Anal. Chem. 1998, 70, 4271-4279
Water Flux across Neutral Carrier Membranes Franz J. Keplinger*
Institut fu¨ r Allgemeine Elektrotechnik und Elektronik, Technical University of Vienna, Gusshausstrasse 27, E359-6, A-1040 Vienna, Austria Artur Jachimowicz
Institut fu¨ r Mikrosystemtechnik, Albert-Ludwigs-University Freiburg, Freiburg, Germany Franz Kohl
Ludwig Boltzmann Institut fu¨ r Biomedizinische Mikrotechnik, Technical University Vienna, Vienna, Austria
We investigated the water flux through neutral carrier membranes caused by the osmotic pressure difference of the solutions on both sides of these membranes. Miniaturized thin-film ion-selective electrodes were used as their extremely small internal electrolyte volume as well as their extremely thin membrane make them specifically suitable for such studies. The dilution of the internal electrolyte due to the transmembrane water flux results in a significant shift of the ISE potentials. A model explaining the potential versus time curve of thin-film sensors was developed. The penetration coefficient of water is determined experimentally with respect to the lipophilicity of the membrane plasticizer used. The inverse of the square root of the penetration coefficient depends linearly on the logarithm of the lipophilicity for almost all investigated membranes. Effective miniaturization of ion-selective structures based on neutral carrier membranes can be achieved using thin-film technology for sensor device fabrication. As a consequence, neutral carrier membranes have to be prepared by thin-filmcompatible processes. In such applications, the volume of the internal electrolyte and the membrane thickness are much smaller than those used for conventional ion-selective electrodes. Hence, understanding the water transport mechanisms through the thin membrane becomes one of the key issues of the miniaturization techniques. A strongly correlated second key phenomenon to be considered in this context is the dilution of the internal electrolyte, which can no longer be neglected as in the case of macroscopic devices. Ion-selective electrodes (ISEs) contain neutral carrier membranes as the ion-selective component, which normally exhibit an average composition of 33 wt % poly(vinyl chloride) (PVC), 66 wt % plasticizer, 1 wt % selective carrier,1,2 and occasionally minor (1) Ammann, D.; Morf, W. E.; Anker, P.; Meier, P. C.; Pretsch, E. Ion-Sel. Electrode Rev. 1983, 5, 3-92. (2) Armstrong, R. D.; Horvai, G. Electrochim. Acta 1990, 35, 1-7. S0003-2700(98)00389-8 CCC: $15.00 Published on Web 09/10/1998
© 1998 American Chemical Society
additives. Membrane properties such as selectivity, lifetime, and electrical behavior are determined by the composition of the membrane. Here the selectivity is mainly defined by the sort of the carrier;1,3 the lifetime of the membrane depends on the lipophilicity of the components4,5 and the electrical behavior on the composition.6-9 A thorough knowledge of the membrane properties is required in order to be able to design ion-selective electrodes with precisely predictable behavior. Especially for miniaturization aspects, effects have to be taken into consideration that are not relevant for macroscopic ISE devices. Neutral carrier membranes selective for cations such as H+, + K , Na+, or Ca2+ are permeable for the one specific cation type only, the so-called sample cation. The cation-transfer number of a membrane for the sample ion is nearly unity.10 This is in agreement with a Nernstian slope of the potentiometric electrode response for this ion.11 Normally, membranes operate under a zero current condition. For a net ionic flux, both ion types would have to be transported simultaneously. But those membranes only permit a very low permeability for counterions and therefore only minor ion transport takes place, influencing the detection limit.12 However, membranes are permeable not only to the primary ions but also to gases and uncharged molecules. These properties can be used for sensing such species.13,14 The species (3) Eugster, R.; Gehrig, P. M.; Morf, W. E.; Spichiger, U. E.; Simon, W. Anal. Chem. 1991, 63, 2285-2289. (4) Oesch, U.; Simon, W. Anal. Chem. 1980, 52, 692-700. (5) Dinten, O.; Spichiger, U. E.; Chaniotakis, N.; Gehrig, P.; Rusterholz, B.; Morf, W. E.; Simon, W. Anal. Chem. 1991, 63, 596-603. (6) Horvai, G.; Gra´f, E.; To´th, K.; Pungor, E.; Buck, R. P. Anal. Chem. 1986, 58, 2735-2740. (7) To´th, K.; Gra´f, E.; Horvai, G.; Pungor, E.; Buck, R. P. Anal. Chem. 1986, 58, 2741-2744. (8) Igelhart, M. L.; Buck, R. P.; Pungor, E. Anal. Chem. 1988, 60, 290-295. (9) Iglehart, M. L.; Buck, R. P.; Horvai, G.; Pungor, E. Anal. Chem. 1988, 60, 1018-1022. (10) Thoma, A. P.; Viviani-Nauer, A.; Arvanitis, S.; M.; Morf, W. E.; Simon, W. Anal. Chem. 1977, 49, 1567-1572. (11) Morf, W. E. The Principles of Ion-Selective Electrodes and of Membrane Transport; Akade´miai Kiado´: Budapest, 1981. (12) Mathison, S.; Bakker, E. Anal. Chem. 1998, 70, 303-309. (13) Meyerhoff, E. M. Clin. Chem. 1990, 36, 1567-1572.
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as the saturation continues, the potential of the sensor should remain constant. When saturation ends, the internal concentration starts to decrease and the sensor signal drifts. With fair knowledge of the amount of salt evaporated and the time elapsed from the moment of dipping into the solution until the beginning of the signal drift, one is able to calculate the water flux rate through the membrane. In parallel, if the osmotic pressure is known, one can determine the membrane-specific material parameters. The thin-film sensor structure exhibits a quick response time because of the relatively thin membrane, which is used without any supporting construction. The high osmotic pressure of the saturated solution and the extremely small internal volume lead to a fast change of the internal concentration. Figure 1. Schematic cross section of the thin-film sensor used to measure the membrane permeability. The internal solution is formed by water intake into the nc membrane caused by the difference of the osmotic pressures.
of interest in our work is water, which can penetrate in the form of vapor. The water transport through the membrane can be driven, for example, by a hydrostatic pressure, by an electric field (electroosmosis15), or by the difference of the osmotic pressures of the solutions on both sides of the membranes (osmosis). In the case of an osmotic driven transport, the water flux that is directed from the membrane side containing less concentrated solution toward the more concentrated solution side tries to equalize differences of osmotic pressure on both sides of the membrane. The water flux stops as soon as the difference in osmotic pressures becomes zero. This is a status where the internal solution contains the same amount of dissolved substances as the sample solution outside. For membrane-coated sensor types, the ionic strength of the internal electrolyte is restricted by the applied technological measures for manufacturing. The water flux is inversely proportional to the membrane thickness, and the shift of the internal concentration will be the faster the smaller the volume of the internal electrolyte. For macroscopic sensor configurations (e.g., Philips IS-561), no significant change of electrode potential occurs due to water intake into the internal volume. The membranes are, here, typically ∼200 µm thick and the internal electrolyte volume is relatively large, being in the range of 1 mL. Miniaturized ISEs, however, use membranes only of some micrometers thick and internal volumes are in the range of nanoliters. In such a configuration, the water flux through the membrane can easily change the internal electrolyte concentration, causing significant signal drift. In the presented study, this drift effect is used to estimate the rate of water flux across ISE membranes and to investigate the influence of major membrane components. Principle. We observe the water flux through the neutral carrier (nc) membrane with the help of a thin-film sensor arrangement (Figure 1). The sensor consists of an Ag/AgCl electrode serving as internal reference electrode, an evaporated KCl layer, and a K+-selective membrane covering the whole structure. During the measurements, water penetrates through the membrane and forms a saturated internal electrolyte. As long (14) Fasching, R. Miniaturisierte Kohlendioxidsensoren. Ph.D. Thesis, Technical University of Vienna, Vienna, Austria, 1997. (15) Fluri, K.; Koudelka, J.; Simon, W. Helv. Chim. Acta 1992, 75, 1012-1022.
4272 Analytical Chemistry, Vol. 70, No. 20, October 15, 1998
THEORY Osmotic Pressure. According to van’t Hoff, the osmotic pressure of an ideal diluted solution can be described by an equation analogous to that for ideal gases. This model assumes that the dissolved substances behave like an ideal gas and that the solvent on both sides of the membrane needs not to be taken into consideration. Therefore, the osmotic pressure Π is, in a first approximation, proportional to the amount of dissolved particles ΠV ) nRT, or with n/V as the molar concentration c the osmotic pressure Π ) cRT is proportional to the concentration. In the case of KCl solutions, which were used for this study, deviations from this ideal behavior can be considered by the osmotic coefficient g.16 The concentration of KCl has to be multiplied by 2 because every molecule consists of an anion and a cation:
Π ) g2cRT
(1)
The osmotic pressure difference between the solutions situated on both sides of the ion-selective membrane is responsible for the water flux through the membrane. EMF. Equation 2 describes the EMF response of the sensors to sample solutions containing the primary ion.
E ) E0 +
γ′K+ c′K+ γ′K+ c′K+ RT RT ) E0 + ln ln F γ′′K+ c′′K+ γ′′Cl-c′′ClF (γ′′ c′′ )2 KCl
KCl
(2)
The second term corresponds to the boundary potentials at the interfaces between sample solution and ion-selective membrane, as well as between membrane and the internal electrolyte, and between the internal electrolyte and the internal reference electrode. The superscripts ′ and ′′ denote the sample and the internal electrolyte, respectively. A change of the internal activity of 1 order of magnitude generates a potential change of ∼120 mV across the membrane. Consequently, the change of the internal concentration is properly detectable (Figure 4). Some minor contributions to the cell potential are neglected in the further analysis. Among them are the diffusion potential (16) Sourirajan, S. Reverse Osmosis; Academic Press: New York, 1970.
at the interface of the sample solution and the bridge electrolyte which is constant (-0.7 mV) and included in E0.11 As the study starts with the first contact of the dry membrane with the sample solution, the membrane is in a nonequilibrium state and therefore an asymmetric potential occurs.17 This asymmetric potential is known to be normally limited to some millivolts.17,18 Equation 2 also neglects another potential component. According to the theory of nonequilibrium thermodynamics, the water flux through the membranes generates an additional potential difference, the so-called “streaming potential”. For an undisturbed potential at the membrane interface, the internal electrolyte film has to be thick compared to the Debye length,19 which is ∼0.2 nm in a saturated KCl solution. This requirement is fulfilled within some seconds and, therefore, not considered any further. One can further assume that the material parameters of the membrane are isotropic throughout the membrane and remain constant over time. The amount of water taken up by the membrane increases with the immersion time.17,20 This swelling phenomenon is controlled by a dual-sorption process21 consisting of a rapid uptake where water is dissolved within the membrane matrix with a diffusion coefficient in the order of 10-6 cm2/s and a much slower process where water droplets within the membrane are formed.22 The second process can be described by an apparent diffusion coefficient of ∼10-9 cm2/s.23-25 (For comparison, the self-diffusion coefficient of water is 2.4 × 10-5 cm2/s at 25 °C.) The amount of water within the membrane depends not only on the membrane composition (influenced by the portions of plasticizer, carrier, and additives) but also on the properties of the surrounding solutions (osmotic pressure). An approximate value for the equilibrium water content can be estimated as 0.5 mol/L.17 This value is small enough that no significant increase of the membrane volume occurs. Expansion of the Internal Electrolyte Volume. The water flux across the nc membrane produces a saturated internal solution first (Figure 1). After complete dissolution of the salt layer, the continuing water flux dilutes the internal solution (Figure 2). Potential during the Saturation Phase. The electrical potential difference of the cell consists of two major components: the membrane potential and the potential difference generated by the internal and the external reference electrode. As long as the internal electrolyte remains saturated, the potential difference according to eq 2 should remain constant. Any drift of it indicates the initial conditioning processes of the membrane have not been completed yet. (17) Du ¨ rselen, L. F. J. Ph.D. Thesis, ETH 8927, Zu ¨ rich, Switzerland, 1989. (18) Du ¨ rselen, L. F. J.; Wegmann, D.; May, K.; Oesch, U.; Simon, W. Anal. Chem. 1988, 60, 1455-1458. (19) Debye, P.; Hu ¨ ckel, P. Phys. Z. 1923, 24, 185-206. (20) Oesch, U. Ph.D. Thesis, ETH 6249, Zu ¨ rich, Switzerland, 1979. (21) Li, X. Transport Behavior of Ions and H2O in Poly(vinyl chloride) Based Ion-Selective Membranes. Ph.D. Thesis, University of Alberta, Edmonton, Canada, 1992. (22) Chan, A. D.; Harrison, D. J. Anal. Chem. 1993, 65, 32-36. (23) Li, Z.; Li, X.; Petrovic, S.; Harrison, D. J. Anal. Chem. 1996, 68, 17171725. (24) Li, Z.; Li, X.; Rothmaier, M.; Harrison, D. J. Anal. Chem. 1996, 68, 17261734. (25) Chan, A. D. C.; Li, X.; Harrison, D. J. Anal. Chem. 1992, 64, 2512-2517.
Figure 2. Initial potential distribution across the sensor (solid line) and the changes caused by the dilution of the internal electrolyte (dashed line)
Figure 3. Schematics of the assumption for the calculation of the concentration at the internal interface of the membrane.
Potential during the Dilution Phase. Due to the decreasing concentration of the internal solution, the osmotic pressure also decreases. Hence, the water flux decreases and the growing rate of the volume of the internal solution slows down. Accordingly, the interface potentials at the internal reference electrode as well as at the internal membrane interface change also. Water Flux through the Membrane. The sensor signal (Figure 4) shows a significant change of the drift rate at the end of the saturation phase. With knowledge of the period of time needed to completely dissolve the salt placed under the membrane, one can calculate the rate of water flux through the membrane during the saturation phase. The increase of the internal volume depends on the amount of salt and on its solubility. For the calculation of the amount of water passed through the membrane, one has also to consider the decreased water concentration in the saturated solution. As the layer thicknesses are small compared to the lateral dimensions, one can neglect the vault of the membrane and the slight increase of the internal surface due to this vault. Hence, one can calculate with a one-dimensional model. Estimation of Internal Concentration Gradients. We consider possible concentration gradients within the internal volume caused by the water flux through the membrane. The corresponding model for this question is shown in Figure 3. Due to the increase of the internal volume, the membrane moves with ∂xm/∂t. The concentration cm at the internal interface is determined at first by the water flux JH2O, which causes an infinitesimal increase of volume within the period dt, and second by K+ ions, which diffuse into this volume. Neglecting any volume change Analytical Chemistry, Vol. 70, No. 20, October 15, 1998
4273
cm )
Jc(xm,t) JH2O
(3)
plus the temporal integral of the water flux JH2O
c′′(t) )
FKCldKCl de +
The diffusion process of the salt is described in terms of Fick’s first law:
∂c ∂x
Jc(x, t) ) -D
(4)
The concentration gradient at the membrane surface is given as
|
|
∂cm ∂t ∂cm 1 ∂c ) ) ∂x x)xm ∂t ∂x x)xm ∂t JH2O
(5)
Inserting eq 5 into eq 4 and the result into eq 3 gives a differential equation for the concentration at the membrane surface:
cm ) -D
∂cm 1 ∂t J2
(6)
H2O
Solving the differential equation by separating the variables gives
( )
2 JH 2O t cm ) cs exp D
(7)
A coupled diffusion of anions and cations occurs in the absence of an external electrical field. Thus, we have to use the diffusion coefficient for KCl (DKCl ) 1.9 × 10-5 cm2/s 26). Even a high water flux that would dissolve the salt layer within 100 s (∂xm/∂t ≈ 6 × 10-8 m/s) gives a time constant of some million seconds in eq 7. This is several orders of magnitude higher than the time needed to dissolve the salt. Hence, one can neglect the influence of the water flux on the internal concentration profile and use one global concentration c′′ for the entire internal electrolyte. Dilution Phase Modeling. The mass of the salt mKCl under the nc membrane is given by
mKCl ) VKClFKCl
(8)
The volume of the electrolyte and the mass of the salt determine the concentration of the internal solution. If values per unity area are used, the dilution phase can be expressed as
c′′(t) )
FKCldKCl d(t)
(9)
The electrolyte layer thickness d(t) versus time is composed of the thickness de, which is formed by dissolving the whole salt, (26) CRC Handbook of Chemistry and Physics, 60th ed.; Weast, R. C., Ed.; CRC Press: Boca Raton, FL, 1980.
4274 Analytical Chemistry, Vol. 70, No. 20, October 15, 1998
∫J t
(τ) te H2O
) dτ
cs
∫J
1 1+ de
t
(τ) te H2O
(10) dτ
whereas the index e denotes the moment when the internal saturation ends. The water flux is assumed to be proportional to the difference of the osmotic pressures between the internal and the sample solution. As a consequence of the very high semipermeability of the nc membranes as well as the zero current conditions, no ion penetration occurs. According to Staverman,27 the reflection coefficient σ equals unity. This is a number defined phenomenologically for the interpretation of osmosis experiments. If one further states the absence of any hydraulic pressure difference, one can describe the dependence of the water flux JH2O on the osmotic pressure difference by a constant which is called permeability coefficient of water PH2O:28,29
∆Π Π′′ - Π′ JH2O ) PH2O ) PH2O dm dm ) PH2O 2000 RT
g′′(c′′)c′′ - g′(c′)c′ dm
(11)
where dm means the membrane thickness. The positive sign indicates the water flux toward to the internal electrolyte. The thickness de is given by
de ) ˆJH2Ote
(12)
ˆJH2O denotes the water flux during the saturated phase. By inserting eqs 11 and 12 in eq 10 and differentiating the result, one obtains the following differential equation:
-
cs dc′′ g′′c′′ - g′c′ 1 ) gscs - g′c′ te c′′2 dt
(13)
The volume of the sample solution is assumed to be sufficiently large so that the water flux going into the sensor cell cannot change its concentration c′. Therefore, only the internal concentration is a function of time. The osmotic coefficients are functions of the composition of the solutions and consequently of their concentration. This dependence is relatively small compared to the variation of c′′. For solving the differential equation, these coefficients can be taken as constant. If the osmotic pressure of the external solution can be neglected with respect to the internal solution, the following simple result will be obtained: (27) (a) Staverman, A. J. Trans. Faraday Soc. 1952, 48, 176-185. (b) Kotyk, A.; Janacek, K. Cell Membrane Transport, 2nd ed.; Plenum Press: New York, 1975. (28) Zaikof, G. E.; Iordanskii, A. L.; Markin, V. S. Diffusion of Electrolytes in Polymers; VSB: Utrecht, The Netherlands, 1988. (29) Koros, W. J.; Ma, Y. H.; Shimidzu, T. Pure Appl. Chem. 1996, 68, 14791489.
t)
( )
te gs c2s +1 2 g′′ c′′2
(14)
Table 1. Composition of the Tested K+-Selective Membranes, Lipophilicity, and Dielectric Constant of the Plasticizera membrane plasticizer
On the other hand, if one cannot neglect the osmotic pressure of the sample solution, eq 13 also can be solved using constant osmotic coefficients g′ and g′′. The result is more complicated, and the internal concentration c′′(t) cannot be shown explicitly. Therefore, the explicit form in t is also preferred in eq 14.
(
t ) tecs
[
)
gs 1 g′ 1 1 + + c - c g′ g′′ s g′′ g′ g′ c c′ cs - c′ cs c′ gs s gs gs
( )
(
) ( )
(
2
×
( )
]
)
g′ g′ cs - c′ c′′ - c′ gs 1 1 g′′ ln ln cs g′ g′ 2 c′′ c′c′′ c′ g′′ g′′
(15)
To determine the permeability coefficient of water PH2O, the effective thickness of the water volume passing through the membrane has to be known:
dH2O ) (FKCl/SKCl)dKCl
(16)
where SKCl is the solubility of KCl in water. The end point te of the saturation process gives the flux, and the osmotic pressure gives the desired permeability coefficient:
PH2O )
FKCl dKCl dm SKCl te ∆Π
(17)
The permeability coefficient is a phenomenological quantity. It is an overall flow coefficient and not a property of the membrane material in general. Hence, it gives no reference to the mechanisms of the permeation. Although the value of PH2O is in general a function of the temperature and the pressure, there is also a little evidence that the permeability coefficient can also vary with the thickness of the membrane.30 EXPERIMENTAL SECTION Apparatus. Potentiometric signals of at least three samples were recorded simultaneously by an eight-channel amplifier using an OPA 128 LM with a nominal leak current of (45 fA. The amplified voltages were measured by a Keithly model 196 DMM combined with a Keithly model 705 scanner. The data were recorded by a personal computer. Measurements were carried out in air-conditioned laboratory environment at 20 ( 0.5 °C. As reference, an Ingold Ag/AgCl double-junction electrode was used with a 1 M lithium acetate outer filling solution. Sensor Preparation. Metal layers were evaporated on a 0.3mm-thick glass substrate and structured subsequently by photolithography. The internal reference electrode was formed by a (30) Hwang, S.; Kammermeyer, K. In Permeability of Plastic Films and Coatings to Gases, Vapors, and Liquids; Hopfenberg, H. B., Ed.; Plenum Press: New York, 1974; Vol. 6.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
BBPA ClP DBS DBP DOA DOP DOS ETH 217 ETH 469 ETH 2041 ETH 2041 BBPA ETH 8045 FPNPE NPOE TOTM
% 66 65 66 65 65 65 66 65 65 66 32.5 32.5 65 62 62 65
Val. [%] log PTLCb,5
rc
1 2 1 2 2 2 1 2 2 1 2
9.333 4.117 6.4-9.334 7.934 6.44,e 4.535 4.733 6.420 7.837 4.220 7.54 5.320 10.133 4.220 8.333 18.538 10.837 4.93 22.033 4.917 13.1f
2 5 5 2
12.833 2.933 5.937 16.839
23.934 4.638
η [mPas]d 20.4 9.036 19.94 14.44 81.440 20.24 902.0 79.739
13.84 243.339
a Membrane matrix was PVC in all cases. b Lipophilicity of the plasticizer determined by thin-layer chromatography c Relative dielectric constant of the plasticizer. d Dynamic viscosity of the plasticizer. e Only Hansch parameter available. f Harmonic mean of the components.
metal multilayer stack consisting of Ti/Au/Ag/AgCl. The effective electrode area of the reference was 200 µm in diameter. The 10-nm-thick titanium film promotes adhesion of the 50-nm-thick Au layer to the substrate. As the top layer, 1.5-µm-thick Ag was evaporated. This Ag layer was chemically chlorided in 3 wt % FeCl3 and 3 vol % HCl solution. The conducting lines were covered with a 2-µm-thick ECVD silicon nitride layer as insulator. Subsequently, salt was evaporated to form a 2-µm-thick film and structured by an float-off technique giving dots of 800-µm diameter. Layer thicknesses were measured with a profilometer (Dek-Tak, Sloan Co.). Membranes. A number of ion-selective membranes were prepared using different plasticizers. All chemicals for the membrane preparation were purchased from Fluka (Selectophore grade) unless indicated otherwise. As the basic properties of the membrane materials were of interest, no anionic additives31,32 were used. The membrane constituents were dissolved in cyclohexanone in a ratio of 1:4 by volume. The compositions are listed in Table 1. The dispensed membranes were air-dried for at least 72 h to ensure that all solvent was evaporated. The membrane thicknesses typically ranged between 4 and 8 µm. They were measured by means of a light microscope. The components used for the preparation were as follows: valinomycin (Val), bis(1-butylpentyl) adipate (ETH 469), bis(2ethylhexyl) sebacate (DOS), bis(2-ethylhexyl) phthalate (DOP), chloroparaffin (ClP), dibutyl phthalate (DBP), dibutyl sebacate (DBS), dodecyl 2-nitrophenyl ether (ETH 217), 2-flurophenyl 2-nitrophenyl ether (FPNPE), 2-nitrophenyl octyl ether (NPOE), tris(2-ethylhexyl) trimellitate (TOTM) (Sigma Aldrich, 99%), 12(4-ethylphenyl)dodecyl 2-nitrophenyl ether (ETH 8045), bis(1butylpentyl) adipate (BBPA), tetraundecylbenzhydrol-3,3′,4,4′tetracarboxylate (ETH 2041), bis(2-ethylhexyl) adipate (DOA), and high-molecular-weight poly(vinyl chloride) (PVC). (31) Meier, P. C.; Morf, W.; La¨ubli, M.; Simon, W. Anal. Chim. Acta 1984, 56, 1-8. (32) Morf, W.; Simon, W. In Ion-Selective Electrodes in Analytical Chemistry; Freiser, H., Ed.; Plenum: New York, 1978; Vol. 1, Chapter 3.
Analytical Chemistry, Vol. 70, No. 20, October 15, 1998
4275
Figure 4. Measurement with two K+ sensors using DOS as plasticizer (solid lines) and corresponding simulations (dotted lines). The curves 1* and 2* refer to the right y-axis where the potential values are transformed according to eq 18. The arrow indicates a sudden liftoff of the membrane. Membrane thickness: (1) 7.3 and (2) 19.3 µm.
Calculation Procedure. Calculations were performed based on eq 15 and using a PASCAL program written for the PC. The activity coefficients of the ions in aqueous solutions were calculated according to the modified Debye-Hu¨ckel equation41-43 using additional terms up to the third order for the high-concentration regime.16 The osmotic coefficients are calculated from the data published in the literature and given in mol/L.16 RESULTS AND DISCUSSION After the sensor is inserted into the sample solution (10 mmol/L KCl), water penetrates through the membrane and produces a visible electrolyte bubble at the internal reference electrode. The area of this bubble is limited by the lateral dimensions of the salt layer at least as long as the internal saturation lasts. A characteristic potential record of two samples with DOS as plasticizer is shown in Figure 4 (curves 1 and 2). The first portion with nearly constant potential indicates the saturation phase. Afterward, the signal starts to drift to more positive potentials pointing to the dilution phase. The drift rate becomes continuously smaller as the osmotic pressure difference decreases. The thicker membrane (curve 2) has, according to the presented theory, a longer saturation phase and a smaller drift rate in the dilution phase. (33) Selectophore; product information. Fluka Chemie AG, Buchs, Switzerland, 1996. (34) Eugster, R.; Rosatzin, T.; Rusterholz, B.; Aebersold, B.; Pedrazza, U.; Ru ¨ egg, D.; Schmid, A.; Spichiger, U. E.; Simon, W. Anal. Chim. Acta 1994, 289, 1-13. (35) Ammann, D. Ion-Selective Microelectrodes; Springer-Verlag: Berlin, 1986. (36) Beilstein’s Handbuch der Organischen Chemie, 4th ed.; Boit, H. G. Ed.; Springer: Berlin, Germany, 1976; Vol. 2/3, Suppl. IV, p 2081. (37) Oesch, U.; Dinten, O.; Ammann, D.; Simon, W. In Ion Measurement in Physiology and Medicine; Kessler, M., Harrison, D. J., Ho¨per, A., Eds.; Springer-Verlag: Berlin, 1985. (38) Dinten, O. J. Ph.D. Thesis, ETH 8591, Zu ¨ rich, Switzerland, 1988. (39) Schlatter, K. J. Ph.D. Thesis, ETH 8624, Zu ¨ rich, Switzerland, 1988. (40) Beilstein’s Handbuch der Organischen Chemie, 4th ed.; Luckenbach, R. Ed.; Springer: Berlin, Germany, 1983; Vol. 9/5, Suppl. IV, p 3181. (41) Hamer, W. J.; Wu, Y. J. Phys. Chem. Ref. Data 1972, 1, 1047-1098. (42) Hu ¨ ckel, E. Phys. Z. 1925, 26, 93-99. (43) Meier, P. C. Anal. Chim. Acta 1982, 136, 363-368.
4276 Analytical Chemistry, Vol. 70, No. 20, October 15, 1998
The numerical simulation according to eq 15 (dotted curves) fits nearly perfectly to the measurement results. Hence, the material parameters of the membrane remain indeed constant during the whole period of the measurement, even when the osmotic pressure decreases to ∼10% of the initial value. The simulation results deviate only at the end of the measurement. The increasing electrolyte bubble strains the membrane and stresses the adherence of the membrane to the supporting silicon nitride layer. After a certain time, the membrane lifts off partially. But the internal electrolyte is still confined hermetically by the membrane. The formation of any liquid junction between external and internal solution can be excluded by the unchanged response to concentration changes of the external solution. In some cases (e.g., curve 1), the membrane responds to the increasing stress with a sudden partial liftoff. As a consequence, the effective area of the electrolyte bubble increases as does the rate of dilution. To pronounce changes of the membrane permeability, one can insert eq 14 in eq 2. It turns out that the quantity E* given by
E* ) exp
(
)
(
γ′K+ c′K+ t 2g′′ F -1 (E - E0) ) E0* 2 2 RT γ′′ + c + te gs K
K
)
(18)
which varies linear with time t. According to eq 17, the slope of E* is proportional to the permeability coefficient PH2O. The results are represented by the almost linear curves 1* and 2* in Figure 4, referring to the right scale. In the case of a sensor with a thin membrane (curves 1 and 1*), the membrane lifts off abruptly, as marked by the arrow on the graph. The slope of curve 1* increases after the partial liftoff (thin solid line), indicating a step of the water flux rate through the membrane. Sudden liftoff causes at the same time a transient potential of ∼2 mV, which vanishes within ∼1 h. It is likely that sudden deformations of the membrane influence the electrochemical potential of ions in the membrane.24 The slight deviations from linearity can be attributed to the concentration dependence of the osmotic coefficient as well as the activity coefficient. In most cases, the liftoff of the membrane does not occur suddenly, but as a slow and steady process depending on the adherence of the membrane to the substrate as well as on its composition. Normally membranes were operated under equilibrated conditions or close to the thermodynamical equilibrium. To reach this state, even thin-film membranes have to be conditioned for days.44 In the presented experiments, however, the membrane tests started from the dry state. Thus, a high signal drift occurs during the initial conditioning phase. Extreme values were obtained for DBS-based membranes, where the signal becomes stable after 2 min and the saturation phase takes only 15 min. The other extreme can be reached by using ETH 2041, which has the highest lipophilicity of the used plasticizers. Here, the initial phase lasts for 0.5 h and the saturation phase takes 7 h. These values correspond to a 5-µm-thick membrane in each case. Sensors with a BBPA-softened membrane showed no significant potential drift within the saturation phase. This phase may be tried to be prolonged with ETH 2041. A 1:1 mixture of BBPA and ETH 2041 (44) Reinhoudt, D. N.; Engbersen, J. F.; Brzo´zka, Z.; van den Vlekkert, H. H.; Honig, G. W. N.; Holterman, H. A. J.; Verkerk, U. H. Anal. Chem. 1994, 66, 3618-3623.
Figure 5. Dependence of the penetration coefficients for water on the lipophilicity for K+-selective membranes based on the indicated plasticizer. The coefficients were calculated according to eq 12. Every data point represents the arithmetic mean of at least three measurements; the standard deviation was better than 10%. [PH2O] ) 10-18 kmol m/m2 s kPa. Regression line, all data points except DOP.
(membrane 11) exhibited an average saturation period, but the low drift rate was given only during the second half of the saturated phase. As shown in Figure 5, the calculated value of the penetration coefficient for water perfectly matches with the regression line, if the harmonic mean of the lipophilicity values of the pure components is set for the lipophilicity of the mixture. After a period of time, which lasts ∼10% of the saturated phase, the potential becomes nearly constant. This behavior, also shown in Figure 4, is very characteristic for the plasticizers DOS, BBPA, and DBS. They all have low dielectric constants (r e 4.5). The plasticizers TOTM, ETH 2041, and ETH 469 have slightly higher dielectric constants and higher lipophilicities. These membranes exhibit small drift rates in the saturated phase of about -1 to -2 mV/h and +2 mV/h for ETH 469. Additionally, the potentials are shifted by +10 mV. With increasing dielectric constant of the plasticizer, this potential shift increases as well. Shifts of about +50 mV for DBP and of about +70 mV for ETH 8045 were observed. Deviations from Nernstian behavior (reduced slope and selectivity) also increase. Membranes based on plasticizers with high dielectric constants such as NPOE, FPNPE, ETH 2017, and ClP gave no useful results. One can suppose that in these cases a part of the salt layer was dissolved in the membrane material during the production. As a result, a streaming potential is built up when water penetrates into the membrane. Because of the inherent cationic permselectivity,1 the potential shifts to more positive values. Therefore the presented method of studying water permeation is not applicable to membranes based on such plasticizers. We observed that a high water flux through the membrane influences the selectivity of the membrane. For a 6-µm-thick, DOS-softened membrane, a reduced selectivity to Na+ of log kKpot+,Na+ ) -0.9 has been measured. Increasing the carrier concentration to 2% almost restored the selectivity (log kKpot+,Na+ e -3.0). One can suspect that the water flux creates a carrier concentration gradient with a reduced concentration at the membrane surface to the sample solution. Therefore we used
higher valinomycin concentrations than commonly given in membrane recipes. In case of NPOE and FPNPE no “normal” sensor response could be obtained, even with valinomycin concentrations of 5%. The lifetime of ion-selective membranes is mainly limited by two processes. First, carrier from the membrane is extracted into the sample solution, leading to a loss of selectivity when the carrier concentration falls below a critical value,38 and second, plasticizer leaks into the surrounding media, which reduces selectivity4 and increases electrical resistance and noise.44 These effects are the higher the higher the lipophilicity of the sample solution and the lower the lipophilicity of the membrane components is. As the test sample in general cannot be subject to change, one has to use membrane components with a lipophilicity as high as possible.4,5 Taking the end point te of the saturation phase, the penetration coefficient PH2O can be calculated according to eq 17. In Figure 5, the square root of the penetration resistance is plotted versus the logarithm of the lipophilicity for all membranes with a detectable end point. With the exception of membrane 6 (DOP), a linear dependency appears. The inability of a partition solvent to accommodate water is a good measure of its lipophilic behavior toward a great assortment of organic solutes.45 Thus, we can put on a scale hydrophilicity as the reciprocal value of the lipophilicity. The lipophilicity P2 is a measure for the distribution of a substance in a specific two-phase system, e.g., water/octanol. To obtain the partition coefficients for another system, e.g., membrane plasticizer/ aqueous solution (P1), one has to use the conversion45,46
log P1 ) a log P2 + b
(19)
where a and b are parameters depending on the new solvent. According to Fick’s first law for steady-state transport, the flux rate is controlled by two factors: the steady-state diffusion coefficient Dw and the concentration of water at the boundaries of the membrane. For hydrophobic polymers like neutral carrier membranes, the diffusion coefficient is independent of the concentration of water within the membrane.28 The relation between partition coefficient Kw, diffusion coefficient Dw, and the permeability of water PH2O can be written as
KwDw ) PH2ORT
(20)
In fact, there are only few data available for the partition and the diffusion coefficient to be able to prove this relation. For a DOAplasticized K+-selective membrane Dw ) 2.5 × 10-6 cm2/s and a water content of 0.15 mol/L are reported.20 These lead to a permeability of 2.8 × 10-16 kmol m m-2 s-1 kPa-1, which is ∼3 times higher than the value obtained by the presented measurements. Due to the complex transport process of water through the membrane, the values cannot be compared directly because the reported total water concentration contains the mobile or “free” water within the polymer matrix and the water that is immobilized (45) Leo. A.; Hansch, C.; Elkins, D. Chem. Rev. 1971, 71, 525-616. (46) Collander, R. Acta Chem. Scand. 1951, 5, 774-780.
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Figure 6. Dependence of the penetration coefficients on the viscosity of the plasticizer of the membrane. Equal symbols denote plasticizers with similar (or almost homologous) constitution.
or “bound” in small droplets. The latter one should give only a small contribution to the water flux as the diffusion coefficient is smaller by orders of magnitude than that of the mobile water.25 Furthermore, one has to keep in mind that membranes in the course of these studies were not equilibrated and the equilibrium content of immobile water could not be reached within the measurement period. The amount of immobilized water within the membrane depends on several factors and the interdependencies are not fully understood yet. As far as known, it depends on the lipophilicity of the carrier but not on the concentration of the carrier.20 Results in the literature17 do not show a correlation between water content and lipophilicity or dielectric constant of the plasticizer used. One can assume in these cases that the “immobile” water content viels the content of the “mobile” water. Simulations have shown that the “immobile” water content exceeds the “mobile” by more than a factor of 10.24 Equation 20 states a Fickian diffusion of the vapor in the homogeneous macromolecular substrate. Many authors have shown that the observed mechanism is “anomalous” or “nonFickian”23 and that Fick’s first law is not applicable to the permeability of homogeneous membranes in such cases.47 Equation 20 shows that the permeability is proportional to the diffusion coefficient of water. According to the Stokes-Einstein relation D ) kT/6πrη, the diffusion coefficient depends on the 4278 Analytical Chemistry, Vol. 70, No. 20, October 15, 1998
reciprocal viscosity of the plasticizer. Therefore, the penetration coefficient is plotted in Figure 6 against the reciprocal viscosity. The plasticizers DOS, BBPA, DOA, and DBS (filled circles), which have a very similar constitution, follow a linear dependence as shown by the solid line. Plasticizers with different constitution may match other linear relations, but there are too little data to prove their evidence. The parameters viscosity and lipophilicity of a plasticizer cannot be calculated from each other, but they are also not completely independent. A large plasticizer molecule (e.g., with long side chains) gives, in general, a more lipophilic plasticizer and increases also the viscosity of the plasticizer. Therefore, the permeability can be expressed only by the lipophilicity (Figure 5) for commonly used plasticizers in K+-selective membranes. The permeability coefficient of plasticizers with a nitro group, such as NPOE, was estimated by observing the structures under the microscope. The internal salt layer was dissolved much slower than with other membrane plasticizers. The permeability for NPOE is ∼10-19 kmol m m-2 s-1 kPa-1. The membranes became milky when exposed to the test solution. This is caused by water droplets within the membrane. Opaqueness took place much faster for membranes with high dielectric constants. Due to this (47) Peterlin, A. In Permeability of Plastic Films and Coatings to Gases, Vapors, and Liquids; Hopfenberg, H. B., Ed.; Plenum Press: New York, 1974; Vol. 6.
effect, the salt crystals under the membrane became hardly visible after ∼1 week. Hence, one can conclude that the water content in the membranes with plasticizers based on a nitro group is higher than in those with other plasticizers. On the other hand, this water has to be mainly immobile to be able to explain the low water permeability of these membranes. This evidence is a highly surprising contradiction, as we had expected a higher dielectric constant to give higher water content within the membrane, which in turn should also give a higher permeability.
ACKNOWLEDGMENT We thank the Austrian Science Foundation (FWF) and the Oesterreichische Nationalbank for funding of this study. We also thank Bui Thi Thu Lan for verifying the specifications of the carrier samples.
Received for review April 7, 1998. 1998.
Accepted July 27,
AC980389X
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