1122
Anal. Chem. 1985, 57, 1122-1126
Time Response of Potentiometric Gas Sensors to Primary and Interfering Species Werner E. Morf, Irmgard A. Mostert, and Wilhelm Simon* Department of Organic Chemistry, Swiss Federal Institute of Technology (ETH), CH-8092 Zurich, Switzerland
A theoretical analysis of the emf response of gas sensors to interfering gases is presented. The treatment considers the example of CO, electrodes and analyzes the tlme and concentration dependence of the interference by aclds HY. The selectlvity exhiblted by such gas sensors after short measuring periods or at low sample concentrations Is determined by the ratio of the permeabliities of the gas-permeabie membrane (PH,/Pco,), while the final equilibrium selectivity is given by the ratio of the acldlty constants of the specles Involved (KHy/Kc,,J. The predlcted tlme- and concentration-dependent changes in selectivity are in agreement with experimental findings for dlfferent sensor systems. The dynamlc response to the primary specles CO, is also treated. The theoretical expresslon derived permits a perfect fit of experlmental time-response curves.
where the activities (parentheses) and concentrations (brackets) refer to the internal solution of the gas sensor. The approximations in eq 1 and 2 are valid if the activity coefficients of all ions can be represented by the mean activity coefficient y+ and if the activities of uncharged species correspond to their concentrations. In all cases where the sample solution contains detectable amounts of relatively weak acids (COz,HY), the mass balance equation for the internal solution reads [HCOS-]
+ C[Y-] Y
= [M+J
(3)
This implies that the concentrations [H+] and [OH-] are negligibly small as compared to the given total cation concentration [M+]. From eq 1-3 the activity measured by the internal pH electrode is then obtained as follows: KCOz[co21 + CKHY [HYl 11-1
Since the pioneering contributions by Stow et al. (I),Severinghaus (2,3), and Ross et al. (4) potentiometric sensors for carbon dioxide and other gases have become an important tool in analytical chemistry (for a review see ref 5 ) . These electrochemical devices are typically composed of a gas-permeable membrane and an internal pH-sensitive electrode cell which responds to the concentrations of volatile acids or bases permeating into the internal electrolyte solution. It was shown by Ross et al. ( 4 ) on the basis of a theoretical model that the response characteristics depend on the membrane properties, the composition of the internal solution, and the variables of geometry. The selectivity behavior of gas sensors was elucidated only recently by Lopez and Rechnitz (6, 7). The results given by these authors indicated that the equilibrium selectivities are determined by the acidity and basicity, respectively, of the interferents rather than by the volatility (see also ref 8). In contrast, Kobos et al. (9) concluded from similar experiments that the observed selectivities of gas sensors reflect the relative solubility of the permeating species in the membrane material. The present treatment analyzes the dynamic response behavior of COz sensors in the presence of interfering gases. It will be shown that the selectivity coefficients are time-dependent quantities. Their limiting values are given by the ratios of permeability coefficients (at the initial steady-state) and by the ratios of acidity constants (at final equilibrium). THEORY Volatile acids may generally interfere with carbon dioxide gas-sensing devices. Such interferenta are capable of diffusing across the gas-permeable membrane and of influencing the pH value of the internal electrolyte by protolysis reactions. The decisive equilibrium constants for COz and for any interferent HY are defined as
0003-2700/85/0357-1122$01.50/0
(H+) =
nr
rm+1
(4)
Hence the emf response of the sensor to primary and interfering gases is given by
E = EoH + S log (H+) = E°COz + s 1% [[c021 + CkHY[HYll HY
(5)
where EoH and Eocqare standard potentials of the electrode cell, s is the slope of the response function, and kHYis the equilibrium selectivity of the sensor for an interferent HY relative to COz
This intrinsic selectivity coefficient can be observed potentiometrically after an equilibrium distribution of dissolved gases has been established across the gas-permeable membrane. Only in this case are the sensed concentration values [CO,] and [HY] (referring to the internal solution film) identical with the concentrations of the sample solution, [CO,], and [HY],. Evidently, the equilibrium selectivity factors increase with increasing acidity of the interferents. According to eq 6, kHY corresponds to the equilibrium constant of the basic exchange reaction HY (sample)
+ HC03- (internal solution) F= COz(sample) + Y- (internal solution)
This reaction proceeds when carbon dioxide sensors are exposed to interferents, until the final equilibrium is reached. Consequently, the dynamic response to interferents is governed by an inward flux of HY coupled to an outward flux of COz and by concomitant changes in the composition of the internal electrolyte. If considerations are restricted to the steady-state exchange of two gases, the following relations apply:
0 1985 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 57, NO. 6, MAY 1985
where A is the active area of the gas permeable membrane, V the volume of the internal solution film interposed between membrane and pH sensor, J the mass flux, and P the permeability coefficient of the subscripted species. From eq 7,8, and 3, the assumption of a steady state is found to imply that JCO,+ J H y = 0 and hence (9) [c021 + PHY[HYl = [co2ls + PHY[HYls where the weighting factor p H Y is given by the permeability ratio
where D is the diffusion coefficient of the subscripted species in the membrane (thickness d ) and k' is the partition coefficient of the species between the aqueous sample or internal electrolyte and the membrane. It is most surprising that the relations 5-10 are formally identical with an earlier theoretical description of the timedependent anion response of silver halide membrane electrodes (IO)which accounted for solubility equilibria at the membrane surface and for diffusion of primary and interfering anions across the aqueous boundary layer. In the present treatment, protolysis equilibria near the pH-sensing membrane and permeation of the substrate species across the gaspermeable membrane are taken into account. Thus the response mechanisms of the two sensor systems indeed turn out to be very similar. In analogy to the former description (10) one can derive the following differential equation from eq 8 together with eq 6 and 9
dY -=
Y([Cods
+ k.HYIHYla) - kHYIHYls
P H Y C (11) Y(kHY - PHY) - kHY where y is the molar fraction of anions Y- in the internal electrolyte and C is an instrumental parameter
dt
Y =
[Y-I [Y-] [HCO,]
+
(12)
If it is assumed that the gas sensor is in contact with initial concentrations [CO2loand [HY], at t < 0 and with the final sample at t L 0, the limiting values of y(t) are (see eq 6 and 12)
Integration of eq 11 now leads to an implicit solution for y ( t )
The fundamental result for the emf response can finally be given in terms of the sample concentrations [CO,], and [HY], and of the time-dependent molar fraction y
These relations offer a formal description of the dynamic
1123
response exhibited by COz sensors in the presence of interferents HY. Of course, analogous expressions may be written for other gas-sensing systems. According to eq 15 and 16, a stepwise change in the sample concentrations results in the following transient emf response:
Evidently, the apparent selectivity, as exhibited by the sensor after comparatively short measuring periods, is dictated by the permeability ratio pHY.The same transient selectivity control by diffusion processes was observed for solid-state membrane electrodes (10-12). In the case of gas sensors, the selectivity parameter pHY is related to the partition coefficient k'of the permeating species (eq 10) which is indeed a measure of the solubility of these species in the membrane material (for homogeneous membranes) or a measure of their volatility (for microporous or air gap membranes) (9). In contrast, the final EMF excursion is determined by eq 18 where the equilibrium selectivity coefficient kHY is given by the ratio of dissociation constants of the acids involved (7)
This clearly shows that a pronounced time dependence of the selectivity should be observable for gas sensors. Such phenomena will be discussed below in more detail.
EXPERIMENTAL SECTION Reagents. All solutions were prepared from chemicals of the highest purity available in doubly quartz-distilledwater. For the electrode response and selectivity studies, the following solutions were prepared NaHC03in a phosphate buffer (pH 7.4), Na2S205 in a KCl/HCl buffer (pH 1.8),NaNOz in a tartrate buffer (pH 3.4), and NazS in a phosphate buffer (pH 7.4). The ionic strength of all buffer solutions was 0.2. Gas-Permeable Membranes. Two types of membrane materials were studied: silicone rubber (Orion C02 membrane 9502-04) and PVC (S 704, high molecular, Lonza AG, Basle, Switzerland) plastified with bis(1-butylpentyl) adipate (BBPA; Fluka AG, Buchs, Switzerland). Two PVC membranes of different thickness (-200 pm, -35 pm) were applied; the membrane composition was 33 wt % PVC and 67 wt % BBPA. These membranes were supported on the sample side with Millipore filters (type SC, pore size 8.0 pm; Millipore S.A., Molsheim, France). The silicone rubber membrane was removed together with a mesh backing from the Orion membrane-spacer assembly and was positioned in the gas sensor with the mesh on the sample side. Electrodes. All experiments were made with modified Philips ammonia electrodes, Model IS-570, having an active surface area of 13 mm2. For a variation of the internal electrolyte volume, one electrode contained a spacer between gas-permeable membrane and pH sensor; the surface area of this electrode was 20 mm2. All electrodes were f i e d with an internal solution of 0.005 M NaHC03 and 0.2 M NaCl. Apparatus. The electrodes were mounted into a flow-through measuring cell (material, Plexiglas; channel diameter, 5 mm). Potentiometric measurements were made with an electrode monitor using FET operational amplifiers AD 515 KH (Analog Devices, Norwood, MA, input impedance 1013a / 2 pF, bias current 4 5 0 fA, capacity neutralization). The data processing system, the display terminal, and the printer used conform to the specifications given in ref 13. Procedure. All measurements were performed at 21 & 1 "C. The procedure used for time response studies and selectivity determinations was the following. After the measuring cell was filled with buffer solution, the base line potential was recorded. Then the cell channel was rapidly filled with a solution of the primary or interfering species in the same buffer (flow rate, 12 mL/min). The flow was stopped and the potential response of the gas sensor was recorded during 1024 s (2'O s, response to COz)
1124
ANALYTICAL CHEMISTRY, VOL. 57, NO. 0, MAY 1985 EMF
[mv]
COz SENSOR SILICONE RUBBER MEMBRANE
[HYIs
E
co,
-SENSORS, RESPONSE TO NO,
lo-' M
12060 -
i
0-
-60 -
- 120 -180j
Figure 2. Timedependent emf response to NO, of carbon dioxide sensors with different gas-permeable membranes (SR (silicone rubber) or PVC of the lndlcated thickness). The curves were measured on lo-' M solutions of NaNO, (pH 3.4). 1
0 '
1000
I
2doo M"
C.
Ct TIME
Figure 1. Timedependent emf response of a carbon dioxide sensor M CO, sample to IO-' M solutions after a step change from a of different gases. The theoretical curves were calculated from eq 14-16 using the values given in Table I for the gas permeabllltles of the sillcone rubber membrane and for the acidity constants of the gases. For [M'] = lo-' M, VdIA = lo4 cm', and DC0zk'C02= cm2/s( 4 ) ,the value Ct = lo3 M-I corresponds to a measuring time of 10's (see eq 13). Table I. Selectivity Determining Parameters of COz Sensors Using Dimethyl Silicone Rubber Gas-Permeable Membranes
species
HY
acidity constant KHy(15), mol/L
SO2
1.7 X
NO,
5.1 X lo4 1.0x 10-7 4.5 x 10-7
H~S
co,
equilibrium selectivity kHY
3.9 X lo4 1.1 X lo3 2.2 x 10-1
1
permeability
initial D H Y k hy ( 4 ) , selectivity cmz/s PHY 3.8 X 1.0 X 3.4 x 2.9 x
10" 10" 10-5 10-5
0.13 0.034 1.2 1
or 2560 s (response to interferents). The internal electrolyte film of the sensor was replaced after each measurement. For further details, see ref 14.
RESULTS AND DISCUSSION Figure 1 shows the calculated emf response of a given gas-sensitive electrode to a stepwise change in the sample solution from lo4 M C 0 2to M HY, where the interferent is SOz, NO,, or H2S. The response to a M COZ sample is also indicated. The computations are based on the selectivity parameters compiled in Table I. The calculated curves in Figure 1clearly illustrate that at least three different types of time-dependent variations of the electrode potential can be encountered. For pure COz samples, of course, the emf response is relatively fast and conforms to the usual expectations (see also below). The response to HzS, on the other hand, is characterized by a potential overshoot (see Figure 1). Such transient response is generally obtained for interferents with pHY>> k H Y , as is demonstrated by eq 17 and 18. A completely different situation is evidently found in cases where kHY >> pHY,e.g., in the presence of serious interferents such as SO2 and NO, (see Figure 1). Here a striking stepwise change in the apparent potentiometric selectivity is observed.
.-
CMt
[mv]
CO, - SENSORS, RESPONSE TO
so,
220 160100 -
40 -20-80-140-
-200-
Figure 3. Time-dependent emf response of different carbon dioxide M solutions sensors to SO,. The curves were measured on 5 X of Na,S,O, (pH 1.8). This is a consequence of eq 15 and 16 which can be replaced by the following approximations for lZHY >> p H Y , yo 0, and yeq= 1: y p~y[HY]$c (0 5 y 5 1) (19)
These relations predict a sharp selectivity increase resulting at the time t = ( J J ~ ~ [ H Y ] ~as C )is- documented ~, in Figure 1. Before this transition time, the interference in COz sensors by SO2 or NO, is much less serious than might be expected from pure equilibrium considerations. After this time, however, the sensors have become completely converted into SO2or NO,-selective systems. The theoretically deduced effects of interferents on gassensitive electrodes are in excellent qualitative agreement with experimental findings (see Figures 2-5). For example, the predicted changes in the apparent selectivity for SO2 or NO, are corroborated. The results document that the observed transition time increases with decreasing permeability coefficient and decreasing concentration of the interferent (see Figures 2-5) and with increasing volume of the internal
ANALYTICAL CHEMISTRY, VOL. 57, NO. 6, MAY 1985
1125
EMF
EMF
CO, -SENSORS ,RESPONSE TO HZS
[MI
[mv!
-20
- 50 -80
- 110 - 140 - 170 -200
-230 0I
I
lb
'
i0
'
3'0
I
4'0
' [mir TIME
Flgure 4. Timedependent emf response of different carbon dioxide sensors to H2S. The curves for PVC membranes were measured on 5 X IO-' M solutions of Na,S (pH 11.5); the curve for the SR membrane was obtained using IO-' M Na,S (pH 8.5). EMF
-5
Imvl
-4
-3
-2
-i
IOS[HY],
Figure 6. Concentrationdependence of the emf response of a carbon dioxide sensor to different gases. The theoretical curves for Ct = IO3 M-' were Calculated from eq 14-16 using the parameters given in Table I.
240 180
In spite of its merits, the presented theoretical treatment is clearly based on an idealized model and therefore cannot explain quantitatively all the effects observed on gas sensors. For example, eq 17 predicts a stepwise response to COz concentrations in the absence of interferents while in reality the approximation to the final equilibrium is not an infinitely fast process. The reason for this discrepancy is that eq 7 and 8 make use of a steady-state assumption even for t 0. For an exact description of the initial time response, the following relations should therefore be applied:
120 60 0
-
-60
- 120 O
' IO
20
I
3b
I
4b
'[mir TIM
Flgure 5. Dependence of the time response of a carbon dioxide sensor on the concentration level of the interferent NO,. The curves were measured on 100, IO, and 1 mM solutions of NaNO,, respectively.
electrolyte layer (AV in Figures 2-4; decrease of the instrumental parameter C). The first point is of special interest. It offers a straightforward explanation for the low sensitivity of COz electrodes to poorly volatile inorganic or organic acids. In fact, the observable selectivity toward species that have a very low permeability coefficient is given by pHy > 1 because the final equilibrium distribution across the membrane cannot be attained within due time. For that reason gas-sensing electrodes are often considered to be nearly free of interferences (4). Concentration-dependent changes in the selectivity coefficients for interferents, as exemplified in Figure 5, must necessarily result in nonlinear calibration plots for these species. Figure 6 shows the calculated emf response curves of COz sensors for SOz, NO,, and HzS. The calculations were based on the assumption that the emf readings for all calibration measurements are taken after a constant period of time. It becomes evident from Figure 6 that the slope of the response curve for H2S (interferent with pHY> k H ~ )is subNernstian, whereas the response to SOz or NO, (interferents with k ~ >> y PHY) is characterized by highly super-Nernstian regions. Such phenomena have been observed very recently by Lopez (7) and by Kobos et al. (9).
where the fluxes Jco2(x,t)and JHy(x,t)in the membrane phase (0 5 x 5 d ) are given by Fick's laws. Unfortunately, rigorous formal solutions can be derived only for limiting cases. For instance, the dynamic response of the sensor to COz in the absence of interferents HY (Le., [HY], = 0 and [HC03-] = [M+] = constant) is determined by eq 5 with
where a, are the positive roots of the following equation: a, tan an =
Ak ho,d V
(22)
For many commercially available COz sensors the geometric parameters are chosen that Ak &d/ V >> 1 holds. In this case, eq 21 reduces to
1126
Anal. Chem. 1985, 57, 1126-1130 (4). The use of PVC membranes in C 0 2sensors is nevertheless attractive because they can easily be modified for simultaneous determinations of pH values and bicarbonate activities (17). Due to the exact knowledge of the dynamic response behavior, a further reduction of the required measuring time should become possible by means of computational methods (18)or electronic circuits (19). Registry No. COP,124-38-9.
A EMF RESPONSE TO
[mvl
co,
100 80 60 -
LITERATURE CITED 40 -
0
-
CALCULATED OBSERVED
20 -
0I
0
'
4'
'
8'
'
1;
'
16 [m,'r TIM
Flgure 7. Calculated and observed emf response of COz gas sensors to the primary speck. Calculations were based on eq 23 using a time
constant (4d2/7?Dco,) of 98 s (thln membrane) and 520 s (thick membrane), respectively (14). This result, describing the dynamic response of optimized gas sensors to the primary species, is quite different from an earlier expression derived from a steady-state approach (4). However, it nicely conforms to experimentally observed time-response curves (see Figure 7) as well as to a similar theory presented by Buffle and Spoerri (16). Since the response to the primary species is usually faster than the equilibration of the sensor with interferents, the approximations involved in the preceding theoretical treatment are absolutely adequate. From the curve fitting in Figure 7 and from other measurements (14) a diffusion coefficient for COz in PVC membranes of cm2 s-l is found. This value is considerably lower and the resulting response time is longer than those for the more common membrane materials such as silicone rubber
-
(1) Stow, R. W.; Baer, R. F.; Randall, B. F. Arch. Phys. Med. Rehabil. 1057, 38, 646. (2) Severinghaus, J. W.; Bradley, A. F. J . Appl. Physiol. 1058, 73, 515. (3) Severlnghaus, J. W. Ann. N . Y . Acad. Sci. 1088, 748, 115. (4) Ross, J. W.; Rlseman, J. H.; Krueger, J. A. Pure Appl. Chem. 1073, 36,473. (5) Arnold, M. A.; Meyerhoff, M. E. Anal. Chem. 1084, 56, 20R. (6) Lopez, M. E.; Rechnitz, G. A. Anal. Chem. 1082, 54,2085. (7) Lopez, M. E. Anal. Chem. 1084, 56, 2360. (8) Mascini, M.; Cremisini, C. Anal. Chlm. Acta 1078, 9 7 , 237. (9) Kobos, R. K.; Parks, S. J.; Meyerhoff, M. E. Anal. Chem. 1082, 54, 1976. (IO) Morf, W. E. Anal. Chem. 1083, 55, 1165. (11) Hulanlcki, A.; Lewenstam, A. Anal. Chem. 1081, 53, 1401. (12) Lindner, E.; Toth, K.; Pungor, E. Anal. Chem. 1082, 54, 202. (13) Wuthier, U.; Pham, H. V.; Zund, R.; Welti, D.; Funck, R. J. J.; Bezegh, A.; Ammann, D.; Pretsch, E.; Simon, W. Anal. Chem. 1084, 56,535. (14) Mostert, I. A., Diss. ETH Zurich, in preparation. (15) SillBn, L. G.; Martell, A. E. "Stability Constants of Metal-Ion Complexes", 2nd ed.; The Chemical Soclety, Burlington House: London, 1964; Spec. Publ. No. 17. (16) Buffle, J.; Spoerrl. M. J. Electroanal. Chem. Interfacial Nectrochem. 1081, 729, 67. (17) Funck, R. J. J.; Morf, W. E.; Schulthess, P.; Ammann, D.; Simon, W. Anal. Chem. 1082, 54,423. (18) Morf, W. E.; Slmon, W. I n "Ion-Selective Electrodes in Analytical Chemistry"; Freiser, H.. Ed.; Plenum: New York, 1978: Vol. 1. ChaDter 3. (19) Luttmann, A.; Muckenhoff, K.; Loeschcke, H. H. Pflugers Arch. 1078, 375,279.
RECEIVED for review November 2, 1984. Accepted January 15, 1985. This work was partly supported by the Swiss National Science Foundation. I.A.M. thanks Orion Research, Inc., for a grant.
Caffeine-Picrylsulfonate Liquid Membrane Electrode for Selective Determination of Caffeine in Analgesic Preparations Saad S. M. Hassan,*l Mona A. Ahmed? and Moshera M. Saoudi Department of Chemistry, Faculty of Science, Ain Shams University, Cairo, Egypt
A ilquid membrane electrode for caffeine prepared from a solution of caffelnepicryisulfonate Ion-palr complex In l-octanoi is developed. I t exhibits Nernstlan response in the range of 10-2-10-6 M caffeine wlth a catlonlc slope of 59 mvhoncentration decade. The electrode has a wlde working pH range (5.5-9.5), fast response time (20 s to 1.5 mln), stable response for at least 30 days, and high seiectlvlty for caffeine In the presence of many organic bases. The results obtained for quantltatlon of 1-1000 pg mL-' of caffeine show an average recovery of 99.5 % and a mean standard deviation of 1.3%. Determination of caffelne in some analgesic preparations gives results in good agreement wlth those obtalned by the United States Pharmacopoeia method. Present address: D e p a r t m e n t of Chemistry, F a c u l t y o f Science, Qatar University, Doha, Qatar (Arabian Gulf). Permanent address: D e p a r t m e n t o f Chemistry, U n i v e r s i t y College f o r Women, Heliopolis, Cairo, Egypt. 0003-2700/85/0357-1126$01.50/0
Caffeine is one of the most important alkaloids consumed in our daily life. It is a mild central nervous system stimulant, is an analeptic, restores mental alertness in fatigued patients, and improves psychomotor coordination. It is present in coffee, tea, cola beverages, and chocolates and used alone or in combination with analgesics in many pharmaceutical preparations for the treatment of headache (1). Determination of caffeine in these preparations, however, is commonly beset with many difficulties. The United States Pharmacopoeia (2), British Pharmaceutical Codex (3), and European Pharmacopoeia (4) recommend three methods for the determination of caffeine after prior separation. These are potentiometric titration with perchloric acid in nonaqueous solvents, extraction from strong alkaline media with chloroform, drying, and weighing as free base, and spectrophotometric measurement at 276.5 nm. These methods are time-consuming, nonselective and inapplicable to low levels of caffeine. A literature survey indicated that caffeine may also be 0 1985 American Chemical Soclety
