=
qwoY-;)
Fca t time t m
=
0.5tR (ml/min)
(PdPo),-
partition coefficient molecular weight of the stationary liquid phase pressure (mm Hg) vapor pressure of pure solute at column temperature (mm Hg) concentration of solute in the liquid phase (mole/l.) gas constant (1-mm/mole- OK) temperature (OK) column temperature (OK) volume of liquid phase (ml) volume of gas phase (ml) retention volume a t column temperature and pressure (ml) V B measured a t the column inlet (ml) V Rmeasured a t the column outlet (ml) mole fraction of solute in the liquid phase mole fraction of solute in the gas phase activity coefficient of solute a t temperature T and pressure P lim. h ( T , P) x2-0
partition ratio number of moles of liquid phase in the column
t
=
t.4
= retention time of a n air peak (min)
fR
ub
uc Ut
uo
v20
vzm qb rlC
171
P
rl.
time (min)
= retention time of the solute (min)
average flow velocity of mobile phase a t any point o n a front o r boundary (cmisec) = average flow velocity of pure carrier gas ahead of a boundary (cmjsec) = average flow velocity of the mobile phase (solute plus carrier) behind a front (cmisec) = average flow velocity of mobile phase a t column outlet after the boundary has emerged from the column (cm/sec) = molar volume of pure solute (l./mole) = partial molar volume of solute at infinite dilution (I./mole) = viscosity of gas mixture a t any point o n the boundary = viscosity of pure carrier gas = viscosity of input mixture (solute plus carrier) = density of stationary liquid phase a t column temperature (g/ml) = empirical factor defined in Equation 17 =
RECEIVED for review May 18, 1971. Accepted July 29, 1971. This work was supported by a Fredrick Gardner Cottrell Grant from the Research Corporation and Grant No. GP27999 from the National Science Foundation.
Performance Characteristics of Permeation Tubes Daniel P. Lucero Electro-Analytical Transducer Corporation, Placentia, Calve 92670 The general operation and characteristics of permeation tubes are examined by their mass transport equations. Their sample emission rates in the steady state, saturation, and depletion stages are analytically described. An expression for the emission rate equilibrium time is presented which shows that the time required to restore emission rate equilibrium after a temperature change is identical to that required for initial conditioning. A relationship between tube temperature, carrier gas flow rate, and sample concentration of the carrier and at the tube outside surface is developed. I t shows that the sample concentrations in calibration gases produced by permeation tubes are entirely related to temperature over a wide range of carrier gas flow and tube emission rates. Permeation tubes can be utilized as a permeameter to conveniently measure the diffusion parameters of materials to different gases.
PERMEATION TUBES are self-contained sources of precisely controlled low level gas flow rates less than 1 ng/sec. They are primarily used t o provide accurate dynamic gas samples over a wide range of concentrations ( I , 2). By injection of the tube emission gas molecules directly into a carrier gas stream, concentrations in the sub-ppm range are conveniently generated at modest carrier flow rates without further dilution. At the present time, the utility of permeation (1) A. E. O'Keefe and G. C. Ortman, ANAL.CHEM., 38,760 (1966). (2) Zbid., 39, 1047 (1967). 1744
tubes is mainly in the preparation of reproducible gas mixtures over a wide range of concentration and complexity (3, 4). This feature permits the dynamic calibration and testing of air analyzers and aids in establishing primary standards for trace gas analysis (5, 6). Analytical techniques are employed in this article t o unify the technology of permeation tubes and clarify the existing confusion regarding their equilibrium characteristics and useful range of operating conditions. The author and many other workers have experienced excessive delays in the calibration of gas analyzers and interpretation of the analytical data produced. For example, analyzer span and signal drifts are observed when calibrating with permeation tubes which have not attained concentration equilibrium of the dissolved calibration gas in the tube wall. Although thermal equilibrium is attained in a few minutes, gas saturation of the tube wall t o equilibrium requires several hours after a temperature change. The tube emission varies logarithmically with time until equilibrium saturation is reached.
(3) M. D. Thomas and R. E. Amtower, J . Air Pollrrt. Contr. Ass., 16, 623 (1966). (4) L. A. Elfers and C. E. Decker, ANAL.CHEM., 40,1659 (1968). (5) W. L. Barnesberger and D. F. Adams, Emiron. Sci. Tech., 3, 258 (1969). (6) F. P. Scaringelli, A. E. O'Keefe, E. Rosenberg, and J. P. Bell, ANAL.CHEM.,42, 871 (1970).
ANALYTICAL CHEMISTRY, VOL. 43, NO. 13, NOVEMBER 1971
GENERAL OPERATION
A permeation tube is essentially comprised of a hollow sealed cylindrical tube fabricated of a relatively inert semipermeable material such as Teflon (Du Pont) (/). It is filled with a gas, which during isothermal operation, coexists in equilibrium with its liquid phase and is exposed t o its surroundings through the tube wall. It may utilize any gas which can be liquefied within practical operating and storage temperature and pressure limits. Consequently, for a given tube, the emission rate is dependent upon and is entirely controlled over a relatively wide range by its temperature. During operation, its temperature is constant and maintained t o within + O , l "C for adequate precision and control of emission rate. At excessively low temperatures, the tube emission rate density (std cc/min-cm2) is negligibly small. At excessively high pressure, a proportionally thicker tube wall is required t o provide mechanical strength. It increases the tube gas equilibrium saturation time. More important, however, are the nonlinearities of tub: emission rate introduced by deviations from Henry's law at high gas pressures. The most common temperature and pressure operating ranges of the tube are 5 t o 40 "C and 1 t o 10 atm. It is also essential that the calibration gas or tube charge gas be virtually nonreactive with the carrier gas or any impurities it may contain. For example, the back diffusion of water vapor in the carrier through the tube walls in some cases limits the useful life of a tube by forming " 0 3 in NO? tubes. In this case the charge gas, NOs, is lost by emission through the tube walls and conversion t o " 0 , . A permeation tube experiences three distinct stages which are characterized by the tube emission rate with time: the saturation, steady state, and depletion stages. Only the steady state stage is useful in producing calibration standards since the tube gas emission rate cannot be effectively controlled in the saturation and depletion stages. In the calibration of gas detection devices, a permeation tube charged with the sample molecular species and in steady state operation is inserted in a carrier gas stream of known flow rate. The sample gas emanating from the tube outside surface and the carrier gas are mixed t o known proportions or predetermined sample gas concentrations against which gas detection devices are calibrated. More concentrated mixtures in sample gas are obtained by decreasing the carrier gas flow rate. Converse changes produce more dilute mixtures.
the tube wall material must be homogenous and isotropic and must not experience phase changes over the operating temperature range. Chemical and physical interaction of the tube material and the sample or carrier gas should be avoided t o prevent altering the diffusion parameters and dimensions of the tube with time. In addition, it is essential that the permeation tube operate as a n isothermal body at constant temperature and that the sample gas pressure at the tube outer surface remain constant. Steady-State Stage. The sample emission rate of a right circular cylindrical permeation tube is related to its material properties, temperature, and dimensions as shown below (7):
(11 tube sample emission rate, std cc/min temperature, OK tube length, cm tube wall material reference permeability coefficient, cc/sec-cm* Torr/cm tube wall material permeability activation energy t o sample gas species, cal/mole universal gas constant, 1.986 cal/mole-"K sample gas partial pressure, Torr tube radius, cm subscripts denoting inside and outside tube surface, respectively The partial pressure difference term of Equation 1 is the diffusion potential. In the preferred operational mode, the tube outside surface sample gas partial pressure is controlled at a constant level near zero. This condition is attained by instantly transporting the sample gas molecules away from the outside surface by forced convection induced by the carrier gas. For this reason the carrier gas flow rate is always maintained at levels sufficient t o provide the convective potential required by the transport process. Equation 1 is simplifizd by operation a t the condition p o + 0. For the liquid-gas phase system in the permeation tube, the equilibrium temperature and pressure are functionally related, at saturated conditions below the critical point of the gas, by the Clapeyron--Clausius equation (8). Thus, the sample gas partial pressure inside the tube is exclusively determined by its temperature. It is expressed by a n integrated form of the Clapeyron-Clausius equation:
wherep,
=
PERFORMANCE CHARACTERISTICS
The permeation tube performance characteristics are principally established by the properties of the sample gas and tube wall material and its dimensions. Their relatively small, constant, and reproducible sample flow rates are attained by maintaining a constant diffusion potential over a single unvaryingly small diffusion conductance. The sample gas partial pressure across the tube wall constitutes the diffusion potential and the tube wall dimensions and wall material sample gas permeability coefficient comprise the diffusion conductance. F o r a given tube of constant dimensions, the potential and conductance variables are exclusive functions of their temperature response characteristics. It is important t o restrict tube operation t o special boundary and operating conditions. Gas transport through the tube wall must be entirely by a solution/dissolution diffusion process-i.e., sample gas leaks through seals, cracks, pores, etc. are absent. To achieve a uniform emission rate density,
AH,
=
C
=
sample gas vapor pressure at reference temperature T,, Torr sample gas average molar heat of evaporation over temperature range T, t o T,, cal/mole a constant equal t o [ A H , ' R T , ] ,dimensionless.
Equation 2 prescribes a constant A H , over the temperature range T, t o T,. Since A H , varies with temperature, a n average value can be employed and reasonable accuracy maintained providing the temperature range is less than 40 "C. It is also important that T, and T, be a t levels sufficiently below the sample gas critical temperature t o assure the specific volume of the vapor is significantly larger than the liquid. Compliance with this condition is assessed by inspection of the compressibility of the sample gases employed (7) R. M . Barrer, "Diffusion In and Through Solids," Cambridge University Press, London, 1951, Chap. 1. (8) S. Glasstone, "Textbook of Physical Chemistry," 2nd ed., D. Van Nostrand, New York, N.Y., 1946, p 450.
ANALYTICAL CHEMISTRY, VOL. 43, NO. 13, NOVEMBER 1971
1745
Table I. Compressibility and Latent Heat of Evaporation of Ammonia and Sulfur Dioxide.
Item Critical pressure. atm Critical temperature, “C Temperature, “C Saturated pressure, atm Reduced pressure Reduced temperature Compressibility factor Latent heat of evaporation, cal/mole @ 10 “C @ 25 “C @ 40 “C
Ammonia 111 132 20 8 0 0 0
5 4 7 079 725 96
5000 4750 4480
Sulfur dioxide 71 157 20 3 0 0 0
7 2 34 043 68 98
5700 5500 5230
Per cent deviation in latent from 25 “C reference @ 10 “C @ 25 “C @ 40 ”C
+5 27% 0 -5 6 9 z
$3 64% 0 - 4 90%
a Data from J H Perry, “Chemical Engineers’ Handbook.” 3rd ed.. McGraw-Hill, New York, N.Y., 1950, pp 204, 205, 208, 250, 275, and 353.
(9). For example, complete conformance is certain when the gas exhibits a unity compressibility factor. At 20 O C the compressibility factors of saturated ammonia and sulfur dioxide are 0.96 and 0.98, respectively, as shown in Table I. Their deviation from unity compressibility is less than 10% which is not regarded excessive (10) and is compatible with the limits of Equation 2. The latent heat of evaporation varies approximately in a linear fashion with temperature and is zero at the critical point (11). However, over a +15 OC temperature range, the per cent deviation of latent heat from that at 25 “C is approximately = k 5 % and +4% for ammonia and sulfur dioxide at the operating temperature limits as shown in Table I. Smaller excursions in AH? and pLfrom Equation 2 are obviously obtained over narrower temperature ranges which are more common in practice (I). It appears that over a 10 t o 40 O C temperature range, the thermodynamic properties of saturated ammonia and sulfur dioxide conform within reasonable limits t o the assumptions leading to Equation 2 and in expressing their vapor pressure levels in terms of their latent heats. A combination of Equations 1 and 2 , reflecting the boundary conditions and simplifying assumptions presented above, yields a n expression of permeation tube steady state sample emission rate in terms of the material and dimensional variables and temperature:
large variation in AHe with T o r for wide temperature ranges. In all cases, the slope of the curvature is larger a t the lower than at the higher temperature, and the curve tends t o be concave downward. Over small temperature ranges, however, the data are linear in the absence of tube wall material phase changes. A phase change is reflected by a n abrupt change in the slope of the line at a specific and discrete temperature. The slope change is due t o an abrupt change of the permeability coefficient activation energy E. Thus, In (qJ data are correlated with 1/Tby two straight lines whose slopes are proportional t o their respective E. Experimental data exhibiting similar behavior have been reported for sulfur dioxide Teflon permeation tubes (12). It appears a phase change occurs near 0 “C. It is common for workers to ascribe this type of behavior to inadequate carrier gas flow control and faulty gas detector or analyzer response. In many cases, great efforts are devoted t o the invastigation of these elements. It is suggested that prior characterization of the permeation tubes by Equations 1 , 2 , and 3 can avert some of these misdirected efforts. Saturation Stage. Steady state operation of a permeation tube is achieved after it experiences a transient stage which follows charging of the tube with the sample liquefied gas or a temperature change. Temperature changes alter the equilibrium condition because the sample gas partial pressure changes with temperature as described by Equation 2 . Thus, a change in temperature establishes a new sample gas concentration equilibrium condition in the tube wall corresponding t o its pressure as defined by Henry’s law (13-15). In both cases, the total equilibrium time is primarily determined by the time required to saturate the tube wall with sample t o its equilibrium concentration. The thermal response of a standard commercial permeation tube is of secondary significance t o the equilibrium time. It affects the equilibrium time only because the wall material diffusion coefficient changes with temperature. The thermal equilibrium time constant is about 10 t o 30 seconds while the equilibrium saturation time constant may be several hours. For radial diffusion transport where the tube length is much larger than its wall thickness ( L >> ro - r,) and outside radius ( L >> ro),the time constant for the saturation process is given by the expression below (13-16): where t,
=
D, =
t, = (roz- r t 2 )In (ro/rt)/Ds (4) permeation tube equilibrium time constant, sec, tube wall material gas diffusion coefficient, cm2/ sec.
+
To attain 99% of the final saturation level, the time required is approximately 5 t . Wall saturation time is independent of the saturation level and the tube length. Temperature affects saturation time only by the variation of D,with temperature which is identical in form t o the thermal variation of the permeability coefficient (7). The tube wall saturates faster at higher than at lower temperatures. Equation 4 can be applied with reasonable accuracy to tubes with L/r, 2 15 and with the magnitude of D, evaluated at the saturation temper at ure.
(9) J. H. Perry, “Chemical Engineers’ Handbook,” 3rd ed.. McGraw-Hill, New York. N.Y., 1950, p 353. (10) 0. A. Hougen and K . M. Watson, “Chemical Process Principles,” John Wiley & Sons, New York, N.Y.. 1947, p 487. (11) Zbid.,p 277.
(12) F. P. Scaringelli, S. A. Frey, and B. E. Saltzman, Amer. Did. Hyg. J . , 28, 260 (1967). (13) D. P. Lucero, AKAL.CHEM., 40,707 (1969). (14) Zbid.,41, 613 (1969). (15) S. Glasstone, “Elements of Physical Chemistry,” 1st ed., D. Van Nostrand, New York, N.Y., 1954, pp 350-2. (16) D. P. Lucero and F. C. Haley, J . Gas Clv-omatogr.. 6, 477 (1968).
2TLP”P, [exp (-E/RT In (r,/rJ
q =-a
- AH,/RT
- C)]
(3)
The temperature response of q. in Equation 3 arises from the temperature dependent properties of the tube wall material permeability coefficient and the sample gas vapor pressure. Thus, qs varies logarithmically with 1jT. A plot of In (qJ against lji“ is a straight line with a negative slope of [(AH? E)/R]. Experimental data will display some degree of curvature, particularly with gas samples where there is a relatively
1746
e
ANALYTICAL CHEMISTRY, VOL. 43, NO. 13, NOVEMBER 1971
For this reason, it is necessary t o condition permeation tubes after charging with the liquefied gas by permitting them t o saturate for several days. Temperature changes resulting from environmental changes and test or experimental requirements disturb the gas equilibrium concentration in a similar manner. It is common practice to store the tubes in a low temperature environment, such as a laboratory refrigerator at 5 "C, to extend their life. In most applications, the tubes operate at higher temperatures. Therefore, the tube sample gas emission rate will drift upward until its tube wall is saturated to its equilibrium concentration. The time required is approximately 5t, as described by Equation 4. Ideally, a permeation tube should be stored and used at a single temperature to avoid inducing the saturation stage thermally. With every change in temperature, the corresponding equilibrium concentration level of sample gas in the tube wall material must be established prior to attaining emission rate equilibrium. This behavior has been noted with a typical butane single-wall permeation tube which had experienced the initial saturation stage (6) upon charging with the sample gas. It required 113 hours to attain emission rate equilibrium after a moderate temperature change. Equation 4 was used with the saturation time reported in reference (6) t o calculate the Teflon butane diffusion coefficient at 1.7 X lo-' cm2/sec. From the same source, the Teflon sulfur dioxide coefficient was determined to be 1.1 X 10-7 cm2/secby the same technique. It is always essential t o allow the permeation tube sufficient time for saturation, after charging with the liquefied gas or changing its temperature, t o maximize accuracy and precision in their sample emission rates. Otherwise this behavior may be interpreted as a signal drift in detector calibration tests employing permeation tube techniques. The emission rates per unit tube length of a sulfur dioxide permeation tube at 20 and 21 "C are 190 and 208 ng/min-cm, respectively (17), and initially a maximum error of approximately 9% in the sulfur dioxide concentration of the carrier gas is present when the tube temperature is changed by that increment. The error decreases with time as the tube wall is saturated with sample gas to the concentration level corresponding to the vapor pressure. A single-wall tube similar t o that described in Reference (6) possesses a time constant of 12.2 hours. It will require approximately 61 hours at 21 "C t o stabilize and minimize the error. In changing temperature from 20 t o 25 "C, the maximum error initially introduced is 3 5 x . At the end of one time constant or 12.2 hours, the error is 13 %. This behavior is a severe limitation o n the utility of permeation tubes since it is impractical to wait several days for the tube emission rate t o stabilize after only moderate temperature changes. However, in applications where temperature is maintained essentially constant such as in air quality monitoring stations, it may not be a serious restriction. It can be surmounted by constructing time-temperature-emission rate charts which provide a correction factor for the emission rate and sample gas concentration in tlie carrier gas stream. Knowledge of the tube sample emission rate in the saturation stage is not of critical importance t o its utility. However, it can be obtained from a solution of Ficks second law in cylindrical coordinates ( 7 ) at the boundary conditions discussed earlier. The solution leads to Bessel functions. A simpler but more approximate solution is obtained from a
one-dimensional single-node representation of the tube wall (13). By means of the simplification, the emission rate is given by the product of Equation 3 and the factor [l - cat], where a = litc. The Depletion Stage. The useful operating period of a permeation tube ends with the condition at which the liquid phase of the sample vanishes because of its depletion. At this time, the tube internal sample pressure is not constant nor solely a function of temperature. It is approximately related to time at constant temperature by an expression derived from Equation 1 and a time-differential form of the perfect gas law: Pid
where P i d
=
= pi
exp
[
-
0.358 RTP, c E I R T
permeation tube internal sample pressure in the depletion stage, Torr
It is noted that pid is the internal sample gas partial pressure of the tube. In this sense, it is equivalent t o pi of Equations 1 and 2. However, the variations of P z d with time and temperature as expressed by Equation 5 is different. Therefore, the internal pressure in the depletion stage is designated by pia to note this distinction from that of Equation 2. Zero time in Equation 5 is taken at the instant the liquid phase vanishes in the permeation tube and as given by Equation 2. If required, the approximate expression for the depletion stage emission rate can be obtained from a combination of Equations 1, 3, and 5. OPERATING CONDITIONS
Permeation tubes offer a convenient and relatively simple means of conducting dynamic calibrations of gas detection devices and performing analytical experiments. However, their successful implementation is contingent on establishing known and closely controlled operating conditions as defined by the particular application and boundary conditions. For applications where these circumstances cannot prevail, corrective factors must be applied. As stated earlier, accurate and precise temperature control is essential in producing exact sample emission rates. Other limits in operating temperature, pressure, and carrier gas flow rate are also critical. Internal Gas Pressure. The liquefied gas pressure ( p , ) must not exceed pressure levels which seriously affect tube dimensions. In addition, it is important that there are no serious deviations from Henry's and Fick's laws at high pressures. Unless a strong interaction exists with the gas solute and membrane material, the gas pressure levels at which Henry's law displays nonlinearities are relatively high for most applications. For carbon dioxide in Teflon, it is about 11 atmospheres (18). Carrier Gas Flow. The main function of the carrier gas is to dilute the sample molecules to the required proportions and transport them out of the system to a gas detector or analyzer. Another equally important function is promoting the boundary condition p o + 0. Thus, it is essential to provide an adequate carrier gas flow rate to remove the sample molecules from the permeation tube outside surface. The rate of mass transport away from the tube surface depends upon carrier gas flow and diffusion moduli in the form
(17) Metronics Dynacal Permeation Tubes, Product Bulletin No.
20-68, Metronics Associates, Inc., Palo Alto, Calif. 94304.
(18) N. N. Li and E. J. Henley, A.Z.Ch.E. J., 10, 666 (1964).
ANALYTICAL CHEMISTRY, VOL. 43, NO. 13, NOVEMBER 1971
1747
OPERATING
IO0
10
SO2 CONCENTRATION AT TUBE
OUTSIDE SURFACE
(3, 1
@
PPM
Figure 1. Sample concentration in carrier gas and at external surface of sulfur dioxide permeation tube Operating conditions Temperature, 25°C; air carrier pressure, 760 Torr; SO2 vapor pressure, 2895 Torr; laminar carrier gas flow; tube length, 30.4 cm; tube outside radius, 0.1092 cm; tube inside radius, 0.0787 cm; tube material, Teflon; carrier gas tube diameter, 2.54 cm; SO: permeability, 2.54 X lO-"cc/sec-cm2-Torr/cm
of the Reynolds and Schmidt groups (19-22). For a permeation tube with its longitudinal axis parallel t o the direction of carrier gas flow, the relationship between the concentration of sample in the carrier gas and the sample concentration at the tube carrier interface is given below: 2.78 y o 'v
+ 0.976 y c Q c l / *
(6)
QC'/*
where y c
=
sample concentration in the carrier, ppm
Qc= carrier gas flow rate, cc/min y o = sample concentration a t the tube outside sur-
face, ppm Equation 6 is a specialized form of a n expression describing sulfur dioxide transport from a tube surface by an air carrier at 760 Torr in laminar flow (19) for the operating conditions listed in Figure 1. It is obtained by equating the rate of sample transport from the tube surface by carrier convection t o Equation 3. The carrier dilution effect on sample concentration is determined by the ratio of the tube emission flow rate t o the carrier gas flow rate. The mole fraction on a ppm basis is given by: y c = 60 X IO6 q s / Q c . This relationship describes the operating line of Figure 1. This equation is solved simultaneously with Equation 6 t o yield the relationship between y , and y o . The solution is obtained graphically as shown below. Equation 6 was employed t o calculate the carrier transport (19) D. 2. Pohlhausen, 2. Angew. Math. Mech., 10,353 (1921). (20) A. P. Colburn, T r a m Amer. I m t . Chem. EHg., 29, 174 (1933). (21) T. B. Drew, Tram. Amer. Inst. Clrem. Eng., 26, 26 (1931). (22) R. B. Bird, W. E. Stewart, and E. N. Lightfoot, "Transport Phenomena," John Wiley and Sons, New York, N.Y., 1960, p 525. 1748
I
I
I
I
VT
IPK
D
,
x",'103
Figure 2. Teflon sulfur dioxide permeability coefficient Permeability coefficients measured with permeationtube permeameter 0 Data from A. E. O'Keefe and G . C. Ortman, ANAL.CHEM.,38, 760 (1966) F. P. Scaringelli, A. E. O'Keefe, E. Rosenberg, and J. P. Bell, ibid., 42, 871 (1970)
lines a t carrier flow rates of 10, 100, and 1000 cc/min. They are graphically illustrated in Figure 1. The intersection of the operating line and the carrier transport lines on Figure 1 yields the solution of Equation 6 and dilution effects t o yield the sample gas concentration a t the tube surface and in the carrier gas ( y J . The ratio of sulfur dioxide concentration at the tube surface to that in the carrier ranges from 1.3 to 4.5 at 10 and 1000 cc/min carrier gas flow rates, respectively. Substitution of the results of Figure 1 for p o in Equation 1, demonstrates that the error introduced by assuming p . = 0 is about 0.1 at carrier flow rates near 10 cc/min and proportionally less at higher carrier flow rates. Thus, the principal boundary condition that p o + 0 is adequately fulfilled over the range of conditions and dimensions listed in Figure 1. The analytical procedure utilized t o construct Figure 1 can be used t o evaluate the performance and accuracy of permeation tubes for other specific applications. It can be used t o perform numerical experiments t o establish the maximum permeation tube dimensions and minimum carrier flow rate t o meet the condition where p o 0.
-
PERMEAMETER APPLICATION
The unique characteristics of permeation tubes provide a convenient and simple means of measuring the common diffusion parameters of some material-gas combinations. They can perform as well as some of the permeameters ordinarily used to perform these measurements (23). In (23) ASTM E-96-66, American Society for Testing and Materials, Philadelphia, Pa,, 1966.
ANALYTICAL CHEMISTRY, VOL. 43, NO. 13, NOVEMBER 1971
this application, identical equipment to that utilized in the dynamic calibration of gas detection devices can be used (6). The limitations of a permeameter or permeameter tubes are those imposed by the critical point of the gas and the mechanical properties of the tube wall material. A gas whose critical point is below that a t which the measurements are t o be performed cannot be used because the emission rate is not described by Equations 1 and 3. I n this casz, the internal tube pressure is described by Equation 5 and the emission rate appears as if the tube is in the depletion stage. A reasonably low internal pressure (pi)level must be maintained to prevent large deviations from Henry’s law and rupturing of the tube wall. Accuracy limitations are imposed only by the dimensional, temperature, and gas detection accuracy of the system. An experimental technique must be implemented t o ensure that thermal and the subsequent mass transport equilibrium are fully established during the measurements. The permeability coefficient is determined by measuring
y, with a detector and using Q c and Equation 1 to compute the permeability coefficient (P,) or the group Poe-*IRT. Figure 2 presents the Teflon sulfur dioxide permeability coefficient determined in this fashion as a function of temperature from data of references (1) and (6). At 25 “C, it is 2.45 X lo-” cc/sec-cm2-Torr/cm. The permeability activation energy ( E ) is 1080 cal/mole as given by the slope (EIR)of the data. The diffusion coefficient (D,) is determined by Equation 4 and from the time required t o establish a steady emission rate after a n abrupt and small change in tube temperature. A plot of log (D)GS. l / T yields the diffusion activation energy (Eo). Once P, and D, are established, the gas solubility in the tube material is calculated from the ratio Pm/Ds at all temperatures.
RECEIVED for review September 30, 1970. Accepted August 9, 1971.
Construction and Calibration of an Apparatus for Absolute Measurement of Total Luminescence at Low Levels Richard Bezman and Larry R. Faulkner Coolidge Chemical Laboratory, Harrard Unicersity, Cambridge, Mass. 02138 An apparatus which features an integrating sphere for the reproducible collection of sample luminescence and a detection system of uniform response with wavelength has been constructed for the absolute measurement of total luminescence from sources of irregular geometry. The instrument was designed especially for use with low-level sources (less than l O I 3 photons/sec). A stepwise procedure permits calibration, repeatable to =t3%, for low luminescence intensities by means of the ferrioxalate actinometer exposed with a high intensity source. The stepwise nature of the calibration gives high confidence in its accuracy, and it is apparently independent of the geometry of the monitored source and the angular distribution, the decay time, and the spectrum (at wavelengths shorter than 600 nm) of its luminescence.
FROMTIME TO TIME,investigations of luminescent materials have demanded measurements of luminescence intensity that are both absolute, in that the results may be expressed in “absolute” photonic units, and total, in that they account for all light emitted a t any wavelength in any direction. This need has appeared most frequently when luminescence efficiencies have been of interest ( I , 2). Of course, methods involving fluorescence, phosphorescence, chemiluminescence, and scintillation measurements currently comprise a n important segment of analytical chemistry. Yet the development of these methods as viable analytical techniques continues to depend upon gradually improved understanding of fundamental processes. Measurements of luminescence yield have historically been a prominent means for advancing such knowledge, and, not surprisingly, the utility of the measure(1) J . N. Demas and G. A. Crosby. J . Phys. Chem., 75, 991 (1971). (2) C. A. Parker, “Photoluminescence of Solutions.” Eisevier. Amsterdam, 1968.
ments has been proportional to the ease and reliability with which they could be made. Only in determinations of fluorescence and phosphorescence quantum yield has measurement of total luminescence met unqualified success. This special case appears because the measurements are taken at steady-state; because a fairly intense, well-defined excitation beam can be used; and because the angular distribution of emission can be made completely random. Absolute measurements are not always needed in this application, because one seeks t o know only the ratio of total emission to the total quanta absorbed. However for luminescence that is not optically excited, emission intensities often change rapidly with time, sample geometries are often not constant or regular, the angular distribution of emission is usually not uniform, and absolute, rather than comparison, measurements must be used t o obtain emission yields of luminescence. It is plain that methods suitable for work in fluorescence spectrometry are not ordinarily useful for chemiluminescence, electroluminescence, or radiation-induced luminescence measurements. Furthermore, the luminescence generated in experimental work is usually a t such a low level that the usual means for determining absolute intensities, such as actinometry, cannot be applied to the sources themselves or to secondary steady-state sources of comparable intensity. Standard emitters, moreover, are generally far too intense for use in the direct calibration of photomultiplier tubes, and attempts at masking usually only aggravate geometric problems. To meet the requirements for our work in electrogenerated chemiluminescence, we have constructed and calibrated a photometric apparatus that yields absolute measurements of total emission regardless of the geometry, decay rate, or spectrum (at wavelengths shorter than 600 nm) of emission. Be-
ANALYTICAL CHEMISTRY, VOL. 43, NO. 13, NOVEMBER 1971
* 1749
