Thermodynamic Measurements by Frontal Chromatography A Practical Experimental Approach C. J. Chen and J. F. Parcher Department of Chemistry, The University of Mississippi, University, Miss. 38677
A partial investigation of the effect of experimental variables in thermodynamic measurements at finite concentrations by frontal chromatography has been carried out. The effects studied include the viscosity, pressure, and sorption effects, and the variation in outlet flow rate caused by each of these effects. The experimental apparatus and techniques have been tested by comparison of the activity coefficient data with comparable data obtained by static experiments or elution experiments at infinite dilution. Comparison data are presented for the systems n-hexane and benzene in squalane, and n-hexane and cyclohexane in n-hexadecane. The comparisons show that this technique is very much faster, but less accurate, than the classical static measurements of isotherms and activity coefficients of nonelectrolytes, and that the viscosity and flow rate of the carrier gas do not influence the activity coefficient measurements. GASCHROMATOGRAPHY is primarily an analytical separation technique. However, since the basic process is an equilibration of one o r more solutes between two immiscible phases, the chromatographic technique may be used to measure physical parameters normally measured by vapor pressure, solubility, o r gas compressibility measurements. Activity coefficients, second virial coefficients of gas mixtures, partition coefficients, adsorption and partition isotherms, and complex formation constants are the most common quantities presently measured by gas chromatography. Additional properties may be obtained from secondary measurements or from temperature variation studies, e.g., surface areas, heat of adsorption, partial molal excess free energy, enthalpy, and entropy of solution. The efficacy of gas chromatography for thermodynamic measurements has been recognized for many years and several reviews have appeared in the literature (1-5) covering this general area. Activity coefficients of nonelectrolytes at infinite dilution, A”, were first measured by Porter, Deal, and Stross (6) in 1956, with no corrections for gas phase imperfections. The theory and techniques for chromatography have been improved considerably and the most accurate measurements have been carried out using the virial equation of state along with an extrapolation to zero pressure correction. Everett (7) derived the following equation for f?” measurements from chromatographic data.
(1) J. R. Conder, in “Progress in Gas Chromatography,’’ (Vol. 6 of “Advances in Analytical Chemistry and Instrumentation”), J. H. Purnell, Ed., Interscience, New York, N.Y., 1968, p 209. (2) J. C. Giddings and K. L. Mallik, It7d Eng. Ckem., 59(4), 19 ( 1 967). (3) R. Kobayashi, P. S. Chappelear, and H. A. Deans, ibid., 59(10), 63 (1967). (4) C . L. Young. Chromutogr. Rer., 10, 129 (1968). (5) H. W. Habgood, in “The Solid-Gas Interface.” E. A . Flood, Ed., Vol. 2, Marcel Dekker, New York, N.Y., 1967, p 611. ( 6 ) P. E. Porter. C. H. Deal. and F. H. Stross. J . Amer. CIzem. Soc., 78, 2999 (1956). (7) D. H. Everett, Trans. Faraday Soc., 61, 1637 (1965). 1738
In f?(Tc,0)
=
In (nlRi“/KV&O) P20(B22
+ P(2B23 - G?”)/RT (1)
- t.?O)/RT
Several authors have made comparative studies of chromatographic and static measurement of fi”(8-11) and the agreement is usually excellent. Elution chromatography has one disadvantage with regard to the measurement of activity coefficients and that is the “infinite dilution” restriction. In the finite concentration range, x2 > 0, the process is severely complicated by several factors : (1) Gas phase nonideality ( 2 ) Variable partition coefficients, Le., nonlinear partition isotherms (3) Surface adsorption effects (4) Mobile phase sorption effects (5) Resistance to mass transfer To overcome the “infinite dilution” restriction, one must supplement the elution technique by controlling the concentration of solute in the carrier gas. This type of chromatography is known as frontal chromatography. In this case, the sample is continuously introduced into the chromatographic column a t a fixed mole fraction in the carrier gas. The recorder response or “frontalgram” is an integral form of the usual Gaussian peak of an eluted sample. This procedure is definitely inferior to elution chromatography as a separation technique; however, the advantage of the additional controlled variable, Le., concentration of solute in the gas phase, makes this procedure the best chromatographic approach for studying solution effects in the finite concentration ranges. Frontal chromatography is experimentally more difficult because of the need for switching gas streams without disturbing the detector or flow rate; and introducing the solute into the carrier gas a t a constant, known mole fraction. The detector requirements are slightly more severe since the detector must be linear over a wider range than usual. HOWever, once the equipment is assembled, the experimental technique is comparable with elution experiments. The first nonanalytical use of frontal chromatography was introduced by James and Phillips in 1954 (12). These workers used frontal chromatography to measure the adsorption isotherms of benzene and cyclohexane on charcoal. Since that time, the technique has been improved and the theory
(8) R. K . Clark and H. H. Schmidt, J . Phys. Cliem., 69, 3682 (1965). (9) A. J. B. Cruickshank. D. H. Everett, and M. T. Westaway, Traus. Faraday Soc., 61, 235 (1965). (10) A . J. B. Cruickshank, M . L. Windsor, and C. L. Young, Proc. Royal Soc., 295A, 271 (1966). (11) A. Kwantes and G. W. A . Rijnders, in “Gas Chromatography 1958,” D. H. Desty. Ed,, Butterworth, London, 1958, p 125. (12) D. H. James and C. S. G. Phillips, J . Chem. Soc., 1954, 1066.
ANALYTICAL CHEMISTRY, VOL. 43, NO. 13, NOVEMBER 1971
A 2
I
3
Figure 1. Schematic diagram for frontal chromatography Gas tank P. Pressure regulator 1.2. Oil manometer A.
developed by Glueckauf (13, 14), and this procedure has been used by numerous authors (15-19) to measure adsorption isotherms of solutes on solid adsorbents. There have been few direct comparisons between static and chromatographic isotherms (15, 16) for systems with nonlinear isotherms; however, the agreement is reasonable, considering the approximations in the chromatographic technique. Krige and Pretorius (20-23) have written a series of papers on the theory of frontal chromatography. This work was limited to so-called stationary fronts and incompressible mobile phases, but included the sorption effect and more recently, Conder and Purnell (24-27) published a lengthy discussion of the theory of frontal chromatography. EXPERIMENTAL Apparatus. A schematic diagram of the instrumentation is shown in Figure 1. The gas chromatograph used was a Microtek GC-2500 equipped with a thermal conductivity detector. The carrier gas was divided into two paths. One flow stream passed through a saturator at constant temperature in a separate controlled constant temperature bath. The other stream passed directly to the column. Either pure carrier gas or saturated carrier gas could pass through the column. Ahead of the columns, a Beckman GC-4 pneumatic gas sampling valve was used to alternate the inlet gas lines to the columns. After the analytical column, the carrier gas passed through either the viscometer or the flowmeter. The inlet pressures are monitored by manometers 2 and 3 and adjusted by the Matheson low pressure regulators. The differential manometer 2 was (13) E. Glueckauf, Nature, 156, 748 (1945). (14) E. Glueckauf, Trans. Faraday Soc., 51, 34 (1955). (15) P. E. Eberly,J. Phys. Chem.,65, 1261 (1961). (16) S . J. Gregg and R. Stock, in “Gas Chromatography 1958,” D. H. Desty, Ed., Butterworth, London, 1958, p 90. (17) J. F. Parcher and P. Urone, Nature, 211, 628 (1966). 33,966 (1961). (18) R. Stock, ANAL.CHEM., (19) P. Urone and J. F. Parcher, ibid., 38, 270 (1966). (20) G. J. Krige and V. Pretorius, ibid., 37, 1186 (1965). (21) Zbid., p 1191. (22) Ibid., p 1195. (23) Zbid., p 1202. (24) J. R. Conder and J. H. Purnell, Tram. Furrrdoy SOC.,64, 1505 (1968). (25) Zbid., p 3100. (26) Zbid., 65, 824 (1969). (27) Zbid., p 839.
B. Detector S . Saturator 3. Mercury manometer
Table I. Physical Properties of the Chromatographic Columns
Column No. 13 15
Liquid phase Squalane 11-Hexadecane
Weight of liquid Per cent phase, Solid support coating gram 60/80 AW-
22.58
2.370
Chrom-P 60/80 AWChrom-P
16.50
1.537
designed to indicate the pressure difference between the two inlet lines. Reagents. The analytical columns used were 1 m X ‘/.,-in. 0.d. Cu tubes filled with coated, acid washed 60/80 Chromosorb P. Squalane and n-hexadecane from Applied Science Laboratories were selected as the stationary phases. Baker GC-Spectrophotometric grade solvents were used exclusively for the solutes. Coating and Analyzing Procedure. The solid support was coated by a method described previously (28). The coated support was analyzed by washing with cyclohexane in a tared filter crucible and using weight differences. The columns which have been prepared and analyzed in our experiment are listed in Table I . Procedure. The inlet pressure difference was monitored o n the differential oil manometer 2, and equalized by means of the Matheson low pressure regulators, P. The carrier gas containing a constant, known mole fraction of solute from the saturator could be introduced into the analytical column by means of the gas switching valve, GSV. The mole fraction of solute was calculated from the inlet pressure and the saturator temperature. After the instrument has been properly adjusted, the flow rate change due to either viscosity or sorption effects could be measured throughout the experiment and the activity coefficients calculated. In the case of activity coefficient measurements, an elution sample was injected prior to each frontalgram to check the column performance through the comparison of the partition coefficient value with literature values. The flow rate change after actuating the gas switching valve was recorded, and the frontalgram was analyzed. The retention distance at various concentrations was read from the frontalgram and the activity coefficient was calculated on an IBM SYSTEM/360 computer. (28) J. F. Parcher and P. Urone, J Gus Chromatogr., 2, 184 (1964).
ANALYTICAL CHEMISTRY, VOL. 43, NO. 13, NOVEMBER 1971
1739
3 i
\
om
L
I
\
L 0 2 4 6 8 1 0 1 2 1 4
0
Time (minutes)
0 0
Figure 2. Sorption frontalgram and flowrate variation in He/n-hexanelsqualane system
1
2
Time (minutes) Figure 3. Viscosity effect
The gas phase viscometer was made from a Perkin-Elmer 154B Vapor Fractometer modified to hold a reservoir of mercury and a capillary tube. The viscosity measurements were carried out using the technique described by Malinauskas, Whisenhunt, and Searcy (29). The flow rates were measured from the residence time of a small air peak in a n empty column in a Fischer Gas Partitioner at the outlet of a n analytical column. The usual soap bubble flowmeters could not be used because of the large hydrocarbon concentrations and a capillary flowmeter and rotameter were ineffective because of the variations in gas viscosity. A mass flowmeter was not applicable because of variations in thermal conductivity of the gas phase in the course of the experiment. RESULTS AND DISCUSSION
The relationship of the measured retention volume, in frontal chromatography, t o the thermodynamic quantity K, has been derived and studied by several investigators (30-34). For systems with a constant partition coefficient: SORPTION EFFECT
V,
=
v, + (1 -
Y)KVl
(2)
The effect of pressure on the retention volume is given by Equation 3 ( I O ) and the retention volume of a system with a nonlinear isotherm, is given by Equation 4 (33,35). PRESSURE EFFECT NONLINEAR ISOTHERM
vr
= Vm
Vr
=
+ KVi(1 + PPJ33 V m + V>(bQ/aC)c
(3)
(4)
Peterson and Helfferich (33) have combined Equations 2 and 4 for the special case of a n elution peak in partially saturated column.
(29) A. P. Malinauskas, S. J. Whisenhunt, and J. Q. Searcy. J . Chern. Educ., 46, 781 (1969). (30) P. C. Haarhoff and H. J. Van Der Linde, ANAL.CHEM.,37, 1742 (1965). (31) [bid., 38, 573 (1966). (32) A. B. Littlewood, “Gas Chromatography,” Academic Press, New York, N.Y., 1962, p 40. (33) D. L. Peterson and F. Helfferich, J. Phys. Chern., 69, 1283 (1965). (34) G. Schay, “Theoretische Grundlagen der Gaschromatographie,” Veb Verlag der Wissenschaf‘ten. Berlin, 1961. (35) F. Helfferich and G. Klein, “Multicomponent Chromatography,” Marcel Dekker, New York, N.Y., 1970. 1740
0
3
Experimental data
__ Calculated curve
An equation of this form was the basis for the work of Conder and Purnell(24-27) who integrated this equation to obtain an analytical solution for Q, the amount of solute absorbed per milliliter of solvent, in terms of flow rates and areas of designated portions of the frontalgrams. The partition isotherms were converted to activity coefficient data for comparison with literature values. F o r the two systems nhexane in squalane and n-heptane in dinonylphthalate, the agreement between static and chromatographic data was acceptable (27). The initial objective of this work was t o test this procedure and expand the general technique to other systems. However, in the course of the investigation, we were forced to provide a different procedure in order to obtain reliable results. The initial phases of the work were carried out using helium as the carrier gas. The flow rate at the outlet of the column changes continuously in the interval 0 < t < t R . This effect is shown in Figure 2 which is a plot of outlet flow rate us. time. This curve is superimposed on the frontalgram (detector response cs. time) to show the variation in flow rate during the experiment. When helium was used as the carrier gas, the flow rate increased continuously during saturation and decreased continuously during the desorption portion of the experiment. This effect is primarily, although not entirely, caused by the gas phase viscosity differences between the helium gas and a binary mixture of helium/benzene. The viscosities of these gases were measured and found to be 210 and 186 ppoise ( Y , = O,l), respectively, a t 60.5 O C . Thus, based on Darcy’s law, the flow rate when the column is filled with helium/benzene should be 1.13 times the flow rate with pure helium in the column. The observed flow rate increase in the interval 0 < I < t R is less than this-i.e., approximately 1.06-which means that the observed flow rate variation is due to a combination of two opposing effectLe., viscosity effect and sorption effect. The effects of gas phase viscosity have been studied previously in elution systems by Haarhaff and Van der Linde (30, 31) and Dyson and Littlewood (36, 37). The effects observed by these authors are in qualitative agreement with the observed behavior in frontal chromatography. (36) N. Dyson and A. B. Littlewood, Trans. Faraday SOC., 63, 1895 (1967). (37) N. Dyson and A. B. Littlewood, ANAL.CHEM.,39, 638 (1967).
ANALYTICAL CHEMISTRY, VOL. 43, NO. 13, NOVEMBER 1971
250
\ Time (minutes)
Figure 5. Sorption frontalgram and flowrate variation in Hz/n-hexane/squalanesystem
Figure 4. Viscosity of vapors and gases at 27 "C
I n order to study the sorption effect and viscosity effect independently, the two effects must be separated. There are several approaches to this problem. The two we chose were to study the flow rate variation in a frontal experiment with helium and hydrogen as the mobile phases with n o solute (eliminate sorption); and to use a carrier gas/solute combination in which the viscosity of the gas is approximately independent of the composition (eliminate viscosity effect). The results of the experiments with helium and hydrogen are shown in Figure 3. Krige and Pretorius (20-23) have developed a theory of frontal chromatography which includes the viscosity effect. The equation developed for flow rate variation with time of a single, undiluted solute is :
points o n a boundary-Le., it is independent of Y . The basic requirement is met only in systems with linear isotherms or isotherms convex to the concentration axis in which diffusion effects are significant. In this study, the primary emphasis is on the diffuse boundary (either front or rear) and not the sharp or stationary front normally used in frontal chromatography theory. In a diffuse boundary, the solute concentration velocity (35) is a function of the solute concentration, so that the boundary shape changes continuously as the boundary passes through the column. The velocity at any point on the boundary is proportional to the velocity of saturated carrier gas in the portion of the column equilibrated with solute (32, 36, 37). Ub
=
ui/(l
+ k)
(7)
Thus the velocity ui must also vary with the boundary composition. The velocity of the front, ub, is related to the velocity of the pure carrier by: Ub = U o { l
+ k(l - Y ) ]
(8)
The velocities on each side of a boundary are related by Equation 9. The solid lines in Figure 3 are a plot of this equation for hydrogen and helium (k = 0) and the data points are experimentally observed flow rates. There is semiquantitative agreement between the observed and calculated flow rate variation. Thus, the viscosity effect can be adequately treated by Krige and Pretorius' theory. An alternate approach to the problem of gas phase viscosity is evident from an inspection of Figure 4. The viscosities of the normal chromatographic carrier gases, e.g., He, Nz, Ar, COz, are in the range of 150-250 ppoise, while the normal solutes are less than 100 ppoise. Hydrogen gas has a viscosity of 88 ppoise at room temperature and the effect of gas phase viscosity can be reduced or eliminated by using H2as the carrier gas. Figure 5 shows the flow rate variation when hydrogen is the carrier gas. In this case, the flow rate decreases when the binary hydtogen/benzene mixture enters the column, even though the viscosity of the mixture in only slightly greater than the viscosity of pure carrier. In this case, the viscosity effect is minimal and the controlling factor is the sorption effect. Krige and Pretorius based their treatment on the concept of "stationary" or sharp fronts. The requirement for a stationary front is that the solute velocity is the same a t all
(9)
In the usual case of different viscosities, Equation 7 and 8 must be altered by the factor ?lO/Tb. Peterson and Helfferich (33) have shown that for nonlinear isotherms, k should be replaced by
dQ h,thus for systems
(dc) V M
with a nonlinear isotherm, different gas phase viscosities, and an assumed incompressible mobile phase.
ub = V b
(1
+
("") 5) b c cv7n
The velocity of the front can be measured by the retention volume of a given point in the boundary. However, in the case of frontal chromatography, there are two distinguishable retention volumes, which are not necessarily equal. The volume of gas passed into the head of the column in the will not necessarily equal the interval 0 < t < tg, i.e., vRI,
ANALYTICAL CHEMISTRY, VOL. 43, NO. 13, NOVEMBER 1971
1741
0
I
I
I
01
I
0.2 I
04 I
06 I
0.8 I
1.0 I
8 0 ".
Oo5t
Figure 7. Activity coefficient of cyclohexane in n-hexadecane
coefficient of n-
Figure 6. Activity hexane in squalane
0 00
0 Static data 0 Experimental data Infinite dilution elution data
volume passed out V R ~even , when corrected to T, and P (35)
v,, = Vr,
Vm
=
vmu.Iq%/uh~h
(12)
+ (bQ/dC)cVl
(1 3)
For the outlet retention volume: Vro
1
Vm
+ (1 - V ( b Q / b C ) c v ~
(14
Thus the usual retention volume, VB,, is a function of the solute concentration, while V R varies ~ with the slope at the isotherm a t point C, but not with 1 - Y. The inlet flowrate is harder to measure, but easier to interpret, while the opposite is true of VRo. The outlet flow rate is also a function of the position of the boundary in the column even in the absence of viscosity effects, and this variation will affect the retention volume measurements. Krige and Pretorius (20-23) have worked out a theory for the flow rate variations in the case of sharp fronts; however, no work has been done on the effects of this flow rate variation in diffuse boundaries. It has been observed in almost all cases studied, that the flow rate change is linear with time. Thus the flow rate can be described by a n equation of the form: Fc = FCo- $t
(15)
+
where is an empirical factor determined by the combined viscosity and sorption effects. $ can be measured from the flow rate variation during the time 0 < t < tR. $
=
dF,/dt
( 1 6)
The retention volume, VRo,is measured from the outlet flow rate. V,,
=
sdr
F,dt
(17)
If Equation 15 is valid, then the integral in Equation 18 may be approximated by: Vro= Fc*t,
tained by integration of Equation 5. The variable of integration must be changed to dy before the integral can be evaluated. This can be done using Equation 20 (24). dC
=
(19)
(P,/RT)dY
Equation 20 has been used in this work to evaluate the partition isotherms and activity coefficients. Conder and Purnell (24-27) integrated a n equation similar to Equation 20 to obtain an analytical solution. We have chosen to carry out a direct graphical integration on the IBM SYSTEM/ 360 using Simpson's rule. The activity coefficients were then calculated from the partition isotherm by Equations 21 and 22 for comparison with static data (38, 39).
In fi(T,, 0)
=
In ( YzP,/X2P20) -
+
Pz0(Bz2 - UzO/RTc P,J:(B22
- (1 - Y)2 (Bz2-
2B23
+ B d - U Z ~ ] / R T ,(22)
Figure 6 represents the data obtained for n-hexane in squalane a t 60 "C. The static data of Ashworth and Everett (38) at 20, 30, and 40 "C and the infinite dilution,f", data obtained from elution experiments are presented on the same graph for comparison. In the limited range studied, xz < 0.35, the agreement with static and other chromatographic data is acceptable, and the primary advantage is that the isotherm was obtained from one experiment of approximately 15 minutes. At present, the data are digitized manually. This is a time consuming step; however, the entire operation-Le., digitization, and computation-usually required less than an hour. This is a remarkable saving in time, but the price is a slight loss of accuracy. Figure 7 is a similar plot for cyclohexane in n-hexadecane (50 "C). Static data are not available for comparison; however, the chromatographic values of Kwantes and Rijnders (11) values o f f " = 0.75-0.77 agree well with our extrapolated value o f f " = 0.78.
(18)
When Fc* is the observed outlet flowrate, corrected to T, and P , at t = 0.5 fR. The partition isotherm may then be ob1742
Elution data Experimental data
(38) A. J. Ashworth and D. H. Everett, Tram. Faraday Soc., 56, 1609 (1960). (39) M. L. McGlashaii and A. G. Williamson, ibid., 57, 588 (1961).
ANALYTICAL CHEMISTRY, VOL. 43, NO. 13, NOVEMBER 1971
:;:I \
h
I
-+" 0.10 O-
.t?N
0 20
0.15
0 301
t
0.20
0
Figure 8. Activity coefficient of nhexane in n-hexadecane
40 80 120 100 Temperature ("C)
Figure 10. '4ctivity coefficient of benzene in squalane at infinite dilution
0 Static data 0 Experimental data
hlartire (40) Kwntes and Rijnders ( / I ) 3 Everett (7) A W
0
Desty and Snanton (41)
Ashnorth and Ewrett (38) 0 This nork
A 0 I-
Figure 9. Activity coefficient of benzene in squalane A 0C 0
Static data Experimental data at 60 "C
The results for n-hexane in n-hexadecane, e.g., Figure 8, are not satisfactory, when presented on a log scale because of the relative expansion of this scale. However, the maximum error in the activity coefficient is less than 3 at x2 = 0.30. All of the results shown in Figures 6 to 8, are for systems in which the activity coefficient is essentially independent of temperature in the limited temperature range studied. The system benzene/squalane is temperature dependent and the results for this system a t 59 "C are shown in Figure 9. In all cases, our results are lower than the static data (39), but agree well with the elution data (11). Figure 10 is a plot of the available literature values o f f " as a function of temperature. The data points represented by the closed circles are well within the range of literature values, but considerably less than the static data. This deviation could be due to temperature effects in the column and/or solid support absorption of benzene. These points are presently under investigation in our laboratory. In previous work in chromatographic isotherms (27), it has been suggested that the particle size should be large, so that the flow rate can be reduced to eliminate the uncertain effects of the compressibility correction factor in the calculation. This approach increases the time required and
may introduce significant effects due to diffusion. All of the data presented in the figures were obtained at the optimum flow rate for the particular column and solute. The effect of flow rate o n the calculated data was observed for the 59 "C experiments in Figure 9. The data shown represent the combined results of four experiments a t 140, 86, 83, and 37 ml/min. The optimum flow rate was approximately 80-85 ml/min; however, a 50 ml/min change in either direction had no significant effect in the results. The . I : values were 0.83, 0.88, 0.89, and 0.95, respectively, and this variation had little o r no effect o n the results. The effect of the viscosity of the carrier gas was investigated and found to be negligible when Equation 20 is used to calculate the partition isotherm. The experimental data in Figure 6 are a composite of three experiments using helium, hydrogen, and nitrogen as the carrier gas. The viscosities of these gases were measured as 211, 97.4, and 196.3 ppoise, respectively, a t the column temperature. The activity coefficients measured with the three differect carrier gases had a relative deviation of less than 2 %. It is doubtful if a chromatographic technique will ever completely supplant the conventional static determination of activity coefficients of non-electrolytes nor are the results presently as accurate. However, the tremendous reduction in experimental time required makes the chromatographic approach a n attractive alternative to the static method. NOMENCLATURE
Subscripts 1, 2 , and 3 refer to the stationary liquid phase, solute, and inert carrier gas, respectively. = second virial coefficient for components i and j Bt, (l./mole> = concentration of solute in the gas phase (moleil.) C = corrected gas flow rate at column temperature Fc and pressure (mlimin) = Fc a t time t = 0 (mlimin) Fc (40) D. E. Martire, Ph.D. Thesis, Stevens Institute of Technology. Hoboken, N.J., 1963. (41) D. H. Desty and W. T. Swanton. J . Phys. Clrmn?., 65, 766 (1961).
ANALYTICAL CHEMISTRY, VOL. 43, NO. 13, NOVEMBER 1971
1743
=
qwoY-;)
Fca t time t
= 0.5tR (ml/min)
m (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
