Theoretical Collection Efficiencies of Adsorbent Samplers Gunnar 1. Senum Environmental Chemistry Division, Brookhaven National Laboratory, Upton, New York 11973
The use of adsorbents in adsorption tube samplers for the collection and preconcentration of volatile components in air samples requires a knowledge of a maximum safe sampling volume or breakthrough volume in order to guarantee a quantitative collection. Previously there have been several arbitrary definitions of a breakthrough volume which have had various dependencies on the component retention volume and, in some instances, on the number of theoretical plates of the adsorbent. As a result of the application of chromatographic response theory to adsorption samplers, a breakthrough volume is defined and explicitly expressed in terms of a required collection efficiency, the retention volume for the adsorbate/adsorbent combination, and the number of theoretical plates of the adsorbent. The specified collection efficiency is guaranteed for an adsorption tube sampler as long as the sampled volume is less than this breakthrough volume. The use of adsorption tube samplers for the collection and concentration of trace volatile compounds in air, e.g., air pollutants, contaminants, etc., for subsequent detection has been extensively reported and demonstrated (1-11). A requirement which is necessary for the collection technique to be quantitative is that the volume of sampled air not exceed the safe sampling volume of an adsorbent for the particular compound (adsorbate) being collected. This safe sampling volume, Le., the adsorbate breakthrough volume, can be defined as the volume of air containing the adsorbate that may be sampled without a significant amount of adsorbate remaining uncollected. This adsorbate breakthrough volume is dependent on the adsorbate retention volume (V,) as has been observed in experimental studies ( 1 ,4 , 5 , 7-11). It is also dependent on the number of theoretical plates (N) of the adsorbent ( 5 , 8 ) ,a point which has been often overlooked in some experimental studies. Nonetheless, in some instances (11, 12) the adsorbate breakthrough volume has been arbitrarily defined as some fraction of the adsorbate retention volume as determined from a conventional gas-chromatographic experiment. Consequently, with the use of this breakthrough volume, it will not be certain whether the adsorbate has been quantitatively collected since the number of theoretical plates of the adsorbent has been neglected in the estimation of the breakthrough volume. It is the purpose here to derive explicitly the adsorbate collection efficiency of an adsorption tube sampler as a function of the adsorbate retention volume, the adsorbent number of theoretical plates, and the sampled volume under the assumption that standard chromatographic theory can be applied to adsorption tube samplers. As has been previously determined by Reilly et al. (12),the adsorbate concentration at the outlet of an adsorbent sampler is
R(V) = C erfc [(N/2)lI2(1- V/Vg)]/2 C erfc [(N/2)1/2(V/Vg+ 1)]/2 (2)
+
in which N is the number of theoretical plates of the adsorbent, i.e.
R(Vb) = fc
in response to an adsorbate concentration C, applied a t the inlet of the adsorbent sampler a$ time t equal to zero. Here, t , is the adsorbate retention time, u is related to the adsorbate chromatographic half-width, and erfc (x)is the complementary error function (13).This can be reexpressed as
(4)
However, it is more realistic to define the adsorbate breakthrough volume, v b , as the sampled volume when a certain fraction, f, of the total collected adsorbate has been allowed to pass through the sampler without collection, i.e.
in which the right-hand side of eq 5 is the amount of adsorbate not collected and the quantity enclosed in parenthesis on the left-hand side is the amount of adsorbate which has been collected. The expression for the outlet concentration R( V), eq 2, can be substituted into eq 5 to get an equation for Vb in terms of N and V,, i.e.
+
2f(Vb/Vg)(N/2)1/2/(1 f) = ierfc [(N/2)lI2(1- Vb/Vg)] T ierfc [(N/2)1/2(1 + Vb/Vg)] (6) in which ierfc (x)is the integral of the complementary error function (13).This equation has been numerically solved (14) for Vb/Vg (the breakthrough volume expressed as a fraction of the adsorbate retention volume) as a function of the number of theoretical plates of the adsorbent, N, and the desired collection efficiency, i.e. collection efficiency = 100(1 - f)
(1)
(3)
V, is the retention volume per gram of adsorbent and Vis the sampled volume per gram of adsorbent. This is the explicit expression, Le., the breakthrough curve, for the adsorbate concentration at the outlet of the adsorption sampler as a function of the sampled volume, V, the adsorbate retention volume, V,, and the number of theoretical plates of the adsorbent, N . This is displayed in Figure 1 as a function N and V/V,. The number of theoretical plates of the adsorbent is solely a function of the adsorbent and is, ideally, independent of the adsorbate and sampler temperature. Again, if N is large, the second term in R( V) is negligible with respect to the first term and can be neglected; consequently, in this approximation R( V) becomes the familiar expression for the breakthrough curve in frontal chromatography. However, both terms in R( V) must be maintained if R( V) is to have the proper limit as N approaches zero; Le., when no adsorbent is present in the sampler, then R ( t ) = C for t 2 0. Previously, in many instances ( 3 , 10, I I ) , an adsorbate breakthrough volume has been defined as the sampled volume when a certain fraction, f, of the inlet adsorbate concentration is detected in the outlet of the sampler, i.e.
R(t) = C erfc [ ( t ,- t)/21/2u]/2
+ C erfc [(tr + t)/21/2u]/2
N = (t,/a)2
.
(7)
The resulting curves as a function of collection efficiency ranging from 80%to 99.9% are displayed in Figure 2. A p p l i c a t i o n a n d Discussion
Standard chromatographic theory has provided a convenient expression for the breakthrough curve R( V), eq 2, given
0013-936X/81/0915-1073$01.25/0 @ 1981 American Chemical Society
Volume 15, Number 9, September 1981
1073
SAMPLING VOLUME/ RETENTION VOLUME
Figure 1. Adsorbate concentration (expressed as a fraction of the inlet concentration) expected at the outlet of an adsorption tube sampler as a function of sampled volume and the number of theoretical plates of the adsorbent (N).
‘0
0 2
0.4
0.6
0 8
1.0
1.2
I 4
SAMPLING VOLUME / RETENTION VOLUME
Figure 2. Adsorbate breakthrough volume (VI,) (expressed as a fraction of the adsorbate retention volume (V,)) is determined on the abscissa from the intersection of the ordinafe, the number of theoretical plates of the adsorption tube sampler, and the curve corresponding to the required collection efficiency.
an adsorbate retention volume and the adsorbent number of theoretical plates. As is well-known, these two parameters can be obtained from a conventional gas-chromatographic experiment by using the adsorbent sampler as a chromatographic column. This method has been shown experimentally to agree with measured breakthrough curves (10). More importantly, this derivation has explicitly given the dependence of the adsorption sampler collection efficiency on N , the adsorbent number of theoretical plates. This is quite apparent in Figure 1, where the breakthrough function R( V) is displayed as a function of N and V/V,, the sampling volume divided by the adsorbate retention volume. The sharpness of the breakthrough curve increases as the number of adsorbent theoretical plates is increased. Thus, it is apparent that the efficiency of an adsorbent sampler will increase with in1074
Environmental Science & Technology
creasing adsorbent theoretical plates. In the case of adsorbent sampler with N = 2, it would be impossible to collect with an efficiency greater than 85%since, even at the start of sampling, 15% of the adsorbate concentration is passing through the sampler without being collected, even though the adsorbate retention volume might be quite large. Thus, the notion that a breakthrough volume can be safely assumed to be a set fraction of the adsorbate retention volume is false, since in some instances (low adsorbent N ) it can lead to nonquantitative collection of the adsorbate. This is especially the case when certain nonstandard chromatographic column materials are used as adsorbents, e.g., various charcoals and chromatographic supports such as alumina, which have a low adsorbent N. A safer method for the determination of the breakthrough volume is to determine N and V, by a conventional gaschromatographic experiment. The breakthrough volume can then be determined from the intersection of the measured N (which is measured a t the expected sampler flow rate) with the required collection efficiency curve as given in Figure 2. For example, it has been experimentally determined (15) that a l/S-in. diameter sampler containing 150 mg of 30-40 mesh Ambersorb 347 has an N of 5 a t a flow of 100 mL/min. Thus, in order to ensure a collection efficiency of 95%, a breakthrough volume of 42% of the adsorbate retention volume is determined from Figure 2; Le., a t a sampling volume of 42% of V,, 5% of total adsorbate which has entered the sampler has not been collected. For the same column, for a sampling volume of 70% of V,, 10% has not been collected. Figure 2 can also be used to estimate the collection efficiency of a sampler when the sampled volume, the number of adsorbate theoretical plates, and the adsorbate retention volumes are known. The breakthrough volume can also be determined from a measured breakthrough curve. In this case, the adsorbate retention volume is the volume a t which 50% of the inlet adsorbate concentration, C, is measured a t the outlet of the adsorbate sampler. The slope a t this 50% breakthrough volume is C ( N / ~ T ) ~ / ~from / V , which N can be determined. As before, Vb is determined from Figure 2 once V,, N , and the desired collection efficiency are known. An examination of Figure 2 reveals that there is a minimum number of adsorbent theoretical plates required to ensure a certain collection efficiency. Thus, for example, it is impossible to collect with 99.9% collection efficiency with an adsorbent sampler with an N less than 10.7 regardless of the choice of sampling volume or adsorbate being collected. Raymond and Guiochon ( 5 ) have given an expression for a maximum sampling volume as
v = V,(1 - 2/N1/*)
(8)
which has also been used by Tanaka (8).According to Figure 2 , this maximum sampling volume corresponds to an adsorbate collection efficiency ranging from -95% a t lower adsorbent theoretical plates to -99.8% at higher theoretical plates. Consequently, this is a reasonably good estimate for a maximum sampling volume which guarantees a t least a 95% collection efficiency. On the other hand, the breakthrough volume given by Brown and Purnell(9) in their Figure 1similarly corresponds to an adsorbate collection efficiency ranging from 80% at lower adsorbent number of theoretical plates to 99% at higher theoretical plates. Brown and Purnell state that their breakthrough volumes were derived for a 99% sample recovery with the use of Cropper and Kaminski’s formula ( I ) , and indeed it does correspond to a 99% collection efficiency when N is greater than 30. However, the failure of Brown and Purnell’s breakthrough volume to correspond to a 99% collection efficiency a t N less than 30 is due to an approximation used in Cropper and Kaminski’s derivation. The breakthrough volumes as derived in this paper are exact for all N since no
approximations are involved. Similarly, Butler and Burke (16) applied Cropper and Kaminski’s approximate formula to an analysis of porous adsorption tube samplers, with the consequent result that their analysis is increasingly inaccurate as N is decreased below 30. The breakthrough volumes as determined from Figure 2 are derived from chromatographic theory assuming a standard Gaussian chromatographic response to a narrow pulse injection of a trace concentration of adsorbate. In some instances, as the concentration of adsorbate is increased, the response is no longer Gaussian but becomes a skewed Gaussian or some other functional form. Breakthrough volume can similarly be derived in these instances by the method given in Reilley (12). However, it is felt that the breakthrough volume as derived from a trace concentration Gaussian response should represent a realistic breakthrough volume regardless of the actual non-Gaussian chromatographic response or adsorbate concentration of the adsorption sampler. This is supported by the observation that, in the majority of instances with increasing trace adsorbate concentration, the response can be expressed as a Gaussian skewed to the upstream side. However, in the instance when an adsorption tube sampler is required to collect larger concentrations of an adsorbate, Le., nontrace concentrations, it is recommended that the adsorbate retention time and the adsorbent number of theoretical plates be determined by the technique of inverse chromatography, as first detailed by Reilley (12). In this technique, a plug of pure carrier gas is injected onto an adsorbent column previously equilibrated with a carrier gas containing the maximum expected concentration of adsorbate. The resulting response appears as an inverse chromatograph, Le., having a negative peak. From this negative peak the adsorbate retention time and the adsorbent number of theoretical plates can be determined, allowing the breakthrough volume with a required collection efficiency to be calculated as described in the text. This breakthrough volume with its required collection efficiency is assured for the maximum expected adsorbate concentration. This argument applies also to the collection of many components with an adsorption sampler, and in these instances the derived breakthrough volume (for the component of interest with the least retention volume) should be regarded only as an approximate safe sampling volume. However, if the component retention volumes are determined at the con-
centrations actually expected during sampling and in the presence of all of the other components by an inverse chromatography experiment, then the calculated breakthrough volume can be regarded as a realistic measure of a safe sampling volume. Similarly, the Gaussian breakthrough volumes are valid for the collection of an adsorbate which varies in trace concentration over the sampling period, as long as the adsorbate concentration on an average extends throughout the entire sampling period. However, a change in the flow rate of air through the sampler can be expected to change the collection efficiency of the sampler since N is slightly dependent on flow. Consequently, N must be determined at the expected sampler flowrate. Literature Cited (1) Cropper, F. R.; Kaminsky, S. Anal. Chem. 1963,35,735. (2) Pellizzari, E. D.; Bunch, J. E.; Carpenter, B. H.; Sawicki, E. E n uiron. Sci. Technol. 1975,9, 555. (3) Parsons, J. S.; Mitzner, S. Enuiron. Sci. Technol. 1975, 9, 1053. (4) Russell, J. W. Enuiron. Sci. Technol. 1975,9, 1175. (5) Raymond, A.; Guiochon, G. J. Chromatogr. Sci. 1975,13,173. (6) Jones, P. W.; Grammer, A. D.; Strup, P. E.; Stanford, T. B. E n uiron,. Sci. Techrtol. 1976,10,806. ( 7 ) Holzer, G.; Shanfield, H.; Zlatkis, A.; Bertsch, W.; Juarez, P.; Mayfield, H.; Liebich, H. M. J. Chromatogr. 1977,142,755. ( 8 ) Tanaka, T. J. Chromatogr. 1978,153, 7. (9) Brown, R. H.; Purnell, C. J. J . Chromatogr. 1979,178,79. (10) Gallent, R. F.; King, J. W.; Levins, P. L., Piecewicz, J. F. “Characterization of Sorbent Resins for use in Environmental Sampling”, EPA Report 600/7-78-054,March 1978. (11) Piecewicz, J. F.; Harris, J. C.; Levins, P. L. “Further Characterizations of Sorbents for Environmental Sampling”, EPA Report 600/7-79-216,Sept 1979. (12) Reilley, C. N.; Hildebrand, G. P.; Ashley, J. W. Anal. Chem. 1962,34,1198. (13) Abramowitz,M., Stegun, I. A,, Eds. “Handbook of Mathematical Fupctions”; U.S. Government Printing Office: Washington, DC, 1964; Chapter 7. (14) Berlyand, 0. S.: Gavrilova, R. I.; Prudnikov, A. P. “Tables of Integral Error Functions and Hermite Polynomials”, Macmillan: New York, 1962. (15) Dietz, R., Brookhaven National Laboratory, private communcation, 1979. (16) Butler, L. D.; Burke, M. F. J . Chromatogr. Sci. 1976,14,117.
Received for reuieu September 29,1980. Accepted May 12,1981.This research was performed under the auspices of the United States Department of Energy under Contract No. DE-AC02-76CH00016.
Comparison of Trihalomethane Levels and Other Water Quality Parameters for Three Treatment Plants on the Ottawa River Rein Otson,” David T. Williams, and Peter D. Bothwell Bureau of Chemical Hazards, Environmental Health Directorate, Health and Welfare Canada, Ottawa, Canada
Tony K. Quon Bureau of Management Consulting, Management Services, Supply and Services Canada, Ottawa, Canada
Introduction
Potable water supplies which contain chlorine as a disinfectant may also contain halogenated organics at levels potentially hazardous to human health. Reactions of chlorine with naturally occurring organic materials (1, 2 ) and with model compounds ( 3 ) in water have been demonstrated to yield halogenated products such as the trihalomethanes (THM). The factors controlling production of trihalomethanes during potable water treatment have been investigated 0013-936X/81/0915-1075$01.25/0 @ 1981 American Chemical Society
for a number of water supplies (4-6). Water parameters, such as, temperature, total organic carbon content (TOC), pH, color, chlorine demand, turbidity, and water type (surface water or groundwater) have been shown to affect trihalomethane production. Also, water treatment practices, such as chlorination, filtration, coagulation, and storage, have considerable effect on the extent of formation of halogenated organics. Studies (4,6-9) have been conducted wherein water quality parameters and treatment practices for potable water treatVolume 15, Number 9, September 1981
1075
