The Structure of Water and Electrolyte Solutions
By RICHARD J. PODOLSKY, PH.D.
Intermolecular forces tend to organize water molecules into a tetrahedral lattice, conferring "crystalline" properties on the liquid. The simple ions, such as Na+, K+, and Cl-,
have dinmensions which are of the same order as the water nmolecule. Therefore, in aqueous
solution, ions can substitute for water molecules in the water lattice. However, because
the force between ion and water molecule differs from the force between 2 water molecules,
the properties of the lattice are perturbed by an ion. Transport processes in electrolyte
solutions are analyze,d in terms of the sp,ecific lattice perturbation produced by each ion.
This approach is contrasted with the classical hydrodynamic model in which ions in solution are treated as spheres in a continuous fluid. The relevance of ionic transport in
aqueous solution to the transport across biologic membranes is brieflv discussed.
Downloaded from http://circ.ahajournals.org/ by guest on September 30, 2016
Theory of Dissociation
ABOUT 70 years ago Arrhenius invented
the theory of dissociation to account for
the conduction of ani electric current through
an electrolyte solution. In his day the textbooks taught that electrolytes were neutral
molecules which decomposed into charged
particles as a result of the applied voltage.
However, while thinking about the measurements of conductance which he was making
for his doctor's thesis, it ocecLrred to Arrheniiis
that the charged particles that make a solution
conduct might exist before current passed
through the solution. This wouLld mean that an
electrolyte dissociated into ions the moment
it dissolved, and that these ions would carry
an electric current wirhen driven by an applied
voltage.
The theory of dissociation worked well in
explaining several important chemical problems of the day. For example, van't HToff was
studying the osmotic pressure and the lowering of the freezing point of solutions. He discovered that a nonelectrolyte produced an
osmotic pressure, or lowered the freezing point,
according to the number of molecules in the
solution. But electrolytes were anomalous;
they had a much greater effect than expected
on the basis of the number of mnolecules. By
taking dissociation into account and calculating the effect according to the nui-nber of particles in the solution, the difference between
electrolytes and nonelectrolytes disappeared.
The question of why electrolytes dissociated
was sidestepped by Arrhenius. A few years
later, though, Thomson, and then Nernst, correlated dissociation with the dielectric constant of the solvent. They pointed out that the
forces between charged particles would be
considerably reduced in a medium of high
dielectric constant. Specifically, according to
Coulomb's law, the force between 2 charges is
inversely proportional to the dielectric constant of the intervening medium. Thus in
water, with a dielectric constant of 80, the
force between ions will be 80 times less than
in the crystal, and there will be a strong
tendency to dissociate. This argument made
the phenomenon of dissociation seem more
sensible, and the Arrhenius theory was generally accepted at the close of the nineteenth
eentury. Biologists were quick to see its implications, and this symposium shows how
fruitful a good idea can be.
Hydrodynamic Model for Ionic Transport
Having worked out the general mechanism
of electrolytic conductance, it was natural for
biologists to try to account for the properties
of specific ions. Thinking centered on aqueous
solutions since water is the most common solvent. At first a hydrodynamic model was used.
In analogy with macroscopic spheres in
liquids, an ion was thought of as a charged
particle embedded in a continuous fluid. When
a macroscopic sphere passes through a liquid,
a frictional force develops which is propor-
From the Naval Medical Research Institute, Beth-
esda, Md.
818
Circulation, Volume XXI, MaV 1960
STRUCTURE OF WATER AND ELECTROLYTE SOLUTIONS
819
a
F?igure 1
The closest packing of spheres. (Republished by
permission of Interscience Publishers.2a)
Downloaded from http://circ.ahajournals.org/ by guest on September 30, 2016
tional to its size: the larger the sphere, the
greater the drag. It did not seem unreasonable
to suppose that the different mobilities of the
ions could be explained in terms of the sizes
of the particles in solution. However, this approach soon led to difficulties, largely because
the size of simple ions is of the same order as
the size of the water molecule. From the ionic
point of view, water is by no means a continuous fluid.
Studies of fluidity provide the clearest evidence that the ions in a solution cannot be
regarded simply as a collection of small
spheres in a liquid. According to classical hydrodynamic theory, adding particles to a
liquid can only increase the viscosity, that is,
make it less fluid. The change in fluidity
should be proportional to the volume fraction
of the added particles.' Although this effect
is used to measure macromolecules, for particles as small as ions it is apparently swamped
by another factor. Solutions of cesium iodide,
for example, are more fluid than pure water,
which is embarrassing for the hydrodynamic
model.2
Structure of Water
We now know that many of the puzzling
properties of ions in water are due to the
unusual nature of water. Water is a very unusual liquid; indeed, as we shall see, water is
more like a crystal than like a fluid.What distinguishes an "unusual" from a
"usual" liquid? One difference is the way
Circulation, Volume XXI, May 1960
b
Figure 2
The face-centered cubic lattice. (Republished by
permission of Nature.2b)
the molecules are packed together. In a
'usual" liquid the molecules can be treated
as hard spheres which interact with each other
only on contact. The most stable packing is
that which maximizes the number of contacts. The spheres will form layers, 2 of which
are diagrammed in figure 1. In the first layer
the spheres are in staggered rows. Those in
the next layer (thinner lines) fall into vallevs
shaped by the first layer. Each sphere has 12
nearest neighbors: 6 in its own layer, 3 in the
layer above, and 3 in the layer below. This is
the closest packing for a collection of similar
spheres.
This array might be more familiar as the
face-centered cubic lattice (figure 2a), the arrangement of the chloride ions in the sodium
chloride crystal. (The sodium ions are small
enough to fit into the spaces between chloride
ions.) The layers in figure 1 are revealed by
sectioning the lattice at 450, as shown in
figure 2b.
The distance between molecules in the liquid
state can be measured by x-ray scattering.
Knowing this, and the molecular weight, we
can easily calculate what the density would
820
PODOLSKY
Downloaded from http://circ.ahajournals.org/ by guest on September 30, 2016
Figure 4
Figure 3
Schematic representation of an isolate(l uwate)
molecule. (Republished by permissione of Researeh.4)
be if the molecules were closely packed.@ Conversely, if the density, calculated oln this basis,
turns out to be correct, the molecules are inideed closely packed. Such is the case for typical, or "usual?" liquids like argon and
methane. But for water (2.9 A betweeni centers) the calculated density is 1.7 Gm. 1/rl.,
nearly twice the actual densitv, which mneans
that the molecules are far from closely packed.
And, indeed, x-ray data show that the average
number of nearest neighbors is not 12, but
between 4 anid 5.3
For the liquid to have this open structure,
there mlust be relatively strong directional
forces between lneighboring water imolecules.
These forces arise from the electroniie distribuition of the isolated water molecule, schematized in figure 3.4 The 4 pairs of valence-shell
electronis in water occupy 4 orbits (the hatched
ellipses) which extend out tetrahedrally froml
the oxygein niucleus, 0. The 2 pairs of electrons
which forin the A and B orbits, the valeniceshell electronis, are associated with the OH
bonds; the other 2 pairs, C and D, are, for obvious reasons, called "lone pairs. " Largely
because the orbits of the "lone pair" electrons
*A cube with an edge of 1 can hold 1/%32 r
spheres in closest packing, where r is the sphere
l adiuls.
The ideal water lattice. (Republished by permis-
sio$n of Acta Polqte (hnica
[Sweden1 .4a)
are directed away from the electrically positive regions of the muolecule, the celnters of negative and positive charge do not coincide. This
electrical asvmmlietry is the source of the
dipole maomenit of the molecule, which, in turn,
is responsible for the electrostatic interaction
between water imolecules and ions.
AVater molecules have a tendency to stick
together by formingio hy drogen bonds. The
bond is dcue to the initeraetion of the "'lone
pair" eleetrons of onie water mnolecule with the
proton of a second water molecule. Since the
4 electroniie orbits are tetrahedral, anid since
each cali be involved in a hydrogen bond, it
is clear that a population of water molecules
w-ill ten-d to form a tetrahedral lattice (fig. 4).
This is the arrangement of the molecules in
ice, and, as we kniow from the low density,
imiuch of the structure remains in the liquid
state also.
We see, theni, that the structLtured natuLre of
liquid water-called "iee-like-iess " by some
authors2° -7-can be traced back to the fact
that each water molecule tends to form hydrogen bonds with 4 other water molecules. Thermual motionis lead to rupture of some of the
hydrogen bonds, so the degree of structure
will depend oni the temperatuLre. To the extent
that water is ice-like, the molecules can be
thought of as distributed amionig the sites of
a tetrahedral lattice.
Circulation, Volume XXI, May 1960
821
STRUCTURE OF WATER AND ELECTROLYTE SOLUTIONS
o
'
2
3q
0
9i
#
0
F
&*
0Al
Ol
J
0C+*
N4"
o
0
0
0
5 i"
pA
56.
C/
oo o
5-
ri 4#
0
'a
Cal
Qr
Cd',
A/3
Y,W
0
Downloaded from http://circ.ahajournals.org/ by guest on September 30, 2016
sa3
Lci'
7e~~~I
Ce4'
5
15
i6#
,45s
0
01
J
0
&
B7
0. 0mu14'
MO
cbo
Cb
gf.
5
0
,57h
r
5+
4oe41
zr,4-
BZn
S1
06-Zr-
017.1
1
Cs
Au
Figure 5
The crystal radii of the atomic ions. (Republished by permission of Cornell University
Press.9)
The obvious difference between water and
ice-the fluidity-reflects the relative ease with
which molecules can jump between lattice
sites in the 2 states. In ice, the molecular coordination is so rigid, and the thermal vibrations are so feeble, that jumps between lattice
sites are extremely rare. At liquid temperatures, however, enough of the coordination is
broken so that the more vigorous thermal motions lead to molecular jumps, or Brownian
motion, between lattice sites. In a sense, each
molecule is locked in a "c age " formed by
interaction with its neighbors. The energy required for the jump, the activation energy, is
really a measure of the tightness of the "cage "
which binds the molecule.8 The activation energy can be influenced by physical factors,
such as temperature and pressure, and, as we
shall discuss subsequently, by introdueing ionls
into the lattice.
The lattice structure accounts for many of
Circulation, Volume XXI, May 1960
the curious properties of water. For example,
the anomalous increase in density between 0
and 4 C. is due to the better packing of the
molecules after some of the structure is
melted. Beyond 4 C. this effect is masked by
the usual expansion resulting from the greater
amplitude of molecular vibration.
Sizes of Ions
Before considerinig electrolyte solutions, I
should like to say a few words about the iolns
themselves. By assigning a 'radius" to eaeh
ion, it is possible to predict a great many properties of ionic crystals. For example. the interionic distances in crystals and the crystal
energy can be reckoned very accurately by
treating the ions as hard balls of the appropriate radius.9
For atomic ions the ionic radius can be correlated with the position of the element in the
periodic table, as shown in figure 5. The radius
822
PODOLSKY
Ei~~~~®O3
0 0 0i
Downloaded from http://circ.ahajournals.org/ by guest on September 30, 2016
1*
a
Ca.
P04 50;~ClO,, MnOQCrO
to
o0
I
0
E*
Pb
I
I
I
1
e
3 4
I
I
5A
Figure 6
Crystal dimensions of some simple ions. (Republished by permission of Cornell University
Press.9a)
of the circle is proportional to the (univalent)
crystal radius of the ion. In a given row, the
ions decrease in size, from left to right, because the increasing nuclear charge for the
same number of orbital electrons tends to pull
the electrons closer to the nucleus. Down the
columns, there is an increase in both the number of orbital electrons and the nuclear charge,
but since there is no change in the net charge,
the radii are somewhat more uniform than
across a row.
A water molecule is very nearly the same
size as the oxygen ion. Since the fundamental
assumption of the hydrodynam-ie model is that
the diseontinuities in the solvent are small
compared with the size of the suspended particle, and since atomic ions are either smaller
than or very nearly the same size as the water
molecule, it is not at all surprising that the
hydrodynamic model is less than adequate.
Even the simpler molecular ions, shown in
figure 6 together with some of the biologically
iunportant atomic ions, would encounter considerable granularity in nioving through
water. The forest is lost for the trees.
Lattice Model for Aqueous Electrolyte Solutions
Suppose an electrolyte is dissolved in water.
To a first approximation, the ions will occupy
the same lattice sites as the water, that is, they
will fit into the lattice substitutionally (fig. 7).
On the left, a water molecule is tetrahedrally
coordinated with 4 neighbors. The black
patches locate the hydrogen nuclei. Since the
structure is held together by hydrogen bonds,
the black patches are opposite the "lone pair '
orbits. On the right, an ion is substituted for
the central water inolecule. This substitution
wixill lead to ehanges in the water lattice. Sincee
Circulation, Volume XXI, May 1960
STRUCTURE OF WATER AND ELECTROLYTE SOLUTIONS
,a
823
a
SUBSTITUTIONAL IONIC SOLUTION
Figure 7
Water structure and a substitutional ionic solution.
WATER STRUCTURE
Downloaded from http://circ.ahajournals.org/ by guest on September 30, 2016
the ion is a monopole rather than a dipole,
its electrostatic field will interact with the
dipole moment of the water molecules and
tend to rotate 2 of the 4 adjacent water molecules. An anion, for example, will attract the
positive ends of the adjacent water dipoles
toward the center of the tetrahedron, and
this rotation will disturb the coordination of
the next shell of water molecules. Of course,
the influence of the ion on the lattice structure
will fall off with distance, and, far from the
ion, the lattice will be unperturbed.
Before leaving this figure, I should like to
point out that the electrostatic interaction of
an ion with water dipoles (in the first shell
and beyond) can, in a sense, be compared with
its interaction with counter ions in a solid
crystal. Carrying this thought further, anl
aqueous electrolyte solution can be taken as
liquid crystal of variable composition. Then
dissociation in water would simply be the
mixing of 2 compatible crystals, a point of
view that might have dissolved sonie coneeptual difficulties of Arrhenius' day.
Transport Processes
It is convenient to think of an ion as a
modified water molecule, considerably different in charge, and different in size. These
differences will change the activation energy
necessary for lattice jumps among sites in
the neighborhood of the ion. The magnitude
Circulation, Volume XXI, May 1960
of the change, which depends on the ionic
species, will be reflected in a corresponding
change in various transport processes. For
example, consider an ion that interacts with
the adjacent water moleeules so that they
move about the lattice more easily. Then the
self-diffusion of water in the presence of the
ion will be greater than in pure water. Also,
since the ion itself is locked in a "cage "
made up of the water molecules around it, the
ion will also move more freely in this case.
Conversely, if the ion-solvent interaction is
such that water molecules near the ion move
with greater difficulty, the ion within the
"cage" will also move less freely.
According to this picture, then, both ions
and water molecules are distributed among
the sites defined by the water lattice. But each
ionic species modifies the structure of the lattice around it in a specific way. The activation
energy for lattice jumps of both the ion and
the water molecules around it, the perturbed
water, will be different from that of the unperturbed water, the difference depending on
the ionic species. The change in activation
energy will be reflected in both the ionic and
the water mobility.
The simplest way of measuring the influence
of an ion on the water lattice is to measure the
fluidity of the solution. All the particles occupying the lattice sites will contribute to
the fluidity: the ions themselves, the water
PODOLSKY
824
log MOBILITY
Downloaded from http://circ.ahajournals.org/ by guest on September 30, 2016
RELATIVE FLUIDITY
Figure 8
Dependence of the limiting mobility of the alk;ali ions
and Dole p)aram/eter B.
perturbed by the ions, and the water uninlfluenced by the ions. If anl ion breaks up the
structure of the waters aroun-d it, the solutiol1
will be nmore fluid than pure water. Coniversely, if an ion interacts with the neighboring particles in such a way as to make it mnore
difficult for themii to move arounrd, the solution
will be less fluid.
This arguimenit canl be turnied arouind to use
the fluidity of the solution as a basis for calculatinog the activationi energy of both an ion
and the water molecules with which it interacts.'0 This activation energy cani then be
used to calculate the mobility of the ions (the
electrical conductivity of the solutionl) and
the mobility of water (the rate of diffusioni of
labeled water through the solutioni).
Analysis reveals that the ioniie mobility
should be exponentially related to the fluiditv
of the solution.'0 To test the result of this
analysis. data for the alkali ions have been
on
the relative fluidity, the Jo-nes
plotted in figure 8. The abscissa is a measure'
of the influence of the ion on the fluidity of
water: with an anion that has no effect on the
water structure, solutions with cations on the
right of zero, e.g., potassium, rubidiun, and
especially cesium, are more fluid than pure
water; sodium, and to a greater extent, lithium, decrease the fluidity of the solution. The
ordinate is the logarithm of the corresponding
mobility. The data fit the expected linear relationi quite satisfactorily. It should also be
nioted that the smaller erystal radius is correlated with the lower mobility, a point which
will be discussed subsequently.
This relation is not restricted to the alkali
ions. Figure 9 displays data for 38 different
species for which both fluidity and mobility
data are available. All the ions have crystal
radii less than 4 A. Three points, in paren*The datum used is the Jones aiid Dole parameter
B.10
Circulation. Volume XXI) May 1960
825
STRUCTURE OF WATER AND ELECTROLYTE SOLUTIONS
Downloaded from http://circ.ahajournals.org/ by guest on September 30, 2016
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0
+0.1
Bi
Figure 9
Dependenc(e of the limiting ionic mobility on the relative fluidity, the Jones and Do le
parameter B. (Republished by permission of the Journtal of the American Chemict
Society.10)
theses, triinethylammonium, tetraethylammoniium, and lanthanum, are clearly out of line.
But the scatter about the expected linear relation does Ilot seem unreasonable, especially
sin-ce the fluidity data are fronm many sources,
some quite old.
The structure-breakinlg-or structure-forming-effects of the ionis are also reflected in
their influence on the self-diffusion of water.
In these experiinents, the diffusion of labeled
water across an electrolyte solutionl is compared with the diffusion through pure water.
Whether the tracer moves througb the solution
more or less rapidly thanl in pure water should
depend on whether the ionis break, or
strengthen, the lattice arounid them, which,
as has been discussed previously, can be decided from the fluidity of the solution (fig.
10). The ordinate is the chanige in the selfdiffusion of labeled water, and the abscissa,
as in figures 8 anid 9, is a measure of the
fluidity of time solutioni. For example, a molar
Circulation, Volume XXI,
May
1960
solution of potassiuim iodide, at 10 C., is about
12 per cen-t more fluid than pure water at that
temperature; labeled water diffuses through
it about 13 per cent faster than in pure water.
The straight line was calculated from the
model ;10 the points are the experimental findings for the 3 salts, KI, KCl, and NaCl, at
the indicated temperatures." That the model
also works in this case is especially significant
siniee the slope anid initercept of the straight
lilne were derived without benefit of adjustable
paramneters.
Ionic Hydration
Until now, I have purposely avoided the
problem of ionic hydration, that is, the question of whether ani ion miigrates alone or with
a number of attached water mllolecules. The
concept of hydration was invelnted to explain
why the ions with smaller crystal radii are
generally less mobile than those with larger
erystal radii. It was argued that the water
dipole would be attracted and locked to the
826
PODOLSKY
(D- Do)
Do
0.15
-
I~~~~~~K 100
0.10
Downloaded from http://circ.ahajournals.org/ by guest on September 30, 2016
KI250
0.05
KCI0100
-
0
NoCI100
* /
O0
c0o05
NaCI250
-01
0.1
0
(B)
RELATIVE FLUIDITY
Figure 10
Dependence of D, the self-diffusion coefficient of water in electrolyte solutions, on B,
the Jones and Dole parameter. (Republished by permission of the Journal of the American Chemical Society.'0)
smaller ions since the electric field at the surface of an ion increases with decreasing
radius. Then the hydrodynamic unit-the
cluster of particles that stick together in
Brownian motion-would actually be larger
for the ions having the smaller crystal radii.
This has always beeii a murky point in the
theory of electrolytes. Direct studies, with
tracers, show that the water around small.
highly charged ions-e.g., aluminum, with a
charge of 3, and thallium, with a charge of 4exchanges, within a few minutes,12 with moleCirculation, Volume XXI, May 1960
STRUCTURE OF WATER AND ELECTROLYTE SOLUTIONS
Downloaded from http://circ.ahajournals.org/ by guest on September 30, 2016
cules far from the ion. Whether water sticks
to these ions for the shorter times involved in
diffusion is not known. If the hydrodynamic
model for ionic transport is put aside, the
evidence for a rigidly bound shell of water on
the smaller ions becomes quite tenuous.
An energetic rather than a geometric factor
probably lies behind the lower mobilities of
the smaller ions. The interaction of the ionie
field with the dipole moment of the adjacent
water raises the activation energy which is
necessary for motion of these waters. This
effect can be large, compared with structure
breaking from disruption of the water lattiee,
in the high fields of the surface of the smaller
ions. If the net result were a tighter "cage"
around the ion, the ion would have a correspondingly lower mobility.
Conclusion
I think the lesson to be drawn from the success of the lattice model in understanding
transport processes in electrolyte solutions is
that the analysis starts with the change in the
solvent due to the ion. This is a turnabout
from the earlier hydrodynamic model in which
the solvent properties were supposed to be Uninfluenced by the ion and the differences
among ionic solutions were attributed to the
sizes" of the ions in solution, an elusive property which could never be pinned dowln. In
the lattice model, on the other hand, the water
structure is changed in a specific way by each
ionic species. This change depends on the way
the lattice adjusts to the differences between
the force field of an ion and that of a water
molecule, or, more simply, on how the ion
"fits" into the water lattice.
With regard to membrane transport, the
relative mobility of ions in the membrane
and in water will be the same to the extent
that ions move through "wide" channels containing water with lattice properties like pure
water. However, if the water lattice is modified by the membrane, as would happen in the
case of "narrow " pores, there is no direct
way of relating transport in the membrane to
transport in water. As in the case of water,
the dominant factor is probably the reciprocal
Circulation, Volume XXI, May 1960
827
interaction of ion anid solvent. This interaction
might be the reason for some of the difficulties
encountered in explaining membrane specificity in terms of either crystal radius or ionic
mobility in water.
1.
References
EINSTEIN, A.: Eine neue Bestimmuung
kuldimensioneai. Ann. Phys. Lpz.
der Mole19: 289,
1906.
la. -: Berielitigung zu meiiner Arbeit: Eine neue
Bestimmung der Molekuldimensionen. Ann.
Phys. Lpz. 34: 591, 1911.
2. GURNEY, R. W.: Ionic Processes in Solution. New
York, MeGravw-Hill, 1953.
2a. RUTGERS, A. J.: Physical Chemistry. New York,
Interscience Publishers, 1954, p. 140.
2b. BARLOW, W.: Probable nature of the internal
symmetry of crystals. Nature 29: 186, 1883.
3. MORGAN, J., AND WARREN, B. E.: X-ray analysis
of the structure of water. J. Chem. Phys. 6:
666, 1938.
4. COULSON, C. A.: The hydrogen bond: A review
of the present position. Research 10: 149,
1957.
4a. FORSLIND, E.: Theory of water. Acta polytechnica 115: 33, 1952.
5. BERNAL, J. D., AND FOWLER, R. H.: Theory of
water and ionic solution, with particular reference to hydrogen and hydroxyl ions. J. Chem.
Phys. 1: 515, 1933.
6. FRANK, H. S., AND EVANS, M. W.: Free volume
and enitropy in condensed systems. III. Enitropy in binary liquid mixtures; partial molal
entropy in dilute solutions; structure and
thermodynamics in aqueous electrolytes. J.
Chem. Phys. 13: 507, 1945.
7. --, AND WEN, W. Y.: Ion-solvent interaction:
Structural aspects of ion-solvent interaction in
aqueous solutions; a suggested picture of
wi-ater structure. Disc. Farad. Soc. 24: 133,
1957.
8. GLASSTONE, S., LAIDLER, K. J., AND EYRING, H.:
Theory of Rate Processes. New York, Mc
Graw-Hill, 1941, chaps. 9 and 10.
9. PAULING, L.: Nature of the Chemical Bond.
Ithaca, Cornell University Press, 1945, chap. 10.
9a. BRAGG, W. L.: Atomic Structure of Minerals.
Ithaca, Cornell University Press, 1937, p. 30.
10. PODOLSKY, R. J.: Transport processes in electrolyte solutions. J. Am. Chem. Soc. 80: 4442,
1958.
11. WANG, J. H.: Effect of ions on the self-diffusion
and structure of water in aqueous electrolytic
solutions. J. Phys. Chem. 58: 686, 1954.
12. HUNT, J. P., AND TAUBE, H.: Exchange of water
between hydrated cations and solvent. J. Chem.
Phys. 19: 602, 1951.
The Structure of Water and Electrolyte Solutions
RICHARD J. PODOLSKY
Downloaded from http://circ.ahajournals.org/ by guest on September 30, 2016
Circulation. 1960;21:818-827
doi: 10.1161/01.CIR.21.5.818
Circulation is published by the American Heart Association, 7272 Greenville Avenue, Dallas, TX 75231
Copyright © 1960 American Heart Association, Inc. All rights reserved.
Print ISSN: 0009-7322. Online ISSN: 1524-4539
The online version of this article, along with updated information and services, is
located on the World Wide Web at:
http://circ.ahajournals.org/content/21/5/818
Permissions: Requests for permissions to reproduce figures, tables, or portions of articles
originally published in Circulation can be obtained via RightsLink, a service of the Copyright
Clearance Center, not the Editorial Office. Once the online version of the published article for
which permission is being requested is located, click Request Permissions in the middle column of
the Web page under Services. Further information about this process is available in the Permissions
and Rights Question and Answer document.
Reprints: Information about reprints can be found online at:
http://www.lww.com/reprints
Subscriptions: Information about subscribing to Circulation is online at:
http://circ.ahajournals.org//subscriptions/