where ro is the radius in the cylinder.
Cz is l/4 as required. The author knows of no simple way to calculate the values of the correlation coefficient, p . The values required are less than the maximum limit of 1 and are reasonable for a fairly strong correlation between the velocity distribution and mass transfer effects. An equation previously derived by the author has recently been used by Kieselbach (10) t o analyze data from several columns by a least squares technique. Unfortunately, this equation was in error, in that the velocitydistribution term was thought to be a 1 fu‘nction of (1~k2 and the correlation term was not included. Thus, the equation corresponded to Equation 27 with C” = 0. However, since C’ is determined principally by early peaks where C’ is much larger than C“k and C”’ is determined largely by late peaks where C”’k2 is much larger than C’k, the values for these coefficients should be reasonably accurate. Kieselbach found experimentally that C’ is of the same order as C”’ or even a little larger (8). Equations 28, however, indicate that this condition is im-
possible. His results may reflect incomplete compensation for system dead volume. In any case, his results suggest that the C3 or velocity-distribution term is large compared with the mass transfer term. It is also notable that the gas diffusion terms observed by Kieselbach vary approximately as the square of particle size. This would be expected for a velocity-distribution term, but not for a mass transfer term, which is related to pore size. The combined gas diffusion terms were found to be larger than the liquid phase mass transfer term when liquid loadings were less than 10% by weight and k was not near unity. In an early work, Jones (6) found gas diffusion dominated liquid diffusion in his columns even a t higher liquid loadings. However, if values of Cs of unity in Equation 26 are assumed, the values of d, to explain Jones’s data are between 1 and 2 mm., an order of magnitude larger than particle size. Channeling in the column packing occurring over dimensions of this order would lead to a large velocity-distribution term that could explain the data. ACKNOWLEDGMENT
The author expresses gratitude to E. I. du Pont de Nemours & Co. for permission to publish this works. The helpful comments of Richard Kiesel-
Gas Chromatography of the C, to
bach, of that company, and of Marcel Golay have been found invaluable. Ann Sheldon of Du Pont carried out the computations of the Cz coefficients in the modified Golay equations. LITERATURE CITED
(1) Bethea, R. M., Adams, F. s., A N A L . CHEM.33, 832 (1961). (2) Giddings, J. C., J . Chem. Educ. 35, 588 (1958). (3) Giddings, J. C., Suture 184, 357 f 1959). (4) Glueckauf,,,E., “Vapor Phase Chromatography, D. H. Desty, ed., p. 29, Butterworths, London, 1958. (5) Golay, M. J. E., “Gas Chroma\ - - - - ,
tography-1958,” D. H. Desty, ed., p. 36, Butterworths, London, 1958. (6) Jones, W. L., Southwide Chemical Conference, A.C.S.-I.S.A., Memphis, Tenn., Dec. 6, 1956. (7) Kenyrd, E. H., “Kinetic Theory of Gases, p. 287, McGraw-Hill, New
York. 1938. (8) Keulemans, A. I. M., “Gas Chromatography,” p. 96, Reinhold, New York, 1957. (9:) Kieselbach, R., ANAL. CHEM. 32, 880 (1960). (10) Zbid., 33, 23 (1961). (11) Klinkenberg, A., Sjenitzer, F., Chem. Ena. Sci. 5. 258 (1956). (12) Loyd, R. J., Ayers, B. O., Karesek, F. W., ANAL.CHEW32, 618 (1960). (13) Ospensky, J. V., “Introduction to
Mathematical Probability,” McGrawHill, New York, 1937. (14) van Deemter, J. J., Zuiderweg, F. J., Klinkenberg, A., Chem. Eng. Sci. 5, 271 (1956). RECEIVED for review November 28, 1960. Accepted March 10, 1961.
C, Nitroparaffins
Isothermal vs. Linear Temperature Programming R. M. BETHEA and F. S. ADAMS, Jr. Chemical Engineering Department, Iowa State University, Ames, Iowa
b The van Deemter equation has been modified to show qualitatively the effect of resistance to mass transfer in the gas phase on the component band width-retention time ratio, as represented by the height equivalent to a theoretical plate. Qualitative predictions as to the effects of flow rate, heating rate, and isothermal level on the separation and resolution of the Clto Ca nitroparaffins have been made and demonstrated experimentally. O p timum resolutions were obtained a t a constant temperature of 50” C. and flow rates of 90 and 60 ml. of hydrogen per minute with a heating rate of 2.9” C. per minute starting from
40’ C. 832
ANALYTICAL CHEMISTRY
M
investigators (3-6, 7, 11, 14) have contributed to the knowledge of gas chromatographic separation by linear time-temperature programming. The results reported here are from a study made to determine the optimum operating conditions for the quantitative separation of the C1 to Ca nitroparaffins with a reasonable analysis time. I n previous work on this problem (@, qualitative separation of all eight nitroparaffins was obtained, but quantitative separation was possible only for nitromethane, nitroethane, 2-nitropropane, and I-nitropropane. The present study includes a comparison of constant temperature operation with linear temperature programming. Variables ANY
studied were carrier gas flow rate, heating rate, and constant temperature level. THEORETICAL
In this report isothermal and linear temperature programmed gas chromatographic analyses are compared. A. modified version of the equation proposed by van Deemter, Zuiderweg, and Klinkenberg (6) was used to explain the effects of the process variables on retention time, t i . In van Deemter’s development, all mass transfer resistances are included in OL, where CY is the over-all mass transfer coefficient per unit volume of
packing. In the development of their Equation 38 H
= 20 +
u
ap = 6 X p / d , For a unit volume of packing,
2uxg/ff
(1
+ KXg/Xi)’
to their Equation 53,
H
2 YDg U
laminar flow (8). For uniform spheres, the specific surface may be expressed as
Xh
+ 2Xdp +
+ X P + xg + xi
= 1
=
(4)
+
1
1
K
Equation 1 may be rewritten as
(Y=(yI+cyII 1
may be modified by substituting ffP
i.
+1
for This separates the effects of resistance to diffusion in the bulk gas stream from the effects in the gas-filled, liquid-coated pores. This separation is necessary, as the gas in the pores is stagnant or a t best in laminar flow. Thus diffusion in the pores would be entirely molecular in nature, because the relative magnitude of the mean free path of the solute molecules is very small compared with an average pore diameter of 0.4 to 2 microns. This range for pore diameter has been reported (1) for Johns-Manville red Chromosorb, which is similar to the crushed firebrick used as the solid support in this work. In the bulk gas phase, D in van Deemter’s Equation 38 is the longitudinal dispersion coefficient and is a combination of molecular and eddy dxusivities, as shown in their Equation 53. No modification of 0x1 is necessary, since this term, representing the resistance to mass transfer in the liquid phase, will be the same mathematically regardless of the physical location of the liquid. The usual assumption may be made that the coating within the pores of the particles is of the same thickness as the substrate coating on the external particle surfaces. With this modification, van Deemter’s Equation 41 becomes l_ = _ l ff
l
K
(1)
a,+&+&
25D,a: = 150D,Xi where as = apk, = 6x9
where the term in brackets is the specific surface of a cylinder with one end (that farthest from the external particle surface) closed. The substrate coats the inside surface and the bottom of the cylinders. The expression for k, remains unchanged, as we are still dealing with mass transfer in a laminar fluid. The resistance to mass transfer in the liquid phase, CY^, has been expressed by van Deemter in Equation 51 as
d;
x,
(2)
This is similar to the correlation for
D,the longitudinal dispersion coefficient] may be expressed as D
=
yD,
+ XU
d,
(7)
the sum of the molecular and eddy diffusivities. Since k = K -X , Xi
(8)
van Deemter’s Equation 38 may be rewritten as
2uX: d:
(1
+ k ) 2 150D,Xzt
or more simply as
The temperature a t any time during a linear temperature programmed run may be expressed as T = to
+ Rn 0 + 273
(11)
For the case of isothermal work, this reduces to T = t~ 273. The molecular dxusivity of a solute in a carrier gas, D,,can be expressed (18) as
+
Do = j
(T89
(12)
wi
2
Is (G)
H has been related ( l a )to &, S, and R by the following equations : Qi
=
sij = ( t j
~ ’ ( 1 KX,/XI)’DIXI
it was assumed that mass transfer resistance in the gas phase may be neglected. The data for their system behave in accordance with this assumption. Resistance to mass transfer in the gas phase may not always be negligible, and the resistance to molecular diffusion in the pores of the packing particles may be significant, especially with low weight ratios of substrate to support (10). Following the type of approach commonly employed in kinetic studies involving beds of fine particles, van Deemter’s Equation 41
L
(3)
Assuming that the macropores may be represented as cylindrical capillaries,
8d2, K X , u
HI the height equivalent to a theoretical plate, is expressed by
ti/wi
-
ti)/li
(14) (15)
We may now rewrite Equation 10 as
where the primed coefficients indicate that the flow rate conversion from linear to volumetric units has been made for the unprimed coefficients in Equation 10. The first two terms of the right side of Equation 18 represent the contributions of eddy diffusion and molecular diffusion in the bulk gas phase. The next three terms represent, in order, the resistance to mass transfer due to diffusion in the interstitial space between particles, within the pores of the particles themselves] and in the liquid layer. Terms 3 and 4 actually describe the same mechanism, but each represents a different physical region where the resistance to mass transfer is applicable. In Equation 18, H has been presented as a function of ti, as in the study reported here, we are primarily interested in changes in peak separation and overlap produced by changes in the process variables under consideration. Whereas other investigators (10, 13) have been primarily interested in optimizing efficiencies] our efforts have been directed toward developing methods by use of theoretical concepts for more rapidly determining optimum operating conditions for future analytical work than is now possible through empirical procedures. Equation 18 will be examined to show qualitatively the effects of each term on retention time. Temperature Effects. The primary effect of an increase in temperature a t a constant flow rate is to increase term 2 and decrease terms 3 and 4 of Equation 18. From a physical viewpoint, this would be expected, since the molecular diffusion increases as T3’2 and the resistance to mass transfer in the gas phase decreases by T3i2. The change in d, due to thermal expansion of the substrate will be minor. The same VOL. 33, NO. 7, JUNE 1961
833
may be said of d h and 1. The particle diameter, dp, will be even less affected by thermal expansion. If terms 3 or 4 were controlling, ti would increase directly as T5/2. For Newtonian fluids only, Di may be expressed as an inverse function of viscosity, stated in Perry (15)as p = ci e-T
(19)
Few substrates fall in this category and we have been unable to generalize the effects of temperature on DI. Assuming a Newtonian substrate,
(20)
If diffusion in the liquid phase were controlling, then t i 2 would increase as eT as shown in term 5. As it is well known that ti decreases with increasing temperature and the first term of Equation 18 does not change with temperature or flow rate, the rate-controlling process in this case must be diffusion in the bulk gas stream as represented by term 2. The dependence of ti with absolute temperature at constant flow rates has been adequately shown (16, f7). These data may be represented as
A plot of relative retention time us. temperature a t R constant flow rate should consist of a family of expdnential curves opening upward for those compounds with t i greater than that of the reference substance and opening downward for those compounds with ti less than that of the reference substance. This relationship has been verified in our laboratory. Changes in the right side of Equation 18 cannot be said to influence only ti, as this equation shows the physical effects on the quantity We have observed in our work that increases in T cause a decrease in wi but the percentage change in wi is not as great as that in ti. This was especially noticeable for components eluted after 1-NP. Golay's work (10) on early peaks, primarily air (whose ti's are practically unaffected by most substrates), related changes in H to changes in w i . His work was considered as evidence for modification of the van Deemter equation to account for diffusional effects in the bulk gas stream. Equation 21 independently permits the prediction of changes in ti caused by temperature changes in constant flow work. As used here, K (and thus k) is similar to the thermodynamic equilibrium constant, which in general increases with temperature. The change in k with temperature provides an additional increase in the denominators of terms 3, 4, and 5 of Equation 18, thus
7.
834
ANALYTICAL CHEMISTRY
further increasing ti, if any of these terms were the rate-controlling step, as temperature increases. Since the reverse is true, under these conditions, the primary rate-controlling step is found in term 2. -4s k also appears in the numerator of term 5, the effect of liquid phase diffusion on ti would be expected to be decreased with increasing temperature. This is a logical assumption, since it is ivvell known that the rate of diffusion in Newtonian liquids increases with temperature-i .e., the kinetic energy of both the substrate and solute molecules increases (18). The combined use of Equations 18 and 21 may make it possible in the future to predict separately the effect of temperature on solute band width, wi. This presupposes exact knowledge of the dependence of k (and hence K ) with temperature. Unfortunately, such data are not a t present available for the great majority of substances used as partitioning agents in gas chromatography. Flow Rate Effects. For a constant mass of solute added, the primary effect of a flow rate increase a t a constant temperature is a decrease in retention time. An increase in flow rate will decrease the mass transfer rate in the bulk gas phase because of the impeding effect of an increased number of carrier gas molecules in the bulk gas phase-i.e., the solute concentration in the bulk gas phase becomes more dilute with a corresponding decrease in concentration gradient from the gas phase to the liquid phase. As F increases a t a constant value of R h , the terms where the influence of temperature predominates should increase in proportion to the length of time that a particular component is e.xposed to the higher temperatures. The temperature effects in terms 2, 3, 4, and 5 of Equation 18 oppose the flow rate effect to some extent. As temperature appears as T3'2 in t e r m 2, 3, and 4 and as e T in term 5, and F appears in all four t e r m only as the first power, the effect of temperature increases by linear programming should gradually become more apparent as F / R h increases ( 5 ) . Flow rate has little effect on k. A flow rate increase has the effect of decreasing term 2 of Equation 18 with a corresponding increase in ti and a decrease in wi if molecular diffusion in the bulk gas stream is the rate-controlling process. This does not happen. A flow rate increase will directly increase terms 3, 4, and 5 with a corresponding decrease in ti, which is known to occur. The controlling rate process then is a combination of one or more of terms 3, 4, and 5 of Equation 18-i.e., the rate of mass transfer. At this point the reader may raise the question: Why not disregard term 4 of Equation 18 and include in term 3 the resistance to mass transfer in the stagnant gas-filled pores? This simplifica-
tion would be possible if only a single standard support were universally used. Baker (1) has demonstrated that both the number and the pore size distribution change with type of support material. Zlatkis, Ling, and Kaufman ($0)have shown that chemical pretreatment has an effect on the retention time a t least partially due to structural changes in the support. These changes are reflected in d h , which appears in term 4. Experiments in this laboratory, which were identical except for chemical pretreatment of the brick, have shown differences in both ti and wi (and thus, H ) , which are most easily explained by inclusion of a term such as term 4. EXPERIMENTAL
Apparatus. The unit used in this work was the F & M Scientific Corp. Model 500A programmed temperature gas chromatograph. The only modification made on this unit was the replacement of the soap film flowmeter by a Fischer and Porter rotameter, Flowrator tube No. 08-150/13 with stainless steel float, calibrated a t opera& ing conditions. No base line drift or changes in flow rate were observed during the linear programmed temperature runs. The sample injection port was maintained a t 200' C. Samples were injected through a self-sealing silicone rubber septum with a IO-pl. Hamilton microsyringe. The carrier gas used was hydrogen (extra dry grade, The Matheson Co.) which was dried before use by passing through a 12-inch length of s/rinch pipe filled with No. 5A Linde Molecular Sieves installed in the inlet. line to the thermal condu2tivity cell. The flow rate through the reference side of the detector was maintained constant a t 25 ml. of hydrogen per minute a t 28" C. The output signal from the detector was supplied to a 0- to 5-mv. Bristol Dynamaster potentiometer, Model 1PH-570. It was necessary to opelate the unit a t an attenuation of X2, which has the sole effect of halving the peak heights, to keep the peaks on the 10inch recorder strip chart. The chart speed used was 30 inches per hour. As the results of this investigation will ultimately be used for the quantitative analysis of the reaction products from a vapor-phase butane nitrator which will contain some oxygenated compounds (chiefly formaldehyde, acetaldehyde, methanol, ethanol, and possibly formic and acetic acids) in addition to the nitroparaffins, an attempt was made to develop a partitioning agent which would give sharp, symmetrical peaks. Packings. The column used throughout this study was a 6-foot length of l/rinch outside diameter copper refrigeration tubing coiled on a 3inch mandrel after being filled with a 2 to 1 mixture by weight of Armeen SD (10 grams per 100 grams of inert support) and Apiezon N grease in the same proportion. The inert support used
+
was the -48 65 Tyler standard screen fraction of crushed and sized JohnsManville Type (3-22 firebrick. The packings were prepared separately (9) and were mixed after preparation by dry screening several times on a 65-mesh Tyler screen. The screening has the additional advantage of removing any fines produced during the substrate impregnation step. The packings were heated in an oven with circulating air stream a t 150" C. for 24 hours before mixing.
b Figure 1. Effect of heating rate on relative retention time Flow rate. 150 ml. Hs/min.
The choice of this mixed packing was based on preliminary studies in this laboratory to determine the most suitable packing for the quantitative separation of nitroparaffins and the oxygenated compounds expected in the product stream from the butane nitrator. A standard sample was made up gravimetrically from eight nitroparaffins, description and symbols of which have been given (a),and was used as a test mixture for 14 columns, each 50 inches long by 1/4-inch I.D. These columns were (quantities per 100 grams of brick) : 1-decanol, P,P'-oxydipropionitrile, Ucon LB 500x (PerkinElmer R packing), THEED (tetrahydroxyethylethylenediamine), squalane, 30 grams each; 2,2,4-trimethyl1,3-pentanediol, 35 grams; Apiezon M, 10 grams; Apiezon L, 10 grams; Armeen SD [a soya amine recommended by Zarembo and Lysyj (19) for the quantitative separation of water and alcohols], 30 grams; Armeen SD, 15 grams; a 2 to 1 mixture by weight of Apiezon T and Armeen SD, each containing 30 grams of substrate; a 1 to 1 mixture by w i g h t of the same packings; a 1 to 1 mixture by weight of Apiezon M, 10 grams, and Armeen SD, also 10 grams; and a 2 to 1 mixture by weight of Apiezon M, 10 grams, and Armeen SD, 10 grams. As the last packing in this list provided the best separation, it was further tested in 6- and 12-foot columns made of l/c-inch copper tubing. The 12-foot column required excessive analysis times to obtain sufficient peak separation and showed unacceptable peak sharpness due to tailing. The 6-foot column seemed to offer the best chance for obtaining the desired separation. The columns tested which provided reasonably good separation of the nitroparaffins caused considerable tailing for oxygenated compounds. Those which provided good separation for oxygenated compounds caused leading of the nitroparaffins. The use of mixed substrates eliminated leading altogether and eliminated tailing except in the methanol and nitromethane peaks. For these tu70 compounds, the amount of tailing observed had no apparent effect on quantitative work. Further studies showed that the substitution of Apiezon N for Apiezon M greatly improved the separation, so an experiment was designed for the sys-
c
I-NP
-
t
"'1,
,
0.3
0
2
4
6
8
12
IO
14
Heating rote ,"G/min.
tematic investigation of this promising area. This packing inverted the elution order of 2-M-I-NP and 2-NB from that already reported (2). Operating Conditions. T h e experimental conditions are shown in Table I, with the retention times of 1-NP corresponding to each set of experimental conditions. Two replicates were made a t random for each set of conditions within each flow rate .group, regardless of type of analysis (constant temperature or programmed temperature) using a 4-pl. sample of the test mixture for each run. Additional replicates were made a t random with respect to type of analysis, level of operation within each type, and flow rate. These additional runs showed that there is no change in column characteristics with time and that the experimental conditions and retention times of the nitroparaffis are reproducible within + 1%. DISCUSSION
The effect of temperature on relative retention time for the nitroparaffins at the optimum flow rate found for isothermal operation (90 ml. of Hz per minute measured a t 28" C.) was to reduce the relative retention time for 1nitrobutane from 2.53 to 2.02 and to increase the relative retention time of nitromethane from 0.25 to 0.38 as the
Table 1. Retention Times for 1 -Nitropropane and Experimental Conditions for Determination of Optimum Operating Conditions for Maximum Separation and Resolution of Nitroparaffins
Flow RateJo F , bll./Min. 60
90
120
150
Retention TimesTMinutesb Temp., ' C. Constant Temperature 40 50 60
70 80
Heating Rate C./Min.
20.21 1 2 T Q T 15 53 8 68 6 65 8.06 6.38 4.40 5.92 4.62 3 . 3 4 4.39 3.22 2.54
7 m 5.59 4.02 2.86 2.31
Linear Temperature Programmingc
7.03 6.28 5.88 5.24 5.05 4.23 Hydrogen flow rate measured at 28' C. 2.9 4.0 5.6 7.9 11.0 15.0
11.82 10.42 9.18 7.66 6.85 5.66
9.73 8.56 7.46 6.53 6.00 4.92
7.41 7.06 6.14 5.39 4.99 4.27
Measured from injection point to appearance of peak maximum height. Starting temperature, to = 40" C.
isothermal level was varied from 40' to 88" C. This effect becomes more pronounced as the flow rate is increased. It was decided to use retention times relative to that of 1-NP for correlating data, since this compound is one of the VOL 33, NO, 7, JUNE 1961
835,
i i 2.484 2.457
e
e
I 0
4
8
12
16
20
F -, Rh
Figure 2.
24
36
40
44
48
*
52
,.
Combined effects of tlow rate and heating rate on relative retention time
major products resulting from the vaporphase nitration of commercial butane, and it will be present in all samples taken for analysis. Reproducibility of results a t constant temperature is within 10.8%. Figure 1 shows the effect of linear temperature programming on relative retention time a t a flow rate of 150 ml. of hydrogen per minute, measured a t 28' C. Each component is eluted a t a characteristic temperature and time. As is seen from Table I and Figure 1, the retention times decrease with increasing Rh. This effect becomes more pronounced a t the lower flow rates, as the sample components have longer residence times in the column a t the lower flow rates. Obviously, the combination of extremely low flows and high heating rates will result in increasingly poorer separation and the relative retention time of all components will approach 1.0. For our system, increasing RA caused a decrease in resolution and consequently a decrease in efficiency; therefore further efforts were directed toward high flow rates and moderate heating rates. Leading diminished markedly with increases in flow rate and heating rate. Tailing presents little problem with the nitroparaffins ANALYTICAL CHEMISTRY
32
mW,/min-"C,
MI. H?/min.: X 60,
836
28
0 90,
A 120,
and the lower oxygenated compounds, with the exception of nitromethane and methanol, which consistently show slight tailing. A starting temperature of 40' C. was chosen as being far enough above room temperature to allow rapid establishment of thermal equilibrium and yet low enough so that acceptable separations are obtainable. Some work was done with starting temperatures of 35' and 50" C. Thermal equilibrium a t the starting temperature was assured by waiting until the recorder base line was constant for a t least 10 minutes before sample injection. The analyses a t the lower starting temperature resulted in unacceptable tailing of the first four constituents (NM through 2-M-2-NP) and unacceptable leading of the last three constituents (2-NB, 2-M-I-NP, and 1-NB). Under these conditions, leading and tailing were approximately equal for 1-NP. With the higher starting temperature, the peaks were greatly sharpened, but were too close together for future quantitative work, especially the pair 2-M-2-NP and 1-NP and the pair 2-NB and 2-M-1-NP. Figure 2 is a plot of relative retention time us. flow rate to heating rate ratio, F/RA,where F is in milliliters of hydro-
V 150
gen per minute, measured a t 28" C. over a range of 60 to 150 and Rh is in degrees centigrade per minute over a range of 2.9 to 15.0. This correlation is presented over a range of 4.0to 51.5 ml. of hydrogen per O C. Figure 2 indicates that the relationship between relative retention time and F/RA for values above 20 ml. of hydrogen per O C. is approldmately linear. With increasing values of F/Rh, the slopes of the curves approach constant values, indicating that at infinite values of F/Rh, the relative retention times will approach their isothermal values a t the starting temperature as has been suggested (6). These values of ti a t 40" C. and a flow rate of 60 ml. of hydrogen are shown on the extreme right side of Figure 2 for comparison. Also apparent from the curves is that a t very low values of F/Rh, no separation will be obtained. The resolution data from the constant temperature runs fall in a family of shaped curves showing maximum peak resolution a t a flow rate of about 90 ml. of hydrogen per minute, which is in agreement with many other studies using l/c-inch columns. Though the data may seem to indicate that even larger values of R may be found a t flow rates in excess of 150 ml. of hydrogen per
--
0.16
I
1
I
I
I
-
b
minute, it WM found that at this flow rate, the peaks were too close together for quaptitative work. The reason for the presence of both maxima and minima in these curves is not known. Values of resolution, R, for the constant temperature runs are presented in Figure 3. Rdl, corresponding to the resolution of 2-M-2-NP from 1-NP, and Rm, corresponding to the resolution of 2-NB from 2-M-1-NPJ test our data most severely. These data form a family of curves similar to those obtained for relative peak separation, S, which indicates that relative peak sharpness, Q,is also changing in a consistent manner within the temperature and flow rate limitations of this study. The Q and S curves are not shown, since their shapes are similar to those for resolution. Since R is a function of Q, the peculiar curvature may be explained in the following manner. Both Q and S are low initially, pass through a maximum a t about 90 ml. of hydrogen per minute, and slowly decrease, but a t different rates. S is initially between 5 and 10% below its maximum value. Above 90 ml. of hydrogen per minute, S remains essentially constant with slight minima apparent a t about 120 ml. of hydrogen per minute. However, Q values beyond their maxima continually decrease. The data obtained using linear temperature programming are presented as
2 .o
Figure 3. Effect of flow rate on resolution for isothermal operation 0
A V X
4OoC. 5OoC. 60°C. 7OoC. 8OoC.
1
I .6
I.4
U c- 1.2 0 +
3 0
1.0
U
.
0.6
1
--I
'
0
2
L
I
I
60
i
-4
X
I
~
!
j
120
90
I I50
~
functions of F/Rh, milliliters of hydrogen per degree centigrade. As seen in Figure 4, the values of 8 4 5 and 867 obtained using various combinations of flow rate and heating rate fall on continuous smooth curves, as would be expected frpm previous work (4, 7). For
0
Q,
0.08 Q,
I
I
I
I
I
I
I
I
T
-
T
-
J
~
~
A
- 0.06 0
Q)
a
0.04
0.02
t
c --,rnl,H~OC. F Rh
Figure 4.
j
values of 8 4 5 above F/Rh = 20 ml. of hydrogen per O C. and So?for the entire range of this correlation, the relationship is approximately linear. This was expected in light of the similar behavior of the relative retention times of 2-M-2N P and 2-NB (Figure 2).
i
Y
l
F, ml.H,/min.
t
> .c
I
0.8
Combined effects of flow rate and heating rate on relative peak separation Ml./min.:
X 60,
0 90,
A 120,
150
VOL. 33, NO. 7, JUNE 1961
837
l
o
l
i
r
I
i
1
r
r
I
10
0
r
I 20
I
I
l
F ,ml.H,/"G.
I
l
l
l
r
r
l
l
r
l
40
30
i
l
I
t
i
j
50
Rh
Figure 5. Combined effects of flow rate and heating rate on resolution Ml./min.:
The differences between any two curves in Figure 2 (representing ti - t,) increase with increasing F/Rh. The absolute value of ti from Table I (1-NP), however, decreases from an initial value of 5.66 milutes a t F/Rh = 4 ml. of hydrogen per O C. to a minimum of 4.23 minutes a t F/Rh = 10 ml. of hydrogen per O C. and then increases nonuniformly because of the conflicting effects of flow rate and heating rate. Thus S will be small a t low values of F/Rh and gradually increases as F/Rh gets larger. Since H i s proportioned a t S2,this means that the right side of Equation 18 must be small, indicating that the contribution of term 2 will be slight. It is the only term of the right side with a direct dependence on T. Term 5 will become smaller faster than terms 3 and 4 as T increases. Terms 1, 3, and 4 make the major contributions to S under these conditions. For a small Rh a t a constant flow rate, S will be larger, so the right side of Equation 18 will be larger. These conditions produce lower average values of T,and term 2 is even smaller. Terms 3 and 4 will make a greater contribution, and term 5 will begin to have an appreciable effect. The contribution of term 5 will become even more apparent as the temperature is lowered. If to is 838
ANALYTICAL CHEMISTRY
0 60,
A 90,
120,
X 150
Ion-ered to liquid nitrogen temperature, the diffusion rate in the partitioning agent under that condition will be extremely low, and term 5 will become dominant.. S will become large. Equation 18 has been used to explain qualitatively the data collected. Further work is needed on this and other systems in order to estimate the magnitudes of the contributions of the physical effects represented by each of the five terms. A mathematical analysis, such as that of Kieselbach ( I S ) , would provide values of the coefficients. The relationship between F/Rh and relative peak sharpness, Q, was found to be approximately linear. In contrast with the isothermal behavior, both Q4 and Q6exhibited a twofold decrease over the range F/Rh = 4 to 50 ml. of hydrogen per 'C. Our data show that halving Rha t constant F increases wi by approximately 35% with a concurrent increase in ti of only 10 to 15 %. Referring to Equation 18, if the left side (proportional to 1/Q;) is increasing, the contribution of term 2 of the right side has become less dominant, as predicted. No values of Q4 or &e deviated more than d=5% from a linear least squares fit, of the experimental data. The combined effects of Q and S on
resolution are presented in Figure 5 . Figure 2 shows that (t, - t i ) gradually increases (but at a decreasing rate) as FIRhincreases. Now w,is known to decrease with increasing F-Le., increasing F/&. R would therefore be expected to be small initially and to increase with F/&. The curvature of R in Figure 5 is more pronounced than that seen for S in Figure 4, since R is the product of Q and S . At high values of F/Rh, Q is lower and tends t o flatten the high end of the R curve. For any combination of Aow rate and heating rate such that F/Rh 8 2 0 ml. of hydrogen per c., acceptable resolutions are obtained. Based on the following considerations, an R 2 0.6 has been taken as the criterion of satisfactory resolution for the nitroparaffin system. This has been tested in the laboratory against seven known mixtures of the nitroparaffins given previously (2). In Figure 3, R46 falls between 1.2 and RB7falls between 0.3 and 0.9 for the work done a t constant temperature. Thus R6, is controlling as to the choice of operating level for analysis a t a constant temperature. Acceptable resolution is obtained a t constant temperatures of 40°, 50', and 60' C. corresponding to total analysis times of 32, 20, and 14
minutes. The combination of some tailing of the 2-M-1-NP and 1-NI3 peaks and excessive analysis time a t 40' C. and overcrowded chromatograms a t 60' C. eliminates these conditions. The optimum R is obtained a t 50" C. a t a flow rate of 90 ml. of hydrogen per minute. Figure 5 shows that for F/Rh ml. of hydrogen per O C., R46 and Rs, are always greater than 0.6. In the linear programmed work, runs at any of the tested flow rates and an Rh 2 4.0' C., per minute produced overly crowded chromatograms-Le., total analysis time times ranged from 15 to 9 minutes as Rh increased. Within the runs made a t Rh 2 2.9' C . per minute, the best compromise between resolution and total analysis time indicates that a flow rate of 60 ml. of hydrogen per minute will produce optimum results. A summary of the optimum operating condition is presented in Table 11. It appears that, for one system, making a basic data survey or "box" by using several widely separated levels of operating conditions as shown in Table I will point out the most fruitful areas for further investigation. It is perhaps too early to state categorically that these areas will also be the best to investigate for still other systems. However, for an equivoluine mixture of alcohols (methanol, ethanol, 2-propanol, 1-propanol, 2-methyl-2-propano1, and 2-butanol) optimum resolution was obtained under the same conditions as those found most advantageous for thr nitroparaffins. This was determined by analyaing the alcohol test mixture under the conditions providing optimum nitroparaffin separation and extending the levels of these conditions to form a box about this central point. The resolution of the alcohols was satisfactory a t the center of the box and became progressively poorer as we moved further from the center. The work done on the alcohol test mixture and incomplete studies on esters, ethers, and ketones indicates that Equation 18 can be used t o explain the effects of temperature and flow rate on these systems as well as for the nitroparaffins. The primary advantage in using linear temperature programming is the production of more symmetrical and evenly spaced peaks than those obtained with constant temperature analysis. A combination of isothermal and programmed temperature operation should result in an improvement in the resolution of the pair 2-M-2-NP and 1-NP and the pair ZNB and 2-M-1-NP. Work is in progress to verify the expected beneficial effects of combined isothermal and programmed temperaturo operation (ramp-function programming). Parameters currently under investigation are flow rate, column length, the duration of the initial constant tem-
perature period, and the heating rate used during the linear programmed temperature period. ACKNOWLEDGMENT
The authors thank D. C. Dangoria and C. C. Hull for assisting with the laboratory work and the calculations.
Table
II.
Optimum Conditions Nitroparaffin Analysis
for
Operational Operational Flow Method Level Rate" Isothermal 50' C. 90 Linear temperature programming 2.9"C./min.* 60 a Measured a t 28" C. b Starting temperature 40' C.
X
= fractional column cross-sectional
a
= over-all mass transfer resistance
area, dimensionless
y
=
X
=
e
= = =
p T
per unit volume of packing, sec.-l constant in van Deemter equetion accounting for tortuosity of gas flow paths, sec.'/cm. constant in van Deemter equation characteristic of the paeking, dimensionless time, min. vist:osity, gram/cm. sec. 3.1416, dimensionless
SUBSCRIPTS A = solute B = carrier gas 11, f , I = substrate
a
= bulk gas phase = gas in pores
r
development
= any sample components = solid support particles = gas phase in van Deemter'e
i,j
1,2,3,4= different constants or functions
NOMENCLATURE
A
=
a
B
= =
B'
=
C = C' =
c
=
D, = D, = d, = dh
=
d, =
E E'
= =
e
=
F
=
G
=
G'
=
H
=
j
= =
k
R h
= = = =
T
=
K
L 1
t = to =
constant in Equation 10, dimensionless specific surface, cm.-l coefficient in Equation 10, dimensionless coefficient in Equation 18, cm. ml./"K.*/I min. coefficient in Equation 10, dimensionless coefficient in Equation IS, min./cm. ml. constant diffusivity of solute A in carrier gas B, sq. cm./sec. diffusivity of solute A in partitioning agent, sq. cm./sec. effective thickness of liquid layer coating each particle, cm. effective pore diameter, cm. effective average particle diameter, cm. Coefficient in Equation 10, cm1.-2 coefficient in Equation 18, 'K,a/2 min./cm. ml. base of natural logarithms, 2.718
...
volumetric carrier gas flow rate, ml./min. coefficient-in Equation 10, dimensionless coefficient in Equation 18, OK.'/' min./cm. ml. height equivalent to a theoretical plate, cm. function o f . partition coefficient, moles solute/mole gas Dhase . moles so1ute)mole liquid phase constant defined by Equation 8 column length, cm. effective pore length, cm. heating rate, C./min. absolute temperature, O K . retention time, min. struting temperature in progrrtmmed tcmpcrature runs,
..
O
c.
u = lincnr carrier gas velocity, cm./
sec. w = peak width measured between inflection tangent intercepts a t the chart base line, min.
LITERATURE CITED
(1) Baker, W. J., Lee, E. H., Wall, R. F.,
Second International Gas Chromatography Symposium, East Lansing, Mich., June 10,1959. (2) Bethea, R. M., Wheelock, T. D., ANAL. CHEM.31, 1834 (1959). (3) Dal Nogarc, S., Bennett, C. E., Ibid., 30,
l l C 7 /\'"VU,. lClCP\ la",
(4) D'a1 Nogare, S., Harden, J. C., Ibid., 31, 1829 (1959). 1 3 ~ ~ Langlois, ~ ~ r W. ~ E., 4 n (5) . . D,~ Ibid., a&, I U I ( I V O V ~ . (6) Deemter, J. J. van, Zuiderweg, F. J., Klinkenberg, A., C h a . Eng. Sci. 5, 271 I~ 19.56). ..__,_
(7) Eggertsen, F. T., Groennings, S., Holst J. J., ANAL. CHEM. 32, 904 ( 1960). (8) Ergun, S., Chew Eng. Progr. 48, 89 (1952). (9) Evans J. B,, Willard, J. E., J. Am. Chem. doc. 78, 2908 (1956). (10) Oolay, M. J. E., in "GBB Chromatography, 1968," D. H. Desty, ed., pp. 61-3, Butterworths, London, 1958. (11) Hab ood, H. W., Harris, W. E., ANAL. 32, 460 (1960) (12) Jones, W.L.,Kieselbach, R., Ibid., 30,1590 1968). (13) KielsJbach, R., Ibid., 33, 23 1961). (14) Martin, A. J., . Bennett, E., Martinez, F. W., informal discuRsion group, Second International Gas Chromatogra hy Symposium, East Lansing, Mich., &no 10, 1059. ( I 5) Perra J. H.k,$, "Chemical Engineer's andboo 3rd ed., p. 372-4, McGraw-Hill New York lf50. (16 Purnell, i. H in "3apour Phsse dhromato raphy,;)'D. H. Desty, ed., p . 52 Acafiemic Press, New York, 195F. (17) gennev. " , H. M.. ANAL. CHEM.30. 2 ' ('1958). (18) Trcybal, R. E., "Mass Transfer 0 crations," pp. 21-4, McGraw-Hill, fw York, 1955. (19 Zarembo, J. E., Lysyj, I., ANAL. ,HEM. 31, 1833 (1050). (20) Zlatkis, A,, Ling, S., Kaufman, H. R., Ibid., 31, 945 (1950). RECEIVED for review September 6 1960. Accepted March 27, 1961. Work supported equally by rcscarch pants from the Engnccring Expcriment Ststion, Iowa State University, and Phillips Petroleum Co.
HEM.
I
b.
VOL. 33, NO. 7, JUNE 1961
899
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