Ionics (2015) 21:1631–1648
DOI 10.1007/s11581-014-1333-7

ORIGINAL PAPER

Membrane potential generation without ion transport
Hirohisa Tamagawa

Received: 13 March 2014 / Revised: 25 November 2014 / Accepted: 26 November 2014 / Published online: 30 December 2014
# Springer-Verlag Berlin Heidelberg 2014

Abstract Current view about cell is that the cell is a waterysolution coated with semi-permeable membrane and there
exists nonzero potential, so-called membrane potential, acrossthe semi-permeable cell membrane. Goldman-Hodgkin-Katz
equation and Donnan theory are the fundamental existing
theories for explaining the cause of membrane potential generation. However, the observations of membrane potential
inexplicable by these existing theories have been repeatedly
reported by a small number of researchers for more than thepast half century. Hence, it is needless to say important toreconsider the membrane potential generation mechanism.
Based on the experimental result shown in this paper, it was
concluded that the existing theories were not genuinely rightfor the explanation of membrane potential generation. Adsorption theory is only a genuinely right theory instead. The
adsorption theory describes that the adsorption of the mobileions on the adsorption sites on the membrane generates themembrane potential. This work introduces the experimental
observation inexplicable by Goldman-Hodgkin-Katz equation
or Donnan theory but is in harmony with the adsorption
theory.
Keywords Membrane potential . Goldman-Hodgkin-Katz
equation . Donnan theory . Ion adsorption

Introduction
Membrane potential is the potential generated across a cell
membrane [1–3]. It changes in accordance with the cell activity. Thus, the membrane potential is one of the indications of
H. Tamagawa (*)
Department of Mechanical Engineering, Faculty of Engineering,
Gifu University, 1-1 Yanagido, Gifu, Gifu 501-1193, Japane-mail: tmgwhrhs@gifu-u.ac.jp

the cell’s biological activities. Goldman-Hodgkin-Katz equation (GHK equation) [1–3] and Donnan theory [1, 2, 4–6] arewell-known concepts of membrane potential generation
mechanisms. GHK equation describes the permeation rate ofmobile ions through the cell membrane, and individual ion
concentrations are fundamental factors in determining themembrane potential. Donnan theory describes that the membrane potential is generated by asymmetric ion distribution
between cell inside and outside due to the existence of immobile ions to which the cell membrane is impermeable [1, 2,
4–6]. Both theories—GHK equation and Donnan theory—
have been successfully employed in predicting the membranepotential behaviors in the recent past [1–6]. Virtually, no one
has doubted these existing theories of membrane potential
generation mechanism. However, a small number of researchers outside mainstream have continuously objected tothese theories [1, 2, 6–8]. The leading scientist among thoseresearchers is a physiologist, Dr. Gilbert Ling. He has explained the drawbacks of existing theories and advocated his
own theory of membrane potential generation mechanism.
According to his theory, the membrane potential is generated
by the immobilization of mobile ions [1, 2, 6]. Mobile ions areimmobilized because of their adsorption on the surfaces ofsubstances constituting the cell, resulting in the nonzero membrane potential.
Independently of Dr. Ling, Dr. Kan Lu Cheng, an electrochemist, proposed a quite similar theory of potential generation mechanism of ion selective electrode such as a glass
electrode [9–13]. Dr. Cheng’s theory describes that the potential detected by the electrode is caused by the adsorption ofions on the electrode surface. He emphasized that theadsorbed ions (immobilized ions) forms a capacitor on theelectrode surface, resulting in the potential generation.
In this paper, the author raises a question again against
the existing theory of membrane potential generation
mechanism and introduces some experimental evidences

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Ionics (2015) 21:1631–1648

in harmony with the theories advocated by Drs. Ling andCheng [1, 2, 6, 9–13].

Theories for membrane potential generation
In this section, the existing theories of the membrane potential
generation mechanism and an alternative theory advocated byDrs. Ling and Cheng are introduced. The existing theories tobe described are GHK equation [1–3] and the Donnan theory[1, 2, 4–6], and the alternative theory is called the adsorption
theory [1, 2, 6, 9–13].

active transport [1–3]. The current and widely accepted concept of cell biology implies that ions are transported throughthe cell membrane by way of ion channels and pumps embedded in the cell membrane [1–3, 6, 7]. The passive ion transport
through the cell membrane is caused by the diffusion of ionspassing through the ion channels. The pump transports theions through the cell membrane against the gradient of ion
concentration, that is, the active transport [1, 2, 6, 7]. Regardless of whether passive or active transport, GHK equation
precisely predicts the membrane potential behavior as longas the ion transport through the cell membrane is induced.
Donnan theory

Existing theory
Goldman-Hodgkin-Katz equation
Considering that two aqueous solutions are separated by asemi-permeable membrane as illustrated in Fig. 1, both left
and right compartments contain the ions X+ and Y−. Potentialof V, which is the potential in the left compartment in reference to the right compartment, across the semi-permeable
membrane, is represented by the GHK equation of Eq. (1).


RT PX ½Xþ ℓ þ PY ½Y− r
V ¼ − ln
ð1ÞF
PX ½Xþ r þ PY ½Y− ℓ

V: potential, R: gas constant, T: absolute temperature, F:
Faraday constant, [m]n: Concentration of m in n-compartment, when m is X+ or Y−, and n is ℓ (left) or r (right), Pm:
Permeability constant of m, which represents the degree ofsemi-permeable membrane permeability to m.
The GHK equation implies that the potential generated
across the semi-permeable membrane is dominated by the
degree of ion transport through the semi-permeable membrane
and the ion concentration [1–3]. Without ion transport throughthe membrane, the GHK equation is invalid for any system.
It is widely accepted that the ion transport through the cell
membrane is caused not only by passive transport but also by

Considering that the two aqueous solutions are separated bysemi-permeable membrane as illustrated in Fig. 2a. Initially,
the left compartment contains ions A+ and B−, while the rightcompartment contains α+ and β−. The semi-permeable membrane is impermeable to A+ but permeable to the rest of ions.
Because of the entrapment of A+ within the left compartment,
the disparity of ion concentration between the left and rightleft compartments is caused over time by the passive transportof ions of B−, α+, and β− through the semi-permeable membrane. Such ion concentration disparity causes the electricalpotential gradient—membrane potential—between the left
and right compartments. Individual ion concentrations andelectrical potential gradient come to settle at constant level,and such a state is the equilibrium state and illustrated inFig. 2b. According to the Donnan theory, membrane potential
across the semi-permeable membrane is the consequence of
the asymmetric ion distribution between the left and rightcompartments caused by the existence of A+ impermeable tothe semi-permeable membrane [1, 2, 4–6].
Basically, the abovementioned two existing theories require ion transport through the semi-permeable membranemore or less. The GHK equation given by Eq. (1) clearly
contains Pm indicating the existence of ion transport. Even
though the ion concentration in the left compartment is sameas that in the right compartment, ion transport can take placeas the equilibrium state ion transport. Hence, GHK equation issemi-permeable membrane

Fig. 1 Two ionic solutions
separated with a semi-permeable
membrane. Both left and rightcompartments contain the ions X+
and Y−, but the concentration of
X+ (Y−) in the left compartment is
not necessarily the same as theconcentration of X+ (Y−) in theright compartment

Left compartment

: X+
: Y-

Right compartment

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Fig. 2 Two ionic solutions
separated by a semi-permeable
membrane. a Initially, the left
compartment is filled with asolution containing substance AB
which can dissociate into A+ andB−, while the right compartment
is filled with substance αβ which
can dissociate into α+ and β−. The
semi-permeable membrane isimpermeable to A+ but permeable
to the rest of the ions. b After awhile, asymmetric ion
distribution is realized because ofentrapment of A+ within the left
compartment: A+

semi-permeable membrane

Ionics (2015) 21:1631–1648

Left compartment: α+: βRight compartment

semi-permeable membrane

(a)

: B-

(b)
valid. However, without ion transport, Pm =0, GHK equation
collapses. Donnan theory does not require continuous ion
transport through the membrane. According to the Donnan
theory, the nonzero potential across the membrane is caused
merely by the asymmetric ion distribution as illustrated inFig. 2b. As long as such an asymmetric ion distribution isachieved, the Donnan theory is valid, even though Pm =0.
However, ion transport through the membrane should be
induced at least once to realize the asymmetric ion distribution
state (Fig. 2b) from the initial state of symmetric ion distribution (Fig. 2a). Therefore, the above two existing theories
require more or less the ion transport through the membrane.

represented by a dashed line in Fig. 3. The positively
and negatively charged layers form a capacitor and potential Φ is generated (see Fig. 3). This potential is detectedby a glass electrode. So, the immobilization of protons
due to their adsorption on the membrane surface is theorigin of (membrane) potential. Furthermore, the glass
membrane does not need to be permeable to ions for themembrane potential generation, the glass membrane only
needs to bear adsorption sites on its surface. This alternative theory is hereafter called the adsorption theory.
According to the adsorption theory, even though two aqueous solutions are separated by an impermeable membranesuch as the glass membrane, nonzero potential is generated

The adsorption theory
Basic concept of the adsorption theory is shown in thissection. For the purpose of showing its essential part andachieving easy understanding, Dr. Cheng’s explanation is
employed [9–13]. Imagine a glass membrane surface incontact with an aqueous solution containing protons,
where the glass is the same type used for a glass electrode. Figure 3 illustrates the interfacial region between theglass surface and the aqueous solution containing protons.
Protons are adsorbed onto the negatively charged sites ofsilanol groups on the glass membrane surface and form apositively charged layer as represented by the thin solidline in Fig. 3. Namely, silanol groups serve as adsorption
sites for protons. The negatively charged adsorption sitesof silanol groups form a negatively charged layer

−OSi―
−OSi―
−OSi―
−OSi―

: H+
: OH-

−OSi―
−OSi―

−OSi―

aqueous solution

glass membrane

Fig. 3 Interfacial structure between the glass membrane and an aqueous
solution containing protons

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Ionics (2015) 21:1631–1648

across the glass membrane. Considering the two aqueous
solutions containing protons separated by an impermeable
glass membrane as illustrated in Fig. 4. Assuming that the
proton concentration in the right solution is less than that in
the left solution (see again Fig. 4), the capacitor formed on theright surface of the glass membrane is totally different fromthat formed on the left surface. Hence, the magnitude ofpotential generated on the right surface, Φ', is different fromthat on the left surface, Φ. Hence, the consequently generated
potential across the glass membrane is the nonzero potentialof Φ - Φ' (≠0 V). So, the adsorption theory does not require theion transport at all for the nonzero potential induction.
Author of this paper, Tamagawa, and his collaborator,
Morita, investigated the potential behavior across the impermeable membrane which separated two KCl solutions [14].
The potential behavior they observed was analyzed by theirown theory. They prepared high and low concentration KCl
solutions separated by a silver wire both ends of which werecovered with AgCl serving as the adsorption sites for Cl− as
illustrated in Fig. 5. Because of the adsorption of Cl− on theleft surface of silver, the left surface of silver became negatively charged. Due to the negative charge, the ions of K+ andCl− in the left KCl solution came to inhomogeneously distribute by obeying the Boltzmann distribution. Hence, the potential represented by the dotted line drawn in the left KClsolution in Fig. 5 must have been generated. The same mustbe true for the right KCl solution, but the disparity of KClconcentration between the left and right KCl solutions caused
the adsorption of larger quantity of Cl− on the right surface ofsilver than on the left surface. It could consequently result in
the potential in the right KCl solution, which was different
from that in the left KCl solution as illustrated in Fig. 5.
Potential in the left KCl solution at the immediate neighborof silver abruptly changes in “Cl− adsorption phase” (seeFig. 5). The potential reaches the bulk phase potential, ϕL,
only a bit away from the left surface of silver. The same is true
for the right KCl solution. When measuring the potential
across a membrane, usually two electrodes are placed in thebulk phase of two solutions. One electrode is inserted into thebulk phase in the left solution, and another electrode isFig. 4 Two aqueous solutions
containing protons separated by
an impermeable glass membrane.
Proton concentration in the rightsolution is less than that in the left
solution. Φ' and Φ (Φ'≠Φ)
represent the potential generated
on the right surface and left
surface of the glass membrane,
respectively

inserted into the bulk phase in the right solution. Therefore,
the potential in the system represented by Fig. 5 must be given
by ϕL-ϕR according to Tamagawa and Morita’s theory [14].
They successfully reproduced the experimentally observed
potential behavior by the use of their theory. They concluded
that the membrane potential was generated not by the permeation of ions through the membrane but by the inhomogeneous ion distribution, which obeyed the Boltzmann distribution, caused by the ion adsorption.
Dr. Ling’s idea of cell membrane potential generation
mechanism is basically the same as Dr. Cheng’s [1, 2, 9–13],
and Tamagawa and Morita’s theory largely draws on thetheories advocated by Drs. Ling and Cheng. Thus, Tamagawa
and Morita concluded that the adsorption theory Drs. Ling andCheng had advocated was a valid theory as the membranepotential generation mechanism.
A number of researchers might say that if the existing cell
membrane potential generation mechanism is wrong, thefoundation of contemporary concept of cell biology collapses.
Therefore, it is quite natural for them to think that the adsorption theory is quite unlikely to be right. However, Dr. Ling’s
research results already provided the answers to such an issueand defied such doubts cast on the adsorption theory [1, 2,
5–7]. To introduce those Dr. Ling’s answers is not the topic
this paper deals with. This paper shows some experimental
results contradicting the existing theory of membrane potential generation mechanism but in harmony with the adsorption
theory advocated by Drs. Ling and Cheng.

Experimental
In this paper, the author especially doubts the necessity of ion
transport for the membrane potential generation. As describedin the “Existing theory”, GHK equation is an explanation of
membrane potential generation. It states that the potential
generation is caused by the ion transport through the semipermeable membrane. Donnan theory is another explanationof membrane potential generation mechanism, and it says that

−OSi―
−OSi―
−OSi―
−OSi―

−OSi―
−OSi―

aqueous solution

glass
glass membrane
membrane

−OSi―

―SiO−
―SiO−
―SiO−
―SiO−
―SiO−
―SiO−
―SiO−

: H+
: OH-

aqueous solution

Ionics (2015) 21:1631–1648

Cl- adsorption phaseCl- adsorption phase

Bolt zmann di str ibut ion

silverlow conc. KCl solution

: K+

AgCl

AgCl

φL

Boltzmann distribution

glass membrane

Fig. 5 Two KCl solutions
separated by a silver at both endsof which were covered with AgCl
serving as the adsorption sites for
Cl−. Dotted line represents thepotential profile expected

1635

φR

: Cl-

high conc. KCl solution
adsorption sites for Cl-

Preparation of solutions and membranes

voltmeter B

N
N-C
W

C

E-C

The author scrutinized the membrane potential generation
mechanism theoretically as well as experimentally. An experimental setup constituted of five compartments divided byfour membranes, as illustrated in Fig. 6, was fabricated. The
five compartments are denoted by N-compartment (North
compartment), S-compartment (South compartment), Wcompartment (West compartment), E-compartment (Eastcompartment), and C-compartment (Center compartment),
respectively. N-compartment and C-compartment are separated by the membrane denoted by N-C as in Fig. 6. Similarly, Scompartment and C-compartment, W-compartment and Ccompartment, and E-compartment and C-compartment are
separated by the membrane, S-C, W-C, and E-C, respectively.
Figure 6 illustrates the setup for the measurement of potentials
between N- and S-compartments by the voltmeter A andbetween W- and E-compartments by the voltmeter B.

Semi-permeable membrane The ion exchange membrane
Selemion CMV was used for N-C, S-C, W-C, and E-C. It is
manufactured by Asahi Glass Co. Ltd. (Tokyo) and commercially available. Selemion CMV contains fixed atomic groupof –SO3H. Since –SO3H creates immobile anions of –SO3− inthe hydrated state, Selemion CMV works as a cation exchange
membrane. It is used for the water purification, and the cationsin the water are adsorbed on the Selemion CMV surface.
Since Selemion CMV is a cation exchange membrane, it isquite obvious that anions hardly pass through Selemion CMV
because of repulsive electrostatic force between the –SO3−
and the anions, while cations are adsorbed on Selemion CMVor easily pass through it because of attractive electrostatic

W-C

Experimental setup

Membrane of N-C, S-C, W-C, and E-C

voltmeter A

the membrane potential is generated by the occurrence ofasymmetric ion distribution as the consequence of ion transport through the semi-permeable membrane. Without the iontransport, neither GHK equation nor Donnan theory is applicable for explaining the membrane potential generation.
Hence, in this study, the author especially focuses on the roleof ion transport through the semi-permeable membrane for themembrane potential generation.

E

S-C
S

Solution in N-, S-, W-, E-, and C-compartments
In the experiments carried out, N-, S-, W-, and E-compartment
were filled with KCl aqueous solutions. KCl solutions wereprepared by dissolving KCl into deionized water. The condition for C-compartment is to be described in the “Results anddiscussion”.

Fig. 6 Experimental setup. The setup constitutes five compartments
separated by four membranes. N, S, W, E, and C represent North-,South-, West-, East-, and Center-compartment, respectively. N-C, S-C,
W-C, and E-C represent the membranes, respectively, separating neighboring two compartments. In this illustration, voltmeter A registers thepotential between the N- and S-compartments, while voltmeter B registers the potential between the W and E-compartments

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Ionics (2015) 21:1631–1648

force between the –SO3− and the cations. Namely, Selemion
CMV is a semi-permeable membrane. Thus, Selemion CMV
was employed in this work as a model of semi-permeable
membrane.
Impermeable membrane According to the adsorption theory,
even though the membrane is impermeable to ions, the potential across the impermeable membrane is generated as long as
the membrane surface has adsorption sites (see Fig. 4) [1, 2, 7,
9–14]. Therefore, it is important to experimentally study the
behavior of potential across an impermeable membrane, too.
In order to verify this concept of adsorption theory, the membranes to which K+ and Cl− solution were impermeable andbearing surface adsorption sites for those ions were prepared.
Using such membranes, the potential across the impermeable
membrane was investigated. Similar experiment was alreadycarried out by Colacicco about 50 years ago [1, 2, 14–16]. In
the Colacicco’s experiment, two ionic solutions were separated by an oil membrane. His membrane contained a minutequantity of detergent. Figure 7 illustrates the interface between
the aqueous solution and oil membrane. Hydrocarbon tail ofthe detergent was anchored in the oil phase because of its
hydrophobicity, while the charged head of the detergent protruded into aqueous solution because of its high affinity towater. Hence, the detergent molecules formed a monolayer as
illustrated in Fig. 7. The charged head served as adsorption
site for the ions bearing the charge of opposite sign to the headcharge of the detergent. The oil membrane served as animpermeable membrane to ions. So, this membrane was animpermeable membrane bearing ion adsorption sites. With the
Colacicco’s experiments in mind, the author attempted toprepare oil membranes impermeable but bearing surface adsorption sites.
Two kinds of impermeable liquid membranes were prepared for this study. One was prepared by dissolving poly(ethylene glycol) 4-nonylphenyl 3-sulfopropyl ether potassium
salt (hereafter called PEG-K) into 1-pentanol, where thisliquid membrane is denoted lm-N. Once PEG-K dissociates,
one end of PEG-K comes to have negative charge. Anotherone was prepared by dissolving 1-decyl-3-methylimidazolium

aqueous solution
phasecharged headhydrocarbon
taildetergentoil membrane
phase

Fig. 7 Detergent molecules forming a charged monolayer at the interface
between aqueous solution and oil membranechloride (hereafter called DMIC) into 1-pentanol, where thisliquid membrane is denoted lm-P. Once DMIC dissociates,
one end of DMIC comes to have positive charge.
PEG-K and DMIC were chosen because of their longhydrocarbon tails and the charge at their heads. Owing to suchlong hydrocarbon tails, it was strongly expected that themonolayer of them were easily formed at the interface between the aqueous solution and the liquid membrane. It was
expected that PEG-K would form a monolayer bearing negatively charged adsorption sites, while DMIC would form amonolayer bearing positively charged adsorption sites. So, the
PEG-K monolayer would adsorb cations, while the DMIC
monolayer would adsorb anions.
Experimental procedure—potential measurement
Typical experimental procedure is explained as follows: All
the compartments shown in Fig. 6 were filled with KClsolutions. Neighboring KCl solutions were separated by themembranes N-C, S-W, W-C, and E-C. Which membrane,
Selemion CMV or lm-N or lm-P, is used as N-C, S-W, W-C,
and E-C depends on the experimental purpose. Potential wasmeasured at room temperature in any experiment shown inthis paper.

Results and discussion
Membrane potential across the semi-permeable membrane
Membrane potential in equilibrium state
Four pieces of Selemion CMV sheet were placed in theexperimental setup (Fig. 6) as N-C, S-C, W-C, and E-C,
respectively. All the compartments were filled up with KClaqueous solutions, and their initial concentrations are shownin the row of “before” in Experiment 1 in Table 1. Then, thepotentials, PN-S, PC-S, PW-E, and PC-E, in the equilibrium state
were measured, where Pi–j represents the potential of icompartment in reference to j-compartment. Right after filling
all the compartments with KCl solutions, the potentials were
unstable. But after a while, say after 10 s, the potentials settleat certain level, and this state is referred to as equilibrium statein this measurement. The potentials, PN-S, PC-S, PW-E, and PC-E
are summarized in the row of “before” of Experiment 1 inTable 1. Then, the concentration of KCl solution in the Wcompartment was disturbed on purpose by replacing the initial
KCl solution in the W-compartment with a new KCl solution,and the potentials in the equilibrium state were measured
again after the disturbance, where the concentration after the
KCl solution replacement is shown in the row of “after”
of Experiment 1 in Table 1. It was impossible to replace theIonics (2015) 21:1631–1648
Table 1

1637

Concentration of KCl solution and potential generated before and after disturbanceExperiment 1a
Concentration of KCl (M)Compartment
N
Beforeb0.001
Afterc0.001
Experiment 2f
Concentration of KCl (M)Compartment
N
Before
0.001
After
0.001
Experiment 3g
Concentration of KCl (M)Compartment
N
Before
0.001
After
0.001
Experiment 4i
Concentration of KCl (M)Compartment
N
Before
0.001
After
0.001
Experiment 5k
Concentration of KCl (M)
N
0.001

S
Sat.d
Sat.

S
Sat.
Sat.

S
Sat.
Sat.

S
Sat.
Sat.

S
Sat.

W
0.001
Sat.

W
0.01
Sat.

W
0.01
Sat.

W
0.01
Sat.

W
0.01

E
Sat.
Sat.

E
Sat.
Sat.

E
Sat.
Sat.

E
Sat.
Sat.

E
Sat.

a

The membrane used is Selemion CMVb“Before” means before replacing the KCl solution in the W-compartmentc“After” means after replacing the KCl solution in the W-compartment

C
1
1

Potentiale (mV)
PN-S
PC-S
140
27
139
27

PW-E
139
4

PC-E
28
27

C
1
1

Potentiale (mV)
PN-S
PC-S
129
27
127
27

PW-E
121
30

PC-E
27
27

C
1
1

Potentialh (mV)
PN-S
PC-S
–
–
–
–

PW-E
–
–

PC-E
–
–

C
0.00001
0.00001

Potentialj (mV)
PN-S
PC-S
–
–
–
–

PW-E
–
–

PC-E
–
–

C
0.00001

Potentiall (mV)
PN-S
PC-S
–
–

PW-E
–

PC-E
–

d

Sat. means saturated KCl concentratione

Pi-j represents the potential of i-compartment in reference to j-compartmentf

The membrane used was Selemion CMV, same as the Experiment 1gConcentration of KCl in individual compartments were the same as those employed in Experiment 2hTime course of PN-S and PW-E are shown in Fig. 9

iConcentration of KCl in individual compartments were the same as those employed in Experiment 3

jTime course of PN-S and PW-E are shown in Fig. 10

kIndividual compartments had KCl solutions concentrations of which were as shown in Experiment 5, which was the same as the KCl concentration
before the disturbance induction in Experiment 4lTime course of PN-S and PW-E are shown in Fig. 11

entire KCl solution in the W-compartment with new one dueto the experimental difficulty, but most of the KCl solution in
the W-compartment was replaced with new one. Experimental
results of Experiment 1 in Table 1 suggest that only PW-E
exhibited significant change after the disturbance, while theothers were virtually not disturbed at all. Another experimentof Experiment 2 was carried out basically by the same procedure of Experiment 1. The exact experimental conditionof Experiment 2 is summarized in Experiment 2 in Table 1.
0.01 M KCl solution was filled in the W-compartment before

the disturbance, while 0.001 M KCl solution was filled in the
W-compartment in Experiment 1. Similar to the experiment 1,
only PW-E exhibited significant change after the disturbance asshown in Experiment 2 in Table 1.
In Experiments 1 and 2, the potential of PN-S was generated
through three compartments of N-, C-, and S-compartment,
where this structure is hereafter called N-C-S system. The
potential of PW-E was generated through three compartments,
too, to be called W-C-E system in the same manner. Bothsystems had C-compartment in common. Since the1638

Ionics (2015) 21:1631–1648

membranes of N-C and S-C are Selemion CMV, they aresemi-permeable membranes. Therefore, the ion transport between N- and S-compartments as indicated by a fine solid
arrow in Fig. 8 must have taken place for the generation ofnonzero PN-S. It suggests that GHK equation is applicable for
explaining the potential generation of PN-S. It is true for PW-E,
that is, the ion transport between W- and E-compartment musthave taken place as indicated by a thick solid arrow in Fig. 8,
and furthermore, it was expected that GHK equation could
explain the potential generation of PW-E. In this experimental
system, ion fluxes indicated by fine and thick solid arrows
must have existed. Thus, it was speculated that the ion fluxesof N-C-S system collided with those of W-C-E system in the
C-compartment. Therefore, the disturbance of KCl solution
condition in the W-compartment in both Experiments 1 and 2
had been the cause of the alteration of not only PW-E but also
PN-S. However, PW-E only was significantly altered after the
induction of disturbance. Hence, it might be possible to derivea conclusion that the experimental observation in Experiments
1 and 2 were not explicable by an existing theory of GHK
equation.
One might argue that the KCl condition of C-compartment
has nothing to do with PN-S and PW-E, because of the following
explanation based on existing theory of GHK equation. Equations (2) and (3) are derived by the use of GHK equation.
RT PK ½Kþ N þ PCl ½Cl− C
PN−C ¼ − lnð2ÞF
PK ½Kþ C þ PCl ½Cl− N

PC−S ¼ −−þ

RT PK ½K C þ PCl ½Cl S
lnF
PK ½Kþ S þ PCl ½Cl− C


ð3Þ

N-C
C

E-C

W

W-C

N

E

S-C
S

Fig. 8 Ion transport passage. Fine arrow represents the ion transportpassage for the generation of PN-S. Thick arrow represents the iontransport passage for the generation of PW-E

PN-S is given by Eq. (4) using Eqs. (2) and (3).
PN−S ¼ PN−C þ PC−S ¼ −
RT PK ½Kþ N þ PCl ½Cl− C
lnF
PK ½Kþ C þ PCl ½Cl− N

−

ð4Þ



RT PK ½Kþ C þ PCl ½Cl− S
ln−þF
PK ½K S þ PCl ½Cl C

Selemion CMV is a cation exchange membrane. Thus, it isalmost impermeable to anion, Cl−. Since Selemion CMV wasused as a membrane of N-C and S-C, the relation of PK >>PCl
must be valid about Eq. (4). This kind of assumption was notuncommon in the electrophysiology field [17]. Hence, Eq. (4)is simplified as Eq. (5).
PN−S ∼−


RT PK ½Kþ N
RT ½Kþ N
ln
ln
¼
−
F
F
P K ½K þ S
½Kþ Sð5Þ

Equation (5) is interpreted as the concentration of Ccompartment had nothing to do with PN-S. With the same
discussion, the concentration of C-compartment had nothing
to do with PW-E. Because of this explanation, it is possible toconclude at this moment that the membrane potential behavior
summarized in Table 1 is explicable by GHK equation. Now,
the author carried out the computation of potential PW-E under
the condition of Experiment 1 by employing the Eq. (6)derived by the same manner for deriving Eq. (5).

RT ½Kþ W
PW−E ∼− ln
F½Kþ E

ð6Þ

It turned out that the PW-E’s before and after the disturbancewere ~210 and ~0 mV, respectively. Former computational
potential was significantly different from the experimental
value of 139 mV, but the latter computational potential wasquite close to the experimental value of 4 mV. The same
computational analysis was carried out under the experimental
condition of Experiment 2. It turned out that the computationally obtained PW-E’s before the disturbance and after the
disturbance were ~150 and ~0 mV, respectively. Former computational potential was a bit different from the experimental
value of 121 mV, and similarly, the latter computational potential was a bit different from the experimental value of
30 mV.
So, it was impossible to derive a firm conclusion about themembrane potential generation mechanism. Therefore, it wasnecessary to further proceed with some experiments to derivea firm conclusion. For the purpose of it, the experimentdescribed in the “Membrane potential in the middle of disturbance” was carried out.

Ionics (2015) 21:1631–1648

1639

Membrane potential in the middle of disturbance
The potential behavior described in the “Membrane potential
in equilibrium state” was scrutinized further by carrying out
another experiment under the same experimental condition as
Experiment 2 in Table 1. But in this experiment, PN-S and PW-E
were measured simultaneously as a function of time. Hereafter, this experiment is called Experiment 3, and its experimental condition is shown as Experiment 3 (same as Experiment2) in Table 1. Figure 9 shows the experimentally obtained data
curved of PN-S and PW-E vs. time, where the KCl solution in
the W-compartment was replaced at the moment indicated by
the arrow.
Right after the KCl solution replacement, PW-E started
lowering down and attained the stable potential in 11 s. During
this 11 s, C-compartment was in transition state, and it was
speculated that the solution condition such as ion fluxes of NC-S system as well as W-C-E system were significantly altered. Therefore, it was expected that PN-S would be disturbed
to some extent at least in the period of the transition state,
though the N-C-S system does not have the W-compartment.
However, the data curve of PN-S in Fig. 9 did not exhibit such aphenomenon but maintained a constant potential. This observation again cast a doubt on the validity of GHK equation.
Still, one might argue that only a minute quantity of thesaturated KCl solution filled in the W-compartment must havepermeated through the membrane W-C into the Ccompartment and such a minute quantity of saturated KClconcentration could not cause any influence on the conditionof KCl solution in the C-compartment, since the concentrationof C-compartment was as high as 1 M (see Experiment 3 inTable 1). Hence, still it is hard to derive some meaningfulconclusion about the membrane potential generation mechanism. For compensating the shortcoming of Experiment 3,
another experiment was carried out as described: The same
experiment as Experiment 3 was carried out by intentionallyemploying quite low concentration 0.00001 M KCl solution
for initially filling the C-compartment instead of 1 M KCl
solution. Hereafter, this experiment is called Experiment 4,

and its experimental condition is shown as Experiment 4 inTable 1. Even if the quantity of KCl solution permeating fromthe W-compartment into the C-compartment was quite small,
KCl solution replacement in the W-compartment must havesignificant influence on the condition of the KCl solution in
the C-compartment, since the initial concentration of KClsolution in the C-compartment was extremely low. Figure 10
shows the experimental result. Still, no variation of PN-S wasobserved even at the transition state.
The experimental result of Experiment 4 again raises a
doubt on the existing theory of GHK equation. But it needs
to be careful for deriving a conclusion. If the experimental
results of Experiments 3 and 4 could be interpreted as thequantity KCl solution permeating from the W-compartment
into the C-compartment through the membrane of W-C was
too small to induce the potential disturbance of PN-S even in
the transient state, those experimental results can be regarded
as the phenomena within the range of existing theory of GHK
equation. In order to clarify this point, the following experiment was carried out: The KCl concentrations of individualcompartments in the experiment were initially the same as
those of Experiment 4 before the replacement of KCl solution
in the W-compartment. Hereafter, this experiment is referred
to as Experiment 5, and the experimental condition is shownas Experiment 5 in Table 1. In Experiment 5, instead ofreplacing the KCl solution in the W-compartment, only a dropof saturated KCl solution was added into the C-compartment
at the immediate neighbor of the membrane W-C. Then, thepotentials PN-S and PW-E were measured as a function of time.
Figure 11 shows the experimental result. Both PN-W and PW-E
after the addition of only a drop of saturated KCl solution weresignificantly disturbed. The addition of a drop of KCl wasdone at t=0 s. So, even the slight change of KCl concentrationin the C-compartment could cause significant disturbance of
PN-S as well as PW-E. Hence, a minute quantity of KCl solution
migration into the C-compartment from the W-compartment
might have caused a significant disturbance of potential in theexperiments in Experiments 3 and 4, but actually, no potential

150
PN-S

100
50
0

potential / mV

potential / mV

150

PW-E

0

PN-S

100
50
0

20

40

60

Fig. 9 Time dependence of PN-S (fine curve) and PW-E (thick curve)
under the experimental condition of Experiment 3 shown in Table 1.
KCl solution replacement in the W-compartment was carried out at the
moment indicated by the arrow

PW-E

0

20

time / s40

60

Fig. 10 Time dependence of PN-S (fine curve) and PW-E (thick curve)
under basically the same experimental condition as Fig. 9, but the KClconcentration in the C-compartment was 0.00001 M not 1 M KCl
solution; replacement in the W-compartment was carried out at the
moment indicated by the arrow

1640

Ionics (2015) 21:1631–1648

potential / mV

150
PN-S

100
PW-E

50
0

0

60

120
time / s180

240

Fig. 11 Time dependence of PN-S (fine curve) and PW-E (thick curve)
after the addition of a drop of saturated KCl solution into the Ccompartment at the immediate neighbor of the membrane W-C. The
initial KCl concentration in the individual compartments and the membranes used were the same as those for Fig. 10

disturbance was observed about PN-S. Therefore, it is strongly
speculated that the membrane potential across the ion exchange membrane was caused not by ion transport throughthe membrane. This conclusion is in conflict with the prediction by GHK equation. The author does not say “Ion transport
never took place in the experiments so far described”. What
we would like to emphasize is “Ion transport must have takenplace in any experiment described above, but the ion transport
might not be the cause of potential generation. The potentials
of PN-S and PW-E must have exhibited significant alteration by
the disturbance, as long as the ion transport was the cause of
potential generation”.
To sum up the experimental results introduced in the“Membrane potential across the semi-permeable membrane”,
the potential generation mechanism between two compartments is not necessarily within the range of existing theoryof GHK equation. Any theory as well as the GHK equation
cannot account for the nonzero potential generation across themembrane, as long as the theory attributes the nonzero potential generation to the transmembrane ion transport. However,still, some may argue that all the above described experimental results are explicable by an existing theory of Donnan
theory [1, 2, 4–6]. Since all the membranes, N-C, S-C, W-C,
and E-C, were not as thin as actual cell membrane, even thosemembranes could be regarded as a phase with large enoughthickness for ions such as K+, Cl−, … . Selemion CMV used as
those membranes are not as thin as the actual cell membrane,
and the thickness of Selemion CMV is around 120 μm by far
thicker than the actual cell membrane. In addition to that,
Selemion CMV contains −SO3H groups, which can dissociate
into immobile fixed charge of −SO3− and mobile charge of
H+. Namely, Selemion CMV forms a phase containing fixed
negative charge in it. Therefore, disparity of K+ and Cl−
concentration must have taken place among all the compartments and all the membranes according to the Donnan theory.
It suggests that the generation of nonzero potential between
any two compartments shown in Figs. 9, 10, and 11 is quite
natural and nothing new from the standpoint of the Donnan

theory. However, in all the experiments so far described, there
existed ion concentration gradient between any two compartments the author focused on. It suggests that there existed ion
fluxes in the experimental systems. Applying Donnan theory
to such a system with ion fluxes is inappropriate, but GHK
equation should be used, as long as the existing theories areright. It is concluded that neither GHK equation nor Donnan
theory can explain the experimental results so far shown.
Membrane potential across the impermeable membrane
Potential across a liquid membrane containing either
negatively or positively charged molecule
Potential between two compartments separated by a liquid
membrane was measured using the setup shown in Fig. 6.
lm-N introduced in the “Membrane of N-C, S-C, W-C, and EC” was prepared and was used as membranes of N-C, S-C, WC, and E-C shown in Fig. 6. N-, S-, W-, and W-compartments
were filled with the KCl solutions; the concentrations ofwhich are shown in Experiment 6 in Table 2, where hereafter,
this experiment is called Experiment 6. C-compartment wasfilled up with lm-N not KCl solution. Since all the membranes
and the solution in the C-compartment were the same solution,
they virtually formed a single membrane separating N-, S-,
W-, and E-compartments to one another. PN-S and PW-E were
measured as a function of time, and the result is shown in
Fig. 12. lm-N is impermeable to water nor KCl. However,nonzero potentials, PN-S and PW-E, were generated and maintained constant. GHK equation is not applicable for explaining
those nonzero potentials because of impermeability of lm-N to
KCl.
Next, the Donann theory could explain the nonzero potential generation. N-C-S system and W-C-E system had Ccompartment in common, and KCl concentration in Scompartment is the same as that in E-compartment. Difference
between those two systems lied only in the KCl concentrationdifference between N-compartment and W-compartment.
Table 2

KCl concentration and the membrane used

Concentration of KCl (M)N
Experiment 6a
0.00001
Experiment 7c
0.00001

S

W

E

C

Sat.b

1

Sat.

lm-Na

Sat.b

1

Sat.

lm-Pc

a
The membrane used was lm-N. lm-N is a mixture of poly(ethylene
glycol) 4-nonylphenyl 3-sulfopropyl ether potassium salt and 1-pentanolbcSat. means saturate KCl concentration

The membrane used was lm-P. lm-P is a mixture of 1-decyl-3methylimidazolium chloride and 1-pentanol

Ionics (2015) 21:1631–1648

1641

potential / mV

200

Similarly, Eq. (10) is obtained.

PN-S

150

h e
i
½Cl− N¼ exp þ ðVN −VW Þ−kT½Cl W

100
50

PW-E

0
-50

0

60

120

180

time / sFig. 12 Time dependence of PN-S (fine curve) and PW-E (thick curve),
where all the KCl solution was separated to one another with a liquid
membrane lm-N

According to Fig. 12, the N-C-S system exhibited about
130 mV, while the W-C-E system exhibited about 0 mV.
The potential difference between them was 130 mV−
0 mV=130 mV and was caused undoubtedly by the KClconcentration difference between N-compartment andW- c o m p a r t m e n t . P o t e n t i a l s i n t h e N - a n d C compartments in reference to the S-compartment are
denoted VN and VC, respectively, and those in the Wand C-compartments in reference to the E-compartment
are denoted VW and VC', respectively. Since the KClconcentration in S-compartment was the same as that in
W-compartment, their electrochemical conditions werevirtually the same in each other. Therefore, it is possible
to derive the relationship of VC =VC'. Let’s focus on theconcentration of K+ in each compartment. Though the
C-compartment was filled with 1-pentanol impermeable
to KCl, an extremely low quantity of K+ could exist as
a counter ion of PEG-K of lm-N. Based on the Donnan
theory, [K+]N: [K+]C is given by Eq. (7), and [K+]W:[K+]C is given by Eq. (8), where e and k represent
elementary charge and Boltzmann constant.




eVN
eVC
½Kþ N : ½Kþ C ¼ exp −: exp −
ð7Þ
kT
kT




eV 0
eVW
½Kþ W : ½Kþ C ¼ exp −: exp − C
kT
kT




eVW
eVC
¼ exp −
: exp −
kT
kT

ð8ÞEquation (9) is derived by the use of Eqs. (7) and (8).
h ei½Kþ N¼ exp −
ðVN −VW Þ
þ
kT
½K W

ð9Þ

ð10Þ

Since the liquid membrane is impermeable to water andKCl, it is quite plausible to believe that the concentration ofK+ and Cl− in the individual compartments were constantthroughout the measurements. According to the experimental
condition of Experiment 6, [K+]N/[K+]W =0.00001, [Cl−]N/[Cl−]W =0.00001, T=300 K, and VN −VW =130 mV. Right
hand side of Eq. (9) is 0.0066 and that of Eq. (10) is 152 bycomputation, and they are totally different from the experimental conditions of [K+]N/[K+]W = 0.00001 and [Cl−]N/[Cl−]W =0.00001, respectively. These results suggest that the
Donnan theory is inappropriate as the explanation of potential
generation cause. The computational results of [K+]N/[K+]W =0.0066 and [Cl−]N/[Cl−]W =152, which was derived based on
the Donnan theory, is invalid in terms of macroscopic electroneutrality, too. It is detailed as follows: The liquid membrane
is impermeable to water and KCl, [K+]W and [Cl−]W musthave been constant, 1 M, throughout the experiment as described already. Thus, [K+]N =0.0066 M and [Cl−]N =152 M,
as long as the Donnan theory is valid. The equation of electroneutrality in the N-compartment is given by Eq. (11).
e½Kþ N þ e½Hþ N −e½Cl− N −e½OH− N ¼ 0

ð11ÞAt the standard condition for temperature and pressure,
proton concentration of water is around 10−6 −10−5 M. Hence,[H+]N~10−6 −10−5 M. Since the ionization constant of water is10−14, [OH-]~10−8 −10−9 M. [K+]N =0.0066 M as shown
above, while [Cl−]N =152 M. So, plugging those quantities([K+]N =0.0066 M, [Cl−]N =152 M, [H+]N ~10−6 −10−5 M,[OH−]~10−8 −10−9 M) into the left hand side of Eq. (11)cannot result in zero. The Donnan theory does not fulfill therequirement of macroscopic electroneutrality. Hence, theDonnan theory cannot be validated. This problem is welldiscussed by Dr. Ling as the violation of macroscopic electroneutrality of Donnan theory [1, 2, 5, 6].
To sum up, neither GHK equation nor Donnan theory can
explain the experimental result shown in Fig. 12. The same
experiment was carried out by using a liquid membrane of lmP, which was introduced in the “Membrane of N-C, S-C, W-C,
and E-C”, in place of lm-N. The exact condition is given inexperiment 7 in Table 2, where hereafter this experiment iscalled experiment 7. The experimental result is shown in
Fig. 13. lm-P is impermeable to water and KCl as well. However, nonzero potentials, PN-S and PW-E, were generated andmaintained constant. By the same argument for Fig. 12, neither
GHK equation nor Donnan theory can explain the experimental
result shown in Fig. 13. Therefore, a new concept is in need as apotential generation mechanism.

1642

Ionics (2015) 21:1631–1648

PW-E

0

Experiment 8-50

Concentration of KCl (M)

-100
PN-S

-150
-200

Concentration of KCl solution and liquid membranes used

Table 3

0

60

120

180

time / sFig. 13 Time dependence of PN-S (fine curve) and PW-E (thick curve),
where all the KCl solution was separated to one another with a liquid
membrane lm-P

Potential across the liquid membrane bearing both negativeand positive charges

Readers might think that T-phase did not contain K+ at all, since theauthor describes that 1-pentanol is impermeable to K+. What the authoremphasizes is that an extremely small quantity of K+ could exist into 1pentanol, but virtually, it could be regarded that no K+ existed in 1pentanol.

N

S

W

E

C

N-C

S-C

W-C

E-C

0.001

Sat.

0.001

Sat.

−a

lm-P

lm-P

lm-N

lm-N

a

C-compartment was not filled with solution, but a cotton thread wasplaced in it

among individual compartments and phase is given by
Eq. (12).
eðPW−T þ PT−E ÞePT−E: exp −
:1
½Kþ W : ½Kþ T : ½Kþ E ¼ exp −
kT
kT

ð12Þ

Employing the experimental result of PW-T +PT-E =100 mV
shown in Fig. 15, [K+]W/[K+]E =0.02 was obtained computationally. According to the data shown in Table 3, actual initialconcentration ratio of K+ between W- and E-compartments
was less than 0.0003, which is by far less than 0.02 computationally obtained. Of course, the initial concentrations of K+ in
W- and E-compartments had been maintained throughout thepotential measurement, since 1-pentanol is virtually impermeable to K+. Therefore, the Donnan theory was ruled out as acause of nonzero potential generation between W- and Ecompartments. Since the GHK equation was ruled out, too,
it was concluded that new concept was needed for the potential generation mechanism explanation.

N: 0.001 M KCla knot: Both threads
are tied here.
N-C: lm-P
W: 0.001 M KCl

C

E: saturated KCl
E-C: lm-N

Another potential measurement was carried out. In this experiment, all the compartments but C-compartment were filled up
with KCl solutions and their concentration is summarizedin Experiment 8 in Table 3. The membranes N-C and S-C
were lm-P, while those of W-C and E-C were lm-N. All four
membranes were connected with quite fine cotton thread as
illustrated in Fig. 14. A small quantity of lm-P (of N-C and WC) and a small quantity of lm-N (of W-C and E-C) wereabsorbed into the cotton thread autonomously. Therefore, allfour membranes became electrically connected to one anotherthrough those fine threads. If thick threads had been usedinstead of fine threads, a large quantity of lm-N and lm-P
would have been absorbed into the threads, and it could cause
the heavy mixing of all four liquid membranes to one another,resulting in the contamination of membranes, N-C, S-C, W-C,
and E-C. Therefore, fine threads were used.
Figure 15 shows the time dependence of PN-S and PW-E.
Obviously, nonzero potentials were generated. Liquid membrane was primarily composed of 1-pentanol. Since both K+
and Cl− were virtually insoluble to 1-pentanol, neither K+ nor
Cl− could be transported through the liquid membranes. Consequently, the generation of nonzero potentials of PN-S or PW-E
is inexplicable by the GHK equation. The applicability of
Donnan theory to this experimental result was considered next.
W-compartment was electrically connected with Ecompartment using a fine thread, and this system is denoted
W-T-E system from now, where T of W-T-E represents the finethread containing lm-N and lm-P. W- and E-compartments
and T-phase all contained K +.1 Potentials between Wcompartment and T-phase and between T-phase and Ecompartment are represented by PW-T and PT-E, respectively.
According to the Donnan theory, the concentration ratio of K+

Liquid membrane

W-C: lm-N

potential / mV

50

S-C: lm-P
S: saturated KCl

cotton thread

1

Fig. 14 Experimental setup. All the compartments were separated by lmN or lm-P as illustrated. All the membranes were connected with two finecotton threads tied each other at the center of C-compartment

Ionics (2015) 21:1631–1648

1643

potential / mV

200

and the liquid membrane. Its hydrocarbon chain was anchoredin the membrane phase and the positively charged head of
DMIC located in the KCl solution. So, the positively charged
monolayer was formed at the interface between the KClsolution and liquid membrane as in Fig. 16.
Cl− in the KCl solution is adsorbed on the positively
charged monolayer. According to the adsorption theory, theconditions (I) and (II) shown below must be establishedconcerning the potential generation of PN-S [1, 2, 5, 6, 9–13].

PW-E

100
0

PN-S

-100
-200

0

30

60

90

120

time / s(I) Anion, Cl−, adsorption on the positively charged sites at
the interface obeys the Langmuir isotherm.
(II) Ion distribution in KCl solution phase obeys theBoltzmann distribution.

Fig. 15 Time dependence of PN-S (dashed line) and PW-E (solid line)

Alternative theory as the membrane potential generation
mechanism
Potential across the liquid membrane
The experimental result of Fig. 15 was considered first. No
existing theories appear to explain the results. Drs. Ling andCheng have emphasized that the ion adsorption is the origin of
membrane potential [1, 2, 5, 6, 9–13]. The interfacial molecular structure between the KCl solution and the liquid membrane can be illustrated as Fig. 16. Since DMIC in lm-P has along hydrocarbon tail, a monolayer consisting of DMIC musthave been formed at the interface between the KCl solution

Fig. 16 Interfacial molecular
structure imagined between the
KCl solution and the liquid
membrane of lm-P

ClK+

Then, the potential profile represented by the dotted curve
shown in Fig. 17 was expected to form. ϕN in Fig. 17 represents the potential in N-compartment at the position sufficiently away from the N-C in reference to the potential to themembrane phase. ϕS in Fig. 17 represents the potential in Scompartment at the position sufficiently away from the S-C inreference to the potential to the membrane phase. PN-S is givenby the difference between ϕN and ϕS as shown in Fig. 17, PNS =ϕN−ϕS.
The author of this paper already derived a formula
representing the potential by taking the Langmuir isotherm

K+

Cl-

K+

Cl-

K+

Cl-

N: 0.001 M KClmagnified

−

− −
−
−

−

N-C: lm-P

W: 0.001 M KCl

C

E: saturated KCl
E-C: lm-N

T- phase

W-C: lm-N−− −S-C: lm-P
magnified

− −

−
− −

S: saturated KCl
Cl- Cl- ClK+

K+

K+

Cl-

Cl- Cl- Cl-

K+

K+
K+

K+
K+

−
Molecular model of DMIC (1-decyl3-methylimidazolium chloride)

counter anion
positively charged headhydrocarbon tail

1644

Ionics (2015) 21:1631–1648

Fig. 17 Potential profile from Scompartment to N-compartment

potential
ClK+

φN

N-compartment
K+
Cl-

K+

Cl-

K+

Cl-

N-C
PN-S

cotton thread in
C-compartment

T- phase

S-C
Cl- Cl- ClK+K+

K+

K+ Cl-

Cl- Cl- ClK+

K+

K+
K+

and the Boltzmann distribution into consideration under theconstraint condition of electroneutrality [14]. Such an approach for deriving the formula of potential is the same asDrs. Ling’s and Cheng’s [1, 2, 5, 6, 9–13]. Applying theformula the author derived, for instance, to the system illustrated in Fig. 17 results in the potential expression given by
Δϕ, Δϕ=ϕN−ϕS, where ϕN and ϕS are respectively given
below.
2
3
rﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ sﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
2
2RT 4 1 K½sTe FCN
1 K½sT
e FCN
ln −
þ
−
þ 15
ϕN ¼ −
F
2 1 þ KCN 2εεo RT
2 1 þ KCN 2εεo RT−

ϕS ¼ −−e KCN ½sTdεlow εo 1 þ KCN

ð13Þ

2
ﬃ3
rﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ sﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
2
2RT 4 1 K½sTe FCS
1 K½sT
e FCS
ln −
þ
−
þ 15
F
2 1 þ KCS 2εεo RT
2 1 þ KCS 2εεo RT

e KCS ½sTdεlow εo 1 þ KCS

ð14Þ

R: gas constant, T: absolute temperature, F: Faraday constant, Ci: concentration of Cl− at the bulk phase in the i-

φS

S-compartmentcompartment (i=N or S), [s]T: concentration of the adsorption
site (positively charged monolayer) formed at the interface
between T-phase and i-compartment (i=N or S), K: association constant between the adsorption site and Cl−, e: elementary charge, εο: vacuum permittivity, ε: relative permittivity ofwater, εlow: relative permittivity of water at the immediateneighbor of adsorption site, d: width of water phase with therelative permittivity εlow.
Based on the above equations, Eqs. (13) and (14), thepotential in the KCl solution at the position sufficiently awayfrom positively charged monolayer in reference to T-phasebecomes lower as the KCl solution concentration decreases.
As illustrated in Fig. 17, KCl concentration in N-compartment
was lower than that in S-compartment. Therefore, it is expected that ϕN is lower than ϕS. Hence, PN-S is negative as inFig. 15 as expected. The same must be true for PN-S and PW-E
in Experiment 7, since lm-P was used. In fact, both PN-S and
PW-E were negative as in Fig. 13. The same discussion so far
described is applicable to PW-E in Fig. 15. The interfacial
molecular structure imagined between the KCl solution andthe liquid membrane is illustrated as Fig. 18. Since PEG-K in
lm-N has long hydrocarbon tail, a monolayer consisting of

Ionics (2015) 21:1631–1648

1645

Fig. 18 Interfacial molecular
structure imagined between the
KCl solution and the liquid
membrane of lm-N

N: 0.001 M KCl

N-C: lm-P
E: saturated KCl

C

E-C: lm-N

W-C: lm-N

W: 0.001 M KCl

S-C: lm-P

＋
＋

＋ ＋
＋

＋

＋

counter cation (K+)

Molecular model of PEG-salt (poly (ethylene glycol)
4-nonylphenyl 3-sulfopropyl ether potassium salt)

hydrocarbon tail(II) must be fulfilled concerning the potential generation of
PW-E in Fig. 15. Then, the potential profile represented by
the dotted curve showed Fig. 19 is expected to form. Basedon the formula derived by the author [14], the potential in
the KCl solution at the position sufficiently away fromnegatively charged monolayer in reference to T-phase becomes higher as the KCl solution concentration decreases.

W-C

＋
＋
＋

K+
Cl-

＋
＋ ＋

K+
Cl-

＋

Cl-

cotton thread in
C-compartment
T- phase

＋ ＋

K+
K+

＋ ＋

Cl-

＋ ＋
＋

PW-E

W-compartment

Fig. 19 Potential profile from Ecompartment to W-compartment

negatively charged headpotential

PEG-K must have been formed at the interface. Its hydrocarbon chain was anchored in the membrane phase, and its
negatively charged head of the anchored PEG-K protruded
in the KCl solution. So, the negatively charged monolayer wasformed at the interface between the KCl solution and liquid
membrane. K+ in the KCl solution was adsorbed on thosenegatively charged monolayer. The conditions (I) and

K+ Cl
K+
ClK+
+
Cl
K+
K
K+
Cl- Cl+K Cl K+
Cl-

E-C

K+ Cl
K+
ClK+
K+ Cl K+K+
Cl- ClK+ Cl K+
Cl-

E-compartment

K+Cl-

S: saturated KCl

＋
＋ ＋

K+
Cl-

＋

K+
K+ Cl

＋ ＋

Cl-

magnified＋ ＋magnified1646

Ionics (2015) 21:1631–1648

Therefore, PW-E in Fig. 19 is positive, and actual PW-E shown in
Fig. 15 was positive as expected. The same should be true for PNS and PW-E in Fig. 12. In fact, PN-S in Fig. 12 was positive, but
PW-E was not and slightly negative. PW-E in Fig. 12 was generated, when KCl concentrations in W- and E-compartments werequite high of 1 M and saturated, respectively. Hence, there was
not so large difference between those two KCl concentrations.
Therefore, PW-E slightly below zero was explicable by the adsorption theory as it was within the range of acceptable experimental error.
Reconsideration of potential across the ion exchange
membrane
The potentials shown in Figs. 9 and 10, which were generated
across ion exchange membranes, are reconsidered in thissection employing the adsorption theory. The experimental
result of Fig. 9 (Experiment 3) is reinvestigated under theadsorption theory. The ion exchange membrane used contains
fixed –SO3H. It dissociates into an immobile atomic group of–SO3− and a mobile cation of H+. Based on the adsorption
theory, the interfacial region between KCl solution and membrane is illustrated as Fig. 20. K+ is adsorbed to –SO3− ofmembrane of Selemion CMV at the interface between the KClsolution and membrane by obeying the Langmuir isotherm,
and all the ions distribute according to the Boltzmann distribution [1, 2, 6, 9–14, 18–26].
Hence, prior to the induction of disturbance, the potential
represented by the dotted line in Fig. 21a must havebeen generated between N- and S-compartments. The same
argument is true for the potential generated between W- and Ecompartments, and the dotted line in Fig. 21b represents the

Validity of the foundation of this study
So far, we have emphasized that both GHK equation and
Donnan theory have shortcomings for explaining the membrane potential generation behavior, and the author has advocated the adsorption theory as an alternative. It is known that

K+

Cl-

N
ClK+

magnified
N-C
W

E

W-C

C
E-C

: H+
: −SO3-

＋
＋

＋

＋
＋
＋

K+

＋

K+

＋

Cl-

＋

Cl-

＋ ＋

Fig. 20 Interfacial structure
imagined between Ncompartment and N-C ofSelemion CMV

expected potential profile before the induction of
disturbance. After the induction of disturbance, the condition(concentration of KCl and degree of ion adsorption) of individual compartments of N-C-S system was unaltered. However, the condition of W-compartment of W-C-E system wassignificantly altered, resulting in the diminish of potential in
the W-compartment as illustrated in Fig. 21b, while the potential profiles in C- and E-compartments remain unaltered,
where the solid curve in W-compartment represents the potential profile expected after the disturbance. Consequently,
PW-E diminishes after the induction of disturbance as illustrated in Fig. 21b. Eventually, PW-E decreases as clearly seen in
Fig. 21b. Therefore, the potential behavior shown in Fig. 9
was observed. Although the KCl concentration in the Ccompartment in Fig. 10 (Experiment 4) was different fromthat in Fig. 9, basically, the same phenomenon as Fig. 9 musthave occurred for Fig. 10.
To sum up, the adsorption theory appeared to be by far
plausible than the existing theories for explaining the cause of
membrane potential generation especially owing to the following points: (i) ion transport is not needed at all; (ii) electroneutrality is fulfilled; (iii) Boltzmann distribution, which isa quite basic concept of thermodynamics, is employed; and(iv) Langmuir isotherm, which is a quite basic concept ofphysical chemistry, is employed.

S-CSIonics (2015) 21:1631–1648

1647
potential

N-compartment
PN-C

K+

Cl-

K+

Cl-

Cl-

＋

＋
＋
＋

potential

＋＋

＋

＋＋

＋
＋

＋

＋

ClK+
Cl-

K+ Cl-

K+
K+

ClCl-

K+
Cl-

E-compartment

Cl-

＋＋

＋
＋
＋

＋
＋
＋
＋

＋
＋
＋
＋

＋
＋
＋
＋

＋

＋
＋
＋

W-compartment

K+

＋

K+

＋

K+

K+

＋
＋

＋＋

Cl- Cl- K+

K+ Cl-

＋＋

K+

-

PC-S

S-compartment

-

K+ Cl

Cl-

-

K+
K+ Cl Cl- Cl
Cl
K+
K+ Cl K+
ClCl +
K
Cl- Cl+
+
K
K
Cl-

＋
＋
＋
＋

Cl-

Cl- K+

K+

＋
＋

Cl-

K+
Cl-

＋
＋
＋

Cl-

Cl- Cl- K+

＋

Cl-

PC-E

＋

K+

PW-E

＋＋

S-C

K+

K+

PW-E

PW-C

＋

PW-C

K+

K+

after the disturbance

PN-S

C-compartment

K+ K+- Cl- ClCl
Cl- K+ClK+
ClClK+
Cl- Cl
K+ Cl
K+ K+ K+
Cl-

Cl-

(a)

before the disturbance

K+ K+

K+

: H+
: −SO3-

＋

N-C

＋
＋
＋
＋

K+

(b)

W-C

C-compartment

E-C

Fig. 21 a Ion distribution and potential profiles in N-C-S for Figs. 9 and 10 before the induction of the disturbance. b Ion distribution and potential
profiles in W-C-E systems for Figs. 9 and 10 before and after the induction of the disturbance

Donnan theory is applicable to the artificial system as well as
living system (a cell) for explaining the potential generation
behavior in those systems [1, 2, 4–6], although the use of
Donnan theory was proved to be unsuitable for the artificial
systems described in this study. Concerning the GHK equation, however, some readers of this paper might have a concern that the use of GHK equation for the analysis of potential
behavior generated in the artificial system such as the setup
employed in this study might be inappropriate, since the GHK
equation is a strong mean for the prediction of real cellpotential analysis in the physiology research field [1–3]. It isquite natural that such a concern is raised, since all the membranes employed in this work did not contain any functional
molecule serving as an ion transporter at all, while it is usually
explained that the cell potential is a consequence of transmembrane ion transport caused by the biological functional
molecules embedded in the cell membrane such as an ion
channel protein [1–3, 5–7]. Therefore, some readers might
think that some part of the foundation of this work—to disprove the GHK equation by analyzing the potential behavior
across the artificial membrane—is wrong in the first place.
But the author of this paper would like to defy this kind ofconcern by the following discussion.
Contrary to our intuition, membrane potential-like phenomenon is observed not only in the living system of cell but also in the

nonliving artificial system. For example, Teorell reported theobservation of action potential-like transmembrane potential in
the artificially built system as early as 1959 [27]. He observed
such a potential generated between 100 mM NaCl solution and
10 mM NaCl solution separated by a porous porcelain membrane
after the imposed constant electric current across the membrane.
Appropriately adjusting the magnitude of electric current imposed,even undamped action potential-like oscillatory potential was
induced. Proteionoid-based microsphere is another artificially created system which exhibits membrane potential-like characteristics [28–31]. Proteinoid-based microsphere consists primarily of
biological molecules of amino acids, but it is artificially created ina laboratory and it does not contain any molecule playing a role ofan ion transporter. However, the proteinoid-based microspherebears the characteristics of potential similar to the real cell membrane potential. Similar to the observation by Teorell describedabove, Ishima et al. observed action potential-like oscillatory
potential in the proteinoid-based microsphere system [28]. Whatis quite intriguing is that such an action potential-like oscillatory
potential was spontaneously induced without any external stimulation unlike Teorell’s observation. The study done by Yoshikawa
et al. is even more intriguing [32, 33]. They made measurement ofpotential between 0.5 M NaCl solution and 0.5 M KCl solution
separated by a porous membrane doped with Span-80. Theyexperimentally observed that the action potential-like potential

1648

oscillation spontaneously started without any external stimulation.
On top of that, their experimental system used no biologicalmaterials unlike the proteinoid-based microsphere. Therefore, nofunctional molecules of ion transporter were employed in the
study done by Yoshikawa et al.
It is not extreme to say that the membrane potential-likecharacteristics are not phenomena particular only to a real cell,
but it is rather commonly observed phenomena even in artificiallycreated systems. Therefore, the author believes that GHK equation
should be applicable even to the artificial system, as long as it isapplicable to a real cell system. As a matter of fact, there are no
theoretical reasons that the GHK equation applicability is limited
to the system consisting of biological living materials such as aliving cell.

Conclusion
Existing theories of the GHK equation nor the Donnan theory
are not enough to fully explain the membrane potential behavior observed in the experiments shown in this paper. On
the other hand, the adsorption theory is in harmony with thoseobservations, and it is strongly backed by the quite fundamental scientific concepts in the thermodynamics and physicalchemistry fields. It is strongly speculated that the adsorption
theory provides with the real cause of membrane potential
generation.
Acknowledgments This research was conducted under the financial
support of the Ministry of Education, Science, Sports and Culture, Grantin-Aid for Challenging Exploratory Research, 26650032, 2014.

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