Solvent effect on membrane transport: Membrane potential and conductance in liquid membrane with mobile ion carrier

Solvent Effect on Membrane Transport: Membrane Potential and Conductance in Liquid Membrane with Mobile Ion Carrier K A Z U O N O M U R A , 1 H I R O Y U K I O H S H I M A , H I R O S H I KAMAYA, AND I S S A K U

UEDA 2

Department of Anesthesia, University of Utah School of Medicine, Salt Lake City, Utah, and Anesthesia Service, Veterans Administration Medical Center, Salt Lake City, Utah 84148 Received January 15, 1985; accepted May 6, 1985 The membrane potential and conductance of a liquid membrane, with dicetylphosphoric acid as a mobile carrier, were measured as functions of the pH of the outside solution, containing HC1 and KC1, while maintaining constant electrolyte concentrations of the inside solution. The effects of membrane solvents with different carbon numbers (1-hexanol, 1-0ctanol, and 1-decanol) were investigated. The transference numbers of each ion were estimated and the overall conductance was resolved into ionic conductances of H + and K ÷. Approximate expressions for the membrane potential and conductance were derived by solving the Nernst-Planck equations, taking into account the Donnan potentials at the membrane/solution interface. For a highly charged liquid membrane, the membrane potential was found to be almost equal to the difference between the Donnan potentials at the two membrane/water interfaces; the contribution from the diffusion potential across the membrane was negligibly small. By curve-fitting of the experimental data on the membrane potential and conductance, the mobility of the carrier, Us, in the membrane was estimated. Also the equilibrium constants were obtained for the association reaction between K + and the carrier, KK, and for the association reaction between H ÷ and the cartier, KH. The mobility of the cartier Us was shown to be close to the mobility of K ÷. The association constants, KK and Kn, increased by a factor of about 10 as the solvent carbon number increased by two. The selectivity of the membrane for H + over K ÷, expressed by Knbn/KKbK (where b is the partition coefficient of ionic species between the membrane and aqueous phases), increased with the increase in the carbon number. © 1985AcademicPress,Inc. INTRODUCTION

Ionic m e m b r a n e conductance is one of the expressions of the membrane transport properties of ions and is generally determined by the concentrations and mobilities of charged species in the membrane, i.e., free ions and charged carrier molecules. The concentrations of these charged species in the membrane phase depend upon the chemical affinity between ions and carrier molecules, as well as the free energy of penetration of the ions into the membrane from the aqueous phase. These On leave from the Chemistry Laboratory, College of General Education, Kyushu University, Ropponmatsu, Fukuoka 810, Japan. z To whom reprint requests should be addressed at the VA Medical Center.

parameters and other physicochemical factors that determine the membrane transport properties are affected by the properties of the membrane solvent in which ion carrier molecules are solvated. The solvent property of the membrane possibly also influences ionic selectivity of the ion-exchanger membranes. In the present study, we used liquid membranes to investigate the solvent effect upon ion carriers. When compared to planar lipid bilayers, liquid membranes have an advantage in that the solvent effect on the ion-carrier molecules can easily be studied by changing the membrane-forming molecules. Liquid membranes also have superior stability, extended lifetime, and larger total membrane area. The effect of membrane solvents on membrane potential has been studied by several

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Journalof Colloidand InterfaceScience,Vol. 108,No. 2, December1985

0021-9797/85 $3.00 Copyright© 1985by AcademicPress,Inc. All fightsof reproductionin any formreserved.

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workers (1-3). Those who deal with neutral carriers have interpreted the solvent effect by the dielectric properties of the membrane solvent on the basis of the Born equation of the electrostatic charging process (3, 4). This model, however, cannot apply to analysis of spe'cific ion selectivity of ion-exchanger membranes. Several theories have been proposed for ion transport through liquid membranes with charged carriers (5-7). Sandblom et al. (5, 6) derived approximate expressions for membrane potential (5) and for the current-voltage relationship in the presence of a single counterion species (6) by assuming local electroneutrality in the membrane. In the present theoretical treatment, we assume that the electric field is constant within the membrane and we use the assumption of electroneutrality only when the Donnan potential across the membrane/solution interface is derived. The constant field assumption, introduced first by Goldman (8), is convenient for deriving analytic results, especially for the case when more than one counterion species is present. Although "local electroneutrality" and "constant field" are physically equivalent, both assumptions are approximately correct only for the bulk membrane phase, that is, they become invalid near the membrane/solution interface and hence they do not always lead to equivalent results. In a previous paper (9) we showed that the electric potential across the membrane/solution interface at equilibrium (i.e., the Donnan potential) diffuses over some distance on both sides of the interface, where neither "local electroneutrality" nor "constant field" can hold. However, the potential-decay distance is usually very small compared to the thickness of liquid membranes. One may, therefore, neglect the diffusive structure of the electric potential at the interface. Nomura et al. (7) proposed a general theory based on irreversible thermodynamics, which takes into account mutual interactions of ionic flows. In the present paper, a theoretical expression of membrane potential and membrane conductance is derived in the case where interactions Journal of Colloid and Interface Science, Vol. 108, No. 2, December 1985

ET AL.

of ionic flows can be neglected so that the usual Nernst-Planck approach is applicable. This report describes an electrochemical study on the pH dependence of the membrane conductance and membrane potential in a liquid membrane system, and the solvent effect of the membrane-forming agents upon these parameters. Liquid membranes were formed in a Teflon filter by impregnating with l-alkanols as a solvent and dicetylphosphoric acid as a mobile ion-carrier. The dc conductance was estimated from the current-voltage relationship, and the ionic membrane conductance was evaluated by the transference number, obtained from the membrane potential at zero electric current. The physicochemical parameters of liquid membrane systems with different solvents were obtained by fitting the experimental data to the theory. THEORY

Consider a planar liquid membrane of thickness l that contains lipid molecules of concentration N at equilibrium. The membrane separates solutions I and II, both containing K +, H +, and CI- ions. We take the x axis perpendicular to the membrane, so that the region 0 < x < l corresponds to the membrane phase, and the regions x < 0 and x > 1 to solutions I and II, respectively. The activities of K + and H + ions in the bulk phase of solutions I and II are denoted by a I, a~, a~ and a~, where subscripts K and H refer to K + and H ÷ ions, respectively, and superscripts I and II to solutions I and II, respectively. Similarly, we denote the numbers of K ÷ ions, H ÷ ions, and free lipid molecules at position x in the membrane by nK(X), nI~(X), and ns(x), respectively. One obtains the relation between the electric current crossing the membrane, I, and the membrane potential, V, when the membrane system is in the stationary state. The following assumptions are made: (1) The membrane is permeable to electrolyte ions, and lipid molecules are allowed to exist only in the membrane phase.

SOLVENT EFFECT ON MEMBRANE

521

TRANSPORT

(2) Free lipid molecules have one negative charge and can react with K ÷ and H ÷ ions in the membrane phase. We assume that these association reactions are strong and fast enough to attain chemical equilibrium. On the other hand, KC1 and HC1 are both assumed to be completely dissociated in the aqueous phase. (3) The concentration of C1- ions in the membrane phase can be neglected. This assumption is reasonable because the membrane has strong negative charges due to the presence of free lipids. (4) At equilibrium, the potential at the membrane/solution interface, i.e., the Donnan potential, diffuses over some distance. The potential distribution at the interface, as well as that of the bulk solution, is assumed to be only slightly distorted by the ionic flows so that these potential distributions practically remain at equilibrium. (5) Under conditions of the present study, the aforementioned distance of the potential decay amounts to about 100 A and is negligibly small compared to the membrane thickness (0.2 mm) (9). We neglect this diffusive structure of the potential at the membrane/ solution interface and assume that the electric field E is constant inside the membrane.

where b~ is the partition coefficient of ionic species a (a = K, H) between the membrane and solution phases, F i s the Faraday constant, R is the gas constant, and T is the absolute temperature. Because the concentrations of the ionic species and neutral species are dilute in the present membrane system (less than total concentration of lipid, i.e., 1.10 -3 M), we have assumed that the activity coefficients of all species existing in the membrane are unity. On the other hand, from the condition ofelectroneutrality at x = +0 and x = l - 0, we obtain

It follows from assumptions (4) and (5) that each solution I and II is equipotential in each compartment. Let the potential of solution I be zero. Then, the potential of solution II coincides with the membrane potential, V, which can be written as

nsK(X) + nsH(X) ~ N.

V = Va + ~i - ~ii

nK(x)+nrr(x)=ns(x)

at

x=+0,

l--0

[3] where we have neglected the C1- concentration (assumption 3). The concentration of free lipids ns(x) is related to nK(X) and nn(x) by the mass action law ns~(X) K~ a = K, H [4] ns(x)n~(x) where ns, is the concentration of lipids complexed with ionic species ol (a = K, H). K~ is the association constant of the respective reactions. We treat the case of strong association (i.e., large KK and Kn) so that [5]

From Eqs. [2]-[5], we find that the Donnan potentials ffi and ~u are given by ~i-

RT 2F

[ 1]

× In (bKak + bHah)(KKbKak + KHbnah) Here, Va is the diffusion potential and ffl and (bn are the Donnan potentials at the interfaces i = I, II. [6] x = 0 and x = l, respectively. The Donnan potentials can be obtained as The electric current I crossing the memfollows. From the condition of chemical equi- brane is given by librium at the interfaces x = 0 and x = l, we I = F(J(~ ) + aCr~) - J(s~)) [71 have

n,(x) = b,ai~exp(-F~i/RT)(a = K, H; i = I , II, a n d a t x = + 0 , 1 - 0 )

[2]

where J ~ ) and J(nm) are, respectively, the fluxes of K + and H + ions, and the contribution from C1- ion has been neglected. The NernstJournal of Colloid and Interface Science, Vol. 108, No. 2, December 1985

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Planck equation for the flux jCm) of charged species a (a = K, H, and S) is

× (a~ - akexp(-FV/RT)) + UHbn × (a~ - alexp(-FV/RT)) - Us{(bKa~

agm)=_U~RT(~

Z,n~FE~ RT ]' 0
+ bHa~)exp(-F(V- (qh - Ou))/RT)

[8] -

where U~ is the absolute mobility of species within the membrane; Z~ = 1 for a = K and H, and Z~ = - 1 for a = S. Recalling that E = constant (assumption 5), we integrate Eq. [8] from x = +0 to x = l - 0, and take the sum of J(Km) + y(Hm) j(m)s Then, we obtain the current-voltage relationship _

I = -

(bKa~ + bHaI)exp(-F(Oi - ,~n)/RT)}] [9]

where we have introduced the diffusion potential Vd, defined as

Va = -El.

.

F2Va exp(-F'bil/RT) - l 1 - exp(-FVd/RT)

[UKbK

[10]

The membrane potential V° at zero electric current is obtained by putting the right-hand side of Eq. 9 to be zero.

R T , rUKbKa~ + Unbnah + Us(b~a~ + bnan)exp(+F(~i - ~n)/RT)] V° = - - f f - m L ~ + Unbna~ + Us(bKaI + bnaI)exp(-F(~, ~ J "

[11]

In accordance with the present experiment, we obtain the membrane conductance Gm defined by

Gm -

Oil F2F (F/ZRT){V°~(~I-Z~n)} ] ~ vo = -T ksinh{(F/2RT)(V ° - ( ~ - On))}] I

N

7 '/2

× (bKa~: + bnaI)l/2(brca~¢ + bnan)mJ × r.VKbKak + UHbna I + Us(bKa~ + bHa n) exp(+F(¢1 - ¢II)]RT)] '/2 I (KKbKa[¢ + KHbHa[~)I/2 J × UKbKan + UHbHa~ + Us(bKaI + bnatn) exp(-F(~x - ~II)/RT).] ~/2 (Klcb~a~ + KHbna~i)m j . [12]

Now we obtain the contributions of the flows o f K + and H + ions to the total membrane conductance G~, which we denote by gK and gH(Gm - gK), respectively. To this end, we rewrite the total electric current I in terms of the flows of membrane permeable ions outside the membrane, which can be observed experimentally: I = IK + IH [13] Journal of Colloid and Interface Science, Vol. 108, No. 2, December 1985

where we have neglected the C1- contribution. We expand IK(V) and In(V) around V = V°. L(v)

= 1~( v °) - g~( v - v °)

+ O [ ( V - V°)21 a - K , H

[14]

where g~ -

o---Pl~o'

~ = K, H

[15]

SOLVENT

EFFECT ON MEMBRANE

TRANSPORT

523

The ionic currents IK and IH must satisfy the relations I,(V,)=O a=K,H [16] where

M KCI and 1 × 10 - 3 M HC1. The pH of the external solution was varied from pH 2 to pH 7, whereas the KC1 concentration was kept constant at 1 × 10-~ M. The liquid membrane was prepared by dissolving dicetylphosphoric V~ = ( R T / F ) l n ( a I / a ~ ) a = K, H [17] acid in water-saturated 1-alkanols at 1 × 10 -3 are the equilibrium potentials for the respec- M. The formed membrane was conditioned tive ions. Evaluating Eq. [14] at V = VK and by soaking it in the internal solution for 24 h. V = VH, respectively and summing them, we The membrane solvent and the ion carrier have were equilibrated with aqueous electrolyte soV ° = tKVK + tHVH [18] lutions before the formation of the liquid membrane. The pH of the aqueous phase was where tK and tH are, respectively, the transferadjusted by HC1 in the range below p H 5, and ence numbers o f K + and H + ions and correlate by phosphate buffer 1 × 10 -3 M a b o v e pH 5, with the ionic membrane conductance and the and measured by a Coming Model 12 pH memembrane conductance as ter (Coming, N. Y.). t~ = g~/am a = K, H [191 The membrane potential at zero electric current as well as at nonzero current was meawhere we have used Eq. [16] and the fact that sured by a pair of calomel reference electrodes I ( V °) = IK(V °) + I H ( V °) = 0, and neglected (Coming) connected to a Keithley Electromhigher order terms ( VK - V°) z and ( VH -- V°) z. eter Model 614 (Cleveland, Ohio). When conEquation [18] coincides with the linear relatinuous recording of the membrane potential tionship between the membrane potential at was necessary, the output of the electrometer zero current and equilibrium membrane powas recorded on a Soltec Model 210 strip chart tentials for the respective ions, which was derecorder (Sun Valley, Calif.). The dc memrived according to the irreversible thermodybrane conductance was obtained from the namics (7). From Eq. [18], we find that tangent of the current-voltage relationship. v°-v~ The dc current was applied through another g,~---Gm a=K,B=H. [20] pair of calomel reference electrodes from a 1.5rC-V~ V dry-cell battery, connected to a decade resister (Electro Scientific Industries Model EXPERIMENTAL DB12, Portland, Oreg.) in series with the Weakly ionized dicetylphosphoric acid was membrane. The membrane current was varied used as a mobile carrier for cations; 1-alkanols in a stepwise manner. The electromotive force were the membrane-forming solvent. The liq- of the battery was found to be stable during uid membrane was supported in a Teflon filter the measurements. Each compartment of (Fluoro-Pore FP100, Sumitomo Co., Osaka, aqueous solution was mixed vigorously by a Japan), which was 200 izm thick and the pore magnetic stirrer driven by water flow supplied size was 1.0 #m. from a constant-volume water pump. All Dicetylphosphoric acid was obtained from measurements were carried out at room temP. L. Biochemicals (Milwaukee, Wisc.) and 1- perature, 24 ___2°C. hexanol, 1-octanol, and 1-decanol were obtained from Sigma. Other reagents were the RESULTS AND DISCUSSION highest grade available and were used without further purification. Water was purified by triThe experimental results for the membrane ple distillation, and once from alkaline potas- potential at zero electric current, V°, are shown sium permanganate solution. in Fig. 1 as a function of pH of external soThe internal solution contained 1 × 10 -~ lution (solution I) for three different memJournal of Colloid and Interface Science, Vol. 108, No. 2, December 1985

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NOMURA ET AL.

moidal shape, and are shifted to high p H direction with an increase in the c a r b o n n u m b e r o f 1-alkanols. F r o m this figure, it is seen that the selectivity o f K + ions is decreased with E --. 0 o the increase in the c a r b o n n u m b e r o f the sol> vent 1-alkanols, over the p H range presently studied. The m e m b r a n e conductance, Gm, was ob-50 tained from the tangent at V = V° along the r ~ i i i i curve plotted for m e m b r a n e current versus 2 4 6 8 m e m b r a n e potential. The m e m b r a n e potential pH on the abscissa at the zero electric current corFIG. l. Membrane potential at zero electric current as a function of pH of external solution. Membrane solvents responds with F °. T h e p H dependence o f are: 1-hexanol/X;l-octanol O; and 1-decanolIq. The curves m e m b r a n e c o n d u c t a n c e for each m e m b r a n e represent theoretical values. solvent is shown in Fig. 3. The three curves in this figure show similar shape with a m i n i m u m a r o u n d p H = 3.5. T h e m e m b r a n e c o n d u c brane solvents, while maintaining the p H o f tance can be written as the s u m o f the ionic the internal solution (solution II) at a constant m e m b r a n e conductances gK and gn, provided value o f 3.1. Because the KC1 concentrations that contribution o f the C1- ion can be neo f both c o m p a r t m e n t s are equal (0.1 M), the glected. O n e can estimate the values ofgK a n d equilibrium m e m b r a n e potential o f K ÷ ions should be zero (Vk = 0); hence, the transference n u m b e r o f H ÷ ions, tH, is calculated according to Eq. [18]. Assuming that the m e m E 10 brane is ideally permselective to cations, the o o o ..1~ er~--'~a o co transference n u m b e r o f K ÷ ions, &, is calcug Io-~ a D ~ a lated according to the relation. I I I I I I 10-~ tH + tK = 1. [21] 50

The obtained transference numbers are shown in Fig. 2. The tH-pH curves show nearly sig-

E O9

10-1

g

10 -2

o

lo-3 0.6

~E

i

E

f

t

I

I

i

i

101

10 -2

o

°

~

0.4

lo-3]

i

2

0.2

i

i

4

f

6

pH 0

i 2

i

~

i

4

i 6

i 8

pH

FIG. 2. Transference numbers of H ions obtained from membrane potential at zero electric current for the different membrane solvents: l-Hexanol A; 1-octanol O; and 1decanol El. Journal of Colloid and Interface Science,

Vol.

108,

No.

2, December

1985

FIG. 3. Membrane conductances (Gin, gH and gK) as a function of external pH. The membrane system and the symbols are the same as Fig. 1. The lines represent the theoretical values. Deviation from the experimental values in the low pH region is probably caused by the contribution from C1- ions, which was neglectedbut became appreciable in the low pH range. Ionic membrane conductances gR and gK were calcuicated from Eq. [20].

SOLVENT EFFECT ON MEMBRANE TRANSPORT gH as a function of the pH of the external solution, by replacing the VH in Eq. [20] with Eq. [17] for a = H, recalling that VI~ = 0 and substituting the experimental values of V° and Gm. The results are shown in Figs. 3b and c. We see that with increasing pH, gH decreases while gK increases. This pH effect corresponds to the increased contribution from K + current to the conductance at elevated pH when the H ÷ concentration in the external solution is decreased. We have derived approximate expressions for membrane potential at zero current, V°, (Eq. [11]) and membrane conductance, Gin, (Eq. [12]), which are found to be functions of the ionic partition coefficients, the ionic mobilities, and the association constants. However, it can easily be recognized from Eqs. [ 11] and [12] that V° depends not on the respective parameters but on the ratios Urt/UK, Us/UK, bn/bK and KH/Kr., and that Gm depends upon these ratios and also on the ratio UK/K~ 2. Equations [11] and [12] reveal that the ionic transport in the liquid membrane is dictated by these ratios, which may reflect the properties of the membrane solvent. Numerical values of Urt, UK, and bH/bK c a n be obtained on the basis of Stokes' law and Born's equation, and those of Us, KH/KK, and Ur./K~ 2 can be estimated by the curve-fitting procedure for the present experimental data on V° and Gin, as described below. Because UK is determined separately, the curve-fitting gives individual values of Us, Ks, and KK. The mobility of ith ionic species, Ui, is related to its Stokes radius, ri,

525

Ui = 1/(67r~r~)

[221

where n is the viscosity of the membrane phase. The numerical values of ~ for each membrane solvent, together with those of other physical parameters, were taken from Refs. [16]-[20]. Because the solubilities of water into these alkanols are 29.0 for 1-hexanol, 20.7 for 1-octanol, and 26.7 mole% for 1-decanol (10), the amount of water, contained in the membrane phase, is large enough to hydrate the ions to the same extent as in the bulk aqueous phase. It is thus justified to assume that the Stokes radius ri in the membrane is equal to that in water because the ion migrating in the membrane appears to be fully hydrated. The values of the mobilities Ug, calculated from Eq. [22] using ri in water, are given in Table I. The partition coefficients of HC1 and KC1 between water and 1-octanol are reported to be 8.24 × 10 -4 and 1.55 × 10 -4, respectively (11). We assumed that bH/bK for the membrane with 1-octanol is approximately equal to the ratio of these values, i.e., 5.3. The values of bn/bK for membranes with other alkanols were determined from the value of bH/bK for 1-octanol by using the Born equation, as shown below. Consider the free energy change for the transfer of the ion, i, from water to a given solvent, AG~. This free energy indicates the difference of the free energies between the ionsolvent interactions in water and in a given solvent, and is usually expressed by the Born equation (12)

TABLEI PhysicalParametersin the LiquidMembraneSystem Solvent

Un (mole.m2"s -1 . j - l ) UK ( m o l e . m 2 - s - l . J -1) Us ( m o l e . m 2 - s - l - J -1) KH (M -~) KK (M -~) brdbK

Knbn/KKbx

1-Hexanol

7.7 × 1.6 X 1.5 × 2.0 × 6.2 × 3.2 1,063

10-13 10-13 10 -13 106 103

1-Octanol

4.6 × 9.7 X 8.8 × 5.0 × 1.0 × 5.3 2,660

10-13 10T M 10-14 107 105

1-Decanol

3.3 × 6.9 × 6.3 × 6.8 × 1.2 × 9.3 5,319

10-13 10-14 10-14 108 106

Journal of Colloid and Interface Science, Vol. 108, No. 2, December 1985

526

N O M U R A ET AL.

81rEor~ N

[23]

~ --

where N is the Avogadro number and Zi, r*, ~0, ~w, and Esdenote the valence of/, radius of i, electrical permittivity of the vacuum, relative electrical permittivity of water, and relative electrical permittivity of the solvent, respectively; r* is the effective ionic radius which takes into account the increase in the surface free energy for the hydrated ion on transferring to the membrane phase (13). Applying Eq. [23] to the transfer of K ÷ and H ÷ ions, and substituting e x p ( - A G ~ / R T ) by partition coefficients, one obtains

: - R T In

bK

87rE-----~

-

-

from CI- ions, which has been neglected in deriving Eq. [ 11], becoming appreciable in the low pH region. A similar argument also holds for the comparison between theory and experiment on the membrane conductance, Gm. As Fig. 3a shows, good agreement is obtained for pH >/ 4, whereas the deviation becomes large in the low pH region. In our theory, the membrane potential V° is expressed as the sum of the diffusion potential I'd and the Donnan potentials ~ I and ~n at the two membrane/solution interfaces (Eq. [ 1]). For highly charged liquid membranes, ~i and ffii (Eq. [6]) are very large, so that the contribution of ~ and ~ i to V° is much greater than that of Vd. Indeed, when F ( ~ - cbn)/RT >> 1, Eq. [11] becomes

"

V° ~

[24] Because ions in the membrane phase are considered to be fully hydrated, as discussed earlier, the radii r , and r~ in Eq. [24] become independent of the membrane solvent. The quantity (1/r* - 1/r~) can be obtained by substituting the values of bH/bi< and cs for 1octanol as well as the value of ~winto Eq. [24]. The ratio bn/bK for membranes with 1-hexanol and 1-decanol can thus be estimated from Eq. [24] after substituting the obtained value of l / r * - 1/r~, and using the values of e~for the respective membrane solvents. The results are given in Table I. The values of Us, KH, and KK for the respective membrane solvents were estimated by the curve-fitting procedure for the experimental data on V° (Fig. 1) and Gm (Fig. 3). The results are also shown in Table I. The best-fit theoretical values of V° and Gm (calculated from Eqs. [ 11] and [ 12], respectively) are plotted as solid lines in Fig. 1. Agreement between theory and experiment for the membrane potential at zero electric current V° is satisfactory, as seen in Fig. 1. In the intermediate and high pH region, the agreement is excellent. In the low pH region, however, the theory overestimates V°. Presumably, this is caused by the contribution Journal of Colloid and Interface Science, Vol. 108,No. 2, December1985

CXal -

-

~II.

[25]

That is, for highly charged liquid membranes, the membrane potential is almost equal to the difference between the Donnan potentials at the two membrane/solution interfaces. Ohki (14, 15) has shown both theoretically and experimentally that the membrane potential of a highly charged lipid membrane is almost equal to the difference between the surface potentials at both membrane surfaces. The surface potential of a lipid membrane plays the same role as the Donnan potential of a liquid membrane. Equation 11 takes a form similar to that of the so-called Goldman-type equation for the diffusion potential (8). However, it must be emphasized that Eq. [ 11] takes into account not only the diffusion potential but also the interfacial Donnan potentials and the flow of carrier molecules. As Fig. 1 shows, V° becomes a limiting value, which we denote by I7° with increasing pH, and the magnitude of 17"oincreases as the carbon number of the solvent 1-alkanol increases. From Eq. [ 11], l7° can be obtained by putting a I = a~ = a~ and a~ ~ 0:

-- 2"--F In

1

b----'K~]\ + KK----~KlJ [26]

SOLVENT EFFECT ON MEMBRANE TRANSPORT which shows that 170 increases with increasing K n / K K . As the curve-fitting results (Table I) indicate, this ratio is f o u n d to increase as the solvent carbon n u m b e r increases. Figure 3a shows that the m e m b r a n e conductance Gm depends considerably on the physical properties o f the m e m b r a n e solvent, and that Gm exhibits small change for high pH. It can be shown f r o m Eq. [12] that as p H increases, Gm b e c o m e s a limiting value Gm, which is approximated by am = 7

~'~-~K ]

"

[271

Because Un, UK, a n d Us show relatively small dependence on the m e m b r a n e solvent, it follows that KH and KK depend strongly on the m e m b r a n e solvent. Table I shows that KH and KK increase by a factor o f about 10 as the solvent c a r b o n n u m b e r increases by two. The selectivity o f the m e m b r a n e for H ÷ over K ÷, expressed by K u b n / K K b K , increased according to the increase in the solvent carbon n u m b e r ; about fivefold increase was observed between 1-hexanol and 1-decanol. We have estimated the mobility, Us, o f the carrier (dicetylphosphoric acid) in the m e m brane (Table I). The numerical value o f Us was f o u n d to be almost the same as that o f UK ( U s / U K ~ 0.9), regardless o f the property o f the m e m b r a n e solvent. In the m e m b r a n e , a dicetylphosphoric acid molecule moves with a velocity close to that o f a K ÷ ion, despite the fact that dicetylphosphoric acid is larger than K ÷. However, this does not seem unreasonable, because the carrier is a rodlike molecule and moves with the long axis in parallel to the direction o f flow, sliding s m o o t h l y in contact with the m e m b r a n e solvent. ACKNOWLEDGMENTS This study was supported by the Medical Research Service of the Veterans Administration, and NIH Grants

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GM25716, GM26950, and GM27670. The authors thank Mr. H. L. Blue for his assistance in preparing the manuscript. REFERENCES 1. Amman, D., Pretsch, E., and Simon, W., Anal Lett. 5, 843 (1972). 2. Garbett, K., Proc. Anal Div. Chem. Soc. (London) 12, 60 (1975). 3. Fiedler, U., Anal. Chim. Acta 89, 111 (1977). 4. Morf, W. E., and Simon, W., Helv. Chim. Acta 54, 2683 (1971). 5. Sandblom, J., Eisenman, G., and Walker, J. L., Jr., £ Phys. Chem. 71, 3862 (1967). 6. Sandblom, J., Eisenman, G., and Walker, J. L., Jr., £ Phys. Chem. 71, 3871 (1967). 7. Nomura, K., Matsubara, A., and Kimizuka, H., Bull. Chem. Soc. Japan 54, 1324 (1981). 8. Goldman, D. E., J. Gen. PhysioL 27, 37 (1943). 9. Ohshima, H., Nomura, K,, Kamaya, H., and Ueda, I., £ Colloid Interface Sci. 106, 470 (1985). 10. Sorensen, J. M., and Arlt, W., "Liquid-Liquid Equilibrium Data Collection, Binary Systems,"pp. 419519. Deutsche Gesellschaft ffir Chemisches Appartewesen, Frankfurt, 1979. 11. Pefferkorn, E., and Varoqui, R., J. ColloM Interface Sci. 52, 89 (1975). 12. Bockris, J. O. and Reddy, A. K. N., "Modern Electrochemistry," Vol. 1, pp. 48-72. Plenum, New York, 1973. 13. Latimer, W. M., Pitzer, K. S., and Slanski, C. M., J. Chem. Phys. 7, 108 (1939). 14. Ohki, S., Phys. Lett. A 75, 149 (1979). 15. Ohki, S., Physiol. Chem. Phys. 13, 195 (1981). 16. "TRC Tables," Vol. I. Thermodynamic Research Center Data Project, Thermodynamic Research Center, Texas A & M University, College Station, Tex., 1984. 17. "CRC Handbook of Chemistry and Physics" (R. C. Weast, and M. J. Astle, Eds.), pp. E52-E54. CRC Press, Boca Raton, Fla., 1981. 18. National Research Council ofU. S. A., "International Critical Tables of Numerical Data, Physics, Chemistry, and Technology," Vol. VII., pp. 211222. McGraw-Hill, New York, 1930. 19. Shkodin, A. M., Sadvonichaya,L. P., and Podolyanko, V. A., Ukr. Khim. Zh. 35, 144 (1969). 20. Robinson, R. A., and Stokes, R. H., "Electrolyte Solutions," 2nd Ed., p. 457. Butterworths, London, 1970.

Journalof Colloidand InterfaceScience,Vol.108,No. 2, December1985