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Journal of Membrane Science 282 (2006) 89–95

Electrical double layer at the peritonealmembrane/electrolyte interface

Nurul Islam ∗, Nisar A. Bulla, Shahina IslamDepartment of Chemistry, Aligarh Muslim University, Aligarh 202 002, UP, India

Received 30 March 2006; received in revised form 30 April 2006; accepted 2 May 2006Available online 10 May 2006

bstract

The resistance (Rx) and capacitance (Cx) in aqueous NaCl solutions across peritoneal membrane of young buffalo were recorded as functionsf concentration, temperature, and frequency. The values of membrane resistance (Rm), capacitance (Cm), reactance (Xx), and impedance (Z) wereomputed. The pattern of Rx, Rm, Xx, and Z, with electrolyte concentration is similar to each other irrespective of their variations with temperaturer applied frequency. The values of electrical double layer capacitance (Cd) were calculated. Plots of Cd versus square root of NaCl concentrationave straight line. The increase in capacitance with increases in concentration and temperature is rapid in the low concentration range and slowsown with successive increases in concentration. These values, however, decrease with increase in applied frequency. Z-values record decrease

ith increases in electrolyte concentration and applied frequency. Increase in electrolytic concentration facilitates the permeation of ions acrosseritoneal membrane. This may be ascribed to the accumulation of ions within the membrane as well as to the electrical double layer formed byhe counter ions at the membrane/electrolyte interface.

2006 Elsevier B.V. All rights reserved.

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eywords: Peritoneal membrane; Capacitance; Electrical double layer; Transpo

. Introduction

The peritoneal microcirculation and peritoneal exchangeccurring in peritoneal dialysis have been reported recently [1].he peritoneal interstitium, coupled in series with the capil-

ary walls, markedly modifies small-solute transport and makesarge-solute transport asymmetric. Thus, although severelyestricted in the blood-to-peritoneal direction, the absorption ofarge solutes from the peritoneal cavity occurs at a high clear-nce rate. Several controversial issues regarding transcapillarynd transperitoneal exchange mechanisms are discussed in thisaper [1]. Aquaporins: roles in renal function and peritonealialysis have also been reported recently [2]. Furthermore, theemodialytic therapies have evolved from the simple, diffusion-

ependent removal of small molecular weight substances fromlood to advanced therapy modalities involving the convectiveemoval of larger uremic solutes [3]. Several investigators have

∗ Corresponding author at: 4/1311, New Sir Syed Nagar, Aligarh 202 002, UP,ndia. Tel.: +91 571 2404788.

E-mail addresses: nxi7@hotmail.com, islamziaul@rediffmail.comN. Islam).

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376-7388/$ – see front matter © 2006 Elsevier B.V. All rights reserved.oi:10.1016/j.memsci.2006.05.007

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tudied the ionic permeability and properties of electrical dou-le layer near the interface between a membrane and electrolyteolution. They have proposed models for understanding the dou-le layer interaction. The electrical double layer formed at theembrane/electrolyte interface is expected to influence and con-

rol the transport of ions as found by these investigators [4–7].t has also been found to be one of the main factors for theelaxation time in electro-osmosis [8–10]. Similarly, the mea-urements of impedance of ionic systems across the membranesrovide valuable data of relevance [10–18]. Lakshminarayana-ah and Siddiqi [19] have discussed the importance of impedanceeasurements, characteristics of polysterene–sulphonic acid

nd interpreted the data in terms of resistance and capacitanceharacteristics of simple membranes. The capacitance and con-uctance measurements were employed to investigate the trans-ort behaviour of ions in many active and passive membranes.uch studies have revealed that the effects of electrolyte con-entration and frequency on the membrane capacitance may be

ue to some structural changes in the membrane rather than thelectrode polarization [20,21].

In addition, passive water transport in biological pores [22]nd comparison of the behaviour of water in different narrow

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0 N. Islam et al. / Journal of Me

ransmembrane pores suggest that an amphipathic-pore is idealor water permeation. Furthermore, either a highly hydropho-ic pore lining or a charged pore-lining region can act as aate [23]. It is suggested that the water permeability is deter-ined from chemical associations between the water molecule

nd sites within the pore, probably in the form of hydrogenonds. The existence of passive water permeability suggestsn alternative model for the molecular water pump; in par-icular of how epithelial cell layers can transport water uphill24].

The effect of interactions in the head groups on the mono-ayer structure and permeability [25] has revealed that theurface layer of the monolayer structure expands and thus,ecreases the thickness of the hydrocarbon layer and increaseshe electrical capacitances. At higher concentrations the exces-ive expansion of hydrocarbon layer increases the tendency toorm micelles, which result in the alteration in the monolayerith increase in ionic permeability [25]. Koji and Takashima

26] have investigated the membrane admittance of culturedyoblasts muscle cells, which indicates that the capacitance

nd conductance of myotube membrane are frequency depen-ent.

The recent studies on the importance of electrical doubleayer include the double layer capacitance dependency on thelectrolyte concentration resulting in a better description of thempedance of sensors [27]. Similarly, the linear-scan voltam-

etry turns out to be the best choice, which can cope withhe double-layer capacitance and severe uncompensated resis-ance [28]. In addition, Mueller and Hirthe [29] have pro-osed models for the equivalent electrical circuits for consol-dated silver and dispersed-phase amalgam involving a doubleayer capacitance, a charge transfer resistance, and an elementttributed to adsorption. Miles and Murray [30] have studiedhe temperature-dependent quantized double layer charging ofonolayer-protected gold clusters. Abragaryan et al. have stud-

ed the distribution of potential on the membrane–electrolyteolution interface [31]. Binder and Lindblom have investigatedhe interaction of the cell-penetrating peptide penetratin withipid membranes as a function of the content of anionic lipid. Theork was aimed at understanding factors, which affect peptideinding to the membranes and its permeation through the bilayer32–34]. Furthermore, the computer simulation studies of modeliological membranes made recently [35] have shown that thelassical molecular dynamics has provided novel insights intohe properties of model biomembrane systems. These include theature of DNA–lipid interactions, the effect of pore-forming [36]ransmembrane peptides on the lipid environment, and the parti-ioning of volatile anesthetic molecules. Simulations conductedt the cell level and with credible numerical values demon-trate that the enzymes positions strongly regulate the membraneermeability for the transported substrate. Depending on bothhe enzymes positions and the membrane charges, the mem-rane may appear either impervious, either permeable or able to

ctively transport a phosphorylated substrate. Globally all hap-ens as if, in function of the enzymes positions, a permeant poreay be regulated, changing from a more closed to a more open

onformation [37].

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ne Science 282 (2006) 89–95

The various utilities of peritoneal membrane are well known1–3]. These include the dialysis in treating patients of uremia.imilarly, the importance of electrical double layer of variedature at the biomembrane/electrolyte interface is equally wellnown. In view of these considerations, the recent studies ofonductance of electrolytes across peritoneal membrane [38]ave been extended. This has been done by taking NaCl asne of the representative cases of the electrolytes studied. Forhis purpose, measurements of resistance and capacitance ofqueous NaCl solutions have been made over the temperatureange: 15–35 ◦C and frequency range: 102–104 Hz. These mea-urements were employed to compute the values of membraneesistance, capacitance, reactance, and impedance as functionsf concentration and frequency. In addition, the values of elec-rical double layer capacitance were computed as a function ofoncentration. The impedance values may be employed to under-tand the mechanism of ionic transport due to the changes pro-uced in the electrical double layer at the membrane/electrolytenterface.

. Materials and methods

Sodium chloride has been taken as one of the represen-ative cases of the fifteen electrolytes for which the specificonductance measurements were reported earlier [38]. NaCl ofnalytical grade (BDH) was used after the usual purification forreparing aqueous solutions in triply distilled water. The fresheritoneal membrane of young buffalo (aged 18–24 months)as obtained from the local abattoir. Its pieces were preserved

n ice-cold Ringer’s solution of pH 7.4. These were washed sev-ral times with distilled water before placing each piece betweenwo halves of the cell. The cell assembly was immersed in a ther-

ostated bath maintained at 25 ± 0.01 ◦C. The resistances andapacitances of aqueous solutions of NaCl were measured bysing an LCR bridge (Elico, Hyderabad).

. Results and discussion

The values of resistance and capacitance measured in aque-us solutions of NaCl across peritoneal membrane at severalemperatures and frequencies are given in Table 1. These resultseveal that the resistance decreases with increases in concentra-ion of NaCl and applied frequency. An increase in temperaturelso causes decrease in the resistance, Rx values. On the oneand, an increase in concentration of the electrolyte causes arogressive accumulation of ionic species within the membrane.onsequently, the membrane becomes increasingly more con-ucting to these ions. This accounts for the decrease in theesistance values. On the other hand, an increase in applied fre-uency results in a fast exchange of polarity between the ionsnd the membrane material. This, in turn, causes the leakage ofhe membrane and thus, decreases the resistance. The biomem-ranes can exist in different structural phases. They seem to

ave liquid crystalline structure at higher temperatures. Theyave loose packing, high fluidity, and high rate of in-planeiffusion of proteins and phospholipids. But at low tempera-ures, the membrane appears to be in gel phase, being more

N. Islam et al. / Journal of Membrane Science 282 (2006) 89–95 91

Table 1Observed values of resistance (Rx, k�) and capacitance (Cx, �F) in aqueous solutions of NaCl across peritoneal membrane as functions of concentration (mol/l),temperature (◦C), and frequency (Hz)

◦C mol/l

0.001 0.002 0.005 0.01 0.02 0.05 0.1 0.2

Resistance (Rx, k�) for several concentrations of NaCl in mol/l15 5.30 4.70 2.30 0.91 0.62 0.24 0.093 0.06820 5.10 4.50 2.00 0.78 0.58 0.15 0.086 0.06125 4.70 4.20 1.80 0.72 0.48 0.12 0.08 0.05530 4.50 3.80 1.60 0.58 0.36 0.10 0.07 0.04635 4.20 3.60 1.30 0.46 0.33 0.09 0.062 0.038

Capacitance (Cx, �F) for several concentrations of NaCl in mol/l15 0.014 0.029 0.048 0.078 0.091 0.38 0.62 0.8520 0.016 0.031 0.050 0.08 0.094 0.41 0.65 0.8725 0.019 0.033 0.053 0.083 0.097 0.45 0.67 0.8930 0.022 0.035 0.055 0.087 0.10 0.48 0.69 0.9235 0.025 0.038 0.059 0.091 0.15 0.52 0.72 0.95

Hz 0.001 0.002 0.005 0.01 0.02 0.05 0.1 0.2

Resistance (Rx, k�) for several concentrations of NaCl in mol/l at 25 ◦C102 4.70 4.20 1.80 0.72 0.48 0.12 0.08 0.055103 4.50 4.00 1.60 0.69 0.46 0.10 0.075 0.053104 4.30 3.90 1.40 0.67 0.44 0.08 0.07 0.05

Capacitance (Cx, �F) for several concentrations of NaCl in mol/l at 25 ◦C102 0.019 0.033 0.053 0.083 0.097 0.45 0.67 0.89103 0.017 0.031 0.051 0.080 0.094 0.43 0.63 0.85

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104 0.015 0.027 0.048 0.077

estrictive to the permeants. Thus, an increase in temperatureesults in a corresponding decrease in resistance. In general, anrrhenius or a non-Arrhenius equation may adequately describe

he behaviour of ionic transport. The type of equation applica-le to a system depends on whether the ionic species are inheir native form or in several possible hydrated forms [39].r else, there are interionic/intermolecular interactions of var-

ed nature in the medium of electrolytic systems. In case theystems are exhibiting an apparently ideal behaviour, Arrhe-ius type of equation may turn out to be reasonably suitableor describing the transport behaviour. However, in the presencef interionic/intermolecular interactions, the non-Arrhenius, aolynomial equation, or apparently an exponential equation [7]ay describe such a behaviour. The non-ideal behaviour appar-

ntly seems to be the case here. A close examination of theselots reveals that initial decrease in the experimental Rx val-es with increase in NaCl concentration is quite fast, the slopealue of which is reasonably high. With successive increasesn solute concentration, the decrease in Rx values slows downnd eventually approaches an almost constant value with slopealue close to zero. This suggests that a saturation point haseached when pores are not easily available for ionic diffusions reported for the specific conductance of dilute solutions [38].he said slope values may represent the outcome of the twotraight lines. One is drawn in such a way that it connects the fast

ecreases while the other connects those of almost no changen Rx values. Consequently, they meet at a sort of thresholdoncentration or the turning point of fast to almost no changen the Rx values. In addition, it is also noteworthy that there

iooa

0.091 0.39 0.59 0.81

s no change in the pattern as well as in the trend of theselots of Rx irrespective of whether their values were recordedt several temperatures or at varied frequencies. On the otherand, the experimental capacitance increases with increases inoncentration and temperature like those of specific conduc-ance (κ). This may be attributed to the changes produced inhe dielectric constant (ε) and the effective thickness (d) of theembrane/electrolyte interface. Increase in temperature causes

ecrease in the values of d, which in turn, increase the valuesf Cx. This is in accordance with the equation for the parallellate capacitor: Cx = ε/36 × 104d. Thus as envisaged, the capac-tance increases with increase in the dielectric constant as wells with decrease in the effective thickness of the membrane.n increase in the electrolyte concentration results in an accu-ulation of ions within the membrane. This causes decrease

n the effective thickness of the membrane due to squeezingf water molecules from the membrane by the incoming ions.onsequently, the capacitance increases with increase in elec-

rolyte concentration. In visualizing the trend of variation inhe behaviour of experimental or computed data at a glance,he graphical display supplements the tabulated results. Such

graphical display of data is expressed in terms of the rele-ant best-fit parameters, which may not necessarily be translatednto or correlated to some physical quantity. These parametersimply represent the best way to reproduce the plot(s) of exper-

mental/computed values if and when so desired. In the lightf such a consideration, the second-order best-fit plots (Fig. 1)f Cx with concentration of NaCl solutions at 15, 20, 25, 30,nd 35 ◦C were made and the relevant coefficients of which are

92 N. Islam et al. / Journal of Membrane Science 282 (2006) 89–95

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ig. 1. Best-fit plots of observed values of capacitance, Cx vs. concentration ofaCl at 15, 20, 25, 30, and 35 ◦C.

iven below:

b[0] = −2.9645 e − 3; b[1] = 8.1487; b[2] = −19.3845;

and r2 = 0.9933;

b[0] = −3.8833 e − 3; b[1] = 8.7274; b[2] = −21.7647;

and r2 = 0.9919;

b[0] = −2.5578 e − 3; b[1] = 9.2301; b[2] = −23.8509;

and r2 = 0.9888;

b[0] = −1.4739 e − 3; b[1] = 9.6164; b[2] = −25.0868;

and r2 = 0.9866;

b[0] = −6.0804 e − 3; b[1] = 10.2468; b[2] = −27.7465

and r2 = 0.9900.

t so happens that these plots seem to quantify the overallehaviour.

In order to study the mechanism of flow of ions throughhe membrane, the impedance, Z along with the mem-rane resistance, Rm and membrane capacitance, Cm haveeen evaluated employing the equation proposed by Lak-hminarayanaiah and Shanes [40] for an equivalent circuitodel: Rm = Rx[1 + (Xx/Rx)2]; Cm = (Xx/Rx)(1/ωRm). The reac-

ance, Xx = 1/ωCx, in whichω = 2πf and f is the applied frequencysed to measure Rx and Cx. It is noteworthy that at relatively highoncentrations where the overall transport kinetics are domi-ated by the interactions between the ion species and the ionhannel protein, the resistance of the bulk electrolyte solutionn the equivalent circuit might not be of much significance.t relatively low concentration the overall transport rate mighte, however, diffusion-limited. For instance, the ratio of R in

.001 M at 25 and 35 ◦C is 4.7/4.2 = 1.11, which is very sim-lar to that of diffusion. In 0.2 M this same ratio increases to.055/0.038 = 1.44, which indicates the presence of rate limit-ng process rather than that of pure diffusion. The plots of Rx

BiT

ig. 2. Best-fit plots of Cx vs. concentration of NaCl at 102, 103, and 104 Hz.

s well as of Xx at the three frequencies: 102, 103, and 104 Hzesemble the Rx plots recorded at several temperatures (theselots are not shown here). Thus, the values of Rx, Xx, Z (as men-ioned below), and Rm obtained experimentally or computedheoretically at either varied temperature or applied frequencyesemble in the pattern of their behaviour with concentrationf NaCl. Consequently, they may be interpreted in a similaranner.The second-order best-fit plots of Cx versus [NaCl] at 102,

03, and 104 Hz are shown in Fig. 2. The corresponding coeffi-ients of the regression equation are:

b[0] = −2.8125 e − 3; b[1] = 9.2360; b[2] = −23.8748;

and r2 = 0.9889;

b[0] = −1.4088 e − 3; b[1] = 8.6872; b[2] = −22.1826;

and r2 = 0.9887;

b[0] = −7.5199 e − 4; b[1] = 7.9779; b[2] = −19.6382;

and r2 = 0.9913.

imilarly, the values of Cm plotted (Fig. 3) against [NaCl] werelso fitted to the second-order regression equation and the rele-ant coefficients are given below:

b[0] = −0.0196; b[1] = 81.1659; b[2] = −191.1693;

and r2 = 0.9926;

b[0] = 4.0976 e − 3; b[1] = 6.7637; b[2] = 7.3726;

and r2 = 0.9805;

b[0] = −8.1101 e − 5; b[1] = 0.1141; b[2] = 0.0619;

and r2 = 0.9762.

y employing the relation: Z = [R2x + X2

x]1/2

, the values ofmpedance have been obtained (Table 2). An examination ofable 2 indicates that the values of impedance decrease with

N. Islam et al. / Journal of Membra

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ig. 3. Best-fit plots of Cm × 103 vs. concentration of NaCl at 102, 103, and04 Hz.

ncreases in electrolyte concentration and applied frequency.his suggests ease in the flow of ions across the membrane.

The electrical double layer theory may also be employed tonterpret the changes produced in the magnitude of the mem-

rane capacitance with changes in electrolyte concentration41]. Such a consideration has been applied to account for theembrane behaviour of varied nature [4–7]. The electrical dou-

le layer capacitance can be evaluated [12,42–45] by employing

dcCa

able 2omputed values of (i) resistance (Rm, k�), (ii) capacitance (Cm × 103, �F), (iii) reaccross peritoneal membrane as functions of concentration (mol/l) and frequency (Hz)5) for several concentrations (mol/l)

z mol/l

0.001 0.002 0.005 0.01

i) Rm values in k� for several concentrations of NaCl in mol/l102 19.71 9.69 6.80 5.73103 4.69 4.07 1.66 0.75104 4.302 3.901 1.401 0.671

ii) Capacitance (Cm × 103, �F) for several concentrations of NaCl in mol/l102 0.144 0.188 0.463 0.733103 0.00106 0.00502 0.0188 0.0612104 0.912 × 10−4 0.616 × 10−4 0.269 × 10−3 0.733 × 1

iii) Reactance (Xx × 102, k�) for several concentrations of NaCl in mol/l102 8.4 4.8 3.0 1.9103 9.36 5.13 0.313 1.99104 0.106 0.0589 0.0332 0.0207

iv) Impedance (Z, k�) for several concentrations of NaCl in mol/l102 9.63 6.38 3.50 2.03103 4.60 4.03 1.63 0.72104 4.301 3.9004 1.4004 0.6703

v) Electrical double layer capacitance (Cd, �F) for several concentrations of NaCl in7.199 10.18 16.10 22.77

ne Science 282 (2006) 89–95 93

ssentially the expression of the proposed equivalent circuit forhe membrane/electrolyte interface:

2Rt/(1 + jωCdRt)] + [Rb/(1 + jωCgRb)]

= [Rm/(1 + jωCmRm)] (1)

here Cg is the specific geometric capacitance, which isssumed to depend upon the structural details of the membraneramework, Cd is the interfacial double layer capacitance, Rbs the bulk resistance of the membrane, and Rt is the chargeransfer resistance between the membrane/electrolyte interfacessuming the transfer to be a single step process. Eqs. (2) and3) are the real and imaginary parts of Eq. (1) [45]:

Rm/(1 + ω2C2mR2

m)] = [Rb/(1 + ω2C2gR

2b)]

+ [2Rt/(1 + ω2C2dR

2t )] (2)

CmR2m/(1 + ω2C2

mR2m)] = [CgR

2b/(1 + ω2C2

gR2b)]

+ [2CdR2t /(1 + ω2C2

dR2t )]. (3)

t higher frequency, Eq. (3) becomes:

/Cm = 1/Cg + 2/Cd. (4)

his equation indicates that the membrane/electrolyte systemay be considered to be composed of three capacitors in series:

he geometric capacitor being placed between the two interfacial

ouble layers [43–45]. When 1/Cg � 2/Cd at high electrolyteoncentration or significant surface charge [12,44], then Cm andg become approximately equal to each other: Cm ≈ Cg. Suchconsideration helped in evaluating the values of Cd by using

tance (Xx × 102, k�), and (iv) impedance (Z, k�) in aqueous solutions of NaCl; (v) values of electrical double layer capacitance (Cd, �F) calculated using Eq.

0.02 0.05 0.1 0.2

5.31 1.16 0.99 0.820.52 0.11 0.084 0.0470.441 0.0802 0.0701 0.03501

1.104 4.05 5.99 8.590.112 0.535 0.639 1.67

0−3 0.139 × 10−2 0.876 × 10−2 0.0101 0.025

1.6 0.354 0.238 0.1771.69 0.037 0.0253 0.01870.0169 0.00408 0.0027 0.00197

1.67 0.37 0.25 0.180.49 0.11 0.079 0.0420.4403 0.0801 0.0701 0.0351

mol/l32.20 48.71 71.99 101.18

94 N. Islam et al. / Journal of Membra

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ig. 4. Best-fit plot of electrical double layer capacitance vs. square-root ofaCl concentration.

q. (4) for different electrolyte concentrations. It appears fromhese results that the increase in concentration of NaCl solutionsesults in a decrease in the value of Cd implying the dependencef Cm on Cd. Similarly, when 1/Cg ≈ 2/Cd, Cm differs fromg. This seems to be due to the absence of charge in the lowlectrolyte concentration.

However, the exact form of double layer capacitanceepends upon the fixed charge, σs and the membrane potential,m. If σs = 0, then [43,44] Cd = ε0εwsinh α/(1/κ)α and foruch lower values of Vm, Cd reduces to Cd = ε0εw/(1/κ) inhich ε0 = 8.85 × 10−14 F/Cm, εw is the dielectric constantf water, α is a constant depending upon the structuraletails of the membrane and 1/κ is the Debye-Huckel length:/κ = 4.31 × 10−8/(2µ)1/2 where µ is the ionic strength of thelectrolyte solution. The value of α is thus obtained by employ-ng the relation: [{ε0εw/(1/κ)Cg}sinh α + 2] = Vm/(2RT/F);r alternatively, CmVm = σp = 4Fc(1/κ)sinh α in whichp is the polarization charge on the capacitor. Ifm � RT/F, then sinh α = α and Cd reduces to ε0εw/(1/κ).hus:

d = ε0εw(2µ)1/2/4.31 × 10−8. (5)

he values of Cd thus obtained by using Eq. (5) for the aqueousolutions of NaCl are given in Table 2. Consequently, linear plotf Cd against m1/2 (Fig. 4) supports the direct dependence of Cdn the square root of the electrolyte concentration. However, its noteworthy that the values of Cd obtained by Eq. (5) differrom those obtained by Eq. (4). Eq. (4) values are 0.014, 0.038,.074, 0.124, 0.230, 1.21, 1.49, and 5.31 at the corresponding

oncentrations. Such a difference has also been reported ear-ier [45] for the parchment-supported nickel phosphate, cobalthosphate, and the complex nickel–cobalt membranes equili-rated with different concentrations of KCl. The said difference

cioo

ne Science 282 (2006) 89–95

eems to be due to the presence of polarizing charge and thetructural details of the membrane matrix [45]. In addition, theay in which the Cd is expressed in the two equations involving

ltogether different terms has inherent difficulties in correlat-ng its values obtained by the two equations. Consequently, thelot based on Eq. (4) shows an apparently linear dependencef Cd on [NaCl] while that based on Eq. (5) shows a non-linearehaviour. In addition, the non-linear plot of the capacitance (Cd)ersus [NaCl] increases rapidly in the low concentration rangend shows a tendency to slow down the initial increases withncrease in concentration. Such a trend has also been observed inhe cases of specific conductance values when successively lessores become available for the transport of ions with increase inoncentration. However, the non-linear plot of Cd against soluteoncentration becomes linear when plotted against m1/2 as statedbove.

Furthermore, the membrane under investigation possesses theositive charge and the counter ions form the double layer at theembrane surface. An increase in concentration of electrolyte

n solution, therefore, causes the counter ions in the form of dou-le layer to be pushed inside the membrane. Consequently, thisesults in a decrease in the effective thickness of the membranend an increase in the ionic charge within the membrane as men-ioned above. In other words, the charge accumulates counterharge, which in turn, can increase the ion channel conductances is quite well known for the “concentration mechanisms” in theiophysics literature of ion channels. Consequently, the mem-rane becomes more conductive to the incoming ions, whichn turn, supports the trend in the behaviour of the membraneesistance under discussion.

. Conclusions

The electrical double layer at the membrane/electrolyte inter-ace influences and controls the transport of ions. The effects oflectrolyte concentration and frequency on the membrane capac-tance seem to be due to some structural changes in the mem-rane. Importance of electrical double layer includes the doubleayer capacitance dependency on the electrolyte concentration.his, in turn, results in a better description of the impedance. The

inear plot of Cd against m1/2 supports the direct dependence ofd on the square root of the electrolyte concentration as envis-ged in the light of the equation, Cd = ε0εw(2µ)1/2/4.31 × 10−8.onsequently, it lends support to the relevant model employed

o explain the behaviour of electrical double layer at the mem-rane/electrolyte interface.

Increase in electrolyte concentration causes progressive accu-ulation of the ionic species within the membrane. Thus,

he membrane becomes increasingly more conducting to theseons. This accounts for the decreases in the resistance val-es. Similarly, increase in applied frequency results in a fastxchange of polarity between the ions and the membrane mate-ial. It is noteworthy that the studies in the behaviour of spe-

ific conductance of several electrolytes and those of capac-tance, resistance, impedance, and electrical double-layer ofne of their representative electrolytes supplement/support eachther.

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N. Islam et al. / Journal of Me

eferences

[1] B. Rippe, B.I. Rosengren, D. Venturoli, The peritoneal microcirculation inperitoneal dialysis, Microcirculation 8 (2001) 303.

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abilities from passive membranes’ potential, J. Non-Equilib. Thermodyn.7 (1982) 159.

[5] G. Cevc, D. Marsh, Properties of the electrical double layer near theinterface between a charged bilayer membrane and electrolyte solution:experiment vs. theory, J. Phys. Chem. 87 (1983) 376.

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