Some Properties of Ionic and Nonionic
Semipermeable Membranes
By ALEXANDER MAURO, PH.D.
Some fundamental properties of barriers are reviewed. The barrier of biologic signifiis the plasma membrane. The role of the barrier in the transport of solvent and
neutral solute species is discussed; 2 fundamental transport processes, namely, diffusion
and mass flow are emphasized. The latter is shown to arise as the barrier offers increasing
impedance to the movement of a given solute species; the barrier is then referred to as
a semipermeable membrane, and the transport of the solvent as osmosis. The osmotic
movement, undoubtedly one of the most important transport mechanisms in physiologic
systems, is shown to arise from a gradient of hydrostatic pressure in the barrier. The
need for the consideration of profiles of thermodynamic quantities is stressed. Finally,
the third thermodynamic quantity, electrical potential, is introduced when ionic species
are considered in the analysis of the "fixed charge" membrane.
cance
THE objective of physiologists dealing
with studies of transport across cell membranes is either to learn what can or cannot
pass across the cell surface as one of the basic
facts about the cell or, by such data, to obtain
some idea about the structure of the membrane itself. It need hardly be emphasized that
the main justification for interest in the
structure of the membrane is the inextricable
relationship between its structure and the
mechanisms which operate at this level of the
cell to bring about the transport of various
species and the associated, higher-order physiologic activity or function, such as propagated activity and secretion. Unfortunately,
although we would like to have a clear and
definite picture of the membrane phase, our
knowledge of its detailed structure has not
advanced too dramatically in recent years.
With the advent of electron microscopy, the
plasma membrane is being visualized as a dark
line or a double line of the order of 100 A in
the myelin sheath, muscle fiber, red cell and
bacteria. (We should have clearly in mind
that many transport studies involve a composite cellular system, such as frog skin, bladder, intestine, colon, capillary and nephron.
It is indeed difficult to decide which cells are
involved here and, moreover, whether the single cell has a symmetric plasma membrane.
Thus, if we desire to keep in mind a simple
cell geometry, it would be well to restrict our
discussions to single cells of the type seen in
muscle and nerve cells, red cells and bacteria.
Furthermore, since we shall be concerned here
with some fundamental physicochemical
mechanisms associated with transport, the
phenomena of pinocytosis and related topics
will be excluded in our discussion.) It is almost a general working hypothesis along the
lines suggested by Daniellil years ago that the
main skeleton of the plasma membrane is a
lipoprotein, bimolecular complex that is either
" eontinuous " or "discontinuous " ( " holes " ).
In this bimoleeular complex, with the hydrophilic groups extending inward to the cytoplasm and outward to the extracellular fluid,
many other molecular entities can be interspersed either radially or along the surface.
It should be stated that to date, the main body
of evidence for the ultrastructure of some
plasma membranes has been acquired by 3
methods of analysis other than electron microscopy, i.e., polarization optics, x-ray
diffraction and chemical degradation studies.
Most of this work has been done on myelin*
*If the Geren theory of myelin formation is correct, then it must be granted that the myelin structure
is a multilayered aggregate of plasma membrane.
Thus, in the years to come, the combination of x-ray
analysis and chemical studies of this system should
supply the most detailed " atomistic " information
about a plasma membrane that has been found by
any preparation hitherto available.
From the Rockefeller Institute.
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846
MAURO
p
port, which for the present can be referred
to as a nondiffusional process, an unambiguous description of the diffusion process is
warranted in order to emphasize the difference. Furthermore, by devoting sonie effort
to a more explicit description of diffusion,
the vexing and confusing problem of the
meaning of "tracer fluxes," "unidirectional
fluxes, ''influx
Distance X
Figure 1
The Gaussiant curve showing chance of finding
particle a distance x from starting point for a
small and large number of executed steps N and N,
respectively.
aiid red cell ghosts, although it would be unfortunate not to nielition that a wealth of data
has been derived from cheniical aiialysis of
bacterial systems.
For our present purpose, let us proceed
with the idea that this lipoprotein structure
is close-packed and the interstices are filled
with water. Those who visualize a predoniinantly radially-ordered lipid skeleton will picture colisiderable order in the inenmbrane, and
will be inclined toward the notioIn of "channels" or "pores." On the other hand, the
combination of the lipid skeleton and other
radially-aligned molecules covered with overlying protein molecules mnight conceivably
give rise to the idea of a network or meshwork
of molecules soaked, so to speak, in water.
Whichever picture is preferred the plasma
membrane, from this rather glib anid simple
description, can certainly be coiisidered as
some barrier to the movenient of ionic and
nonionie species. Indeed, it is precisely some
of the phenomenologic properties which arise
in systems acting as barriers that will concern
us.
We must now consider what fundamental
physical mechanisms can be involved iii the
transport of various molecular species across
the region of the membrane. The mnost fundaniental mechanism which warrants attentioni
is, of course, diffussion. Since we must presenltly consider an alternative mode of trans-
''outflux'' and ''turn-
over rates" nlight be seeni inore clearly.
The most basic kinematic description of the
diffusion process was given by Einstein2 in
1905. This was extended by Smoluchowski in
1915 and most recently by Chandrasekhar in
1942.3 Einstein's discovery indicated that if
a particle executes a "random walk, " then
a group of similar particles, acting without
nutual interference, will distribute themselves in space and timne according to the basic
diffusion equationl
D ax2
Thus, the diffusion equationi is accoulited for
by an explicit description of the displacements
of a single partiele. Let us examine his arguinents: in outline, a particle executes the
"'random walk' '-in 1 dimension-if the a priori probability of jumping a unit step in the
forward or backward direction is equal. It is
clear that this movement goes on for all time,
subject to this condition of equal probability:
The only question that can be asked further
about the particle is the chaniee of finding it
a certain distance in the positive or negative
direction from the startiiig point after a total
niumber of steps have been executed. It turnls
out that the functioii describiiig this probability is the familiar Gaussian curve (fig. 1).
It is important to see most clearly what is
implied bv this function so far as the behavior of the particle is conieerned. The funcetion states that starting out at any poitnt, the
chance of finding the particle a certaiii dis-
a1t
=
*1In this equation,
e = change in concentration per uInit tinme.
D = constant.
-c
the secon(lderivative of conicentationi witlh
respect to distance.
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IONIC AND NONIONIC SEMIPERMEABLIE MEMBRANES
847
tance on either side of the starting point is
symmetric and the chance "spreads" out the
greater the number of steps executed by the
particle. Notice this is the only basic description of the behavior of the particle that is
possible-it is probabilistic. One might say
the particle will wander quite aimlessly on
its "Gaussian walk."
It is important to emphasize that thus
far we have not introduced any ideas about
the energetics involved in the jumping behavior. This will be dealt with later. It is evident that some physical mechanism exists to
impart energy to the particles and, thus, to
effect an average frequency of displacement.
As soon as we begin to consider a distribution
of "Gaussian" particles such that at any moment we have a concentration of particles as
a function of distance, then, as was shown by
Einstein in the paper cited previously,2 the
concentration function will change with time,
resulting in a relationship that is expressed
by the fundamental Fick equation, usually
referred to as Fick's Equation II
at-
Dx2~
We can invoke another relation which is
most fundamental since it expresses the law
of conservation of matter, namely, the continuity equation,
aG
Dt
ai
ax
and thus proceed from Fick's Law 11 to the
flux equation (Fick's Law I) known by the
familiar term of "Fick's law"
J--D de
dx'
where J is the number of particles moving
through a unit area per unit time.
As we have stated above, Einstein indicated
mathematically how Fick's Law II springs
naturally from the movement of many Gaussian particles. However, he also demonstrated
a few years later4 in an "elementary" lecture
to chemists-which he was urged to give by
Prof. Lorentz-how one could proceed directly
from the Gaussian particle consideration to
the flux equation, namely, Fick's Law I. Since
Xj X2
x
x
Figure 2
A. Left. Sketch of the particles distributed with
varying concentration. The 2 compartments of
equal size are shown on either side of the point x.
B. Right. Plot of the concentration of particles as
a function of the distance x. The concentration at
the center of each compartment is seen as cl and e2,
i.e., the mean concentration.
this points up most clearly the fundamental
nature of the movements described by the
phenomenologic flux equation, it is instructive to reproduce his analysis with some interpolations and comments.
Before proceeding, we must be aware of an
important property of the Gaussian particle:
if the particle is observed repeatedly at constant intervals of time r, the arithmetic mean
of the squares of the displacements, A2, is equal
to 2D , where D is a constant equal to 1½2 nl2,
n is the jumping frequency and I is the length
of the unit step. Let us now choose a region
at x in a distribution of particles (fig. 2A)
whose concentration as a function of x is seen
in figure 2B, and then confine our attention to
2 rectangular compartments of equal size on
either side of x as shown. The width of the
elements are chosen to be JAY/2 cm. The sides
are unit area (1 cm.2). Each of the particles
contained in either element will suffer an individual displacement, so that a distribution
of displacements in time r will result; the
root mean square of this distribution is vZ'.
Thus, it is clear that for the population of
particles in each compartment, one half will
suffer a displacement +J\/s2 and one half
-JA2. These conditions are the direct consequence of the fact that the particles are subject to the Gaussian probability function.
Since the width of the compartments is
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MAURO
848
Conc.
I-
--
---
2A-
100 90 80 70 60 50
255
5
S
5
5
5
Figure 3
A. Top. Plot of concentration that varies linearly
with distance x. B. Bottom. Compartments showing
total number of particles moving equally in both
directions and the net number from left to right
in the interval of time.
small, it is reasonable to consider the concentrations c1 and c2 at the center of each conmpartment to be the mean concentrations in
the respective compartments. Thus the number of particles crossing to the right through
the unit area at x is
V2c1VN
and to the left
:L/2 C2 2
The net number is then
dN-/2VA2 (c1-c2)
Since this transfer occurred in a time r, we
have the number of particles per unit time,
i.e., the flux is
dN
=
also we note that
de
dx
,24
(c1-c2),
(C1 - c2)
2z
Thus,
2 (c1- c2)
dN _
A2\ de
/2
dt =r
VA
dx
If we were to consider smaller and smaller
intervals of time, remembering that the term
r2
A2
2- is
a
constant, nanmely, D
dN
dt
we
then have
de
dx
the familiar Fick's Equation I. D is known
as the "diffusion coefficient" of the particle.
It is instructive to apply this treatment to
a distribution of particles whose concentration varies linearly with distanee x. The width
of the compartnients corresponds to a certain
interval of time. The number of particles in
each compartment satisfies the condition of a
linear concentration profile. As explained
previously, particles in each compartment will
nmove out in both directions, namely, one half
to the left and one half to the right. The net
transfer betweeln each compartment is seen to
be constant and proceeds from regions of high
to regions of low concentration.
This analysis enables us to grasp the esseinee
of the mode of movement of individual particles involved in the process of diffusioni.
Moreover, we are now in a position to define
a nondiffusional process: any movement of
particles that involves a comnponient that is
iionrandom is thus to be classed as nondiffusiona]. The pure case, of course, comes to mind
in Poiseuille flow, where the gradient of the
pressure is associated with lamiinar flow of
particles. The degree of rectilinear flow can,
of course, vary so that groups of particles cani
move along nonrectilinear paths and thus be
classed as nonlaminar or turbulent flow.
In general, if a solute is present at a given
concentration difference, a diffusion flow of
the solute will obtain; conceurrently, a diffusion flow of the solvent species will take place
in the opposite direction, with a diffusion coefficient equal to that of the solute species. If
the solute-solvenit diffusion is allowed to take
place across a very coarse barrier, e.g., a sinitered glass filter, the only effect of such a
barrier is to reduce the available cross-seetional area for diffusion.
Thus far in our discussion the barrier has
Inot given rise to any unusual effects worthy
of special consideration. However, if the barrier should be modified so that the barrier region begins to offer an impediment to the
movement of particles, then a marked increase
in the movement of solvent into the solution
phase will occur. The maximum flow of solvent occurs when conditions of infinite impedance to the movement of solute particles
through the barrier are attained; at this poinit
the barrier is usually characterized as a semiCirculation, Volume XXI, May 1960
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IONIC AND NONIONIC SEMIPERMEABLE MEMBRANES
permeable membrane, namely, impermeable to
the solute but permeable to the solvent. This
marked movement of water has been known
to biologists for several centuries and has
been referred to as osmosis. It is undoubtedly
one of the most important effects associated
with semipermeability. The question is how
should we look upon this phenomenon, i.e.,
what causes the movement of water-is it a
diffusional or a nondiffusional process? It is
interesting that both points of view prevail
among both physiologists and physical chemists. Since several important points are involved here with regard to the general subject
of semipermeable membranes, it is worthwhile
to discuss the matter in some detail.
If a collodion membrane is arranged between 2 compartments and means are provided via a capillary tube for viewing the
movement of water across the membrane, it is
observed that the relationship between the
rate of movement of water and the log of the
mole fraction of water in 1 of the compartments-the other being pure solvent-is linear.
The movement of solvent is seen to occur from
the pure solvent to the solution. It is important to emphasize that the collodion barrier
is absolutely impermeable to the solute species
used to establish the mole fraction of the solvent. If, for a given mole fraction, hydrostatic
pressure (in excess of the atmospheric pressure present in both phases) of sufficient magnitude to bring the rate of water movement
to zero is applied to the solution, it is found
that the magnitude of this pressure is equal
to the quantity (RT/V) lnN 20 where R is the
gas constant, T is the temperature in degrees
Kelvin, V is the partial molar volume of
water and N is the mole fraction of water.
This quantity is known as the "osmotic pressure" of the solution.* In dilute solution in
which the N His close to unity, the expression reduces to its equivalent, RTe, where c
is the concentration of the solute species. Re*Two other parameters related to the "'osmotic
pressure" are "lowering of vapor pressure" and
"lowering of freezing point." All 3 are related to
the mole fraction of the solvent.
849
peating the above procedure
at a different
value of N HO establishes the fact that the
pressure necessary to reduce the flow of water
to zero is always equal to RTc over a wide
range of dilute solutions. The equivalence of
the mole fraction term, i.e., the "osmotic pressure" of the solution, to the hydrostatic pressure is expressed by the familiar equation:
dt =K (APP-RTc)
where dn
dt
the flow of water per unit time
leaving the solution, K is a constant of proportionality, and AP is the excess hydrostatic
pressure in the solution with respect to pure
solvent.
The immediate question then arises: what
is the nature of the constant K? This is another way of asking about the nature of the
movement of the solvent across the membrane
when it is acted upon either by a hydrostatic
pressure or by a difference in the mole fractions of the solvent across the membrane. The
most direct way of establishing whether K is
a diffusion-permeability coefficient for the barrier under investigation is to apply the more
fundamental form of the diffusion equation;
as indicated by the theory of irreversible
thermodynamics, this equation should be expressed in terms of the gradient of the chemical potential,5' 6 namely,
dn = DA _ dp.
dt
RT dx
where D is the diffusion coefficient of the solvent, A the area of the available "pores," c
the concentration, and ,u the chemical potential. We shall make the reasonable assumption
that the membrane is "uniform" and thus
that the applied AP gives rise to a linear gradient, namely AP/Ax is a constant. Remembering that only pure solvent is present in
the membrane, the chemical potential is simply a function of pressure, thus,
Ay = VTAP and A= V P
is
Ax
and
finally,
Ax
dn DA V AP DA.AP (2)
dt RT
RT Ax
Ax
since eV = 1. The diffusion permeability co-
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850
MATTRO
Table 1
Flux in moles/sec. per dyne/em.2
Membrane
Group I
Group II
Group III
,f
Diffusion
flux4
Total observed
flux
Ratio
diffusion
/total
1.2 X 10-13
5.6 X 10-14
1.1 X 10-14
8.8 x 103.1 10-12
3.9 X 10-13
1/7'30
1/5
1/316
X
25
efficient DA/Ax can be evaluated by performing a tracer experiment with H201 subject
to the familiar form of Fick 's equation,
namely,
DA
(dn
_i
IitH21
Ax
E
HI
15
0
(V1-
o 10
H(
OTc
By sampling the 2 compartmients at suitable
intervals of time and by using the mass speetrometer to determine the concentrations of
H20'" present, the integrated form of the
above equation (see 8) can be invoked to calculate DA/Ax of the membrane. Having established this parameter, we can then estimate
the flow of water which moves by diffusioil
across the barrier when a pressure is applied
by means of equation (2). Data of this
kind7 8 are seen in table 1 for 3 groups of
collodion membranes (see also fig. 4). The
membranes are essentially of the same thickness but have acquired different "pore" sizes
for aqueous flow by suitably modifying the
procedure used to prepare the mnembranes.
The first fact shown by the data is that, in
all 3 groups, the diffusion component, due to
a gradient of chemical potential resulting
from the pressure gradient, is small with respect to the total flux; therefore, the flow of
solvent must have the character of a nondiffusional flow. Many authors0m12 have considered that the flow obeys Poiseuille's law, and
have imagined the barrier to consist of uniform cylindrical pores. These authors have
then proceeded, using comparable data obtained on biologic cells,' to calculate an average "pore" diameter. The second fact is the
convergence of the nondiffusional and diffu*In biologic studies, the movement of water is
induced by osmosis siiaee it is virtually inipossible in many cass to apply a AP across the
cell surface.
usually
I*
01
: 20
C,
. 11
I
0
10
20
30
40
50
60
Centimeters Hg
Figure 4
Relationship between flow and hydrostatic pressure for 3 groups of membranes. Note flux in
cc./mn. per cm. Rg can be converted to moles/sec.
per dyne/cm.2 by multiplying by .7 X 10-7. (Republished by permission of the Journal of General Physiology.8)
sional component when "coarse' membranes
are compared (group I) with the "tight"
membranes (group III). The pertinent data
appear in column 4 of table 1. This convergence supports the eoncept of Poiseuille
flow through pores,8 but somne reservations
should be held about the validity of using the
Poiseuille conductaniee for flow in "pores" of
very small dimensions.
At this point, it is pertiiient to consider
osmotic flow once again, i.e., the flow associated with the presence of an iiupermeant
solute which serves to establish the mole fraction of the solvent at less than unity. Since
the previously described " osmometer " experiment has demonstrated that the mole fraction
term, i.e., the "osmotic pressure" is exactly
equivalent to the hydrostatic pressure, it follows that the mode of transport of water during osmosis and during the application of a
pressure must be identical. Consequently, our
previous discussion indieates that this flow
must be nondiffusional. A further consideration of this matter will now be used to cast
some light on the origin of osmotic flow and
to stress the general importance of considerCirculation,
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Volume XXI, May 1960
IONIC AND NONIONIC SEMIPERMEABLE MEMBRANES
Membvane
5olution
la
Steady 5tate
851
Pure 5olvent
'RMnH2O,,
p
P
5olute conc.
I
Equilibrium
Sout cono
I
_
_
_
_
_
Figure 5
A. Top. Profile of solute concentration, chemical potential of solvent and hydrostatic
pressure for the steady state. B. Bottom. Profile of the same system for the condition of
equilibrium brought about by applying AP to the solution.
ing the "profile " of thermodynamic quantities within barriers.
With the aid of figure 5, we can see the
profile of the chemical potential of the solvent
in the solution phase. Note that the decrement in chemical potential At, is equal to
RTlnNH,O where a value of NHH2O different
from unity has been established by the presence of the absolutely impermeant solute. It
is apparent from a consideration of the interface between the solution and the barrier that
just inside the barrier, where there is only
pure solvent, the continuity of the chemical
potential function can only be satisfied by
another component of the chemical potential,
i.e., VAP. Thus, on the solution side of the
interface the decrement in chemical potential
is RTlnNH O and, in the barrier, -YAP.
It follows, then, that a drop of pressure, -AP,
niust exist at the interface of the barrier and
the solution, and thus serves to act as the
"driving force" for the osmotic flow. The
pressure profile whieh results is seen in figure
5A. Note that the condition of thermodynamic equilibrium is attained whenl a hydrostatic pressure, AP, which is clearly
(RT/V) lnNH20
is applied to the solution. Such a maneuver
is actually carried out with the osmometer to
establish the thermodynamic parameter of the
solution, (RT/V)lnN , which for dilute solutions reduces to its equivalent RTe. The
profile of chemieal potenitial for the conditions
of equilibrium is seen in figure 5B.
The argument pursued here is essentially
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852
MAURO
similar to that advanced by Garby in 195713
and might be classed as a thermodynamic approach. Unfortunately, there is lacking at
present an explicit kinetic theory which explains the origin of the pressure drop, and
thus the osmotic flow. Incidentally, the explicit treatment of the pressure profile in a
barrier seems to have been carried out for the
first time by Schl6gl in 195514 in an attempt
to explain the origin of anomalous positive
and negative osmosis in ionic membranies. We
shall not pursue this matter further except
to emphasize the importance of recognizing,
in general, the existence of the hydrostatic
pressure throughout the membraile phase,
especially for the understanding of ordinary
osmosis.
To underline the role of the pressure gradieit which arises for the condition of absolute
semipermeability, it is instructive to deal with
the case when 2 solutions are present, one containing an absolutely impermeant species and
the other a permeant species.
However, before proceeding, it should be
stated that if the "osmometer" experiment
were performed with a "leakyv" solute, the
effect observed with a given RTc would be less
than the corresponding AP. This is the other
striking property of the osmotic mechanism
which can be succinctly expressed by writing
the osmometer equation given above in its
nore general form,
ddn
K (A P-cFRTc)
where C is a constant-referred to by Staverman15 as the "reflection coefficient"-that
takes on a value approaching zero for very
permeant species and unity for absolutely
impermeant species.
With this in mind we can now consider the
behavior of the case in which 2 solutions interact with a given barrier. It is clear that the
permeant species gives rise to a negligible
pressure drop. Thus, within the barrier, the
gradient of pressure which is due to the
presence of the impermeant species in the
other solution is a "driving force" common
to all species in the membrane. This common
"driving force" imparts a mass flow to both
solvent and permeant solute. Simple and ele-
gant experiments demonstrating this effect
have been conducted by Mesehia and Setnikar"6 on a collodion menmbrane which has
the characteristics of group I cited previously.
Unawarei-ess of the pressure drop in the barrier would pronlpt one to predict that solutions of identical mole fraction, e.g., dextran
vs. urea, would give rise to zero movement of
water, especially if the eustomary use of the
chemical potential of the solvent in either
phase is used in a "discontinuous" treatment
of the barrier. Although this matter will not
be pursued in detail, it will suffice to state
that a "discontinuous" treatment of a barrier
mtust be a "complete" treatmnent involving
chemical potentials of all species, as carried
out by Kedem and Katchalsky.17 Otherwise,
an attempt can be made at a "continuous" approach such as we have outlined above in
order to establish the thermodynamic profiles
within the barrier and thus to predict the
movement of the various species.
Thus far in our discussion we have been
dealing with the characteristics of semipermeable barriers that arise primarily because
the meshwork or network of "porous" material constituting the menmbrane presents a
simple mechanical hindrance to the solute
species. However, it is possible to observe a
broad class of membrane activity which gives
rise to selective ionic permeability and electroniotive forces in additioni to osmotic effects
without involving direct mechanical blocking
of ionic movements. The kernel of this new
mechanism is the Doiinan effect. The most
direct way to appreciate this mechanism is to
imagine a gel made up of macroions, such as
protein or other polyeleetrolyte, and, of
course, of appropriate mobile ions of the same
sign (" coions " ) and of opposite sign (" counterions"). If the gel block is arranged to
separate 2 solutions conitaining coions and
counterions at the same concentration, the
gel phase and the 2 solutions will enter into a
symmetric; ' Donnan equilibrium. One of the
important consequences of this state is that
ions of the sanme sign as the macroions are
present at low concentration approaching
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853
IONIC AND NONIONIC SEMIPERMEABLE MEMBRANES
vanishingly small magnitude as the concentration of macroions is increased. Without
entering into a detailed thermodynamic treatment of the Donnan system, it will suffice
to state that all mobile ions tend to be distributed so that the total chemical potential
of each species is a constant over the entire
geometry. Disregarding for the moment the
role of the pressure component of the chemical
potential, we must now consider another important component, the electrical potential.
Analysis indicates that an electrical potential
variation or profile must exist throughout the
interface of the gel and the solution arising
from a statistical diffuse " double layer. "18 In
fact, it is the interplay of this profile of electrical energy and the concentration component
of the chemical potential that brings about the
equilibrium condition. If the solutions have
different concentrations, the state now is
" asymmetric, " that is, the 2 gel-solution interface regions remain very close to the Donnan
equilibrium, but throughout the gel a diffusion
regime of ions is established. (Profiles of potential and concentration can be seen in figures 6 and 7; these profiles were19 obtained
from a realistic model.) If the macroion concentration is very large with respect to the
ions in either solution, the "tilt" of the concentration profile throughout the gel is minimal, and thus diffusion is minimal. The gel in
this case is referred to as being semipermeable
to the electrolyte, but selectively permeable to
the counterions present in the gel. If the polyelectrolyte is associated with a 3-dimensional
network of polymers to which ionogenic
groups are attached by chemical forces, this
matrix as a whole will display exactly the
same properties as the gel and is referred to
as an ionic membrane, or, to emphasize the
immobility of the ionogenic groups, as a fixedcharge membrane. The theory of such a barrier as we have outlined is contained in the
papers of Teorell20 and Meyer and Sievers.
The more complete treatment which takes into
account the role of pressure profiles as well as
the concentration and the potential has been
carried out by Schldgl.4 It should be emphasized that by increasing the density of
N EGATIVELY CHARGED M EM BRAN E
(POLY STYR ENE SULPHON IC ACID)
221
20d
18
16n
14-
1210-
86-
420-
5040an
i-
30-
-J
0
I
71,
AV
20-
10-
0-
t
ir
A
-10-
I
02i0
SOLUNTIH
| 7 6 5
4 3 2
SI
|10I2NH
Figure 6
Model of ionic membrane constructed by use of
multicompartment cell. Polystyrene sulfonic acid
provides negatively charged macroions. The profiles of concentration aKnd potential are seen
throughout the "membrane." (Republished by permission of the Journal of General Physiology.19)
cross-linking, the matrix will eventually display, in combination with the Donnan effect,
the properties of mechanical hindrance to solute species, suggesting to many investigators
the concepts of "pores" and "channels."
This brief treatment of some properties of
"inert" membranes, both ionic and nonionic,
Circulation, Volume XXI, May 1960
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854
MAURO
POSIT VE LY
CHARGED M EM BRAN E
N )
( GEL AT
3.
14:
r..
6.
12-
-J
I0-
IJ
:
8-
7.
(I)
6-
8.
0
2
4-
-J
-J
2-
-j
OJ
9.
30U)
200
-J
10-
1 0.
TI
-J
zv
0-
SOLUTION-_1
7
6
10 3N H C
_
5 4
3
_
2
SOLUTION2
10-2N
11.
HC 1
Figure 7
1-.
Model of positively charged membrane using gelatin to provide positive macroion. (Republished by
permission of the Journcal of General Physiolo-
13.
g.'Jt 9)
should serve to illustrate the interrelationlship
between various physical chemical parameters
in relatively simple systems anid perhaps to
shed though feebly, some light on the cauldron of activity in physiologic mnembraines.
References
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Circulation, Volume XXI, May 1960
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Some Properties of Ionic and Nonionic Semipermeable Membranes
ALEXANDER MAURO
Circulation. 1960;21:845-854
doi: 10.1161/01.CIR.21.5.845
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