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avoiding the interference from these aromatic amines. Refrigeration oil samples to be analyzed are usually withdrawn from refrigeration compressors with chlorofluorocarhon refrigerant dissolved in them. However, the removal of refrigerant is not necessary prior to the AC-GPC procedure, since neither dichlorodifluoromethane nor chlorodifluoromethane with which refrigeration oils were saturated a t atmospheric pressure was found to interfere with the determination of oligomers in the oils.
ACKNOWLEDGMENT The author thanks T. Imamura and J. Enomoto for their fruitful discussions. volume of eluent(benzene), mL Figure 4. Relationship between recoveries of TCP and amounts of benzene made to flow in an AC clean-up procedure. Sample: Oil C
which contains 0.5% (w/w) TCP taining TCP, the determination of oligomers should be done twice: first, the determination of oligomers I-IV and VI by the ordinary AC-GPC method described in the Experimental section and, second, the determination of oligomer V by the modified AC-GPC method described here. Aromatic amines added as antioxidants are another example of potential interference. Low molecular weight aromatic amines such as N-phenyl-@-naphthylaminedo not interfere, because they can be separated from P E T oligomers by GPC. However, aromatic amines with higher molecular weights than that of N,N’-diphenyl-p-phenylene-diamine do interfere with the determination of oligomers. A similar procedure to the elimination of the interference caused by TCP is thought to be effective for
LITERATURE CITED S.D. Ross, E. R. Coburn, W. A. Leach, and W. B. Robinson, J . Po/ym Sci., 13, 406 (1956). R. Giuffria, J . Polym. Sci., 49, 427 (1961). I. Goodman and E. F. Nesbitt, Polymer, 1, 384 (1960); J . Polym. Sci , 48, 423 (1960). L. H. Peebles, M. W. Hoffman, and C. T. Albett, J. Polym. Sci., Pari A- 1 , 7 , 479 (1969). H. Zahn and P. Kusch, T e x L l n d . (Moenchen-Gladbach,Ger.), 69, 880 (1967). D. R. Cooper and J. A. Semlyen, Polymer, 14, 185 (1973). S. Shiono, J. Enomoto, K. Shimamura, and K. Aiba, Reito, 53, 23 (1978). S. Shiono, J. Enomoto, K. Shimarnura, and S. Watanabe, presented at the annual meeting of American Society of Heating, Refrigerating and Air-Conditioning Engineers, Detroit, Mich., June 1979. S. Shiono, J . Polym. Sci.. Part A- 1 , in press. G. W. Recktenwaid, Anal. Chem., 31, 1742 (1959). S.Mori, S.Iwasaki, M. Furukawa, and T. Takeuchi, J , Cbromafogr., 62, 109 (1971). L. M. Zaborsky 11. Anal. Cbem., 49, 1166 (1977). M. Fujita and R. Tsuda, Shinku Kagaku, 16, 101 (1969).
RECEIVED for review June 5 , 1979. Accepted August 17, 1979.
Ohm’s Law, Fick’s Law, and Diffusion Samplers for Gases E. D. Palmes” and R. H. Lindenboom New York University Medical Center, Institute of Environmental Medicine, 550 First Avenue, New York, New York 10016
The first demonstration that molecular diffusion could be used for the quantitative collection of atmospheric gases was made by Palmes and Gunnison ( I ) . The theoretical transfer of the test gas through a tube of known dimensions was estimated using Fick’s First Law. The results clearly showed that rates of atmospheric sulfur dioxide and water vapor transfer through tubes having an efficient absorbent on the closed end and the other end open to the contaminated atmosphere could be predicted accurately by applying Fick’s law and using coefficients of diffusion taken from the literature. In the ideal situation, working a t a fixed temperature and using at the closed end of the tube an absorbent which is 100% efficient, Le., concentration at absorbent surface = 0, the rate a t which gas is transferred through the tube by diffusion can be stated by the equation:
JA = D(A/L)c (1) where J = diffusion flux (mol/cm2/s),A = cross sectional area of tube (cm,), I) = coefficient of diffusion (cm2/s),L = length of tube (cm), and c = concentration of contaminant gas (mol/cm3). Using this equation to calculate theoretical transfer rate and exposing samplers to known gas concentrations for various times showed that the predictions can be confirmed with great accuracy over a wide range of tube 0003-2700/79/035 1-2400$01 O O / O
lengths and diameters. A more detailed discussion of the principle of this type of sampler and its application to NO, measurement was given by Palmes et al. (2). When we adapted the NO, sampler for the measurement of NO, (31, it became desirable to reduce the sampling rate. The solution adopted was to seal a full-length, smaller diameter tube inside the larger one and thereby reduce the effective cross section of the tube and the sampling rate. Another possibility, not tried prior to publication, was to insert shorter lengths of smaller tubing into the sampler and to produce, in effect, two tubes in series; this, of course, raised the question as to the manner in which two resistances to diffusional flux could be added. It has been demonstrated by others that there is a strong similarity between Fourier’s law of heat flow, Ohm’s law of electrical current, Poiseuille‘s law of liquid flow, and Fick’s law of diffusion; the similarities between these laws are treated quite comprehensively by Castellan ( 4 ) . We shall concentrate on the similarity between Fick‘s law and Ohm’s law. It should be noted that Nadeau et al. ( 5 )had mentioned this similarity in a discussion of a sampler based on permeation through a membrane; their treatment was only descriptive, however, since permeation constants, which include membrane thickness, must be determined empirically. In the diffusion SamC 1979 American Chemical Society
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Table I. Resistance of Two Tubes in Series to Diffusional Flux NO, captured, 5'%
Tube 1 (Fixed Length)
L,,
LIA'
cm
cm-'
run 1
measureda run 2 run 3
av.
0 1.52 3.02 5.99 7.07
9.96 27.1 44.0 77.3 89.5
100 34.8 22.5 13.5 11.7
100 100 34.9 32.8 21.2 22.3 12.4 13.8 10.8 12.0
100 34.2 22.0 13.2 11.5
100 36.8 22.6 12.9 11.1
Quantities of NO, collected by samplers for each run are given as percent of the corresponding quantities collected by unaltered samplers with dimensions A , and L , ( L , = 0 and A'IL' = A , / L , ) . Values for the samplers in which L , = 0 for runs 1, 2, and 3 were 33.3, 36.4, and 3 6 . 3 nmol Relative diffusional fluxes are preNO,, respectively. dicted from dimensions of tubes by substituting in: A ' / L ' 1 A,/L, 100.
Absorbent
Plastic Cap
RESULTS AND DISCUSSION
Figure 1. Schematic diagram of diffusion sampler
pler, the coefficient of diffusion of a gas in air and the geometry of the tube can be treated separately, making it possible to examine this similarity between the two laws quantitatively. For calculating diffusional flux through the tube we used Equation 1 and for electrical current through a conductor we used:
I = E/R
- -pred.b
(2)
where I = current (C/s), E = potential difference (V), and R = resistance (ohms). The units of flow for diffusion and current respectively are, therefore, mol/s and C/s. The flow is caused by the difference in potential in one case and the difference in concentration in the other. Finally, the flow is proportional to the conductance, 1/R, for electricity and AIL for diffusion. Thus, the "resistance" to diffusional flux can be expressed as LIA. By analogy, resistance of two tubes in series should be additive.
EXPERIMENTAL To test this relationship, a series of NOn samplers were modified as shown in Figure 1. Without tube 2 or its holder, the device is the original NOz sampler described in detail elsewhere (2); it will suffice here to say that in all cases the closed end of the tube contains a matrix coated with triethanolamine which absorbs N O P rapidly and quantitatively. Tube 1 is nominal 3/8-inchi.d. and tube 2 is nominal 1/8-inchid., '/,-inch 0.d. acrylic; one end of tube 2 fitted snugly into a quarter-inch hole in a thin polyethylene cap. A group of samplers in which the length of tube 2 was varied from 0 to essentially the full length of tube 1 were all exposed in three separate runs and the quantity of NO2 captured was determined by a colorimetric procedure ( 2 ) . The total resistance to diffusion of the two tubes in series (L'IA') was calculated from the relationship: (3)
where Ll and Al are length and cross-sectional area of tube 1, and L, and A , are length and cross-sectional area of tube 2.
In all cases A I was 0.713 cm2,L1 was 7.10 cm, and A2 was 0.079 cm2. Table I gives L2 in cm and L'iA'in cm-' for the samplers. The quantities of NO2 captured by the samplers in each of three runs are shown as percent of the amount captured by the unaltered (L2= 0) samplers. Actual quantities of NO2 captured by the unaltered samplers in each run are given in footnote a. Relative diffusional fluxes predicted from tube dimensions are given in the last column. Linear regression analysis comparing experimental values with those predicted from A'/L' gave the following results for runs 1, 2, 3, and average, respectively: slope 0.995, 1.007,0.993, and 0.999; intercept -0.07, -1.59, 0.06, and -0.52; correlation 0.999 in all cases. Thus, the results f i t the theory well within limits of accuracy of the test systems, and demonstrate that diffusional resistances in series, like electrical resistances, 'ire additive.
ACKNOWLEDGMENT We are indebted to Jerome Solomon for his helpful discussions and suggestions during the preparation of this manuscript. LITERATURE CITED (1) Palmes. E D Gunnison. A F Am Ind Hyg Assoc J 1973, 3 4 , 78-81
(2) Palmes, E. D.; Gunnison, A. F.;DiMattio, J.; Tomczyk, C. A m . I d . Wg. Assoc. J . 1977. 37. 570-577. (3) Palmes, E. D ; Tomczyk, C. A m . Ind. Hyg. Assoc. J 1979, 40, EIRR-qql ----..
(4) Castelhn, G. W. "Physical Chemistly"; Addison-Wesley: Reading, Mass.,
1964; Chapter 26.
( 5 ) Nadeau. J. S.; Treen, M. E.; Boocock, D.G. B. Anal. Chem. 1978, 5 0 , 1871-1873.
RECEIVED for review June 8, 1979. Accepted September 17, 1979. This work was supported by Grant No. GO 177042 from the U S . Bureau of Mines and is part of a center program supported by Grant NO. ES00260 from the National Institute of Environmental Health Sciences. The contents contained herein were developed through the use of funds provided by the U.S.Department of the Interior, Bureau of Mines, and by this notice the Bureau does not agree or disagree with any of the ideas expressed or implied in this publication.
