Frontal Analysis Chromatog raphy Experimental Study of Flow Rate Changes Due to Solute Sorption, and Retention Characteristics of Sharp Fronts G. J. KRIGE' and VICTOR PRETORIUS Department of Physical and Theoretical Chemistry, University of Pretoria, Pretoria, South Africa
b An experimental test is made of theoretical expressions previously derived for the retention times of solute fronts and the rate of flow during frontal analysis when sorption effects are important. The experiments are conducted on a column packed with activated carbon, using an equimolar mixture of methane and carbon dioxide, undiluted with carrier, as sample. Values of the mass distribution coefficients are estimated from the corresponding adsorption isotherms of these gas-solid systems, and a close correspondence between theory and experiment is obtained.
A
paper (4) reported a theoretical study of the role played by sorption effects in frontal analysis, assuming that sharp fronts are formed. It was shown that if the sample inlet concentration is sufficiently high, the flow velocity of the mobile phase behind each front exceeds that ahead of the front, and fluctuates with time until the last front has emerged from the column. Theoretical expressions were derived for the retention times and volumes of the fronts, and for the rate of flow during frontal analysis, when a binary mixture of solutes, assumed to be incompressible, is continuously injected into a chromatographic column. An experimental test of this theory is described in the present paper. Since a prior knowledge of the values of the distribution coefficients, and their dependence on the mole fraction of each solute, is required for this purpose, it was found most expedient to use gasadsorption chromatography with permanent gases, in a mixture of known composition, as samples. Distribution coefficients could then be estimated from data for individual adsorbates. The investigation was further simplified by continuously introducing an undiluted binary solute mixture into the column. Under these conditions the mole fraction of the less strongly retarded solute Temporary address, Department of Chemistry, University of British Columbia, Vancouver, Canada.
between the first and second fronts is so that all mole fractions and unity (4, distribution coefficients were available once the adsorption isotherms of the gas-solid systems had been determined.
independent of the effective diameter of the particles (6). The methane was supplied by Matheson and Co. A mass spectrometric analysis showed that it was 97.3y0pure. The carbon dioxide was obtained from African Oxygen Co., and is claimed to be 99% pure. For simnlicitv the samnle eases were not dilute'd wi;h helium' beyore injection. A mixture of methane and carbon dioxide was made by bleeding first the one and then the other pure gas into an evacuated cylinder. The mole fraction of each solute in the mixture was 0.5, and was determined by measuring the pressure of the first pure gas and of the mixture in the cylinder. Before experiments were conducted, the cylinder was allowed to stand for 72 hours to ensure complete mixing of the gases by diffusion. 1 -
THEORY
The expressions derived (4) for the retention times of the solute fronts (fa, ib) and the variation of the flow rate a t the column outlet (uc, u,) with time assume the following form when XIi X z i = I-i.e., XCi= X,"= 0, XI" = 1:
+
PREVIOUS
Determination of Adsorption Isotherms. The adsorption isotherms of methane and carbon dioxide on activated carbon were determined by a volumetric method on a conventional apparatus (IO). The principle underlying this method is briefly the following.
u. = uoqi - (1 75
2u,qig+t -u2 + m)
where and
EXPERIMENTAL
Chromatographic experiments were carried out on a column packed with activated carbon (British Drug Houses). The samples were a mixture of pure methane and carbon dioxide. Helium was used as a carrier. The carbon was activated in an oven at 160" C. for 16 hours. Although the isotherms were determined on a 40- to 60-mesh fraction, the internal surface area of the carbon is so large that the amount of gas adsorbe,d is essentially
The pressure, volume, and temperature of an amount of the adsorbate are measured before it is admitted to an evacuated, thermostated tube containing the adsorbent. The gas is then admitted to the tube, and its pressure, volume, and temperature are measured once equilibrium has been established. The volumes are converted to milliliters a t normal temperature and pressure, and the difference between the two readings divided by the weight of adsorbent in the tube yields the volume of gas adsorbed in milliliters a t normal temperature and pressure per gram of adsorbent. The accurate determination of the amount of gas unadsorbed a t equilibrium depends on a precise knowledge of the dead volume of the adsorption apparatus. This was evaluated by expansion measurements using helium, the adsorption of which was assumed to be negligible. The isotherm may be determined either by fixing the volume and temperature and measuring changes in the pressure, or by kceping the temperature and pressure constant, and measuring the decrease in the volume. The former, simpler, method is preferable for VOL. 37, NO. 10, SEPTEMBER 1965
1191
of the adsorbent surface. The convenient parameter b may be written as (2J1' SA7&Q/RoT b&Q/RaT -~ b= (8) T" * n, (2*MR,T) 1'2
no is proportional to am, and hence bo should theoretically be independent of
T. The applicability of Equation 7 to the gas-solid systems used in this study may be tested in two ways. First, it can be rearranged in the form
P,cm.Hg Figure 1. Adsorption isotherms of methane on BDH activated carbon a.
b. E.
1
a
+ 17'C. + 80OC.
1
ba,p bp
+
(7)
The Langmuir theory assumes that a , is determined solely by the geometry
p,c m. Hg Figure 2. Adsorption isotherms of carbon dioxide on BDH activated carbon a. b. C.
1192
-13OC. 17' C. ++ 80OC.
ANALYTICAL CHEMISTRY
1 1 1 X - f ba, p am
_ = -
- 20°C.
equilibrium studies such as were conducted here, and was adopted. Experimental adsorption isotherms of methane and carbon dioxide on activated carbon a t three different temperatures are given in Figures 1 and 2. The experimental points obtained a t low temperatures suggest that the relation between the amount of gas adsorbed and the pressure may be described by a Langmuir-type isotherm-i.e., (9) a=-
On plotting p / a against p , a straight line of slope l / a , and intercept l / b a m should be obtained. Alternatively, it may be written as
Figure 3. Analysis of data for methane in Figure 1 according to Equation 10
(10)
and a plot of l/a against l / p should be a straight line of slope l / b a m and intercept l/a,. I n Figures 3 and 4 the experimental results obtained for methane and carbon dioxide a t -20°, -13", and 4-17' C., have been analyzed in terms of Equation 10. The approximate linearity of the plots indicates that the Langmuir-type isotherm may be used for the gas-solid systems employed in the range of temperatures covered. I t is noteworthy that the intercepts of the lines with the I / a axis-Le., the values of 1/am-are virtually independent of the temperature. This provides further justification for the use of Equation 7 . The characteristic parameters in the isotherm for each gas were determined with a view to obtaining the best possible fit to the experimental points in Figures 1 and 2. Higher precision was obtained in the values of a,, a t the lower temperatures by determining them from the slopes of plots of p / a against p rather than by using Equation 10. The results are given in Table I. KO attempt was made to evaluate am for the curves a t 80" C., since the isotherms are approximately linear, and inaccurate results would be obtained. The values of a,,, in Table I are approximately constant, and for the purpose of fitting Equation 7 to the experimental curves an average value, Cimj was used for each gas. Then, from Equation 7 ,
The value of b a t each experimental value of a and p was calculated from Equation 11 and the value of 8, in Table I. The average value of b a t each temperature is given in Table I. The heat of adsorption, Q, and the temperature-independent parameter, bo,
+- 2OOC. 17OC.
a. b.
in Equation 8 were determined from the values of b by plotting log ( b V'?) against 1 / T . Their values are also given in Table I. The accuracy of the values of a,, bo, and Q are not indicated in the table. However, if they are used in conjunction with Equation 7 t o plot the adsorption isotherms of methane and carbon dioxide a t each temperature, the curves fall within approximately 3% of the data in Figures 1 and 2. Adsorption isotherms of gas mixtures are difficult to obtain ( 2 1 ) . However, the close conformity of the isotherms of pure methane and pure carbon dioxide with Equation 7 suggests that the mixed Langmuir isotherm should be used to describe the adsorption of a mixture of
E
z
0 0
I
.
0.1
l
0.2
*
l
0.3
l/p, (c m.Hg )-' Figure 4. Analysis of data for carbon dioxide in Figure 2 according to Equation 10 a.
b.
+ 17OC. - 13OC.
these gases, The values of d, for the tJyo gases do not differ much from one another. N o serious error is thus made if the common value of a,,, in the mixed isotherm, amrn,is taken as the arithmetic mean of the values determined for the two pure gases (fd). The volume of solute 1 adsorbed is then (12)
and the corresponding expression for solute 2 is bnam"Xzp a2 = -~ 1 (biXi b2Xz)p
+
+
(13)
For the present system subscripts 1 and 2 refer to methane and carbon dioxide, respectively. X i and X z denote the mole fractions of the solutes in the gas phase, and bl and bz have the same meaning as b in Equations 7 and 8. The values of bl and bz may be calculated a t any temperature in the approximate range -20" to 100" C. from Equation 8 and the data in Table I. The value of is the average of the values of 8, in Table I-viz., 31.59 ml. a t normal temperature and pressure per gram of adsorbent. Mass Distribution Coefficients. The mass distribution coefficients are determined by dividing the volume of gas adsorbed a t equilibrium by the corresponding volume of gas in the mobile phase, both expressed in the same units. For simplicity, all distribution coefficients are evaluated a t the average column pressure during an experiment, p . I t may easily be shown from Equations 12 and 13 and the ideal gas law that, for a mixture of two sorbable gases of mole fractions X 1 and XB,
and
where, in general,
For a single solute diluted with inert carrier to a mole fraction X i ,
I n Equations 14 to 17, k X denotes the mass distribution coefficient at an arbitrary mole fraction, p a is the weight of adsorbent per unit column volume, and E is the total fractional void volume of the packed column. p , = 76 cm. of Hg and T , = 273"A. The average column pressure is given by (7)
[SAMPLE from qlindv
PRESSURE REGULATOR-
$
~~CARRIEF~~~
%WAY SOLENOID VALVE
VALVE
To MANOMETER To COLUMN
Figure 5. Schematic diagram of inlet system for injection of permanent gases
For values of p,/p. less than 1.4, p is equal to l / Z ( p , po) to within 1%.
+
Chromatographic Apparatus. T h e basic apparatus consisted essentially of a sample and carrier inlet system, a chromatographic column of copper tubing, and a thermal conductivity detector of the semidiffusion type (Gow-Mac, Model 9285). All components were thermostated in a forced circulation air bath to within 0.5" C. The column outlet was maintained a t atmospheric pressure. One arm of the detector was sealed, trapping a volume of air which served as a reference. The signal from the detector, which was energized by a 6-volt wet storage battery, was fed directly to a recording potentiometer (Philips). A soap bubble flowmeter was used to measure the volumetric flow rate a t the column outlet. Since the flow velocity changes with time, errors arising from this source were kept small by limiting the time of measurement to a sufficiently small value in all cases. The experimental results given below were obtained on a column (column B) 100 cm. in length, 0.63 cm. in i.d., packed with 60- to 80-mesh BDH activated carbon, which was held in place with glass xool plugs. The weight of the packing per unit column volume, p a , was 0.55 gram per cc. A stream of helium was passed through the column a t an elevated temperature until a steady base line and reproducible results were obtained.
Method of Sample Injection. Continuous introduction of permanent gas samples was achieved with the inlet system shown schematically in Figure 5. To avoid pressure surges when injection is commenced, i t was necessary to incorporate a column bypass system in the inlet, through which the sample could be directed when not required for an experiment. 'l'wo solenoid valves (Automatic Switch Co., Models H T X 831442 and H T X 82627) were used for this purpose. The positions of the valves prior to sample introduction are depicted in Figure 5. Carrier gas from a cylinder passed through the column, while sample gas from a cylinder passed through the needle valve (Hoke, Inc.). The latter was adjusted so that the flow resistance of the sample inlet system was the same as that of the column. The sample was introduced by switching the three-way solenoid valve into its alternate position. Suitable connection of the circuits for the two- and three-way solenoid valves assured that the carrier stream into the column was simultaneously interrupted. After the last front had broken through, the column was purged in preparation for the next experiment by switching the solenoid valves back to the positions shown in Figure 5. I t was possible to vary the inlet pressures for sample and carrier introduction independently by means of two pressure regulators (Negretti and Zambra, Model 20 AG-XZ and Precision Type R 182). RESULTS AND DISCUSSION
Retention Times of Solute Fronts. Since the theory applies strictly oiily to a mixture of incompressible solutes ( 4 ) , the retention times of the fronts were determined a t a flow velocity for which the pressure drop along the column was small. The details of the experimental conditions, and the corresponding values of the parameters required for the theoretical prediction are given in Table 11. of f, and la, The values of the mole fractions, distribution coefficients, and gas viscosities were determined as follows. Since the solutes were undiluted with carrier, X C a = 0 and X I u = .1 (4). kin was determined from Equations 16 and 17 with X j = 1, pa = 0.55 gram per
Table I.
Values of Characteristic Parameters in Equations 7 and 8 for Methane and Carbon Dioxide On BDH activated carbon, determined from experimental points in Figures 1 and 2 am, ml. at dm, ml. at 6, X 104, Temp., NTP/g. 6 X lo2, NTP/g. (A.)l'z/ Q, cal./ Adsorbate ' C. adsorbent (cm. Hg)-l adsorbent cm. Hg mole hIethane 80 0.319 29.02 1.26 4332 Carbon dioxide
++-2017 +80 +I7 - 13
:
36 67 27.37
:
35 55 32.76
1.40 4.29 0.917 5.43 14.3
34.16
1.45
VOL. 37, NO. 10, SEPTEMBER 1965
5007
1193
~
Table II. Parameters Used for Prediction of fa and fb Experimental conditions Column length, L, cm. 100 Column temp., C. 80 2.8 Pressure drop over column, pi - p o , cm. Hg 66.6 Average column pressure, p , cm. Hg Flow velocitv at column outlet after breakthrough of 0.69 second frok, u., cm./sec. Helium Carrier gas carbon dioxide Methane Sample X,' = X2' = 1 1 2 Inlet mole fractions Gas viscosities 2.254 X Ahead of first front, qc, poise 1.323 X 1OF4 Between first and second fronts, q o , poise 1.692 X Behind second front, qi, poise Mass distribution coefficients 5.16 Solute 1 between first and second fronts, k l a 4.82 Solute 1 behind second front, kt' 13.86 Solute 2 behind second front, k~' O
+
Table 111. Theoretical and Experimental Values of Retention Times of Solute Fronts la,
sec.
b
- 10,
sec.
b j
sec.
787 1377 Experimental 590 1 . Sorption Effects Negligible Theoretical 893 1261 2154 Relative error, % 51.4 60.3 56.4 2. Sorption Effects Important Theoretical 601 827 1428 Relative error, % 1.9 5.1 3.7
cc., e = 0.8 (I), and values of the other parameters at 80" C. given in Table I (b, a,) and Table I1 ( p ) . kl' and k2' were calculated from Equations 14 to 16 with X1 = X Z = I/t, P. = 0.55 gram per cc., c = 0.8, and values of other parameters given in Tables I and 11. a m m = 31.59 ml. at normal temperature and pressure per gram of adsorbent. The viscosity of the gas ahead of the first front is that of helium (6); between the first and second fronts it is that of methane ( 5 ) . The viscosity of the gas mixture behind the second front was calculated from the viscosities of methane and carbon dioxide (5) using Wilke's equation (8)-viz.,
1 194
ANALYTICAL CHEMISTRY
methane and carbon dioxide, respectively. v* refers to the viscosity of the pure gas. The theoretical and experimental retention times of the solute fronts are compared in Table 111. The former were calculated by assuming that (1) sorption effects are negligible and (2) sorption effects are important. In case 1 f = L(1 k)/u,, and the results in Table 111 were obtained by using the values of L, u,, kl" and k2s in Table 11. Values of f, and f b pertaining to case 2 were calculated from Equations 1 and 2 and the data in Table 11. The experimental fronts were only a few seconds wide; retention times in the table were found from the profiles by assuming that t = f when the concentration corresponds to half the height of the step. I t is clear from Table I11 that sorption effects play a significant role in reducing the retention times of the fronts under the present conditions, and that a serious error can be introduced in the predicted values of f, and t 5 when this mechanism is neglected. Although the verification of the theor] presented in the previous paper (4) is subject to limitations imposed by experimental uncertainties associated with the adsorption isotherms, Table 111 shows that for most purposes it permits a reasonably accurate estimate of the retention times of the fronts. Rate of Flow during Frontal Analysis. T h e theoretical expressions for the change in the flow rate at the column outlet with time during frontal analysis of a binary solute mixture were also tested experimentally under t h e conditions given in Table 11. The theoretical and experimental results are compared in Figure 6. The solid lines were calculated from Equations 3 and 4,using the data in Table 11. The agreement between theory and experiment is particularly good in the interval before breakthrough of the first front. Although the curves deviate slightly in the region between the first
+
-
0
0
12 16 20 24 t,min. Figure 6. Variation of flow rate at column outlet during frontal analysis of a binary solute mixture
4
8
Experimental conditions given in Table II, and theoretical curves calculated from Equations 3 and 4 0 Experimental Theoretical
---
-
and second fronts, the discrepancy is always less than about IO%, which is reasonable in view of the approximate isotherms employed for the gas mixture. NOMENCLATURE
Unless otherwise stated, subscripts 1 and 2 refer to the less and more strongly retarded solute of a solute pair, respectively, and subscripts a and b, respec'tively, refer to the first and second fronts which break through at the column outlet when a binary solute mixture is continuously injected. Other nomenclature is explained in (4). a
= volume of gas adsorbed per
a,
= volume of gas adsorbed per
unit weight of adsorbent unit weight of adsorbent at infinite pressure 8, = average value of a, amm = common value of a, for two gases adsorbed simultaneously b = convenient parameter, Equation 7 bo = convenient parameter, Equation 8 g, g+ = convenient parameters, Equations 5 and 6 = dummy index j M = mole weight of gas NA = Avogadro's number = number of adsorption sites per no unit surface area of an adsorbent = pressure P = average pressure of a column P pn = 76 cm. of Hg Q = differential heat of adsorption R, = gas constant T = absolute temperature
T,
= 273'A.
t
= total fractional void volume
of a packed column
P.
= viscosity of a solute = weight of adsorbent per unit
7,
= convenient temperature-inde-
7”
column volume wndent Parameter, EWation 8 = convenient parameters, Equations 20 and 21 ACKNOWLEDGMENT
G. J. Krige is indebted t o the Director General of the Atomic Energy Hoard for permission to participate in this project.
LITERATURE CITED
( 1 ) Berge, P. C. van, Pretorius, Lr., J . Gas chromalog. 2,235 ( 1964). ( 2 ) Boer. J . H. de. “Ilvnamical Character ’ o f Adsorption,” p. &, Clarendon Press, Oxford, 1953. (3) I M . , p. 55. (4) Krige, (;. J., Pretorius, V., ANAL. CHEM. 37. 1186 (1965). (5) Lange, ‘IV. A., Forker, G,., &I., eds., ‘[Handbook of Chemistry, 5th ed., pp. 1588-91, Handbook Publishers, Sandusky, Ohio, 1944. (6) McBain, J. W., “Sorption of Gases
and Vapours by Solids,” p. 65, Routledge and Sons, London, 1932. ( 7 ) Purnell, H., “Gas Chromatography,” Chap. .5, Wiley, New York, 1962. (8) Reid, R. C., Sherwood, T. K., “Properties of Gases and Liquids,” p. 200, RIcGraw-Hill, New York, 1958. ( 9 ) Young, D. M., Crowell, A. D., “Physical Adsorption of Gases,” p. 106, Butterworths, London, 1962. (10) Ibid., Chap. 8. ( 1 1 ) /bid., Chap. 11. (12) Ibid., p. 353. RECEIVED for review February 2, 1965. Accepted June 9, 1965.
Frontal Analysis Chromatography Theoretical Treatment of Stationary Front Widths Neglecting Radial Perrnea bility Fluctuations G. J. KRIGE’ and VICTOR PRETORIUS Department of Physical and Theoretical Chemistry, University of Pretoria, Pretoria, South Africa At sufficiently high sample inlet concentrations in frontal analysis, front broadening processes can be balanced by front sharpening processes, and a stationary front is then formed. Theoretical expressions are derived for the widths of stationary fronts taking sorption effects into account. The continuous injection of a single solute, as well as a binary solute mixture which yields well-resolved fronts at the column outlet, is considered. Stationary fronts can arise with linear, type I, and even type 111 distribution isotherms when sorption effects are present. Results obtained are more general than those existing in the literature, and are compared with expressions derived by other authors.
I
been shown theoretically (14), and verified experimentally (15), that sorption effects in frontal analysis at high sample inlet concentrations cause significant fluctuations in the flow velocity of the mobile phase in a chromatographic column, and complicate the expressions for the retention times and volumes of sharp fronts. I n the present paper a theoretical study is made of the effect of sorption mechanisms on the shapes and widths of the fronts observed when both a single solute and a binary solute mixture are continuously injected into a column7 i.e., it is no longer assumed that sharp fronts of zero width are formed. The treatment is simplified considerably a t T HAS
Present address, Department of Chemistry, University of British Columbia, Vancouver, Canada. Permanent, address, Atomic Energy Board, Pelindaba, Republic of South Africa. 1
this stage by stipulating that radial variations in the permeability of the column packing are negligibly small; the other basic assumptions pertaining to the study of preparative chromatography by frontal analysis as a whole have been stated in (14). Various authors (1, 3, 4 , 9 , 18, 19, 21) have deri\ ed expressions for the shapes and widths of the fronts formed when nonideality operates in conjunction with nonlinearity and/or sorption efferts. It has been shown that, at sufficiently high concentrations, the unchecked spreading of the front due to nonideality (front broadening processes) can be counteracted to a lesser or greater extent by nonlinear and sorption phenomena (front sharpening processes). After sufficient time has elapsed the two processes can balance one another, and the shape and width of the front no longer change as it moves down the column. Fronts of this type have been referred t o as stationary fronts (3, 4,18, 19,21). One of the most important differences between frontal analysis and elution development is that stationary fronts may be formed when the former technique is used. The front resolution function, R , defined as (12, 17)
is then proportional to the column length, L, and not to as is the case when the distribution isotherm is linear and flow rate changes due t o solute sorption are negligible. This suggests that by employing conditions under which stationary rather than nonstationary fronts are formed, the mini-
dc
mum column length required to yield a given separation could possibly be significantly reduced. Glueckauf and Coates (9) have derived expressions for the shape of a stationary front for a solute which follows a Freundlich or Langmuir type distribution isotherm, but have neglected sorption effects and nonideality due to processes other than lateral nonequilibrium. Schay and his associates (3, 4, 18, 19) have incorporated the effects due to fluctuations in the flow rate for different types of isotherms, but have made simplifying assumptions regarding nonideality. These are that the plate height is due to either longitudinal diffusion in the mobile phase or lateral nonequilibrium in the stationary phase; no attempt was made to consider these effects in conjunction with one another. Rosanquet and Morgan ( 1 , 2) have investigated the formation of stationary fronts when flow rate changes due to solute sorption play a n important role, but have considered only linear distribution isotherms. The phenomenon of stationary fronts is investigated in detail in this paper. Theoretical expressions are derived which are not subject t o the assumptions made in the treatments referred to above, and are compared with the existing results in the literature. GENERAL CONDITIONS UNDER W H I C H STATIONARY FRONTS ARE FORMED
For the purpose of the present discussion it may be assumed that the shapes and widths of solute fronts are determined by three factors in addition t o the column length : VOL 37, NO. 10, SEPTEMBER 1965
1 195
