pplication of a Piezoelectric Quartz Crystal as a Partition Detector Development of a Digital Sensor Morteza Janghorbani and Harry Freund Department of Chemistry, Oregon State University, Corvallis, Ore. 97331 AT-cut piezoelectric quartz crystals coated with low vapor pressure materials are evaluated as digital sensors in completely digital detection systems. Mathematical relations expressing detector performance as a function of system parameters are developed. Specifically, a response equation in terms of solutesolvent parameters is derived and i s extended to cover the effects of equilibrium temperature. Also, the response time of the detector is described mathematically. The theoretical predictions are tested employing both equilibrium and gas chromatograpic quasiequilibrium conditions. The sensor is applied to detection of sulfur compounds commonly present in pulp mill effluents, and application is made to on-line data acquisition and processing from a gas chromatograph.
QUARTZ CRYSTALS find extensive use as the frequency determining element in electronic crystal oscillators. King ( I ) and Karasek ( 2 ) have used such crystals, coated with a stable low vapor pressure liquid, as fast, sensitive gas chromatographic detectors. Typically two oscillators are frequency controlled utilizing reference and sample crystals. The two rf outputs are heterodyned, the resultant beat frequency is rectified and displayed on a n analog strip chart recorder. The result resembles in appearance that from a thermal conductivity detector. Guilbault (3) has employed crystals coated with mercury(I1) salts for detection of low concentrations of organophosphorous compounds. These workers have pointed out several advantages of this kind of detector, including detector sensitivity increase with solute boiling point, ability to differentiate between polar and nonpolar peaks, fast response, and ease of construction. Although these features are attractive, the potentially most significant characteristic of the transducer is its digital nature. The need for inherently digital transducers has been recognized and their major advantages over their analog counterparts have been discussed ( 4 ) . Especially the present trends towards greater utilization of digital computers in chemical instrumentation make development of such transducers highly desirable. This paper describes the characterization and development of a piezoelectric digital transducer. Mathematical relations characterizing such a partition detector are developed and tested. The detector is applied to on-line data acquisition and processing from a gas chromatograph, and t o monitoring sulfur compounds commonly present in pulp mill stack effluents. THEORETICAL DEVELOPMEN’S Partition Detector at Equilibrium with the Gas Phase. Sauerbrey (5) has shown that the frequency shift of a quartz (1) W. H. King, Jr.. ANAL.CHEM..36, 1735-9 (1964). (2) F. W. Karasek and K. R. Gibbins, J . Chromatogr. Sci., 9, 535-40 (1971). (3) G. G. Guilbault, Ai7al. Chim. Acta, 39, 260-4 (1967). (4) A. E. Schuler. 1/7striu?z.Teciinol., 16, 41-6 (1969). (5) G. Sauerbrey. Z. Phys., 155, 206-13 (1959).
crystal, Af, due to deposition or removal of some material on or from the crystal surface is : Af
=
mAW
(1)
where rn = a constant whose magnitude is determined by the frequency of the oscillating plate, frequency constant of the crystal cut, density of quartz, and the effective area of the vibrating plate. A W = mass deposited on or removed from the surface(s) of the crystal. Suppose such a crystal is coated uniformly with a liquid X which has a negligible vapor pressure and is capable of dissolving a gas Y such that at equilibrium the following relationship holds over the concentration range of interest:
where W,,, = weight of gas Y dissolved per unit volume of compound X,g ml- ; W , = weight of gas Y per unit volume of gas phase, g ml-I; and Ku,, = partition coefficient of gas Y in liquid X For a total volume V , of liquid X present on the effective surface of the crystal, combination of Equations 1 and 2 yields :
Af
=
inK,,, V , W ,
(3)
where Af = frequency shift due to dissolution of gas Y in V, ml of liquid X If the detector volume, defined as that volume of space containing W , grams of gas Y at equilibrium with the liquid X,is V , ml, Equation 3 may be written as: mK u , z v~( wid v D )
Af
(4)
Equation 4 describes the behavior of a partition det,ector at equilibrium with the gas phase. It applies only to cases where the dominant mechanism of solute pick-up is dissolution and not to other mechanisms such as substrate adsorption. Partition Detector Used in Gas-Liquid Chromatography. Assume that a partition detector is connected to the outlet of a gas chromatographic column and that the experimental parameters are such that a condition of approximate equilibrium can be assumed. Employing the concept of “imaginary plug” (6) and making use of Equation 4, it can be shown that:
a,
=
m.K,,,. Vz(W,tlF)
(5)
where a , = Afl.ArZ = incremental peak area for the gas chromatographic peak; A f t = VD/F; F = flow rate of mobile phase; and W , , = total weight of component Y present in the detector volume for the time the “imaginary plug” is inserted. Summation of these incremental areas over the entire peak results in Equation 6: (6) H. M. McNair and E. J. Borelli, “Basic Gas Chromatography.” Varian Aerograph, Walnut Creek, Calif., 1969, p 83.
ANALYTICAL CHEMISTRY, VOL. 45, NO. 2, FEBRUARY 1973
325
GAS
LIP. COATING
CRYSTAL
I
Figure 1. Case of a semi-infinite column of gas diffusing into a thin layer of liquid
20
40
60
80
100
Sime,sec.xro6
Figure 3. Theoretical response plot for the trailing edge of a step input
, 288
278
Figure 2. Case of (a) a thin-layer electrochemical cell, and (6) dissolved gas diffusing out of a thin liquid layer
= i=l
Figure 4. Theoretical behavior of partition detector sensitivity at various temperatures
a,
=
rn.Ky,,. V,.(l/F)
i=l
W,,
(6)
n
and since
W T i = WT total weight of component i injected i=l
into the column:
LEADING EDGE. Assume a column of air of semi-infinite length saturated with hexane in contact with one side of a crystal coated with a finite thickness of squalane. The situation in illustrated in Figure l a . One may apply Fick‘s second law to diffusion of hexane into the squalane coating. The following boundary conditions prevail.
(7) A,
=
(1) C
total area under the peak due to component Y
Equation 7 describes the behavior of partition detectors employed in gas-liquid chromatography under conditions of (approximate) equilibrium. Theory of Partition Detector Response Time. Responsetime relations are discussed for a theoretical step input. They take into account only diffusion into and out of the liquid coating and do not include any effects due to concentration variations in the gas phase. Theoretical plots are calculated for hexane (solute) diffusing in squalane (liquid coating). 326
308
n
n
A,
298
Tern p. PK
=
Co; X
5 0 at any time t
(2)C=O; O < X < l a n d t < O (3)C#O-+KCo;O < X < l a s t + m
where K = the partition coefficient of hexane between squalane and air. Assuming a single reflection term (Figure lb), the integrated form of Fick’s law becomes (7): (7) J. Crank, “Mathematics of Diffusion,” Oxford University Press, New York, N.Y., 1956.
ANALYTICAL CHEMISTRY, VOL. 45, NO. 2, FEBRUARY 1973
Figure 5. Gas handling apparatus
XI
(8)
Equation 11 below, derived by Littlewood ( I O ) expresses K u , z in terms of solute-solvent parameters if the pair follows Raoult’s law.
where Cafis approximately equal t o the product of COand the partition coefficient of hexane between air and squalane. Equation 8 is exponential in nature and shows that for diffusion of hexane in squalane and for x = I ninety-eight per cent of detector response will be attained in less than 100 milliseconds (8). TRAILING EDGE. Hubbard (9) has solved Fick’s law for the concentration-time-distance relationship for electrolysis in a thin layer electrochemical cell. His boundary conditions, evident from Figure 2a, are
where P20 = vapor pressure of solute at temperature T OK; R = universal gas constant; y = activity coefficient of solute X i n solvent Y ; p = density of the liquid phase; and M1 = molecular weight of solvent. Assuming that y is constant over the temperature range of interest, combination of Equations 10 and 11 yields :
X
- erf 21 -
2dDt
< 2’ < I and t < 0 C(1,t) = 0 for t > 0
C(x,O) = Cofor 0
C(0,t)
=
If P20varies with temperature according t o the integrated form of Clausius-Clapeyron equation :
The equation describing this system is: C-
co
Then
(9) Since Equation 9 is symmetrical with respect t o x = 1/2, it should also apply if a plane were inserted at x = 1/2 dividing the cell into two equal halves (7). Retaining the original coordinate system and applying the concepts to a crystal coated with a liquid layer, yields the model sketched in Figure 2b. Two concentration-time profiles are plotted in Figure 3, one at the crystal surface and the other a t the midpoint in the liquid film. The 9 8 x response should be obtained in less than 0.1 msec. Effect of Temperature on Detector Sensitivity. Sensitivity can be expressed as the frequency shift per unit concentration of the component t o be detected:
where S
=
sensitivity, Hz conc.-l
(8) M. Janghorbani, Ph.D. Thesis, Oregon State University, Corvallis, Ore.. 1971. (9) A. T. Hubbard and F. C. Anson, in “Electroanalytical Chemistry,” Vol 4, A. J. Bard, Ed., Marcel Dekker, New York, N.Y.. 1970, 13 212.
mV,pR where H = -- e-B. rM1
Figure 4 presents the effect of temperature on sensitivity using Equation 14 and assuming Hconstant over the temperature range of interest. The plot is for SO, which has a con1 stant A = 3274.7 calculated from the slope of log P cs. -- (11). T EXPERIMENTAL
This section describes both the methodology and the equipment used in various parts of the investigation. All chemicals are reagent grade, all coatings are GC-grade, and the SO2 is anhydrous grade obtained from Matheson Gas Company. Gas Handling Apparatus. Figure 5 shows the glass apparatus used. The main portion consists of a 500-ml flask A, l/2-in. i.d. column CL1, crystal housing B and manometer MI, all made of Pyrex (Corning Glass) glass. The rest of the (10) A. B. Littlewood, “Gas Chromatography,” second ed., Academic Press, New York, N . Y . , 1970. (11) R. C. Weast, Editor-in-Chief, “Handbook of Chemistry and Physics,” 47th ed., The Chemical Rubber Co., Cleveland, Ohio, 1966.
A NALYT ICAL C H EM ISTRY, VOL. 45, NO. 2, FEBRUARY 1973
327
R
II
Figure 6. Hexane peaks reconstructed from digital data for four different runs
I: 0.5 )L.
hexane
2: 0 . 3 pL hexane 3: 0.1
apparatus is also made of Pyrex glass except for certain connections which are either Tygon (Norton) or vacuum tubing, whose lengths are kept to a minimum. Evaluations of various coatings were performed as follows. The coated crystal was placed in housing B and dry N, was flushed through until stable frequency readings were obtained. Housing B was then closed off and 1-ml increments of pure SOs, premixed SO, in Nz, or Nz saturated with other sulfur compounds were injected into housing B via port Pz. The equilibrium frequency reading obtained was the average of 5-10 consecutive readings not varying by more than i l Hz. After the last increment was added and equilibrium was reached, dry Ns was flushed through housing B to return the system to its original state. Test of detector sensitivity to temperature was made by obtaining two frequency shift-SOr concentration plots at two temperatures. Housing B was either placed in ice-water mixture or left at room temperature. The ratio of frequency shift at the two temperatures for each concentration was then calculated from experimental data. Small concentrations of SOr in N, were made by evacuating the main system, (A, and CLl), injecting the appropriate quantity of SO, via PI, using a Hamilton gas tight syringe, and bringing the system pressure to one atmosphere by introduction of dry Nz via ST1. The system was then allowed to stand for a few hours before samples were taken from port P1. Concentration of SOzin the system was calculated from a knowledge of the volume of the system. Gas Chromatographic Partition Detectors. The active portion of the detector used was constructed of Teflon (Du Pont) and had a calculated volume of 0.4 ml. Details of its construction are described elsewhere (8). Gas Chromatograph. A Carle Basic Gas Chromatograph was used with two 1-m Chromosorb G columns containing Carbowax 1540 and dinonyl phthalate (DNP) as stationary phases. The detector was connected to the column outlet by 328
a
pL
hexane
means of a Teflon (Du Pont) coupling block. The manufacturer's recommendations were followed with regard to column operating parameters. The column and injection ports were operated at about 62 "C, with a He carrier gas flow rate of 10-1 5 ml/min (except where noted otherwise), and the partition detector was used without temperature control. Each sample injected into the column consisted of a 1-p1 mixture of two or more of the following: n-pentane, nhexane, n-octane, and benzene. The detector coating was squalane unless noted otherwise. To establish linearity between A , and V,, crystals containing SAIB on only one side (that facing the detector inlet) were used. Hexane was used as sorbate. Appropriate correction for the exposed uncoated surface was obtained by measuring the uncoated crystal response to the same amount of hexane. Taking onehalf the resultant Afyielded a correction of 90 Hz/side. Instrumentation. The crystal transducer employed is an AT-cut quartz crystal (exactly 9 MHz, gold plated, International Crystal Manufacturing Company) treated appropriately depending on the particular experiment. It is placed either in housing B of Figure 5 or in the GC-detector. The crystal is activated by a modified Pierce oscillator whose output is fed into a JFET source follower buffer stage before being connected to a frequency counter (Heath Universal Digital Instrument, EU-805). The output of the counter is either printed out on a Hewlett-Packard 562A digital printer or interfaced to a general-purpose computer (Control Data 3300) for on-line data acquisition. Details of instrumentation are described elsewhere (8). Crystals .were coated by the following procedure. A known volume (2-10 1.1) of a known concentration of the coating material in a volatile solvent (chloroform or methylene chloride) was deposited on the crystal surface by means of a hypodermic syringe and the solvent allowed to evaporate. The crystal was then placed in an oven at 60-70 "C for several hours so that the coating spread uniformly. Prior to em-
ANALYTICAL CHEMISTRY, VOL. 45, NO. 2 , FEBRUARY 1973
10000
I n-Octane
+Octane
I~=(-B.*9.)+(36906145.)V
A Y =(l8**123.)+(41214.* 1 0 5 % ) ~ 8000
6000 c
I
W
i,
/
c?“
//
2
“%4000
a
/
/
LL
n-Hexane
Q
Ay = (-24.* 21)+ (6012669) v
6.)V 2 00
/
2000
Vo Iu m e ,$I. t (1420.r 49.N
Figure 8. Peak height us. injected sample volume Volume, $,
70.0,.
I
Figure 7. Peak area us. injected sample volume
,
/
180%
/
m
ploying the crystal in a given experiment, its frequency was (frequency shift due to the coating measured and Afcoating material) was determined.
I
/
RESULTS AND DISCUSSION
Characterization of Gas Chromatographic Detector; Test of Equation 7. Equation 7 was developed employing the “plug” concept and condition of approximate equilibrium. The purpose of this portion of the study is to test the validity of the equations developed in the Theoretical section and also to establish applicability of such a detector as a digital transducer for gas chromatographic systems. LINEARITY, REPRODUCIBILITY, AND RANGEOF THE DETECTOR. Figure 6 shows typical detector response to 4 different runs of hexane each at 3 different concentrations. Generally, per cent standard deviations better than 5 were observed for various peaks. Figure 7 shows plots of peak area (A,) 5s. volume injected for n-pentane, n-hexane, and n-octane. Area measurements are made by summing up the measured frequency shifts under a given peak correcting the resultant sum for base line. Since the measurement interval between each two consecutive points under the peak is constant, the resultant sum is directly proportional to the peak area. Furthermore, for all peaks used in this work the number of points per peak exceeded ten (12). Sample volume and weight ( W , of Equation 10) are of course related by density. Data of Figure 7 show a very high degree of linearity between A Y and WT as obvious from the best fitting straight lines. The best fitting straight lines were calculated using a least square computer routine. It is instructive to observe that peak heights are also highly linear functions of sample volume as seen from data of Figure 8. Peak heights are obtained simply by correcting the maximum frequency shift in a peak for base line. From the data (12) A. H. Anderson et til., in “Advances in Chromatography,” A. Zlatkis, Ed., Marcel Dekker, New York, N.Y., 1970, p 78.
I
600
I
-
1800
3000
vg ,cc./g Figure 9. Peak area cs. V , for three temperatures
of Figures 7 and 8, it appears that either method should be satisfactory for quantitative analytical determination. ‘The peak height method is less time consuming if data are processed manually, however. As for the operating range of the detector, it depends on the nature of solute used. For n-pentane, oscillations were sustained for peak containing as much as 1.5 pl; whereas, for hexane 0.8 pl injections overloaded the detector. DEPENDENCE OF A, ON K g , z . Because K u , z is directly proportional to V , (10) and because experimental data on retention volumes (V,) of n-alkanes on squalane are available, linearity of A , cs. V Bis reported. Plots of normalized peak areas for n-pentane, n-hexane, and n-octane cs. their respective Vu’sat three widely different temperatures are presented in Figure 9. The numerical values of V,’s for each compound at 25 and 50 “C were calculated from experimental data at 80 and 100 O C (13) using the equation given by Schupp (14). From these plots, it is clear that A , is linearly related (13) W. 0. McReynolds, “Gas Chromatographic Retention Data,” Preston Technical Abstracts Co., Evanston, Ill., 1966, pp 308-9. (14) 0. E. Schupp 111, “Gas Chromatography,” Interscience, New York, N.Y., 1968, p 24.
ANALYTICAL CHEMISTRY, VOL. 45, NO. 2, FEBRUARY 1973
329
Table I. Effect of Temperature on Sensitivity of Partition Detector
1200
SO2
added, ml 0.5 1.o 1.5
2.0 2.5
Figure 10. Peak area cs. volume of liquid coating 14000
i
10000
-
v!
u
r
aAeooo -
t
/ / _ '
.02
.06
.IO
.I4
-22
.I8
I / F , min./ml.
Figure 11. Peak area cs. inverse of carrier gas flow rate 3ooor
4000
P
I
o---o Carbowax 400,24.59:
P
Ql
0/0s02,by vol.
Figure 12. Response plots of liquid coated crystals to various concentrations of SOz in Nz to (and therefore to K V J and that the linearity is temperature independent in the range of 25 to 80 OC. DEPENDENCE OF A , ON V,. As seen from data of Figure 10, peak area varies linearly with increasing amounts of liquid coating. The length of the error bars appearing with each point are one standard deviation for that point. 330
So~clSn.5~c
2.40 2.32 2.30 2.36 2.34
Mean 2.34
720
1.7
DEPENDENCE OF A , ON FLOW RATE. Figure 11 shows the plots for such a relationship for hexane and benzene. Over the range of flow rates tested, peak area is seen to be inversely proportional t o carrier gas flow rate, confirming again the legitimacy of Equation 7. Detector Response Times. As shown theoretically, detector response time for the case where diffusion into and out of liquid coating is the only retarding mechanism should be less than a second. However, the observed characteristics are also a function of system dead volume, flow rate of carrier gas, diffusion coefficient of the solute in the carrier gas, and efficiency of mixing. Streams of pure nitrogen and nitrogen saturated with hexane were alternatively switched into the detector volume while recording detector output. From 10 t o 90% of the final detector response was achieved in 1.1-1.2 seconds for both leading and trailing edges of the response curve (8). The curves are analogous t o those observed by Blaine (15)in the transfer function analysis of the response of a continuous spectrophotometric analyzer. The mixing and sweeping of the detector cell accounts for the long time constant. Dead volume for the apparatus is 1.21.5 ml. Also in the theoretical development for the trailing edge, the assumption was made that C(l,t) = 0 which is not realized in practice. However, one can conclude that subsecond response time can be obtained through the use of small detector volumes. Effect of Temperature on Sensitivity. Table I presents data on sensitivity ratios for SOz on SAIB a t 0 and 22.5 OC for various concentrations of SOz employing the housing B of Figure 5 as explained under the Experimental Section. Employing Equation 14, one calculates a theoretical ratio as follows :
Using the appropriate values for TI and Tz, one obtains a ratio, R, of 2.29. Comparing this t o the experimental value of 2.34 from Table I, one finds agreement to within 2.5%. Evaluation of Coatings for Sulfur Compounds. The nature of the coating used depends on the particular application for which the detector is intended. The coatings must possess several characteristics : stability, sensitivity and reversibility, low vapor pressure, and ease of application. The first two factors are self explanatory and must be compatible with the particular application. One must realize, however, that in this application the terms reversibility and sensitivity are contradictory and must be compromised. The last two factors deserve further elaboration. Since the amount of coating applied is in the microgram range, slight evaporation of the coating material will result in detector drift and will also change detector response characteristics according to Equa(15) R. E. Blaine, Ph.D. Thesis, Oregon State University, Corvallis, Ore., 1969.
ANALYTICAL CHEMISTRY, VOL. 45, NO. 2, FEBRUARY 1973
Table 11. Some Properties of Liquid Coatings Used Name Carbowax 400 Carbowax 20M
For mu1a Vapor pressure, micron C H ~ ~ H [ C H ~ O C H Z ] ~ & H ~ O H 10-5 ... CHzOH[CH20CHz],CHzOH 11
= 455
Dinonyl phthalate
5
x
10-5
Polyphenyl ether
(36 ’-Oxidipropionitrile
CN-CH~CH~OCHXCH~CN SAIB C,zHi,O,(CH,COz)z((CH,),CHCO,), Triethanolamine (CHz0H)d Amine No. 220 Ci7HdNGHdCzH50H Squalane C30H62 a C = Chloroform; M = Methylene chloride. b P = Polar; I = Intermediate; N = Nonpolar. Extrapolated from data of S. J. Hawkes (16).
x lo-*
