Interfacial acid–base equilibrium and electrostatic potentials of model Langmuir–Blodgett membranes in contact with phosphate buffer

Colloids and Surfaces A: Physicochem. Eng. Aspects 171 (2000) 207 – 215 www.elsevier.nl/locate/colsurfa

Interfacial acid–base equilibrium and electrostatic potentials of model Langmuir–Blodgett membranes in contact with phosphate buffer Jordan G. Petrov a,*, Dietmar Mo¨bius b a

Institute of Biophysics, Bulgarian Academy of Sciences, 1 Acad. G. Bonche6 Str., Block 21, 1113 Sofia, Bulgaria b Max-Planck Institute of Biophysical Chemistry, P.O. Box 2431, D-37082 Go¨ttingen, Germany

Abstract The effect of a cationic Langmuir–Blodgett (LB) multilayer of varying thickness on pKi of the weak acid 4-heptadecyl-7-hydroxy coumarin (HHC) located at the multilayer-phosphate buffer interface is investigated. The amphiphilic fluorescent dye is embedded in a neutral methyl arachidate (MA) monolayer that has been deposited atop of the LB-film during dipping. Such a system is considered as an asymmetric model membrane built up of docosyl ammonium cations and phosphate counter-ions (HPO24 − ). Its electrostatic properties are compared with those of the previously studied LB-membrane of Cd-arachidate [1] consisting of arachidate anions and Cd2 + counter-ions. The fluorimetric titration of HHC in the neutral matrix at the multilayer-phosphate buffer interface shows that pKm/w at the membrane–water interface increases with increasing membrane thickness, reaching saturation at about 250 A, . The plateau of pKm/w =6.8 found for this system significantly differs from the plateau value of 10.6, observed for the Cd-arachidate multilayer-phosphate buffer boundary [1], and from pKa/w = 8.2 obtained at the air – phosphate buffer interface [2]. The shifts, DpKi =pKa/w −pKm/w, imply positive membrane – water Gouy – Chapman potentials for all studied thicknesses of docosyl ammonium phosphate (DCAP) multilayer, and negative cm/w potentials for all Cd-arachidate membranes. The plateau values, obtained for membranes more then 250 A, thick, are c m/w = + 81 and − 195 mV, respectively. Thus, the membrane– water interface appears charged, in spite of the presence of a neutral MA monolayer at the LB-film-phosphate buffer boundary. The cm/w/d dependencies can be well fitted with the equation cm/w =

c s/m +c m/w cosh(kd) sinh(kd)

describing the variation of the double layer potentials of asymmetric thin films with film thickness at constant surface charge densities [21a]. The fit of this equation to the experimental data for cm/w /d yields the Gouy – Chapman −1 potential at the glass-LB membrane interface, c , of the diffuse double layers at the s/m s/m and the Debye length, k and m/w interfaces. The values obtained show that the cationic membrane has two positively charged surfaces with different (small) charge densities, while the anionic membrane has a positive s/m and a negative m/w interface, both

* Corresponding author. 0927-7757/00/$ - see front matter © 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 7 - 7 7 5 7 ( 9 9 ) 0 0 5 5 8 - 0

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having large charge densities. The values of k − 1 enable estimation of the concentration of the free divalent charges in the membrane, which appear to be of the order of (4 – 5)× 1022 m − 3. The dipole potential at the interface cationic membrane–phosphate buffer is positive and linearly increases with increasing membrane thickness. It results from the different density of DCAP dipoles deposited on the solid substrate at dipping and withdrawal. For anionic membrane the density of Cd-arachidate dipoles in the adjacent monolayers is the same, and only the last MA monolayer contributes a small positive dipole potential that is independent on membrane thickness. © 2000 Elsevier Science B.V. All rights reserved. Keywords: Model membranes; Interfacial potentials; Langmuir – Blodgett-films; Interfacial pH-indicators; 4-Heptadecyl-7-hydroxy coumarin

1. Introduction It was shown in previous investigations that the interfacial dissociation constant pKi of the weak acid 4-heptadecyl-7-hydroxy coumarin (HHC), embedded in a neutral matrix of methyl arachidate (MA) at the solid – liquid interface, depends on the chemical composition of the solid substrate [3,1]. The substrates used were quartz or glass covered with a Langmuir – Blodgett (LB) monolayer [3] or multilayer [1], and the liquid phase was 10 − 2 M phosphate buffer. Such systems could be considered as simple asymmetric model membranes (with adjacent solid and liquid phases) whose molecular structure could be well characterized and varied in a controlled manner (Fig. 1). It was found that pKi of HHC in a MA matrix located at the membrane – water interface, pKm/w, differs from pKa/w at the interface air – water. The shift, DpKi =pKm/w −pKa/w, was different in sign, when the s/m and m/w interfaces (see Fig. 1) were separated by a cationic or an anionic monolayer

Fig. 1. Schematic presentation of the asymmetric model Langmuir – Blodgett membrane. s, glass substrate; m, LB-membrane with variable thickness d; w, phosphate buffer solution.

[3]. If a LB multilayer of Cd-arachidate deposited on silanated (hydrophobic) quartz was used as a spacer, pKm/w increased with increasing its thickness and reached saturation at 250 A, [1]. This dependence was interpreted as due to free bulk charges in the multilayer which give rise to diffuse double layers at the s/m and m/w interfaces. The membrane–water Gouy–Chapman potential, cm/w, resulting from the distribution of the free charges in the membrane, shifts the interfacial acid–base equilibrium of HHC compared to the air–water interface, because no free charges are present in air. The values of cm/w and pKm/w obtained for the asymmetric membrane vary with its thickness when the diffuse double layers at the s/m and m/w interfaces overlap and become constant when this thickness exceeds the doubled Debye length. In the present investigation the Cd-arachidate multilayer is substituted with a LB-film of docosyl ammonium phosphate (DCAP) and the interfacial pK of HHC and the electrostatic potentials of the two systems are compared. The present and the previous [1] model membranes have the same adjacent phases (glass and phosphate buffer) and the same neutral matrix monolayer of MA at the solid–liquid interface. However, they are built up of different surfactants; arachidic acid anions in Ref. [1], and docosyl ammonium cations in this study. Oppositely charged are also the incorporated counter-ions, Cd2 + , respectively, HPO24 − [4–6]. Therefore, if the chemical composition of the LB-multilayer determines the nature of the free charges in the membrane, the shifts, DpKi = pKm/w − pKa/w, and the Gouy–Chapman potentials, cm/w, should have different signs for the two systems compared. Checking this hypothesis

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mersed in the phosphate buffer during the following titration of HHC at the membrane–water interface. The deposition process was characterized by the transfer ratios defined as, t=

Fig. 2. Fluorescence intensity I, measured at 450 nm, vs. pH of the phosphate buffer being in contact with the membrane. One (), five () and nine ( ) monolayers of docosyl ammonium phosphate separate the glass surface from the last methyl arachidate + 4-heptadecyl-7-hydroxy coumarin monolayer at the membrane–water interface. The arrows show two inflection points of the titration curves observed for the cationic membrane.

might shed more light on the mechanism of charging of the neutral MA membrane – water interface and on the origin of the membrane potentials.

(1)

where GS and GL are the monolayer densities on the solid, respectively on the liquid substrate, DAL is the area that has been occupied by the transferred monolayer at the air–water interface, and AS is the solid surface area on which the LB deposition takes place. The fluorescence of HHC depends on the interfacial electrostatic potential that regulates pH and degree of dissociation of the dye at the interface. Therefore, monitoring the fluorescence intensity at the membrane-buffer boundary one can titrate HHC and determine its interfacial pKi [8]. The dye was excited at 366 nm, where its anionic form predominantly absorbs, and the fluorescence intensity at 450 nm, I, was measured as a function of pH of the phosphate buffer. The degree of dissociation was calculated from the formula

2. Materials and methods Docosyl ammonium chloride (DCA) has been synthesized and characterized as described in Ref. [7]. Merck methyl arachidate for chromatographic purposes and 4-heptadecyl-7-hydroxy coumarin purchased from Molecular Probes were used. The buffer solutions were prepared with Na2HPO4 or NaH2PO4 of AR purity and Milli-Q (Millipore) water. Their pH was adjusted with HCl and NaOH. DCA was spread as 1 mM chloroform solution on 1 ×10 − 2 M phosphate buffer of pH 7.5. After evaporation of the solvent the monolayers were compressed to 30 mN/m and transferred on hydrophilic glass slides at constant withdrawal (dipping) speed of 10 cm/min. LB-multilayers consisting of uneven number of monolayers of DCAP were built up in such a way. A mixed monolayer of MA+HHC with a molar ratio 400:1 was then transferred at 20 mN/m during dipping atop of the DCAP-multilayer. The asymmetric membrane thus obtained remained im-

GS DAL = GL AS

a=

I−Imin Imax − Imin

(2)

where Imin and Imax are the plateau values of I at low and high pH, corresponding to the undissociated and the anionic forms of HHC, respectively. For interfacial potentials that do not depend on pH, pKm/w is equal to the pH value at which a= 0.5 because HHC is a monobasic acid in the studied pH-interval [9]: pKi = pH− log

a 1− a

(3)

3. Results and discussion

3.1. Fluorimetric titration of HHC in neutral MA matrix located at the cationic membrane–phosphate buffer interface Fig. 2 shows some of the titration curves for HHC in MA matrix atop of LB-films containing

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one, five and nine monolayers of DCAP. They show two inflection points (see the arrows), while only one inflection was observed for HHC in the same matrix titrated atop of Cd-arachidate multilayers [1]. The two inflections for the cationic membrane do not result from different ionization equilibriums of HHC, because this dye dissociates as a monobasic acid in the investigated pH range [9]. They might originate from adsorption or penetration of different phosphate ions from the liquid phase at/into the membrane. The cationic model membrane consists of n DCAP monolayers and a MA monolayer, so that its thicknesses d can be presented as: (4)

d=ndDCAP + dMA

The DCAP and MA monolayers have been deposited in a solid condensed state, so that their molecules are closely packed and vertically oriented. Therefore, one can substitute the monolayer thicknesses, dDCAP and dMA, with the corresponding all-trans molecular lengths. This gives dMA = 27.5 A, . dDCAP was calculated from the formula: 2dDCAP =2dNH+ +dHPO2 − +42dCH2 +2dCH3 3

4

(5)

Eq. (5) reflects the structure of the DCAP multilayers proposed on the basis of IR data in Ref. [10]; it shows that the HPO24 − anions form a single layer between the NH3 + heads of the adjacent monolayers. dNH+ was estimated from the 3 , ) and the radius of crystal radius of NH+ 4 (1.5 A

Fig. 3. Dependence of pKm/w on the membrane thickness d obtained from the titration curves below the first plateaux.

HPO24 − was taken 3.0 A, , assuming that it is close to the crystal radii of SO24 − and CrO24 − [11]. X-ray diffraction values of dCH2 = 1.27 A, and dCH3 = 1.42 A, were used [12]. This combination of data yields dDCAP = 32.6 A, . If one assumes that the membrane–water potential remains constant up to the pH value corresponding to the first plateau of the titration curves one could evaluate pKm/w from Eqs. (2) and (3). The dependence of pKm/w on membrane thickness, obtained in such a way, is shown in Fig. 3. The previously found value of pKm/w =6.2 for one monolayer of eicosylamine phosphate deposited on glass was also included [3]. One can see that pKm/w increases with increasing d and reaches saturation at about 250 A, .

3.2. Diffuse double layer potential at the membrane–buffer interface pKa/w of HHC in the same MA matrix monolayer, but located at the air–water interface is 8.2 [2]. This value is by 0.6 units larger than the bulk one, pKb = 7.6, determined in Ref. [13] for the soluble 4-methyl-7-hydroxy coumarin (MHC) in 10 − 2 M phosphate buffer. According to the commonly accepted interpretation this difference is due to the location of the chromophore of HHC at the interface where the dielectric constant is lower than the dielectric constant of bulk water, ob = 78. From the interfacial value of pKa/w and the dependence pKb = f(ob) obtained for MHC in dioxan-water mixtures [14] one finds that pKa/w = 8.2 corresponds to oa/w = 45. The asymmetric LB-membrane investigated in this study has the same last MA+ HHC monolayer contacting with the same liquid phase. Therefore, one can assume that the water structure at the m/w and a/w interfaces is the same, and om/w = oa/w = 45. Then the observed difference pKm/w − pKa/w represents the pure effect of the distribution of free charges in the membrane giving rise to the Gouy–Chapman, cm/w. As shown in Ref. [1], cm/w can be determined from the equation: pKm/w − pKa/w = − Fcm/w/2.3RT

(6)

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orientation is the same [1]. When GS at dipping and withdrawal is different, GS,¡ − GS,  gives the number of uncompensated dipoles per cm2 of a bilayer with contacting head groups:



GBL = GS,¡ − GS,  = GL

Fig. 4. Gouy –Chapman potential at the membrane – water interface, cm/w, vs. membrane thickness d. cm/w was evaluated from the shifts of pKm/w with respect to pKa/w at the air – water interface.

Fig. 5. Transfer ratios of docosyl ammonium phosphate monolayers at withdrawal and dipping (the top of the triangles shows the direction of the solid substrate motion).



1 1 − t¡ t 

(7)

Fig. 5 shows that the transfer ratios at withdrawal, t , exceed those at dipping, t¡, so that GS,¡ \ GS,  for the present system Therefore, the uncompensated dipoles are located in the even layers deposited at dipping and have their center of negative charges (phosphate anions) closer to the liquid phase and center of positive ones (ammonium groups) closer to the solid. This orientation is the same as in the solid condensed monolayer of DCAP at the air–water interface and corresponds to positive dipole potentials and dipole moments [15]. Summation of GBL for all deposited bilayers gives the number of uncompensated dipoles per cm2 of the LB-film, GLB, reduced by the dipole density in the first monolayer deposited on glass, G1. Unfortunately, G1 cannot be specified, because the attachment mechanism of the first DCAP monolayer to the hydrophilic glass surface is unknown. For this reason GLB − G1 = GBL versus n is plotted in Fig. 6. It can be seen that GLB −G1 linearly increases with n (correlation coefficient 0.9997) with a slope 0.79× 1014 cm − 2 giving the effective contribution of each DCAP monolayer to the total number of dipoles in the membrane.

Fig. 4 presents the dependence of cm/w on the membrane thickness d obtained via substitution of the data from Fig. 3 in Eq. (6). It shows that all cm/w values are positive and decrease with increasing d. A saturation at 81 mV is observed above 250 A, .

3.3. Uncompensated dipoles and dipole potential of the cationic model membrane Fig. 5 shows the transfer ratios at withdrawal and dipping versus the number of deposited DCAP monolayers, n. For an Y-type of deposition the adjacent monolayers have opposite dipoles that cancel each other if their density and

Fig. 6. Number of uncompensated dipoles per cm − 2 of the Langmuir – Blodgett film, GLB, reduced by the density of dipoles in the first monolayer deposited on glass, G1, vs. number of deposited monolayers, n.

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Neglecting the interlayer polarization one can present the total transversal polarization of the membrane, PÞ,m, as a sum of the polarizations of the first DCAP monolayer, the subsequent DCAP bilayers and the last MA monolayer: (8)

PÞ,m = PÞ,1 +% PÞ,BL +PMA i

Each component of PÞ,m is equal to the dipole moment per unit volume of the corresponding part of the membrane: PÞ,m =

mÞ,1G1 + dDCAP

mÞ,BL % GBL i

+

% dBL

mÞ,MAGMA dMA

(9)

i

mÞ,BL is the normal dipole moment component of a DCAP molecule in the deposited bilayer. The dipoles in the first DCAP layer are oppositely oriented to those in the last MA monolayer and mÞ,1 and mÞ,MA have different signs. The same holds for the first and the third terms of the right hand side of Eq. (9), so that the main contribution to the total polarization of the membrane is the one of the DCAP bilayers given by the second term. Utilizing the flat capacitor model we obtain the potential difference across the membrane resulting from the fixed uncompensated dipoles in it: P d DVm,dip = % Þ,i i oio0 i =

mÞ,1G1 + o1o0

mÞ,BL % GBL i

oBLo0

+

mÞ,MAGMA oMAo0

(10) It is assumed that the first term giving the contribution of the first DCAP monolayer deposited on glass is the same, but with a negative sign as the effective contribution of each of the next monolayers. The third term is substituted by DVMA,L =550 mV, determined for a MA monolayer of the same density and molecular orientation at the air – phosphate buffer interface [16]. To evaluate the main second term the density of uncompensated dipoles in a bilayer GBL can be calculated from Eq. (7) and the normal component of the molecular dipole moment of DCAP

in the bilayer, mÞ,BL, can be substituted with the molecular dipole moment of DCAP in a solid condensed monolayer at the air–phosphate buffer interface, mÞ,L. The latter can be obtained from previous experimental data [15], namely DVL = 785 mV, ca/w = 85 mV and GL = 4.85× 1014 cm − 2, and the formula for a flat capacitor DVL = ca/w +

mÞ,LGL o mo 0

(11)

Adam and coworkers [17] assumed, that the dielectric constant of a solid condensed monolayer, om, is between 5 and 10. These limits give mÞ,L between 1.9 and 3.8 D. Helmholtz postulated om = 1. This value results in dipole moments that are much smaller than the expected from the summation of the dipole moments of the chemical bonds. Davis and Rideal [18] and Demchak and Fort [19] removed this discrepancy considering the monolayer as a three-layer capacitor: DVL = ca/w +





m1 m2 m3 + + G /o o1 o2 o3 L 0

(12)

The subscripts 1, 2, 3 indicate the regions of hydration water, head groups and hydrocarbon chains, respectively. Different authors have reported different values for m1/o1, o2 and o3 [19– 21], but their substitution in Eq. (12) together with the above data for DVL, ca/w and GL gives practically the same result for a DCAP monolayer, namely m2 + m3 = 2.59 0.1 D. Deposited LB monolayers and Langmuir monolayers at the air–water interface with the same density and molecular orientation differ by the contribution of hydration water, m1/o1, if polarization of the adjacent layers is neglected. In such a case m2 + m3 should be representative for mÞ,BL in the LB-membrane, and oBL can be taken as an average of o2 = 7.6 and o3 = 5.3 reported in Ref. [17]. Thus, substituting in Eq. (10) the effective dipole density of a monolayer in the membrane for G1 = 0.79× 1014 cm − 2 (Fig. 6), mÞ,1 = −2.5 D, mÞ,BL = 2.5 D, GBL from Fig. 6, o1 = oBL = 6.4, and mÞ,MAGMA,L/oMAo0 = DVMA,L = 550 mV, DVm,dip is obtained. The plot of DVm,dip versus d is shown in Fig. 7.

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3.4. Comparison of the Gouy–Chapman and total interfacial potentials of the cationic and anionic model membranes

Fig. 7. Dipole potential of the cationic membrane, DVm,dip, calculated from the number of the uncompensated dipoles in the Langmuir –Blodgett multilayer, molecular dipole moment and dielectric constant estimated from the three-capacitor model of Demchak and Fort [19].

Figs. 8 and 9 compare cm/w and the total interfacial potentials, Fm/w = DVm,dip + cm/w, of the cationic and anionic model membranes. The DCAP membrane exhibits positive Gouy–Chapman potentials at the neutral interface between the MA monolayer and phosphate buffer, which decrease with increasing of d. For the Cd-arachidate multilayer, cm/w is negative and increases in absolute value (becomes more negative) with increasing of d. Plateau values of + 81 mV, respectively − 195 mV, are achieved at the same thickness of about 250 A, . Both total potentials at the membrane–water interface are positive, but the Fm/w/d dependencies for the cationic and anionic membrane have opposite trends. This is due to the significant difference of the dipole components. For the cationic system DVm,dip is large and increases with d, because each deposited DCAP bilayer adds uncompensated dipoles. The Cd-arachidate multilayer does not contain uncompensated dipoles, because the monolayer density at dipping and withdrawal is the same. Only the last MA monolayer gives rise to DVm,dip that is small and independent of d.

3.5. Comparison of the experimental data with some theoretical predictions Tredgold and Smith [22] solved the Poisson’s equation for a LB multilayer being in contact with air. They considered fixed dipoles causing a total polarization Pm of the multilayer and bulk charges with density Cm creating a diffuse double layer at the multilayer–air interface. Their solution predicts the following dependence of the total interfacial potential Fm/a on multilayer thickness: Fm/a = Fig. 8. Total interfacial potential, Fm/w = DVm,dip +cm/w, and its Gouy – Chapman component, cm/w, at the membrane – water interface versus the thickness of the cationic membrane, d. The solid line shows the fit of Eq. (14) at fixed c m/w =81 mV and Debye length k − 1 = 50 A, . The fit gives c s/m = 25 9 5 mV.

Pmd eCm 2 + d omo0 2omo0

(13)

The first term on the right hand side stays for the dipole potential presented in more details by Eq. (10). The second term gives the dependence of the Gouy–Chapman potential on the thickness and bulk charge density of the multilayer. In the

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previous study [1] it has been shown that the experimental cm/w/d data for the Cd-arachidate system do not follow Eq. (13). Here another theoretical expression is fitted to the experimental cm/w/d data for the cationic and anionic systems (see the solid lines in Figs. 8 and 9). This is the equation cm/w =

c s/m +c m/w cosh(kd) sinh(kd)

(14)

describing the variation of the diffuse double layer potentials of an asymmetric thin film with its thickness at constant surface charge densities [23,24]. The fits with c m/w =81 mV for DCAP and c = −195 mV for Cd-arachidate respecm/w tively, gave the potentials, c s/m, at the interface

solid substrate-LB-membrane when d“ , and the Debye lengths, k − 1. The cm/w/d dependence for the anionic membrane is very well represented by Eq. (14) giving c s/m = 2079 5 mV mV and k − 1 = 559 3 A, . The coincidence between the experimental cm/w/d data for the cationic membrane and this relationship is worse; the two free parameters are obtained with significant uncertainties. The situation improves if recall that dsat : 250 A, for both systems and fix k − 1 : 50 A, . With such reduction of the number of the free parameters for the cationic membrane one obtains c s/m = 259 5 mV. The above presentation of the cm/w/d data implies another expression for the total interfacial potential of the asymmetric model membranes that should be fulfilled when the interfacial charge densities remain constant at varying membrane thickness: n

Fm/w = % 1

mÞi Gi c +c s/m cosh(kd) + s/m oio0 sinh(kd)

(15)

3.6. Bulk and interfacial charge densities of the cationic and anionic membranes The diffuse double layers at the s/m and m/w interfaces overlap at small membrane thicknesses and the interfacial potentials, cs/m and cm/w vary with membrane thickness as shown in Figs. 8 and 9. If one assumes that the thickness at which cm/w comes to saturation, dsat : 2k − 1, and that the free charges in the membrane are divalent ions their density Cm can be determined substituting this relationship in the expression for the Debye length [25]: k−1 =

Fig. 9. Total, Fm/w, and Gouy–Chapman, cm/w, interfacial potentials at the membrane–water interface vs. the thickness of the anionic membrane (cm/w/d data from Ref. [1]). The solid line represents the fit of Eq. (14) at fixed c m/w = −195 −1 mV. The fit gives c = 559 3 A, . s/m = 2079 4 mV and k

'

omo0kT 2z 2e 2Cm

(16)

For om = 6.4 and 25°C one finds Cm : 7.4×1021 m − 3. This estimation, although rather rough, has the advantage of not being related to any particular mechanism causing the dependence of cm/w on d. One can determine Cm from Eq. (16) utilizing the values of k − 1 obtained from the fit of Eq. (14) which presumes that the interfacial charge densities are independent on membrane thickness.

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Table 1 Comparison of the Gouy–Chapman potentials and interfacial and bulk charge densities of the asymmetric cationic and anionic model membranes System

c s/m (mV)

c m/w (mV)

ss/m (C/m2) or (A 2/charge)

sm/w (C/m2) or (A 2/charge)

Cm (m−3)

Cationic (DCAP) membrane Anionic (Cd-arachidate) membrane

+25 +207

+81 −195

+3.3×10−4 (48 500) +0.41 (39)

+3.4×10−3 (4700) −0.26 (61.5)

4.5x1022 3.7x1022

Thus, one finds Cm =(3.7 9 0.5) × 1022 m − 3 for the anionic system (k − 1 =55 93 A, ) and Cm : 4.5× 1022 cm − 3 for the cationic system (k − 1 : 50 A, ). ss/m and sm/w can be evaluated from the Gouy– Chapman’s theory [26]:

References [1] [2] [3] [4] [5]

zec s/m ss/m = 8omo0kTCm sinh 2kT sm/w = 8omo0kTCm sinh

zec m/w 2kT

[6] [7]

(17)

The values thus obtained for z =2 (divalent charge carriers), the corresponding Gouy–Chapman potentials and the bulk charge densities of the cationic and anionic membrane are presented in Table 1. They show that both the s/m and m/w interfaces of the cationic membrane are positively charged, but carry different charge densities. The anionic membrane has a positive s/m and a negative m/w interface with charge densities that are by two or three orders of magnitude bigger.

[8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19]

Acknowledgements

[20]

J. Petrov thanks the Alexander von Humboldt foundation for the scholarship that enabled this investigation at the Max-Planck Institute of Biophysical Chemistry. The authors thank Mrs Gisela Debuch and Mr Werner Zeiss for their skillful professional help. A part of the work was done at the Institute of Biophysics of the Bulgarian Academy of Sciences and was supported by grant No K-417 of the Ministry of Education, Science and Technology.

[21] [22] [23] [24] [25]

[26]

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