Gaseous contaminant dosimeter with diffusive material for regulating mass uptake

A gaseous contaminant dosimeter apparatus for collecting, for subsequent analysis, a gaseous contaminant in proportion to its average concentration in the ambient atmosphere over a predetermined collection period. The gaseous contaminant dosimeter apparatus includes a closed chamber containing a medium capable of chemically or physically combining with the selected gaseous contaminant, and porous diffusive material formed from a material through which the contaminant may diffuse at a rate that is proportional to its atmospheric concentration and substantially unaffected by convective movements of the ambient atmosphere, is mounted in fluid impeding relation with the chamber. The diffusive material includes at least two layers of microporous membrane material having a multiplicity of pores which individually have effective cross-sectional dimensions that are smaller than the mean free path length of the contaminant, the membrane material being mounted on the opposite sides of a porous support substrate.

BACKGROUND OF THE INVENTION 
1. Field of the Invention 
The present invention relates generally to the fabrication of a dosimeter 
which is operable to measure the time-weighted concentration of one or 
more gaseous contaminants in an ambient atmosphere, and more specifically 
to the selection of particular starting materials, and the fabrication of 
a diffusive material which permits the passage of a selected gas or gases 
in a gas mixture solely by a diffusive mechanism in proportion to a 
concentration gradient of the selected gas or gases across the same 
diffusive material and independent of the convective movement of the 
impinging gas mixture. The subject diffusive material adapted to be 
manufactured in continuous sheets and thereafter formed into any desired 
sizes or shapes. 
2. Description of the Prior Art 
The prior art is replete with numerous examples of sampling apparatuses 
which are operable to detect a wide range of gaseous contaminants in 
assorted operational environments. For example, in the field of monitoring 
gaseous contaminants which may reside from time to time in the ambient 
atmosphere, much of the recent art has been directed towards constructing 
dosimeters which employ passive means to regulate mass transfer of the 
particular gaseous contaminant to be detected between the ambient 
atmosphere containing same and a selected collection medium, thereby 
eliminating the need for an active pump. Such passive dosimeters typically 
have operational characteristics which include no moving parts, can be 
fabricated inexpensively, are simple to utilize, and can be easily affixed 
to employees for purposes of making personal "breathing zone" 
measurements. These "breathing zone" measurements permit a more accurate 
risk assessment to be conducted than what was heretofore possible with the 
more traditional fixed-site area measurements performed with more 
elaborate or technologically cumbersome instrumentation. 
The authors, Palmes and Gunnison in an article entitled "Personal 
Monitoring Device for Gaseous Contaminants," American Industrial Hygiene 
Association Journal, 34, 78-81 (1973) disclosed such a passive dosimeter 
which measured concentrations of a selected gas by measuring the quantity 
of the gas which diffused through a single orifice of known size to a 
collection element, where the concentration of the selected gas was 
maintained at zero. 
Although substantial prior art exists, all passive dosimeters disclosed 
heretofore have utilized one of only two basic mass transport mechanisms 
thereby achieving the desired objective of regulated mass transfer. These 
basic mass transport mechanisms include permeation which takes place 
through a solid polymeric membrane, and bulk gas diffusion. 
Passive dosimeters which employ the mass transport mechanism of permeation 
typically are configured in a form wherein a solid polymeric membrane is 
disposed in an attitude between an ambient atmosphere containing a gaseous 
contaminant to be detected and a collection medium for same. As should be 
understood, the gaseous contaminant "dissolves" in the solid polymeric 
membrane and mass uptake occurs when a concentration gradient is 
established across this same polymeric membrane. The concentration 
gradient is created, of course, when the collection medium adsorbs or 
absorbs as appropriate, the contaminant in question. Under steady-state 
conditions the amount of material which will typically pass into a passive 
dosimeter in a given time "t" is illustrated by the formula: 
EQU W=kA(C.sub.a -C.sub.i)t/L (1) 
where W=the weight of the material collected expressed in micrograms; k=the 
empirically determined permeation coefficient expressed in square 
centimeters per minute; A=the area of the permeation membrane exposed 
expressed in square centimeters; C.sub.a =the concentration of gaseous 
contaminant in the ambient atmosphere to be tested expressed in micrograms 
per cubic centimeter; C.sub.i =the concentration of the gaseous 
contaminant contained inside the dosimeter (normally zero provided that an 
efficient collection medium is used); t=the time of sampling expressed in 
minutes; and L=the length (thickness) of the permeation membrane which is 
expressed in centimeters. Values of k for polymeric silicon membranes, 
which are considered the most permeable, and therefore preferred, as 
disclosed in the reference authored by K. D. Reizner and P. W. West 
entitled "Collection and Determination of Sulfur Dioxide Incorporating 
Permeation and West-Gaeke Procedure," Environmental Science and 
Technology, 7, 526-532 (1973) are indicated as lying in a range between 
0.001 and 0.01 square centimeters per minute. 
Passive dosimeters which employ the mass transport mechanism of permeation 
have three major advantages. Firstly mass uptake by the mechanism of 
permeation which takes place through a solid polymeric membrane appears to 
be substantially resistant to disturbance occasioned by the variable 
convective movements of the surrounding ambient atmosphere which are 
normally encountered during most sampling applications, and therefore no 
secondary protective design features need be employed. Secondly, the 
utilization of a solid permeation membrane has the attendant 
characteristic of being capable of retaining solid or liquid collection 
media, again without the incorporation of secondary design features. 
Thirdly, a permeation membrane may be manufactured as a sheet of 
substantially continuous material therefore allowing considerable latitude 
with respect to the area and shape of material to be incorporated into a 
dosimeter. 
While the previous prior art devices and practices have achieved numerous 
laudable benefits, they have a multiplicity of shortcomings which have 
detracted from their usefulness. For example, dosimeters employing the 
mass transport mechanisms of permeation have several major drawbacks: (1) 
The rate of mass uptake, by permeation, must be empirically determined for 
each selected gaseous contaminant to be detected and frequently for each 
individual dosimeter because gas "solubilities" cannot in reality 
accurately be predicted from theory and may vary widely even within single 
lots of commercially available membrane; (2) very thin and often fragile 
membranes must be employed to achieve practical sampling rates; (3) the 
time required to achieve an equilibrium rate of mass uptake can be 
relatively long as compared with the concentration fluctuations of the gas 
contaminant to be detected in the ambient atmosphere, hence the 
contaminant sample collected may not accurately reflect the time-weighted 
average measure; and (4) the rate of mass uptake may be adversely affected 
by changes in the temperature or ambient humidity. These several 
shortcomings have heretofore frequently offset the benefits derived from 
employing permeation dosimeters, and as a result the preponderance of 
passive dosimeters now being utilized are of the bulk diffusion type. 
It should be understood that the passive dosimeters disclosed to date have 
generally incorporated one or more substantially still pockets of air 
which individually have macroscopic dimensions relative to the mean free 
path length of the gaseous contaminant to be detected, and which is placed 
between the ambient atmosphere to be sampled, and the selected collection 
medium. The contaminant is collected according to Fick's First Law of 
Diffusion which is set forth below: 
EQU W=pD.sub.b A(C.sub.a -C.sub.i)t/L (2) 
where W=the weight of the material collected expressed in micrograms; p=the 
porosity of the material through which the gas contaminant is diffusing 
(the fractional void volume, which is generally accepted as being equal to 
one (1) in an open system); D.sub.b =the bulk gas diffusion coefficient 
expressed in square centimeters per minute; A=the area of the permeation 
membrane exposed expressed in square centimeters; C.sub.a =the 
concentration of the gaseous contaminant contained in the ambient 
atmosphere expressed in micrograms per cubic centimeter; C.sub.i =the 
concentration of the gaseous contaminant contained inside the dosimeter 
(this being normally zero, provided of course, that an efficient 
collection medium is used); t=the time of sampling expressed in minutes; 
and L=the length (thickness) of the permeation membrane expressed 
centimeters. It has been empirically determined that the bulk gas 
diffusion coefficients for molecules with molecular weights of 300 or less 
which diffuse through the air lie in a range between 3 and 10 square 
centimeters per minute under ambient temperature and pressure conditions. 
It should be understood that molecules with molecular weights of 300 or 
less are most likely to have a measurable vapor pressure. 
Gaseous dosimeters that employ the mass transport mechanism of bulk 
diffusion to regulate mass uptake of a selected contaminant have several 
noteworthy advantages. Firstly, dosimeter performance can be accurately 
predicted from theory by simply substituting diffusion coefficients 
derived from experiment or theory into equation (2) which was discussed 
above; Secondly, intra- and inter-dosimeter sampling rates are 
substantially precise because of the ability to accurately form bulk 
diffusion channels of substantially uniform dimension; thirdly, the rate 
of mass transfer is substantially independent of the effects of pressure 
and humidity and will generally vary with temperature only to an amount 
expressed as T.sup.1/2 ; and fourthly, the time required to achieve an 
equilibrium rate of mass uptake typically is rapid as compared to the 
concentration fluctuations of the gas contaminant in the immediate ambient 
atmosphere to be tested. 
The disadvantages which are attendant with the utilization of bulk 
diffusion dosimeters are a result of shortcomings inherent in their 
respective designs. For example, bulk diffusion dosimeters need to 
incorporate secondary design features to prevent convective air movement, 
which takes place adjacent to the dosimeter, from disrupting the still 
pocket of air necessary to regulate mass uptake, and to retain the 
collection media which might otherwise be released through an open 
diffusion channel which is generally present in such devices. Two 
approaches have been utilized to overcome the above noted shortcomings. 
The first approach has been to employ one or more substantially circular 
diffusion channels which are individually closed at one end by the 
collection medium and which further have a ratio of length-to-diameter 
which exceeds a minimum valve of three. U.S. Pat. No. 4,235,097 and an 
article authored by W. J. Lautenberger, E. V. Kring, and J. A. Morello 
entitled "A new personal badge monitor for organic vapors" found in the 
American Industrial Hygiene Association Journal, 41 737-747 (1980); and 
the article written by R. H. Brown, J. Charlton, and K. J. Saunders, 
entitled "The development of an improved diffusive sampler," American 
Industrial Hygiene Association Journal, 42, 865-869 (1981); discuss this 
principal in greater detail. In practice, however, ratios of ten or 
greater are commonly required to satisfactorily attenuate the deleterious 
effects of convective air movements thereby leading to disadvantageously 
reduced sampling rates. The second approach is to utilize a sheet of 
substantially macroporous material as a "wind screen." For example, U.S. 
Pat. No. 3,950,980 to Brown et al. discloses the use of two or more layers 
of porous material having effective pore sizes in a range between 0.1 and 
100 micrometers which are used to attenuate convective gas movement so as 
to create one or more thin layers of placid gas within an enclosure. 
Further, U.S. Pat. No. 3,985,017 to Goldsmith discloses the use of a 
porous sheet having preferred effective pore sizes in an effective range 
between 5 and 50 micrometers that permits unhindered diffusion, and which 
is disposed in an attitude at the entrance of an enclosure containing an 
internal honeycomb structure that substantially inhibits convective 
movement. It should be appreciated, however, that the latter problem has 
been most often addressed by utilizing a self-supporting or otherwise 
solid collection medium, although parenthetically it should be noted that 
U.S. Pat. No. 4,265,635 discloses the use of a porous hydrophobic film 
(50-80% porous having pore sizes in the range of 0.1-3.0 micrometers) 
placed over the end of a plurality of diffusive channels and operable not 
to interfere with the passage of gaseous contaminants between the ambient 
air to be tested and a liquid collection medium. 
Therefore, it has long been known that it would be desirable to have a 
gaseous contaminant dosimeter that can incorporate the performance and 
design features of both permeation and bulk diffusion type dosimeters 
while simultaneously avoiding the detriments individually associated 
therewith, and which further is particularly well suited to being 
transported easily by employees, can be manufactured in a compact 
configuration and which is operable to provide accurate concentration 
measurements for the gaseous contaminants to be detected. 
SUMMARY OF THE INVENTION 
Therefore, it is an objective of the present invention to provide an 
improved gaseous contaminant dosimeter. 
Another objective of the present invention is to fabricate a diffusive 
material which can be produced in continuous sheets, is substantially 
self-protecting against the deleterious effects of convective air 
movement, and which further is capable of containing either a solid or a 
liquid collection medium in the fashion of solid permeation membranes. 
Another objective of the present invention is to fabricate a diffusive 
material that has a high rate of mass transfer and exhibits uniform 
performance characteristics when fabricated in quantity. 
Another objective of the present invention is to provide a diffusive 
material which has performance properties which are predictable based on 
theory and/or a minimum of empirical data, is rapidly responsive to gas 
contaminant concentration fluctuations, and which further exhibits a small 
or otherwise predictable dependence upon environmental variables in the 
manner of bulk diffusion. 
Another objective of the present invention is to construct an inexpensive 
and versatile passive dosimeter using a source of continuously fabricated 
diffusive material. 
Another objective of the present invention is to provide a diffusive 
material that regulates mass uptake of a gas contaminant to be detected in 
a gas mixture, most commonly air, by a collection medium, at a rate which 
is proportional to the gaseous concentration of the contaminant and 
substantially unaffected by the convective movement of the entraining gas 
mixture. 
Another objective of the present invention is to provide a diffusive 
material which takes on the form of a laminate and which has two 
substantially identical outwardly disposed sheets of microporous PTFE 
membrane, the individual membranes having a predominance of pores with 
effective cross-sectional dimensions which are smaller than the mean free 
path length of the gaseous contaminant in the ambient atmosphere, and 
larger than the molecular size of the same contaminant, the individual 
membranes bound to the opposite sides of a macroporous polyethylene core. 
Another object of the present invention is to provide a diffusive material 
wherein the majority of the resistance to mass uptake is exhibited by the 
collection medium and is confined to the outer microporous layer of PTFE, 
the resistance to mass uptake substantially governed by the elastic 
collisions of the gas contaminant molecules with the pore walls. 
Another object of the present invention is to provide an improved gaseous 
dosimeter wherein mass transfer takes place in accordance with "Knudsen 
regime" diffusion theory, said mass transfer being proportional to the 
concentration gradient created across the diffusive material as the 
collection medium adsorbs or absorbs the contaminant as appropriate, and 
further is inherently resistant to disturbance from convective air 
currents in the immediate vicinity of the dosimeter. 
Another object of the present invention is to provide an improved dosimeter 
wherein solid or aqueous solution collecting media can be retained by the 
diffusive material with the latter substantially prevented from 
penetrating same by the hydrophobic properties exhibited by PTFE. 
These and other objects and advantages are achieved in the apparatus of the 
instant invention wherein there is provided an improved gaseous 
contaminant dosimeter that is operable to collect, for subsequent 
analysis, a selected gaseous contaminant in proportion to its average 
concentration in the ambient atmosphere during the collection period, and 
which includes a glass vial containing either a liquid or solid collection 
medium, the glass vial having an open end which is sealed by a piece of 
diffusive material that is held in place by a threaded cap which has an 
orifice formed therein; communication between the gaseous contaminant in 
the ambient atmosphere and the collection medium taking place through the 
piece of diffusive material.

DESCRIPTION OF THE PREFERRED EMBODIMENT 
Referring more particularly to the drawings, the apparatus of the subject 
invention is best understood by a study of FIG. 1. As shown therein, a 
container or vial generally indicated by the numeral 20 defines a void 32 
and has a neck 33 which has formed therein a raised thread 34 that is 
operable screw-threadably to mate with a cap generally indicated by the 
numeral 22. The cap 22 has an orifice or opening 35 formed therein which 
permits fluid flow communication between the ambient atmosphere 36 and the 
void 32. The cap further is operable to secure a piece of appropriately 
dimensioned diffusive material 21 in fluid impeding relation in the neck 
33 of the container 20. 
As should be understood, the fabrication of a diffusive material 21 that 
would meet the objectives of the invention begins with a consideration of 
the properties of microporous PTFE membranes 37. Those skilled in the art 
will readily recognize that PTFE is marketed under the trademark 
Teflon.RTM. by E. I. Dupont Co. Manufacturer's data provided by W. M. Gore 
& Associates for typical PTFE membranes 37, are set forth in TABLE 1 and 
show that resistance to air and water permeation in response to a pressure 
gradient across a PTFE membrane of selected pore size is inversely related 
to the pore size. After due consideration of the problems related to 
physically providing support for the PTFE membranes, the need to resist 
convective air movement at the exterior surface of the diffusive material 
21, the desirability of preventing a source of aqueous collection media 31 
from penetrating through the diffusive material, and the objective of 
fabricating a simple dosimeter whereby a decision would not have to be 
made by field personnel concerning the proper orientation of the diffusive 
material in the neck 33 of the container 20, the symmetrical laminate 
structure, which is best shown in FIG. 1, was selected. The manufacturer 
of the PTFE membranes shown in TABLE 1 provided four experimental 
laminates wherein PTFE membranes having individual pore sizes of 0.02, 
0.2, 1.0 and 10 micrometers, respectively, were thermally bound in a 
fashion so as to preserve their microporous characteristics, to both sides 
of a 1/16" thick (1.588 mm.) rigid sheet of substantially porous (50% void 
volume) polyethylene. This was done in order to investigate the 
relationship of the pore sizes and the abilities of the individual PTFE 
membranes 37 to resist convective air movement and to retain the aqueous 
collection media 31. As should be understood, manufacturers of PTFE 
membranes 37 employ a "bubble point test" to determine the pore size of 
the respective membranes. During the bubble point test, pressure is 
applied to a wetted membrane for purposes of blowing bubbles. This 
relationship of pressure with the production of bubbles is thereafter 
correlated and the appropriate pore size is assigned to the PTFE membrane. 
TABLE 1 
______________________________________ 
Void Minimum 
Vol- Air Flow Water 
Pore Size 
Thickness ume Rate (1) Entry Pressure 
______________________________________ 
0.02 .mu.m 
0.003 inches 
50% 3 mL/min-cm.sup.2 
350 PSI 
0.2 0.0025 78 75 40 
0.45 0.003 84 170 20 
1.0 0.003 91 530 10 
3 0.001 95 1200 2 
5 0.001 95 5700 0.5 
10-15 0.0005 98 14600 0.25 
______________________________________ 
(1) Measured at a pressure drop of 4.88" of water. 
The gaseous contaminant dosimeters of the instant invention, which are 
generally indicated by the numeral 30, were constructed of the design 
which is best illustrated by reference to FIGS. 2 and 3. As shown in FIG. 
3 the dosimeter 30 includes a clear glass vial 20 having a void 32 of a 
capacity of approximately 16 mL. The void 32 receives an aliquot of 
aqueous collection media 31. As earlier discussed the cap 22 is adapted to 
retain a disk of diffusion material 21 is fluid impeding relation in the 
neck 33. The cap further is operable to exert sufficient force on the 
diffusive material to prevent the seepage of the collection media from 
around the edges of same when the dosimeter 30 is placed in the preferred 
inverted orientation shown in FIG. 3 thereby bringing the collection 
medium into contact with the diffusive material 21. The rigid core 11, of 
the diffusive material, maintains the relative dimensional stability of 
same while it is retained by the cap in an appropriate fluid impeding 
relationship in the neck 33. When appropriately assembled the only 
communication between a gas contaminant (not shown) in the ambient 
atmosphere 36 and the collection medium 31 is through the diffusive 
material 21. 
The abilities of the experimental laminates or diffusive material 21 to 
resist convective air movement and simultaneously retain a predetermined 
volume of aqueous collection medium 31 were tested in a series of 
experiments wherein the gaseous contaminant dosimeters 30 were threaded 
into open top caps which had been affixed to perforations in a tubular 
manifold, not shown, and in such a fashion that the exterior surface of 
the diffusive material to be tested was presented to the inside portion of 
the manifold. The aqueous collection medium 31 was placed in each 
dosimeter 30 and a test atmosphere containing a gas contaminant was passed 
through the manifold under essentially laminar conditions at linear 
velocities between 50 and 280 feet per minute (fpm), a range encompassing 
the average velocity of convective air movement encountered during 
personal sampling (National Institute of Occupational Health and Safety 
Contract No. 210-78-0115-0000). The results obtained from this 
experimental inquiry are shown in TABLE 2. 
TABLE 2 
______________________________________ 
Sampling Rate (cm.sup.3 /min) at Given Face Velocity (1) 
Membrane 
Pore Size 
50 fpm 100 fpm 200 fpm 
280 fpm 
______________________________________ 
0.02 7.8 8.2 7.8 8.8 
0.2 13.9 14.8 21.4 28.7 
1.0 24.0 29.7 46.3 61.5 
10 34.7 39.3 55.9 60.3 
theoretical sampling rate 
31.6 
for pure bulk diffusion 
______________________________________ 
The dosimeters 30 contained a collection medium 31 consisting of 5 mL of a 
0.05% aqueous solution of 3-methyl-2-benzothiazolone hydrazine 
hydrochloride (MBTH) and were exposed to a test atmosphere of 
approximately 0.3 parts per million (ppm) formaldehyde (1/10th of the 
level allowed by the Occupational Health and Safety Administration for 
workers) for a period of approximately 4 hours. After exposure to the 
contaminants an oxidizing reagent consisting of ferric chloride and 
sulfamic acid was added to each dosimeter to produce a color which was 
later quantified by utilizing a spectrophotometer. The aforementioned 
method is the one recommended by the American Public Health Association 
(Method 117, Tentative Method of Analysis for Formaldehyde Content of the 
Atmosphere (MBTH-Colorimetric Method-Application to Other Aldehydes, pp 
308-313 in Methods of Air Sampling and Analysis, APHA Intersociety 
Committee, Washington, D.C.). 
The test results summarized in TABLE 2 indicated that all of the diffusive 
materials 21 could retain the aqueous collection media 31 under quiescent 
experimental conditions. However, the diffusive material constructed from 
10 micron pore size PTFE membranes 37 could not retain the collection 
media when subjected to mild agitation similar to that which would 
normally be experienced during personnel sampling. Of the three remaining 
test diffusive materials only the one fabricated from PTFE membrane of the 
smallest pore size, that is 0.02 microns, successfully resisted convective 
air movement and provided a regulated rate of mass transfer. Further, it 
was observed that the rate of mass transfer was lower than what would be 
predicted by applying Fick's Law for Bulk Gas Diffusion which was set 
forth earlier and indicated as equation (2). 
The individual resistances of each of the layers of the diffusive material 
21 to mass transfer were obtained from the overall apparent sampling rates 
by utilizing an analogy which draws a relationship between electrical 
resistance and diffusional resistance. This is discussed in greater detail 
in an article authored by E. D. Palmes and R. H. Lindenboom entitled 
"Ohm's Law, Fick's Law, and Diffusion Samplers for Gases," Analytical 
Chemistry 51, 2400-2401 (1979). In that article an equation was put forth 
which stated: 
EQU Total Diffusional Resistance.varies.1/S.sub.tot =1/S.sub.core 
+2/S.sub.membrane layers (3) 
where S.sub.tot, S.sub.core, and S.sub.membrane layers are the sampling 
rates of laminated materials as a whole expressed in cubic centimeters per 
minute. This of course includes the porous plastic core 11 and microporous 
PTFE membrane layers 37, respectively. Using this formula, it was 
determined that the surface layers, that is the PTFE membrane 37, had a 
mass transfer resistance three times higher than that of the porous 
plastic core 11 even though they had a void volume equal to, and a 
combined thickness of only one tenth that of the porous plastic core. 
Upon completion of these observations, it was subsequently determined that 
mass transfer through the diffusive material 21 having PTFE membranes 37 
with a pore dimension of 0.02 microns was dominated by Knudsen diffusion, 
the subject diffusion being named after M. Knudsen who discovered this 
phenomena in 1909. As should be understood, Knudsen diffusion is a 
transport mechanism clearly distinguishable from bulk gas diffusion, that 
is, bulk gas diffusion applies when the cross-sectional dimensions of a 
diffusion channel are much smaller than the mean free path length of a gas 
molecule in a gas mixture. The means free path length is the average 
length a gas molecule must travel before colliding with another gas 
molecule. In the ambient atmosphere 36 the mean free path length is 
approximately 10.sup.-5 cm, and thus pores of 0.02 micrometers 
(0.2.times.10.sup.-5 cm) meet this criteria. Those skilled in the art will 
readily recognize that within a Knudsen diffusion channel the probability 
of a gas molecule colliding with another gas molecule is very small as 
compared to the probability that it will collide with the wall of the 
diffusion channel. Therefore the mass transfer of a gas contaminant 
through diffusive material dominated by Knudsen diffusion becomes 
dependent upon the collisions of individual gas contaminant molecules with 
the walls of the diffusion channel, and substantially independent of the 
collisions with one another or other gas molecules present in the gas 
mixture. Inasmuch as convective movement in the ambient atmosphere is 
propagated by means of intermolecular collisions, it should be readily 
recognized that mass transfer through a Knudsen diffusion channel is 
inherently resistant to the interference occasioned by convective air 
movements in the immediate vicinity thereof. 
Although the pores in which the Knudsen diffusion mechanism occurs are 
small as compared to the mean free path length of the gas molecules, they 
are large as compared to the dimensions of the gas molecules themselves. 
Typically, the diametral dimensions of molecules with molecular weights of 
300 or less, that is, those likely to have a measurable vapor pressure, 
lie in a range of between approximately 2 and 10 Angstroms (0.002 and 
0.01.times.10.sup.-5 cm.) It should be understood, therefore, that a 
well-defined theoretical framework has been derived from the kinetic 
theory of gases that describe the properties of diffusion which take place 
under Knudsen conditions. For example, the articles authored by E. A. 
Mason and A. P. Malinauskas (1983), entitled Gas Transport in Porous 
Media: The Dusty-Gas Model, Elsevier Science Publishing Company, Inc., New 
York, N.Y.; and the article authored by R. E. Cunningham and R. J. J. 
Wiliams (1980), entitled Diffusion in Gases and Porous Media, Plenum 
Press, New York, N.Y. discuss this subject. More particularly it has been 
empirically determined that the transport of a gas molecule through a 
capillary tube of circular cross-section with a given radius r is 
proportional to a Knudsen diffusion coefficient which is calculated by 
utilizing the formula: 
EQU D.sub.Kn =[2r(8RT/.pi.M).sup.1/2 ]/3 (4) 
where D.sub.kn =the Knudsen diffusion coefficient expressed in square 
centimeters per minute (cm.sup.2 /min); r=the radius of the individual 
pores expressed in centimeters, (cm); R=the gas constant expressed in 
(gms-cm.sup.2 -mole-.degree.K.); T=the temperature expressed in degrees 
Kelvin (.degree.K.), and M=the molecular weight of the gas contaminant 
expressed in grams per mole. In practice, the Knudsen diffusion mechanism 
occurs in porous solids that frequently have a random structure that 
differs significantly from the relatively perfect dimensions of laboratory 
capillary tubes. Knudsen diffusion which occurs through such porous solids 
is described by an equation similar to, and containing terms found in, 
equations (1) and (2) which were discussed earlier. 
The equation that describes the Knudsen diffusion mechanism which takes 
place through such porous solids is set forth below: 
EQU W=pD.sub.Kn A(C.sub.a -C.sub.i)t/L.differential. (5) 
The ideal Knudsen diffusion coefficient derived from equation 4 is reduced 
by an empirical "tortuosity" factor .differential. which typically lies in 
a range between 3 and 7. It has been discovered that the values of an 
effective Knudsen diffusion constant are defined as the ratio of D.sub.Kn 
/.differential. and have been found to lie in a range between 0.1 and 2 
square centimeters per minute and are thus substantially intermediate in 
value as compared with the analogs constants which define bulk gas 
diffusion and permeation. 
The results obtained from the testing of the variously dimensioned 
diffusive material 21 and which are set forth in TABLE 2 indicated that 
the diffusive material constructed from PTFE membranes having a pore size 
of approximately 0.02 microns, and in which Knudsen regime diffusion 
applied, appeared to satisfy the invention objectives of maintaining a 
constant rate of mass transfer while being exposed to a range of 
convective air movements and simultaneously retaining the liquid 
collection media without the need for secondary protection features. In 
order to determine whether the diffusive material could be fabricated in 
sufficiently large quantities while simultaneously retaining substantially 
uniform performance characteristics, approximately 100 square feet of 
diffusive material 21 was fabricated, and several hundred disks or pieces 
of diffusive material were cut out in random patterns. The disks were 
utilized in a set of experiments which endeavored to examine the amount of 
gas contaminant collected as a function of the air concentration of the 
same gas. The results of these experiments are summarized in TABLE 3. 
TABLE 3 
______________________________________ 
(.mu.g/L)min 
Number of Amount of Relative 
of Dosimeters 
Contaminant Collected, 
Precision 
Exposure (1) 
Exposed Expressed in micrograms 
(2) 
______________________________________ 
34 20 0.42 4.4% 
71 20 0.89 5.1 
143 20 1.66 5.7 
205 20 2.50 6.2 
334 20 3.81 3.2 
______________________________________ 
(1) The test dosimeters were exposed to test atmospheres containing 
formaldehyde at concentrations ranging between 0.1 and 1 microgram per 
liter (approximately 0.1 to 1 ppm) for periods of approximately 4 hours. 
(2) The relative precision is the standard deviation of the amount of 
contaminant collected expressed as a percentage of the mean. 
The test results demonstrated that the entire lot of randomly shaped 
diffusive material allowed a selected gas contaminant to be collected with 
relatively excellent precision at a rate which was substantially linearly 
proportional to its air concentration. A least squares analysis applied to 
a plot of the micrograms of contaminant collected vs. the microgram-hours 
of exposure yielded a line having a slope of 11.3 mL/min, intercept 1.25 
mL/min, and a correlation coefficient of 0.991. 
In order to determine whether the gaseous contaminated dosimeter 
performance of the instant invention could be satisfactorily predicted on 
the basis of theory and a minimum amount of empirical data, a new series 
of experiments were conducted which endeavored to examine the relationship 
of the amount of gas contaminant collected as a function of the air 
concentration of that contaminant for a variety of different gases. 
Applying equation 4 noted above to the instant situation it should be 
expected that the rates of mass transfer for various gases through a 
selected Knudsen diffusive material should vary in proportion to the 
inverses of the square roots of their various molecular weights. The 
results of these experiments are summarized in TABLE 4, below: 
TABLE 4 
__________________________________________________________________________ 
Observed 
Calculated 
Sampling 
Sampling 
Difference 
Contaminant 
M. Wt. 1/(M. Wt.).sup.1/2 
Rate (1) 
Rate (2) 
(2) 
__________________________________________________________________________ 
Formaldehyde (3) 
30 gms/Mol 
0.183 11.3 mL/min 
12.9 mL/min 
-13.8% 
Sulfur Dioxide (4) 
64 0.125 9.6 8.8 +7.8 
Ammonia (5) 
17 0.243 18.1 17.1 +6.0 
Water Vapor (6) 
18 0.236 16.3 16.6 -1.7 
__________________________________________________________________________ 
(1) The observed sampling rates were obtained by exposing test dosimeters 
to a constant concentration of each contaminant for time periods spanning 
at least a fivefold range. The least squares analysis slope of a plot of 
amount collected vs (concentration .times. time) yields the sampling rate 
(2) A linear relationship between the sampling rate and the inverse of th 
square root of the molecular weight of the selected contaminant is 
predicted by equation (4). A least squares analysis of a plot of sampling 
rate vs. 1/(M. Wt.).sup.1/2 was therefore performed and yielded a 
satisfactory result (slope = 77.0 [(Mol. Wt.).sup.1/2 -mL/min], intercept 
= -1 [ (Mol. Wt.).sup.1/2 -mL/min], and correlation coefficient = 0.9318) 
The values of the least squares line were used to compute calculated 
sampling rates by substituting in known values of 1/(M. Wt.).sup.1/2. The 
last column shows the percent difference between the sampling rate 
computed from the least squares line and the observed value. 
(3) Formaldehyde was collected and analyzed as described in TABLE 2. 
(4) Sulfur Dioxide was collected in an aqueous solution of buffered 
formaldehyde and analyzed using a modified WestGaeke pararosaniline 
procedure. 
(5) Ammonia was collected in an aqueous sulfuric acid solution and 
analyzed using a modified Nessler's Reagent procedure. 
(6) Water vapor was collected by placing solid desicated molecular sieve 
in the dosimeter (inverted so that the molecular sieve was in contact wit 
the diffusive material), and analyzed by computing the weight gain during 
the exposure period. 
These test results clearly showed that performance date acquired with 
respect to the rate of mass transfer of one or more gases through a 
selected diffusive material can be utilized to predict the rate of mass 
transfer of a new gas through the same diffusive material. 
The assorted test results indicated that a gaseous contaminant dosimeter 
having a Knudsen type diffusive material 21 would exhibit characteristics 
wherein mass uptake could be predicted to be proportional to the ambient 
concentration of the selected contaminant and would further be inherently 
independent of the convective gas movement over a practical range of 
values. Further the test results indicated that the diffusive material 
would inherently retain the aqueous or solid collection media 31 without 
secondary design features. Moreover it was clearly established that the 
diffusive material could be manufactured in sufficiently large quantities 
while maintaining uniform performance characteristics. As should be 
understood once the performance characteristics of a Knudsen type 
diffusive material is empirically determined for one or more contaminants, 
its performance characteristics with respect to other contaminants can be 
easily and satisfactorily predicted. Further by combining equation (4) 
with the known dependence of C.sub.a (and C.sub.i if applicable) the rate 
of mass transfer by a Knudsen type diffusion material can be shown to vary 
predictably with temperature and pressure as a function of P/T.sup.1/2. 
Finally it has been determined that the response time can be shown by 
theory to be equal to the equation L.sub.2 /6D.sub.Kn and is typically 
rapid, as compared to the fluctuations in the gas contaminant 
concentration. 
The diffusive material 21, as constructed from commercially available 
starting materials, and shown in FIG. 1, includes two PTFE membranes 37 
having a 0.02 micron pore size, and a thickness of approximately 0.003 
inches which are individually thermally bound to the opposite sides of a 
macroporous rigid core layer 11 of polyethylene having a thickness of 
approximately 0.0625 inches. Other materials of substitution will 
hereinafter be discussed in greater detail. 
The physical characteristics that permits the diffusive material 21 to 
resist the deleterious effects of convective air movements is that Knudsen 
diffusion predominates in the PTFE membranes 37. To characterize the PTFE 
membrane structure, such as that shown in FIG. 4, manufacturers of same 
must specify the effective pore size 14 of the PTFE membrane material 37 
be performing one or both of two tests which are set forth below. The 
first test is a bubble point test which was discussed earlier, wherein 
increasing pressure is applied to a wetted sample of PTFE membrane until 
the first steady continuous stream of bubbles appears. Using a 
semi-empirical formula the pressure at which bubbles first appear can be 
related to the maximum pore size present in the membrane. The 
manufacturer's literature utilizes the following formula: 
EQU P=4K.sigma. cos (.phi.)/d (6) 
where P=the bubble point pressure; K=the shape correction factor; 
.sigma.=the surface tension, .phi.=the liquid-solid contact angle; and 
d=the pore diameter. The average pore size of the PTFE membrane is then 
estimated by assuming a normal distribution of pore sizes bounded at the 
upper end by the maximum pore size indicated by the bubble point test. 
The second test which can be employed for purposes of selecting a PTFE 
membrane 37, which has a suitable pore size wherein Knudsen diffusion 
predominates is an air flow rate test. In the air flow rate test the rate 
at which air flows through a selected PTFE membrane 37, which has been 
subjected to a slight pressure gradient, is measured. As earlier 
discussed, the data for both tests are summarized in TABLE 1. 
In order to select a suitable microporous PTFE membrane 37 for use in the 
present invention it should be understood that no amount of pressure can 
force bulk gas transport through a true Knudsen diffusion channel, 
therefore, with respect to the bubble point test noted above, a successful 
PTFE membrane is one which would resist bubble formation until pressures 
are reached that would physically disrupt or deform same. With respect to 
the data shown in TABLE 1 this disruption or deformation process occurs in 
the case of the 0.02 micrometer PTFE membrane at a water entry pressure of 
350 pounds per square inch (PSI). Such test results indicate that even the 
upper bound pore sizes in the same PTFE membrane are highly resistant to 
bulk gas movement induced by a pressure gradient, and therefore can be 
expected to resist convective bulk gas movement. In order to select a 
suitable PTFE membrane utilizing the air flow rate test it should be 
understood that the air flow measurement takes place in the presence of a 
slight pressure drop. This flow of air is necessary to demonstrate that 
the PTFE membrane is porous and not solid. If the pressure drop of 4.88" 
of water, used as the test condition in TABLE 1, is expressed as a 
concentration gradient, (since one unit describing pressure is the number 
of molecules per unit volume), and a value for D.sub.Kn,eff =(pD.sub.Kn 
/.differential.) is obtained from the data shown in TABLE 4, then in that 
event the measured air flow is within a factor of two of that which would 
be computed assuming that the entire air flow was generated by Knudsen 
diffusion. 
Having utilized the aforementioned criteria to identify suitable samples of 
PTFE membranes one should further note that the efficiency of mass 
transfer through a diffusive material in which Knudsen diffusion applies 
varies directly as the void volume and indirectly as to the thickness. 
Reported values for the former typically lie in a range for example 
between 0.1 (porous silica-alumina catalysts) and 0.5, that is PTFE 
membranes 37 as utilized in the instant invention with the preference 
being to employ materials with the highest available void volume to 
maximize mass transfer efficiency. As earlier indicated, Equation (5) may 
be used to compute the range of acceptable thicknesses for particular 
application, although parenthetically the preference would most often be 
to select the thinnest available material for purposes of achieving the 
highest rate of mass transfer. Further the preferred membrane material 
would be one which does not substantially react with, that is adsorb or 
absorb the gaseous components passing through it. In the present invention 
PTFE membranes 37 were selected as one of the most inert substances 
commercially available. Other porous materials which may be used as a 
"Knudsen diffusion" surface layer for regulating mass transfer include for 
example PVF which is otherwise known by the trademark Tedlar.RTM.. This 
material theoretically could be manufactured with pore sizes in the 
Knudsen range. Further, mixed acetate and nitrate esters of cellulose can 
be obtained with a pore size of 0.025 micrometers and comparable physical 
specifications. The "Knudsen diffusion" surface, whatever its individual 
composition, must exhibit the property of hydrophobicity which would 
permit it to retain an aqueous collection medium 31 without further 
structural limitations. This is a highly desirable feature inasmuch as 
many methods which are recommended by recognized advisory agencies for the 
accurate and specific collection and measurement of selected gaseous 
contaminants involve collection of same in aqueous collection mediums 31. 
Examples include, but are not limited to, the various methods recommended 
by the American Public Health Association and the National Institute of 
Occupational Health and Safety for the determination of ammonia, 
acetaldehyde, acetic anhydride, amines, formic acid, hydrazine, hydrogen 
bromide, hydrogen chloride, hydrogen fluoride, hydrogen cyanide, hydrogen 
sulfide, chlorine, sulfur dioxide, nitrogen dioxide, and ozone. Further, 
one skilled in the art will readily recognize that it is possible to treat 
other surfaces so as to give them the trait of hydrophobicity. For 
example, one can treat mixed acetate and nitrate esters of cellulose with 
an application of silicon. 
In the present invention an overall laminate type structure was selected in 
order to provide physical support for the selected membranes 37. Use of a 
support material 11 may or may not be necessary for other candidate 
Knudsen type membranes. If desired, other supporting or moderating type 
layers may be used in combination with the selected Knudsen type membranes 
to confer the desired properties. Porous support materials 11 which may be 
utilized include but are not limited to porous plastics such as 
polyethylene, polypropylene, polycarbonate, and polyurethane; or porous 
woven or fritted glasses; or sintered or other porous metals such as 
stainless steel. In an endeavor to limit the influence of such supports on 
mass transfer, they should be selected so as to have a minimum thickness 
required for their role, and a maximum porosity (void volume). As should 
be understood Equation (2) can be used to select appropriate candidate 
materials which can be substituted in the place of the porous support 
material 11. 
The gaseous contaminant dosimeter 30 of the present invention utilizes a 
vial 20 which is manufactured of glass, in combination with a standard 
septum type cap 22 which secures a disk of diffusive material 21 in fluid 
impeding relation in the neck 33. Assembled from easily available 
materials, such a gaseous contaminant dosimeter is inexpensive and 
reusable. Further, the area of the diffusive material 21 exposed to the 
contaminant gas may be easily changed to modify the rate of collection if 
this is desirable. Moreover it should be readily recognized that glass is 
relatively inert, and can contain a wide variety of chemical reagents 
without inducing unproductive or interfering side reactions. Indeed, the 
methods referred to earlier and which are recommended by recognized 
advisory agencies for the accurate and specific measurement of gas 
contaminants utilizes a method that involves the placing of a collection 
medium 31 in a glass "bubbler" not shown, and drawing air having the 
gaseous contaminant to be detected through the collection medium by means 
of a pump also not shown. Further, organic gases are frequently collected 
by drawing air through a glass tube containing activated charcoal by means 
of a pump. For selected applications, other solid sorbents such as silica 
gel could be used. 
The gaseous contaminant dosimeter of the instant invention also simplifies 
analysis procedures after the selected gaseous contaminants have been 
collected. For example, when a liquid collection media 31 is used, 
developing reagents can be added directly to the vial 20 thereby 
developing a color reaction. The gaseous contaminant concentration can 
then be determined by comparing the developed color to a comparison card 
or by inserting the device directly into the sample well of a colorimeter. 
Moreover with pre-packaged reagents an analysis of this sort can be 
conducted on the job site by relatively unskilled personnel. 
Alternatively, aliquots of liquid collection media may be withdrawn from 
the vial 20 for subsequent analysis by gas or liquid chromatography, 
spectroscopy, ion-specific electrochemistry or any of the analytical 
techniques commonly in use. When solid sorbents are employed desorbing 
solvents, such as carbon disulfides, can be added directly to the vial 20 
and an aliquot of same can be subsequently withdrawn for latter analysis 
by employing gas or liquid chromatography or other desired means. 
Therefore, it will be seen that the gaseous contaminant dosimeter apparatus 
of the instant invention is adapted to enhance the efficiency, speed, and 
accuracy with which the concentration of assorted gaseous contaminants can 
be determined in selected operational environments; provides a fully, 
dependable and practical means by which individual "breathing zone" 
measurements can be performed for selected personnel; and further is 
operable to retain both aqueous and solid sorbents with the attendant 
benefits associated therewith; the gaseous contaminant dosimeter device 
being of both sturdy and dependable construction and relatively 
inexpensive to manufacture and maintain. 
Although the invention has been herein shown and described in what is 
conceived to be the most practical and preferred embodiment, it is 
recognized that departures may be made therefrom within the scope of the 
invention which is not to be limited to the illustrative details 
disclosed. 
Having described my invention, what I claim as new and desire to secure by 
Letters Patent is: