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By William K. Fowler Fundamentals of passive vapor sampling assive vapor-sampling devices are gaining Pwide acceptance among industrial hygienists in settings where exposures of personnel to the air, and the other face is in contact with the trapping medium, so that the entire diffusion or permeation zone lies within the membrane. In a few potentially hazardous vapors must be measured. In designs, however, there is a layer of air between the contrast to an "active" sampler, in which the air inner face of the membrane and the trapping me sample is brought into contact with a detector or dium; this air layer constitutes an additive diffu- collector device by forced convection or pumping, sional resistance in series with the permeation resis the passive sampler typically collects the species of tance provided by the membrane. A typical permea interest (i.e., the analyte) from its immediate sur tion sampler is shown in Figure 2. roundings by virtue of the natural diffusion' (or permeation') of the species into the sampler and from there into or onto a trapping medium or Fick's first law of diffusion "sink." The amount of analyte thus collected is re The rate of diffusion of analyte molecules from lated to the integrated dose or time-average concen the open air at the sampler inlet to the "sink" or tration of the analyte in the sampled environment. analyte-trapping material at the other end of the Relative to active sampling systems, passive sam diffusion zone is governed by Fick's first law of dif plers are generally simple in construction and re fusion:4 quire no power for operation. Moreover, they are small and light in weight, are easy to prepare and use, and are often low in cost.' U = -DA -- dx (1) Diffusion and permeation samplers A diffusion sampler typically consists of a tube, a parallel cluster or matrix of tubes, or an item of hardware providing tube-like pores or channels with an absorbent, adsorbent, or reactive material located at one end of the diffusion zone formed by the tubes, pores, or channels. The other end of the diffusion zone is generally open to the atmosphere. A diagram of a simple tube-type diffusion sampler is shown in Figure I. A permeation sampler differs from a diffusion sampler primarily in that the rate-limiting analyte concentration gradient (i.e., the resistance to mass transport) occurs within a permeable membrane or other permeation barrier positioned between the at mosphere being sampled and a "sink" or trapping medium as described for the diffusion sampler. Thus, one face of the membrane is in contact with where U is the diffusive transport rate (mol/sec), D is the analyte diffusivity (i.e., diffusion coefficient) in air (cmVsec), A is the diffusion path cross-sec tional area (cm2), x is the distance along the diffu sion path (cm), and c is the analyte concentration at point x (mol/cm3). This equation may be integrated over the length, L, of the diffusion path to yield a useful expression for the analyte sampling rate. Under normal operating conditions, it may be as- SORBENT OR ANALYTE "SINK" Dr. Fowler is Senior Chemist and Program Manager for Chem ical Detection Methodology, Southern Research Institute, Bir mingham, Alabama. The author wishes to thank Dr. H. Kenneth Dillon, Certified Industrial Hygienist, for his helpful suggestions during the preparation of the manuscript. 80 : DECEMBER 1982 Figure 1 A simple tube-type diffusion sampler 3H Q09S00 SAMPLER BODY . PERMEABLE membrane Like gaseous diffusion, diffusion within a perme able membrane (i.e., permeation) is also governed by Fick's first law, and therefore the above-de scribed relationships also hold for membrane per meation samplers. For many such devices, however, the diffusion zone is wholly confined to the interior Figure 2 A typical membrane-type permeation sampler. of the membrane; therefore, U in the above equa tions is the diffusive transport rate through the sumed that the concentration of analyte vapor at the surface of the trapping material is zero and that analyte concentration at the sampler inlet is equal to the ambient concentration, C0. With these assump tions, the result of the integration of Eq. (1) is as follows: membrane (Um), D is the diffusion coefficient of the analyte species within the membrane (D,,), and C,, should be replaced with another symbol (say, Cm) that represents the analyte concentration in the membrane at its outer surface. Moreover, the di mensions A, X, and L are physical dimensions of the membrane. (Let Am and Lm be the area and V = DAC (2) L Within a given exposure time, t (in seconds), the amount, M (in mol), of analyte collected by the sampler is as follows: thickness of the membrane, respectively.) To obtain membrane-specific versions of Eqs. (2) and (3) in this manner [i.e., by integration of Eq. (1) over the membrane thickness], one must assume that the analyte concentration at the inner membrane sur face is zero and that the analyte concentration in the M = Ut = DAC"t L (3) Note that the "effective" volume sampling rate (Z, in cm'/sec) is given by DA/L.' Hence, if Z for a given sampler is, for instance, 2 cmVsec, then that sampler will accumulate during a 1-sec interval the amount of analyte that is present in 2 cm3 of the ambient atmosphere, exactly as would a conven tional pump-operated sampling tube sampling at the same rate. Note also that Eq. (2) resembles Ohm's law, / = E/R, where / is the current, E is the electromotive air immediately adjacent to the outer membrane surface is the same as the ambient analyte concen tration. These assumptions are probably at least ap proximately valid for most membrane permeation samplers and for most real sampling situations. Note that Fick's first law by itself does not suffice to relate the ambient analyte vapor concentration (CJ to any measurable parameter associated with the permeation sampler. According to Henry's law, however, the analyte concentration in the mem brane is directly proportional to the analyte concen tration in the air adjacent to the membrane: potential, and R is the resistance.6 Specifically, U in Eq. (2) is analogous to current; DC,, to electromo Cm = QC, (4) tive potential; and L/A to resistance. Because elec trical resistances in series are additive, diffusional resistances {L/A) connected in series between the ambient atmosphere and the analyte-trapping me dium should also be additive. This was found ex perimentally to be the case.6 Frequently in instances where two or more series- where Q is a proportionality constant that contains Henry's law constant. Clearly, therefore, Eq. (4) can be substituted into the membrane-specific ver sions of Eqs. (2) and (3) to obtain the needed rela tionships. Eq, (3), for example, then becomes: M = Umt = QP"A"<Ct (5) linked diffusional resistances occur in a sampler, the resistor nearest the sample inlet is a microporous membrane or other similar covering that serves as a "windscreen." The windscreen prevents the inner diffusion gradient from being disrupted by air movement in the vicinity of the inlet. As long as the pores or channels in the windscreen are great er than about 1 pm in diameter,' the windscreen's effect upon the diffusion characteristics of the sam pler can be determined straightforwardly with Eq. (1).''" Frequently, the windscreen's contribution is negligible. At least one group of researchers chose to define the product QDm as the membrane permeability,* but most researchers in the field of permeation sam pling have found it convenient to lump all of the constant terms into a single "permeation con stant," and hence Eq. (5) may be rearranged to give: K = L.*. - *L QDmAm M (6) 3M 009801 AMERICAN LABORATORY : 81 In practice, K is usually determined for a permea tion sampler by measuring M after exposure of the sampler for time t to standard test atmospheres con taining known concentrations of the analyte. Be cause large variations in membrane thickness (Lm) from one sampler to the next are common,''11 K must be determined individually for each sampler. Experiments with a variety of membranes have dis closed that many membrane materials exhibit a per meation constant that varies with the analyte con centration, " This is a highly undesirable character istic for a permeation sampler. Fortunately, how ever, this has not been a major problem with mem branes fabricated from polydimethyl siloxane (di methyl silicone). Determination of diffusivity, D The diffusivity of a molecular species in air is a function of certain intrinsic properties of the species and may be measured experimentally5 or may be calculated from any of a variety of empirical and serniempirical equations. In a study of nine such equations,14 it was concluded that the equation of Hirschfelder, Bird, and Spotz agreed most closely with experimental values of D for high-molecularweight compounds, whereas the Chen and Othmer equation or the Wilke and Lee equation provided more accurate values for low-molecular-weight va pors. In this study, however, many of the calculated results were not within 5% of the observed val ues, which suggests that the determination of D may be a significant source of error in passive diffusional sampling. A typical value of D for an en vironmental pollutant (such as dichloroethylene) is about 0.1 cmVsec,1' but values of D for different species vary too widely for an "average" value to suffice in Eq. (1) for all organic pollutants.' Effect of environmentalfactors The most significant environmental factors likely to affect the performance of a diffusion-type sam pler are the temperature, pressure, and humidity of the atmosphere. Changes in temperature and pres sure result in changes in the analyte diffusivity ac cording to the following equation: D = K'T" P (7) where T is ambient temperature, P is atmospheric pressure, K' is a proportionality constant, and n is a number that kinetic theory predicts to be 1.5," but that may actually be as high as 2.1.''" To ap- 82 : DECEMBER 1982 predate the magnitude of the dependency of D upon T and P, note that an increase in T from 5 to 35 C causes a 16% increase in D even when n is only 1.5, and an increase in P from 28 to 32 in. Hg causes a 14% decrease in D.` The rate at which a diffusion sampler collects the analyte species, as given by Eq. (2), does not depend on T and P in the manner given for D in Eq. (7). This is because C,,, which appears in Eq. (2) along with D, also depends on Tand P. Changes in Tand P produce changes in the volume occupied by a given mass of atmosphere according to the ideal gas laws, and therefore, the atmospheric concentration of an analyte species (C,,), expressed as a mass per unit volume, must vary in direct proportion to P and in inverse proportion to T\ ^ T (8) If Eqs. (7) and (8) are substituted into Eq. (2), it will be seen that the sampling rate U [and M in Eq. (3)] is directly proportional to T" 1 and is completely in dependent of P. It is appropriate to examine the effect of Tand P on the analyte concentration that might be calcu lated from Eq. (3) after measurement of M, the total amount of analyte collected. First, it is con venient to rearrange Eq. (3) as follows: Now, let us assume that D for the analyte is accu rate at T - T, and at P = /*, (i.e., D = D,) and that a sampling experiment is conducted at T - T2 and P = P,, The calculated value of C,, is given by Eq. (7) as follows: k C, (calc) = \ D,AT (10) The true value of C,, could be computed, however, if the value of D were known accurately at T: and /Mi.e.,ifD = D,): C,, (true) = --ML-- DiAt (il) Thus, the ratio C,, (calculated)/^ (true) = DfD,, and after incorporation of Eq. (7), this expression becomes: C, (calc) = Di ^ P. / C,, (true) D, P, l T, (12) 3M 009802 VAPOR continued Clearly, therefore, both temperature and pressure fluctuations can lead to an error in the calculated analyte concentration. A number of researchers apparently feel, how ever, that it is appropriate to correct all measured ambient pollutant concentrations to the equivalent concentrations at some standard temperature and pressure by use of the ideal gas laws.4*1'1' This pro cedure was recommended by the National Institute for Occupational Safety and Health (NIOSH) and was incorporated into the regulations of the Occu pational Safety and Health Administration (OSHA).1' According to this procedure: C,, (corrected) = C,, (true) Jj- Ts,d P2 (13) where TSld and Piti refer to the chosen standard temperature and standard pressure, respectively, and Ti and Pi are as defined previously. If T, in Eq. (12) is chosen to be Tai and P, is chosen to be P!ld, then Eqs. (12) and (13) can be combined as follows: C* Mc) = ( Ti y-1 C,, (corrected) ( T'sld I (14) 84 : DECEMBER 1982 Hence, if D is accurately known at the standard temperature and pressure, then the analyte concen tration measured by a diffusion sampler at any given temperature or pressure will differ from the corrected true concentration only in proportion to 7"*1. (There is no dependence upon P at all.) For this reason, researchers often state simply that dif fusion sampler error is a function only of Ty,t where it is assumed that n = 1.5 (i.e., n - 1 = Vi), even though the error is actually a function of T"/P as given by Eqs. (7) and (12). The situation is further complicated by the frequent use of the concentra tion unit, parts per million, because vapor concen trations given in this unit are independent of atmos pheric temperature and pressure. When this unit is used, diffusion sampler error is always a function of T"-] and is independent of P. This circumstance seems to have led to ambiguity and consequent mis understanding among workers in the field of indus trial hygiene dosimetry. With regard to the effect of humidity upon diffu sion sampler performance, humidity has essentially no effect upon the diffusion parameters of Eq. (2), provided that the sampled atmosphere does not contain enough water vapor to cause an appreciable change in the mean molecular weight of air. This is a valid assumption in most industrial hygiene appli cations. However, humidity can substantially di minish the saturation capacity of the analyte-trap ping medium, especially if the trapping medium is a solid sorbent material. Although membrane permeabilities are, in gen eral, drastically affected by temperature,11 this does not seem to hold true for membranes prepared from polydimethyl siloxane. For example, no significant temperature effects were observed among silicone membrane samplers designed for the determination of hydrogen sulfide," chlorine,50 or vinyl chlo ride. ,*1' Although rather substantial temperature effects were noted among samplers of :his type that were intended for use in the sampling of carbon monoxide55 and sulfur dioxide,11'51 these effects were nevertheless small in relation to those observed among other Types of membranes. Tl s apparently unique property of silicone membranes has been ex plained in terms of the very small activation energy of permeation for many substances in silicone rub ber.* The effects of atmospheric pressure and of hu midity upon the performance of a membrane per meation sampler are probably not significant.15 Sampler response time Considerably different concentration readings for workplace pollutants have resulted from sam plers positioned only a few feet apart on a worker's body.15 Obviously, therefore, a sampler may be ex posed to quite sudden changes in analyte concentra tion at any point during a given sampling interval, provided that the sampler or the air around the sampler is moving. Thus, it is important that the sampler be able to respond rapidly to a change in analyte concentration. The response time of a diffusion sampler is the time required for the sampling rate, U {Eq. (2)], to adjust completely or nearly completely to a sudden change in analyte concentration in the atmosphere. A simple and convenient measure of response time is the average residence time of the analyte within the diffusion zone of the sampler.4*1'1* If a linear concentration gradient is assumed in a tube-type diffusion sampler (see Figure 1) such that c = C,, at the tube inlet and c - 0 at the surface of the trap ping medium, the average concentration of analyte in the diffusion zone is C,,/2. Moreover, the volume of the diffusion zone is equal to the volume of the tube, A L, where these terms are as defined for Eq. (2). Note that the amount, M, of analyte to be found within the diffusion zone is given by: 3M 009803 AMERICAN LABORATORY : 85 VAPOR continued M= 2 05) If this value is substituted for M in Eq. (3) and the equation is solved for t, the result is the residence time of the analyte in the diffusion zone of the sam pler: tr = ^ 2D (16) Other authors have employed slightly different ver sions of this relation," Derivations e Eq. (16) from Fick's second law of diffusion have been published showing that at time t = the diffusive transport rate, U, has under gone approximately 63% of the full change that it will ultimately undergo in response to a step change in analyte concentration.1 The rate of change of U decreases exponentially with time, so that a time in terval equal to several times is required for the oc currence of a change in U that is equal or very near ly equal to the full anticipated change. Equation (16) predicts that the response time of a diffusion sampler for a given analyte of fixed diffusivity should depend only on the square of the length of the diffusion pathway. If a microporous membrane (whose pores may be only 0.0025 cm long) is employed in the diffusion path, the re sponse time should be extremely fast unless the diffusivity of the analyte suffers as a result of the small dimensions of the pores.1'" Typically for diffusion samplers, however, the response time varies from about 0.5 sec5 to several minutes.,`'1 Although it is possible to calculate the response time of a membrane sampler," accurate values for the necessary parameters are not generally avail able, and therefore response times are usually mea sured experimentally in the laboratory. For silicone membranes, response times of less than 1 min have been achieved for a number of different ana lytes'' "'2" and have been found to be on the order of a few minutes for certain other analytes.'5'21 These response times are probably satisfactory for most applications of passive samplers. Effect of air face velocity The velocity of the air around the passive sampler can affect its rate of analyte uptake. The diffusivity itself is independent of air movement, and thus the adverse effect of moving air arises only from its ability to alter the length (i.e., the diffusional resis tance) of the diffusion pathway. Generally, it is the increase in length of the diffusion pathway caused 86 : DECEMBER 1982 by stagnant air conditions that leads to an error in sampling,7'2' This problem results from the deple tion of the analyte species in the air immediately ex ternal to the sampler inlet. Note that this extension of the sampler diffusion gradient causes an effective increase in the L term of Eq. (2), thereby decreasing the diffusive transport rate, U.li Hence, air stagna tion invariably leads to erroneously low results. It can be shown from mass transfer theory that the diffusive resistance experienced by a passive sampler due to an external analyte concentration gradient is inversely proportional to V*, where V is the face velocity of ambient air relative to the sam pler inlet.4 This relationship suggests that the exter nal diffusive resistance should diminish rapidly with relatively small increments of V above zero until a velocity level is reached beyond which the sampler performance quickly becomes virtually insensitive to velocity. This critical minimum velocity has been observed and reported by various researchers for their respective samplers, and it is usually about 15 ft/min.4'2'25 For dosimeters worn by workers in in dustrial atmospheres, however, face velocities this low are rarely experienced.4'7 In addition to the problem due to low face veloc ities, the opposite problem also may be encountered due to very high face velocities. This problem arises from a disturbance of the sampler internal diffusion gradient near the sampler inlet so that the gradient is effectively shortened and the diffusion rate is in creased. This problem is especially severe for the single, open-tube-type samplers and is most severe when the wind impinges upon the sampler inlet at a 120 to 135 angle with the sampler tube.1,17 Air velocity effects of both types may be min imized by maximizing the length of the sampler in ternal diffusion pathway.2,'2S However, lengthen ing the diffusion pathway also increases the sampler response time [Eq. (16)] and decreases the diffusive transport rate [Eq. (2)]. Moreover, in the design of a passive sampler, care frequently must be taken to limit the diffusive transport rate so that the sam pler's analyte-trapping medium is not saturated when working at the upper end of the ranges of ana lyte concentrations and sampling times. Hence, this factor must also be taken into account when op timizing the length of the diffusion pathway. Inter estingly, a diffusion pathway that is from 3 to 8 times longer than it is wide has proven to be optimal for a considerable variety of passive diffusion sam plers.5''''17'24'25 In principle at least, membrane-permeation sam plers are subject to the same adverse effects of stag nant air as described previously for diffusion sam- 3M 009804 piers. However, the cross-sectional area of a perme ation sampler "inlet" (i.e., membrane surface area) is often far larger than the inlet cross-section for a diffusion sampler. Accordingly, a permeation sam pler collecting analyte species at the same absolute rate (mol/sec) as a diffusion sampler may not dis play nearly as great a tendency to deplete the air of analyte as does a diffusion device. Thus, the perme ation sampler may not be as likely as the diffusion sampler to produce an external analyte concentra tion gradient, and in practice, air stagnation has not been a problem for the permeation sampler, '2*2'*27 Because air movement cannot affect the analyte concentration gradient within or behind the mem brane, the internal gradient-disruption effect of high wind velocities described above in connection with diffusion samplers cannot occur in permeation samplers. Diffusion versus permeation sampling Both the diffusion sampling technique and the permeation sampling technique offer a unique set of advantages and limitations for environmental sampling. Generally, diffusion samplers are amen able to thermal desorption into a gas chromatograph;24,2i'2' they can be mass produced cheaply enough for one-time, throw-away use;2 and they do not require calibration.2 However, they may be sub ject to errors caused by variations in air face veloc ity and also by fluctuations in temperature. More over, the trapping media that are suitable for use in diffusion samplers are confined primarily to ad sorptive or reactive solids (as opposed to liquids, which are useful in permeation devices). These sol ids, in turn, are more susceptible than liquids to the deleterious effects of atmospheric humidity.12 Permeation samplers, on the other hand, are vir tually free from humidity effects (especially when a liquid analyte-trapping medium is employed); they can make use of almost any analyte-trapping me dium (liquid or solid); they are not especially sus ceptible to errors caused either by variations in wind velocity or, if a silicone membrane is used, by vari ations in temperature; and they generally can be used repeatedly.2 However, permeation samplers also tend to be costly, and they typically require cal ibration.2 Even when calibrated, permeation sam plers may exhibit a variable working concentration range (and variable detection limits) because of the variation in membrane permeabilities from one sampler to the next.20 The field of passive sampling technology is cur rently in a state of rapid development, and passive samplers of both the diffusion and permeation types are continuing to appear frequently in the marketplace. References 1. HARRISON, J.W., LAWLESS, P.A., GILBERT. D.E., and WHITE, J.H., Research Triangle Institute, EPA (ESRL) Re port EPA-600/2-76-034, NTIS PB-256-910, "Development strategy for pollutant dosimetry," February 1976. 2. WEST, P,w,, Am. Lab. 12(1), 35 (1980). 3. EVANS, M,, MOLYNEUX, M,, SHARP, T,, BAILEY, A., and HOLLINGDALE-SMITH, P,, Ann. Occup. Hyg. 20, 357 (1977). 4. TOMPKINS. F.C., JR. and GOLDSMITH, R.L., Am. tnd. Hyg. Assoc. J. $8, 371 (1977). 5. LAUTENBERGER, W.J., KRING, E.V.. and MORELLO, J.A., Am. Ind, Hyg. Assoc. J. 41, 737 (1980). 6. PALMES, E D. and LINDENBOOM, R.H., Anal. Chem. 51, 2401 (1979). 7. PURNELL. C.J., WRIGHT, M.D., and BROWN, R.H., Analyst 106, 590(1981). 8. BAILEY, A. and HOLLINGDALE-SMITH, P.A., Ann. Occup. Hyg. 20, 345 (1977). 9. NELMS, L.H.. REISZNER, K.D.. and WEST, P.W., Anal. Chem. 49, 994 (1977). 10. JONES, L.C., BILLINGS, C.E., and LILIS, C,, Am. Ind. Hyg. Assoc. J. 42, 104(1981). 11. HARDY, J.K., STRECKER. 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P.W., Environ. Sci. Techno!. 13. 1087(1979). 24. BROWN, R.H. and WALKIN, K.T., "The performance of a tube-type diffusive sampler for organic vapours," pre sented at the American Industrial Hygiene Conference. May 18-23. 1980, Houston, TX. 25. BROWN, R.H., CHARLTON, J., and SAUNDERS, K.J., Am. Ind. Hyg. Assoc. J. 42. 865 (1981). 26. HERL, F.J. and MANNING, M.P., Am. Ind. Hyg. Assoc. J. 41, 778(1980). 27. NADEAU, J.S., TREEN, M.E., and BOOCOCK. D.G B., Anal Chem. 50, 1871 (1978). 28. OROF1NO, T.A. and USMANI. A M., Am. Lab. 12 (7), 96 (1980). 3H 009805 AMERICAN LABORATORY : 87