hQUID
257
ION-EXCHANGE hdEMBRANES WITH WEAKLY IONIZED GROUPS
Liquid Ion-Exchange Membranes with Weakly Ionized Groups. 11. The Resistance and Electromotive Force of a Thin Membrane’ by John Sandblom2 Department of Physiology and Committee on Mathemathical Biology, University of Chicago, Chicago, Illinois 60637 (Received September 1 , 1967)
Previously developed theories for liquid ion-exchange membranes, in particular the conclusions of part I, are tested on a thin (0.65-mm) membrane formed by dissolving the acid cation exchanger bis(2-ethylhexy1)phosphoric acid in amyl alcohol. This system is shown to conform reasonably well with the assumptions on which the theories are based, notably completely trapped sites with weakly ionized groups and a convectionfree membrane. The transients of the emf and the membrane resistance are measured simultaneously following step changes in external-solution conditions containing mixtures of HC1 and NaC1, from which it is concluded that the emf is established instantaneously long before the profiles have reached their steady states. Measurements are also made of the steady-state resistance for various external solutions and applied electric fields which confirm the theoretical predictions that the resistance is practically independent of the electric field but strongly dependent on the external-solution compositions. The ranges of concentrations in these experiments are chosen such that the co-ions are excluded from the membrane. However, experiments are also performed with HC1 in different concentrations on the two sides of the membrane, and a strong rectification tendency is observed when the co-ions are not excluded which is also predicted by the theory.
Introduction Liquid ion-exchange membranes have primarily been studied because of their resemblance to cell membranes3-6 and recently also because of their electrodespecific p r ~ p e r t i e s . ~ JA liquid ion exchanger consists of a water-immiscible organic solvent, usually of low dielectric constant, in which is dissolved an ionic component of proper size and configuration to make it insoluble in ~ v a t e r . ~Several *~ types of such systems have been characterized with respect to their physicochemical properties,l0f” of which the partition coefficients and the complex formation by the ionic constituents are the most important parameters in determining their behavior as membranes.12*1a By introducing a number of simplifying assumptions the transport properties of liquid-ion-exchange membranes have also been subject to theoretical analysis, where the membranes have been regarded as mobile-site membranes14J5 containing varying degrees of ion pair formation.16j16 I n part I of this series a theory for the case of strong association was developed and is expected to describe the behavior of most types of weakly ionized liquid ion-exchange membranes. This as well as earlier treatments, however, have been confined to the steady state which assumes the interior of the membrane to be convection free, and consequently these treatments do not apply to such experimental situations in which the membrane has been deliberately stirred“ 318 or where it has been thick enough to permit convection in the i n t e r i ~ r . ~ , ~Special J ~ J ~ experimental arrangements are therefore required to test the steady-state theories, and in the case of a single counterion this has been accomplished in a “model” system designed to
satisfy the idealizing assumptions.21 By enclosing a solution of HC1-2-propanol in a polyvinyl tubing sealed at both ends with Ag-AgC1 electrodes, a model system (1) This work was supported by research grant GB-4039 from the National Science Foundation and was aided by U. S. Public Health Service General Research Support Grant FR-5367 and Training Grant 6-T1-GM-833. (2) Department of Physiology and Medical Biophysics, University of Uppsala, Uppsala, Sweden. (3) R. Beutner, “Physical Chemistry of Living Tissues and Life Processes,”, Williams and Wilkins, Baltimore, 1933. (4) W. J. V. Osterhout, Cold Spring Harbor Symp. Quad. Biol., 8, 51 (1940). (5) K. F. Bonhoeffer, M. Kahlweit, and H. Strehlow, Z. Phys. Chem. (Frankfurt am Main), 1, 21 (1954). (6) Data Sheet on Ca2+ Electrode No. 92-20B, Orion Research Inc., 1966. (7) G. Eisenman, Anal. Chem., 40, 310 (1968). (8) G. M. Shean and K. Sollner, Ann. N . Y . Acad. Sci., 137, 769 (1966). (9) R. Kunin and A. G . Winger, Angew. Chem. Int. Ed., Bngl., 1, 149 (1962). (10) A. L. Myers, W. J. McDowell, and C. F, Coleman, J . Irmrg. Nucl. Chem., 26, 2005 (1964). (11) T. Shedlovsky and H. H. Uhlig, J . Gen. Physiol., 17, 663 (1933). (12) M. Dupeyrat, J . Chim. Phys., 61, 306, 323 (1964). (13) M. Kahlweit, H. Strehlow, and C. 9. Hocking, Z. Phys. Chem. (Frankfurt am Main), 4, 212 (1955). (14) F. Conti and G. Eisenman, Biophys. J.,6, 227 (1966). (15) J. Sandblom, G. Eisenman, and J. Walker, Jr., J . Phys. Chem., 71, 3862, 3971 (1967). (16) J. Sandblom, Ark. Fys., 35, 329 (1967). (17) 0. D. Bonner and J. Lunney, J . Phys. Chem., 70, 1140 (1966). (18) H. L. Rosano, P. Duby, and J. H. Schulman, ibid., 65, 1704 (1961); H. L. Rosano, K. Breindel, J. Schulman, and A. Eydt, J . Colloid Sci., 22, 58 (1966). (19) M. Kahlweit, Arch. Ces. Physiol., 271, 139 (1960). (20) K. Sollner and G. M. Shean, J. Amer. Chem. Soc., 86, 1901 (1964).
Volume 73, Number 1 January 1969
JOHN SANDBLOM
258 was obtained which functioned as a mobile-site membrane, the H + ions behaving as trapped sites and the Cl- ions behaving as permeable counterions.21 With suitable precautions the interior of this membrane could be kept convection free. The advantage of having well-defined boundary conditions made this system a particularly useful one for testing the basic elements of the theoretical treatments.21 It is also of interest, however, to examine the extent to which the theory can predict the behavior of a liquid ion-exchange membrane in contact with aqueous solutions. For this purpose a membrane has been made from a commercially available liquid ion exchanger and has been studied under such experimental conditions that the requirements of the theory are met. The experiments have been carried out under steady-state conditions with a convection-free membrane, and the results have shown reasonable agreement with the theory. Studies on this system may therefore be of some relevance to biological membranes in which lipid-soluble carriers have been postulated to exist and where the interior hydrocarbon region is likely to be convection free in view of the bimolecular arrangement. The system should also be useful for comparing liquid and solid ion-exchange membranes with respect to their rectification and other steady-state properties, a comparison which the usual nonconvection-free liquid membranes have not permitted. ?’he Xystena Studied. In preparing a membrane in which the effects of association (ion pair formation) can be conveniently studied, it is desirable to select a system whose chemical properties are simple and well defined. Furthermore, in order to conform with the assumptions of the theories, the experimental system should come as close as possible to meeting the following requirements: (a) the counterions and sites are univalent and behave ideally except insofar as they can associate through a simple law of mass action to form neutral ion pairs; (b) the sites are unable to cross the membrane-solution interfaces; (c) the membrane interior is convection free; and (d) in addition the diffusion of counterions should be membrane controlled. The property (a) can be obtained by a proper choice of liquid ion exchanger, whereas the properties b-d aIso depend on the experimental s i t ~ a t i o n . ~ ~ ~ ~ The liquid ion exchanger used was the acid cation exchanger B2EHPA (bis-(2-ethylhexyl)phosphoric acid) having the steric formulag CHL& CH3(CHz),CHCH2O CH, ( C H JaCHCH20
I
CHZCH3 B2EHPA generally forms monomers (ion pairs) or The Journal of Physical Chemistru
dimers in organic solvents,10 and the branching of its hydrocarbon chain makes it sparingly soluble in water. However, it is only in the acid form in which BBEHPA behaves ideally, since ion-exchange studies indicate that the Na+ salt of BBEHPA forms higher order aggregates of the form NAS-SHS, where S is the anion of B2EHPA.10 Furthermore, the Na+ salt is highly soluble in water, although its affinity for organic solvents is greater than for water. The properties of a liquid ion exchanger depend to a greater extent on the nature of the solvent, particularly with respect to the dielectric constant and the water content. N-Amyl alcohol was chosen because it combines a relatively low water solubility (2.7 g/100 ml of HzO) with a favorable dielectric constant, which does not cause the ionization of BBEHPA to be unduly snppressed. The conductivity is therefore sufficiently high to permit an evaluation of the limiting conductances and dissociation constants by conductometric methods according to Fuoss and Kraus.22 The water content of the membrane will depend on the concentration of BBEHPA and other ions when the membrane is in contact with aqueous solutions. Consequently, the degree of hydration of charged species in the membrane is expected to vary with concentrations. In strong support of this is the observed concentration dependence of the ionic selectivities in a chiiiolin membrane, which was shown to be a result, of variations in the mobilities due to changes in the degree of hydration.5 Therefore, one might expect deviations from ideal behavior with respect to the mobilities and standard chemical potentials of the ions. On the other hand, it is reasonable to assume that the uncharged species have constant mobilities, since these depend only on the molecular size of the molecules and the viscosity of the membrane which is not expected to vary with small changes in the water content. Measurements osf Basic Parameters. The basic parameters in terms of which the membrane properties may be characterized appear in the theoretical treatment of part I, namely, the limiting equivalent conductances (XOHS and X O N ~ S ) , the dissociation constants (KII and K N ~ the ) , transference numbers ( t and ~ ha), the limiting partition coefficients (/‘CH//CN~), and the mobilities of the ion pairs (uHSand uNas).Except for the mobilities of the ion pairs all these parameters have been determined by cIassicaI electrochemical methods (see Table I). The limiting conductances and dissociation constanls for the acid and its sodium salt have been calculatcd from conductance data by E i ~ e n m a n . ~Since these calculations must rely on conductance values which are close tQ the conductivity of pure amyl alcohol, the (21) J. L. Walker, Jr., G. Eisenman, and J. Sandblom, J . Phus. Chem., 72, 978 (1968). (22) R. A. Fuoss and C. A. Kraus, J . Arne?. Chem. Soc., 5 5 , 476 (1933); 57, 488 (1935); Trans. Faraday SOC.,32, 594 (1936).
259
LIQUIDION-EXCHANGE RfEMBRAXES WITH WEAKLY IONIZED GROUPS Table I HBZEHPA
XO, ohm-' cm2 mol-1 K , mol cm-a
28.6 2.26 X lo-@
t Xo (ion pair), ohm-'
0.6 2.7
x
...
NaB2EHPA
11.4 x 10-7
5.6
NaCl
HC1
20.83
5.07
...
3.68 3.08 x 0.0031
x
0.037
... ...
0.8
2.7
... ...
cm2 mol-1
results may not be quite accurate, but the values are consistent with those obtained from conductance measurements of NaCl and HC1 in amyl alcoh01.~ The transference number of hydrogen was measured with glass electrodes according to a method described by GemanLZ3 A liquid junction was formed by bringing two different solutions of B2EHPA in amyl alcohol in contact with each other and measuring the potential difference across the junction with the glass electrodes. The transference number for hydrogen determined by this method was found to be 0.6 from which also t N a and ts can be calculated, using the values for XOHS and XO,vaS.
The value for l i ~ / k ~ \was . , calculated from the distribution coefficients of HC1 and NaCl between water and amyl alcohol. These were measured by equilibrating aqueous solutions of HC1 and NaC1 with amyl alcohol. Samples of the amyl alcohol were then redissolved in water and analyzed for chloride by electrometric tritration. The distribution coefficients S between alcohol and water obtained this way were 0.037 and 0.0031, respectively, for HC1 and KaC1. From conductance measurements Eisenman' found these values to be 0.025 and 0.0025, which are in good agreement with the more direct measurements described here. Squaring the ratio of the distribution ~ ~ in the calcucoefficients gives the value of k H / k used lations. The remaining parameters, namely, the mobilities of the ion pairs (UHS and U K ~ S ) ,may be determined from the limiting currents when all other parameters are In view of their size and lack of charge, it rjeems likely that the ion pairs, whether they contain hydrogen or sodium, have equal mobilities. Being the predominant species in the membrane they will also determine the kinetic behavior; e.g., the time course of relaxation from one steady state to another following a step change in external-solution conditions. These facts provide an easy method to calculate the mobilities of the ion pairs from kinetic measurements as will be described in the section on Results. Table I summarizes the results of all these measurements of the basic parameters. In order to study the steady-state properties of the B2EHPA-n-amyl alcohol system in the form of a thin convection-free membrane, a suitable matrix for the
liquid ion exchanger is required to maintain a stable membrane in contact with aqueous solutions. It was found that Nillipore filters did not have the appropriate wetting properties for the system to form such a stable membrane. Instead a method was developed, in collaboration with Eisenman, by which the liquid ion exchanger was placed in a small hole drilled in a Lucite disk where it formed a stable, well-defined membrane in contact with the aqueous solutions. The dimensions of the hole (0.65-mm length and 0.1-mm width) ensured a convection-free interior for which there was also experimental evidence, e.g., the ability of the membrane to rectify the electric current by skewing the profiles. Experiments described in the lClethods section were also performed to test requirements b and d. The following schematic representation illustrates the various components and phase boundaries of the system
I'I
(')
I+ aq
x-/ Iss-lI+ x-
1
oil
~
(")
aq
where X- is the anion (co-ion), I +is the counterion, and S- is the dissociated bis(2-ethylhexy1)phosphate ion. Cells of this type were first studied by Beutner and have subsequently been termed Beutner cells with oleophilic saltsn6 It has also been demonstrated that the behavior of these cells depends on the manner in which they are formed, ie., where the junctions are located and how the various phases are preequilibrated with each other before the junctions are formed.13 This is not important in our system, however, since the measurements were carried out in the steady state and the external solutions had been preequilibrated with the membrane material.
Method The liquid ion exchanger was prepared by dissolving B2EHPA (Union Carbide, 2.99 M ) in n-amyl alcohol (Baker and Co.) to obtain solutions of 10 and 1 vol yo which were subsequently used in the experiments. In all cases these solutions were preequilibrated with N HCl, but since the membrane, being only 0.65 (23) A. Gemant, J . Chem. Phys., 12, 79 (1944).
Volume 73, Number 1 January 1969
260
JOHN
Figure 1. A schematic picture of the chamber and the membrane showing the inlet holes for the solutions (A), the solution compartments (B), the Lucite disk (C) with the hole containing the membrane (D), a set of 0 rings to clamp the disk (E), current-deliveringAg-AgCI electrodes (F), recording electrodes (G), and magnetic stirrers (H) with
mm thick, equilibrated quickly with the external solutions, the experiments that were carried out at steady state did not require this preequilibration, except that it seemed to increase the stability of the membrane. The membrane solutions were then placed in a transparent Lucite disk with a thickness of 0.65 mm. A hole had been drilled in the disk (diameter of drill, 0.1 mm) and when a drop of membrane material was placed over the hole it was immediately sucked in. Since the Lucite material was wetted by the amyl alcohol but not by water, the membrane remained stable when the disk was dipped in aqueous solutions which had been preequilibrated with the membrane material. The area of the hole was calibrated by measuring its resistance in lo-* N HC1 and the value of 0.95 X lo-' om2was thus obtained for the area of the hole. The disk containing the membrane material waa mounted in a chamber shown in Figure 1 after which the external compartments of the chamber were filled with the aqueous solutions through the openings (A). The potential was measured between one pair of AgAgCl electrodes, the other pair being used for delivering current. At the end of each compartment a magnetic stirrer could be attached as shown in Figure 2, but the stirring appeared to have little effect on the measurements and was not used in most experiments. The electric potential between the recording electrodes was measured with a Corning pH meter (No. 12) with an input resistance of 10-13 ohm. Since a continuous recording of the potential was desired, a Rustrak strip-chart recorder with a chart speed of 1 in./hr was connected to the pH meter. The current delivered through the membrane was obtained from ordinary dry cells (45 V), and when smaller steps of current were desired a series of nickel cadmium cells were used, each with a stable potential of 1.25 V. The resistance of the membrane varied between 106 and 108 ohms, and the batteries were therefore connected via a 109-ohm resistor in series with the membrane. In all cases the aqueous solutions had been preThe Joulnolof Ph&d
Chmiatry
30
60 0
30
SANDBLOM
1 I&, 60
Figure 2s. The time course of the membrane potential at zero current following step changes in the external-solution conditions. The left compartment contained a solution of 0.01 N NC1, and the membrane, containing a 10% BZEHPAamyl alcohol solution, wm initially preequilihrated with lo-' N HCI. The right compartment was filled with solutions of compositions indicated in the figure.
'.It,
30
60 10
I Irn,") 60
Figure 2b. The time course of the membrane resistance for the corresponding solution compositions of Figure 28. The resistance changes were measured by applying a constant current of 5 X 10-V A and recording the electric potential.
equilibrated by vigorous shaking with excess membrane material after which the solutions were allowed to sediment for a t least 10 min. The experiments were performed a t room temperature. That the experimental system behaved like a mobilesite membrane fulfilling the requirements a-d was tested by several different methods. The resistance of the membrane as calculated from the geometry of the system and data obtained by conductance measurements was found to agree with the directly measured values (see Figure 3c), indicating that the resistance of the membrane was determined by its bulk properties. Next the time constant for establishing the steadystate profiles was measured under identical conditions for two membranes of different thickness (0.5 and 2.5 mm). Decyl alcohol was used instead of amyl alcohol in this experiment, since it had a larger viscosity and therefore a somewhat better stability in the bigger hole. The change in resistance during the exchange of hydrogen for sodium was followed, and the time constant for this process turned out to be approximately propor-
LIQUID ION-EXCHANGE MEMBRANES WITH WEAKLY IONIZED GROUPS
O.OliHCi
1
///
-0,031 0.01'L.Ci
/
/
-0.02 I
a.
-0.4
-0.3
-0.2 -0.1
/ 4 2 1*0,3 10.4
t0.l
/
*0.5
-
V(voi0
+0.01 I
10.0
001 NaCI 0,0001 HCI
'.
-0.03
-004
. V(V0llt
+0.03" ,.Ob+
4
+o.oll
+0.02 r003f
Figure 3. The current-voltage characteristics for various external-solution conditions. The left side of the membrane was exposed t o 0.01 N HC1 and the right side was exposed to the solutions indicated in the figures. Positive current flows from left to right and the left compartment is considered to have ground potential. The circles represent the experimentally measured values and the dotted lines are calculated from the values given in Table I using the equations of' part I.
tional to the square of the membrane thickness, further substantiating the fact that the rate-limiting step was determined by diffusion in the membrane phase and not by the exchange across the membrane-solution interfaces. The latter process will, however, be rate limiting for thinner systems, since the activation ener-
261
gies are much larger for diffusion across the boundaries than for diffusion in the bull: phase of the membrane. 1 8 , 2 2 The occurrence of concentration-polarization phenomena may be used as experimental evidence for the existence of trapped siles. If the sites have had time to become polarized under the influence of the applied field, a diffusion potential will be produced which gradually decays when the current is turned off. In a dissociated system this polarization potential can reach values of the same order of magnitude as the applied potential12l whereas stronger association requires higher applied potentials in order to give tile same concentration polarization.lb In the experiments reported here the polarization potentials varied between 0 and 15 mV, depending on the magnitude of the applied potentials which ranged from 0 to 0.5 Ti. An important factor which needs to be controlled is the extent of co-ion exclusion. The external solutions contained HC1 and NaCl in different concentrations, and by keeping these sufficiently dilute with respect to the concentration of B2EHPA in the membrane, the C1- ions could be effectively excluded from the membrane phase. The range of concentrations suitable for the experiments can be determined from a series of potential measurements that were carried out on a thick system a t different dilutions of the external solutions (see ref 7, Figure 2 ) . With a 0.3 M (10 vol 7') concentration of the exchanger in amyl alcohol the potential had a practically ideal Nernst slope (58 nivltenfold change in concentration) in the concentration range 10-100 mM for both HC1 and YaC1. Below 10 mM the effect of the solubility of NaB2EHPA becomes an important factor and above 100 mM the co-ions are no longer effectively excluded. In some of the experiments the effects of incomplete co-ion exclusion have been studied by diluting the BBEHPA in the membrane and increasing the concentrations of the external solutions.
Results kfembrane Potential at Z e m Current (Emf). The solutions used in this series of experiments were HC1 and 9aC1 in such amounts that the total concentration on each side of the membrane was kept constant and equal to 0.01 N . The membrane phase consisted of a 10% solution of HB2EHPA in amyl alcohol preequilibrated with 10-2 N HC1. In each experiment the left compartment was filled with N HC1 preequilibrated with 10% HB2EHPA-amyl alcohol, whereas the right side of the membrane was exposed to solutions containing mixtures of HC1 and NaC1. Of these mixtures the pure NaCl solution was preequilibrated with 10% NaB2EHPA-amyl alcohol and the other solution with 10% HB2EHPA-amyl alcohol. (24) J. T.Davies, J . Phys. Chem., 54, 185 (1950). Volume 73, Number 1
January 1969
JOHN SANDBLOM
262 The potential at zero current was measured across the membrane, and the time course of the potential change was recorded beginning immediately after the compartments were filled. Figure 2a shows the typical time course of such a potential change, and the emf is seen to be established essentially instantaneously. In most experiments, however, an initial rapid phase lasting from 0 to 1 min was observed during which the potential rose about 5-15 mV to its final value. This initial phase was always accompanied by an increased membrane resistance, higher than that which would be predicted from the dimensions of the hole. It was therefore attributed to a certain amount of excess membrane material extending beyond the hole which was gradually washed away during the early phase. Further evidence that the emf is established instantaneously in liquid ion-exchange membranes was obtained from measurements on a thick membrane (ea. 1 cm). I n this system, designed as an electrode, the emf was established within a few minutes, whereas it would take several days to achieve a true steady state in a membrane of this thickness. To show that the emf had established its final value before the profiles had achieved a steady state, the time course for the corresponding resistance change was recorded simultaneously and is shown in Figure 2b. The resistance was measured by applying a constant current of 5 X lop3pA and recording the potential change. The time constant T D for the relaxation of the resistance is seen to be ca. 10 min and may be used to calculate the mobilities of the ion pairs. It was pointed out that the process which determines the kinetic behavior of the membrane is a simple diffusion of the ion pairs, and, since the mobilities of these are presumably equal, they are related to the time constant TD by the relationship
- (CLF)~ i?D RT+Xo
TD=----
d2
where d is the membrane thickness, D is the diffusion coefficient, and R, T , and F have their usual meaning. Expressed in units of equivalent conductance a value of 2.7 was thus obtained for the mobilities of the ion pairs. These experiments demonstrate an important phenomenon which was theoretically predicted for liquid ion-exchange membranes with weakly ionized groups,15 namely, that the instantaneous value for the emf of the membrane following a step change in external-solution conditions is equal to the value which it attains in the steady state, Therefore, a stationary or quasi-stationary state of the emf i s reached immediately following a step change in external-solution conditions, zche.i.eas the resistance approaches a steady-state value over a certain period of time which depends on the time constant for establishing the steady-state projiles. The same phenomenon has also been predicted25 and observed in dense fixed-site membranes (e.g., glass)26and forms the The Journal of Physical Chemistry
basis for analyzing their electrode-specific properties.26 It has therefore been important to test experiment)ally the predicted agreement between steady-state and instantaneous emf’s in liquid ion-exchange membranes since these have also been made into electrodes with ion-selective proper tie^.^^^' It should be emphasized, however, that this test requires a thin, convection-free membrane in order to achieve a true steady state. Current-Voltage Characteristics. HCI-NaCl. The same experimental arrangement that was used in measuring the emf was also used in measuring the membrane resistance a t steady state for various applied potentials. The concentrations of the solutions and of the exchanger were also the same as those used in the previous experiments. In Figure 3 is shown the current-voltage characteristics for various external-solution conditions. The circles represent the measured values, whereas the dotted lines are calculated from the equations of part I using the values for the parameters given in Table I. The curves in all three figures are seen to have a practically linear shape, exhibiting only a slight nonlinearity which is predicted by the theory. However, a certain deviation from the theory is seen to occur particularly for the case shown in Figure 3a with lo-* N NaCl in the right compartment. This deviation may be explained by possible errors in the parameters of nTaB2EHPA, since the measured conductivity of 10% NaB2EHPAamyl alcohol mas found to be 30% higher than that calculated from the values given in Table I. This in turn may be due to the formation of triple ions or other higher order aggregate~,~3 but it may also be due to a concentration dependence of K resulting from changes in the water content of the membrane. In spite of the deviations, however, the theoretically predicted and experimentally measured I-V curves shown in Figure 3 are quite similar with respect to their general shape. For a fixed-site membrane or a mobilesite membrane with completely ionized sites and counterions, one would expect that the resistance changes observed following changes in external-solution conditions (Figure 2b) would also give rise to a distinct rectification in an interval of about *125 mV around the V o potentiaL14~25 The absence of rectification in the actual case i s therefore a distinguishing jeatul’e of liquid ion-exchange membranes with weakly ionized groups. The slight nonlinearity of the I-V curves in Figures 3a and b is seen to deviate toward higher resistances when the potential is negative and toward lower resistances when the potential is positive. For negative potentials the sodium ions are being carried into the membrane, and in part I it was shown that their higher degree of ionization would give rise to a greater non(25) F. Conti and G. Eisenman, Biophvs. J., 5 , 247 (1965). (26) G. Eisenman in “The Glass Electrode,” Interscience Publishers, New Yorlr, N. Y., 1966.
263
LIQUIDION-EXCHANGE MEMBRANES WITH WEAKLY IONIZED GROUPS
the membrane resistance, which will therefore continue to decrease as higher fields are applied. HC1. The object with this set of experiments was to examine the effects of co-ions on the electrical properties of the membrane. The conditions were therefoye chosen so as not to exclude the co-ions from the membrane phase which is illustrated by the following representation of the cell
a- -io
+O.l
H+
(’1
I (uA)
c.
-0.5
r05
+ 1.0
rrV(Y0lt)
r15
Figure 4. The current-voltage characteristics for external solutions containing various concentrations of HC1. The solution conditions and the concentrations of the exchanger are indicated in the figures. A comparison between the rectification ratio measured directly from the curves and calculated from eq 45 of part I is also shown in the figure. Positive current flows from left to right and the left compartment is considered t o have ground potential.
linearity on the negative side which is therefore confirmed experimentally. The nonlinearity for positive potentials in the direction of decreasing resistance is thought to be an effect of co-ions. These will have a larger tendency to enter the membrane on the left side, where the exchanger is more weakly ionized and the Donnan exclusion is not as effective. An inflow of co-ions will tend to decrease
I ~
8(”> H+C1- HS ~H-tCl~
The external solutions were maintained at different concentrations levels (c”/c’ = l O / l ) . Figures 4a and b show the current-voltage characteristics at two different concentrations of BBEHPA, 10 and 1%)with the same external-solution conditions. With a membrane concentration of 10% B2EHPA the co-ions are excluded and the resistance is seen to be essentially ohmic (Figure 4a). In the more dilute membrane, however, the co-ions are not completely excluded and the current-voltage characteristic shows a distinct rectification (Figure 4b). In Figure 4c the same phenomenon is demonstrated with 10% BBEHPA and with 10 times higher external-solution concentrations. The resistance of the membrane is seen to be about 10 times lower in Figure 4c than in Figure 4a, whereas the rectification is the same in both cases. This indicates that the factor which determines the rectification tendency of the membrane is the ratio between external-solution concentrations and the concentration of the exchanger. Iloreover, the rectification is in such a direction that the membrane behaves like a fixed-site membrane with negatively charged sites,27 where the rectification is due to a “washing-out” effect of co-ions.28 This is understandable from the theoretical conclusions of part I, according to which the strongly associated sites will maintain a fixed distribution owing to the presence of ion pairs. In Figure 4 are also inserted two values for the rectification ratio, namely, ? “ m e a d which is obtained directly from the curves and ?“&d which is calculated from eq 45 of part I with the values given in Table I. The calculated values are seen to be considerably higher than the measured ones, which may partly be due to incomplete dissociation of HC1. This is not taken into account in the theoretical derivation which assumes complete dissociation of the C1- ions. Kevertheless, the relative magnitudes as well as the direction of the rectification agree with the theoretical predictions. (27) T. Teorell, Progr. Biophys., 3, 305 (1953). (28) R. Schlogl, 2. P h y s . Chem. (Frankfurt am Main), 1, 305 (1954).
Volzime 73, Number 1
January 1969
264
NOTES
Discussion The theoretical treatment of part I assumes the exchanger to be weakly ionized and a criterion for this is given by
where E,* is the concentration of the exchanger and K m a x is the largest of the dissociation constants, in this case K N ~ With . 10% BBEFIPA (&* = 0.3 1V)the left side of the inequality is equal to 23.5 and a 4% error is therefore made by neglecting the diffusion of dissociated forms (cf. part I). The errors in the individual determinations of the parameters given in Table I will also influence the quantitative agreement between theory and experiment. The largest error probably lies in the separate determinations of Xa and K , whereas the agreement with theory seen in Figure 3c shows that the product X O ~ for HBBEHPA is correct. The largest discrepancy between theory and experiment is seen from Figure 3a to be connected with VO,the potential a t zero current which is more sensitive than the resistance to errors in the values of Xo and K . Although the dissociation constants were calculated from conductance data, an independent check can be obtained by measuring the ion-exchange equilibrium constant K H N a related to the dissociation constants by
Orme and S a n d b l ~ mmeasured ~~ this parameter by an extraction procedure and obtained a value ten times lower than that given by Eisenman, which brings the calculated V o50 mV closer to the measured value. It is therefore obvious that the parameters given in Table I contain many errors, and since the theory is also based on a number of idealizing assumptions, an exact agreement between theory and experiment is not to be expected. Nevertheless, the experirnenk have shown that the system can adequately serve the purpose for which it was designed, namely, to demonstrate the behavior of a liquid membrane with trapped sites and a convectionfree interior. The theory has also proved to be successful in predicting the most important phenomena K observed in this system and should therefore be useful as a basic model for liquid ion-exchange membranes.
Acknowledgment. I wish to thank professor George Eisenman, with whom this investigation was started, for his many valuable suggestions and for his helpful criticism of the manuscript.
(29) F. Orme and J. Sandblom, unpublished results.
NOTES
Onsager’s Reciprocal Relation.
An
Examination of Its Application to a
Simple Membrane Transport Process by E. H. Bresler Research Division, Veterans Administration Hospital and Department of Medicine, Tulane University School of Medicine, New Orleans, Louisiana 70112
and R. P. Wendt Department of Chemistry, Loyola University, New Orleans, Louisiana 70118 (Receized Mag 8, 1068)
During the past 15 years several nonequilibrium thermodynamic theories of membrane transport1-4 have been developed. Because of the need for physicochemical rigor in this area of research the efforts of The Journal of Physical Chemistrg
these theoreticians were met with enthusiasm. However, we feel that there are some fundamental difficulties with the theories which limit their usefulness if they are applied prima facie. In particular, we will show that the Onsager reciprocal relation-the most fruitful theorem of nonequilibrium thermodynamicsis not valid as applied by one of the theories to a simple membrane transport process. Although our criticism may apply with some niodiiication to all of the theories cited above, we will restrict our discussion to the theory developed in 1958 (1) J. G. Kirkwood in “Ion Transport across Membranes,” H. T. Clark, Ed., Academic Press, New York, N. Y., 1954, pp 119-127. (2) 0.Kedem and A. Katchalsky, Biochem. Bzophys. Acta, 27, 229 (1958). (3) S. R. de Groot and P. Mazur, “Non-Equilibrium Thermodynamics,” North-Holland Publishing Co., Amsterdam, 1962, Chapter XV. (4) R. Schlagl, “Stofftransport durch Membranen,” Steiiikopff Verlag, Darmstadt, 1964.
