velocity region where molecular diffusion is dominant.) No significant difference exists between the plate height-mean velocity plots for He and X2 carrier gases (at constant outlet pressure) as shown in Figure 5 . The same data plotted as H / % us. x shows, by contrast, a very wide divergence. It is impossible to get experimentally meaningful C, value because of the masking effect of CL. The value of C 1 ,obtained by a procedure similar to method U . is 0.53. Preparative Scale Columns. Large columns may be expected, on theoretical grounds, to show a trend toward increasing C, values as opposed to the magnified C1 connected with glass heads. The problem has received no prior experimental attention, however. I t is reasonable to believe that the deterioration of efficiency in large columns is associated with the gas phase (notahle with the increased diffusion distance from column center to column side), and thus in no way affects the C1 term. Since the Ci 1488
I
400
ANALYTICAL CHEMISTRY
Coincidence shows that
term is quite often larger than the C, term in conventional (analytical) columns, this shift mag not be large enough to obscure Ci. This will depend on the particular circumstances of the experimental work and especially on the column diameter. Preparative scale columns are unique in that the gas phase terms are expected, based on theory, to be a strong function of column length. This is due to the fact that there is a slow transition from the purely flow-pattern effects to the usual diffusion-dominated form of C,. Additional length enables a more complete transition to occur'. Unless care is taken the C, values obtained from experimental data ail1 reflect this complication by varying with column length. For a fully developed C, term one should choose a column of sufficient length that lateral diffusion will become fully operative. The criterion for this has been discussed elsewhere. Figure 6 indicates the type of results which might be expected from some large-diameter columns. A small
Ck is
1000
negligible
but definite gap exists between the but its magnitude is rather uncertain due to the closeness of the curves and the lack of precision in the data. Xethod %. indicates that C I = 0.016. This is larger than expected based on DeFord, Loyd, and hyers' results using analytical columns with the same solid support but a different liquid ( 2 ) . The difference may be due to instrumental errors or it may be connected with the difference in liquids. The value of C,' (C, a t one atmosphere) for He, based on Equation 12, was 4 X giving a w value of 1.3. This is a very low value considering the nature of preparative scale processes. I t may be that in the short 1-meter column studied the C, term was not yet very well developed. In addition the precision of the data leaves something to be desired in the det,,rmination of Ci and C, values. I?nfortunately there is no experimental work in the literature which would help resolve these questions. A% final conclusion on this matter will have to an ait further experimental work.
G/j, plots,
CONCLUSIONS
Certain broad trends have been predicted and confirmed esperimentally in the above study of the four techniques of gas chromatography. However there are enough exceptions to these trends to indicate that a great deal of additional studj. is needed to get the maximum efficiency from gas chromatographic columns. ACKNOWLEDGMENT
The authors thank S . C. Saha and G. H. Thompson for obtaining the data on the conventional and t h e glass bead columns, respectively. G. E. Jensen constructed and operated the preparative apparatus.
0
LITERATURE CITED I
40
I
60
I
80
I
100
I
V , (cm./sec.) Figure 8. This plot for gas solid column shows the major role played by gas phase terms
(1) Dal Nogare, S., Chiu, J., ANAL. CHEM.34. 690 11962).
(2) DeFord,’ L). ~ .Loyd, , R. J., Ayers, B. O., Ibid., 35, 426 (1963). ( 3 ) Desty, D. H., Goldup, A., “Gas Chromatography 1960,’’ R . P. W. Scott, ed., p. 162., Butterworths, LVashington, 1962. (4) Desty, 1). H., Goldup, A4., Sw:nton, W. T., “Gas chromatography, Tu’. Brenner, et al., ed., Chap. VIII, Academic Press, Kew York, 1962. ( 5 ) Giddings, J. C., J . Gas Chronzatog. 2, 167 (1954). (6) Giddings, J. C., Unpublished results, 1964. ( 7 ) Giddings, J. C., Mallik, K. L., Eikelburger, AI., Ibid., 34, 1026 (1962). (8) Ibid., 35, 1338 (1963). (9) Ibid., 36, 1170 (1964). ( l o j Giddings, J. C., Seager, S. L., Stucki, L. I
