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Hydration Structure and Intermolecular Interaction in Polyelectrolytes.

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Table 2.
Kinetic constants of peptide-enzyme interaction.
Pepsin
( K M or K I . moleil)
No.
Peptide
(23)
(24)
(25)
(26)
(27)
(28)
(29)
Ac-Leu-Tyr-NHCH3 LL
Ac-Tyr-Leu-NHCH3 DD
Ac-Leu-Tyr-NHCH, LD
Ac-Tyr-Leu-NHCH, LD
Ac-Leu-Tyr-NHCH, DL
Ac-Tyr-Leu-NHCH, D L
Ac-Leu-Tyr-NHCH, DO
KM
= 2.7
K1 [a]
K I [bl
KI [bl
=
5.8
x 10-3
x 10-3
=
x
=
x
1.2
1.3
KI [bj = 1.5
KI [b] = 1.8
K I [bl = 7.5
Chymotrypsin
(KI,
molell)
x 10-2
x
Y 10-3
havior of all the dipeptides (25)-(29) which are not
topochemical analogs of (23). Their interaction with
pepsin cannot be described by equations for competitive inhibition. These peptides exhibit “mixed” inhibition with noncompetitive inhibition strongly predominating (a = 1.8-3.2).
Even more definite results were obtained in studies of
the interaction of protected dipeptides (23), (24), (26),
and (27) with chymotrypsin. The process studied was
the inhibition by these dipeptides of chymotrypsincatalyzed hydrolysis of p-nitrophenyl pivalate. In this
case the inhibition constants of the dipeptides could
be compared without determination of the Michaelis
constant which gives only an approximated picture of
the binding of the substrate to the enzyme. As is shown
in Table 2, the KI values for the retro-enantiomers
(23) and (24) coincide within the limits of experimental error. The dipeptide (26) binds with chymotrypsin less efficiently, and compound (29), which is
an antipode of the dipeptide (23), and is usually a
priori regarded as an inhibitor, showed no inhibiting
effect under the experimental conditions.
Received: July 8, 1968
[A 706 IEl
German version: Angew. Chem. 81, 523 (1969)
Hydration Structure and Intermolecular Interaction in Polyelectrolytes
By G. Zundel[*l
In hydration, the intermolecular interaction is of decisive importance, since the ions
modify the properties of the hydration water molecules, and the water molecules in turn
have a strong influence on the interaction between the ions. These processes can be studied
in detail with the aid of I R spectroscopy, which in addition provides a picture of the
hydration structure. IR spectroscopy also shows thaf the excess protons are in energy
bands and allows the detection of the proton dispersion forces acting between tunneling
protons. The results of I R studies on polyelectrolytes contribute to our understanding of
the many biological processes that depend on the behavior of ions.
1. Introduction
In biological events, intermolecular interaction is just
as important as chemical bonding. This “intermolecular” interaction is due to weak bonds, e.g. hydrogen
bonds, linking molecules or the functional groups of a
macromolecule. It is important in particular to the hydration processes, and hence to all biological processes
involving ions.
Methods of molecular physics that have little effect on
the system are particularly suitable for the investigation of intermolecular interaction. Since IR quanta
have relatively low energies, they cause no appreciable
changes in the systems, and IR spectroscopy accordingly offers a promising method.
The intramolecular vibrations occur in the middle
infrared region. The bands in this region provide information about the changes in the molecules due to
[ * ] Priv.-Doz. Dr. G. Zundel
Physikalisch-Chemisches Institut der Universitst
8 Miinchen 2, Sophienstrasse 11 (Germany)
Angew. Chem. internnt. Edit.
Vol. 8 (1969) 1 No. 7
the intermolecular interactions, since these interactions
influence the potential wells in the molecules and so
displace the IR bands. Moreover, the bands due to
intermolecular vibrations can be observed in the far
infrared. This could yield direct information about the
intermolecular bonds, which are very important to our
knowledge of the nature of the liquid state. Practically
no such investigations in the far infrared have however
been carried out as yet.
One difficulty that arises in the spectroscopic study of
homogeneous liquid electrolyte solutions is that in
addition to the water of hydration, such solutions
usually also contain water that is influenced little or
not at all by the ions, and the TR bands of this water
mask the bands due to the water of hydration. IR
spectroscopy is therefore best suited to the investigation of very concentrated solutions, and particularly
to the study of polyelectrolytes.
The present article deals with investigations on organic
ion exchangers (salts and acids derived from polystyrene). In these substances, the ions of the one kind
are fixed to a polymeric network (fixed ions), while
499
those of the other kind move more or less freely in
this network. Ion exchangers of this type are simple
model substances for systems of biopolymers.
A brief survey of the I R bands that provide information
about the intermolecular interaction in these substances[*] will serve as a basis for later discussion.
These are firstly the bands due to vibrations in the
anions. Figure 1 shows the antisymmetric (1200 cm-1)
an absorption continuum in the case of the acids if they
are dissociated. If the acids are not dissociated, but
associated, this is shown by a pair of bands due to the
OH or OD groups of the acid (see Fig. 5).
2. The Salts
The fixed ions ( 1 ) - ( 5 ) each contain either three or
two substantially equivalent XO bonds (Fig. 2 together with Table 1). The mesomeric bond resonance
is therefore very extensive in the anions. The -SO3and -SeO3- ions, so far as they are isolated from their
surroundings, thus have a pyramidal structure, i.e.
C 3 v symmetry.
2.1. Cation-Anion Interaction
-7krn-l)
Ir17071/
Fig. 1.
I R spectra of a) polystyrenesulfonic acid hydrated with HzO
- _ at 98 % relative humidity [*I, . . . . thoroughly dried membrane;
b) polystyrenesulfonic acid hydrated with D20 - at atmospheric
humidity over saturated BaClz solution in DzO; c) N a + salt of polyat 98 % relative humidity
styrenesulfonic acid hydrated with H20 -. . . . thoroughly dried membrane; d) N a + salt of polystyrenesulfonic
acid hydrated with D20 - a t atmospheric humidity over saturated
BaCI2 solution in DzO. For positions of the bands due to vibrations of
the anions and acid groups see Table 1. Stretching vibrations HzO
(3700-2800 cm-I), DzO (2750-2050 cm-I), scissor vibrations H20
(about 1640 cm-I), D20 (about 1206 cm-I, masked in Fig. I).
[*I The spectrum was recorded while the membrane was in equilibrium
with water vapor.
and the symmetric (1040 cm-1) SO stretching vibrations of the -Sol- ions ( I ) in the sodium salt of polystyrenesulfonic acid, as well as the antisymmetric and
the symmetric stretching vibrations of the S=O double
bonds (1350 and 1172 cm-1) and the stretching vibration of the SO single bond (907 cm-1) of the -S02OH
group (6) in the undissociated polystyrenesulfonic
acid. Secondly there are the bands due to the water of
hydration (stretching vibrations and scissor vibration).
Thirdly, interesting information can be derived from
171
The antisymmetric stretching vibration of a group
having CjVsymmetry is degenerate, i.e. two vibrations
have the same wave number 181. However, in the spectra of thoroughly dried membranes of the salts of
polystyrenesulfonic acid a doublet is found (Fig. 3)
instead of the expected single band at 1200 cm-1 [*I,
showing that the degeneracy is removed. This splitting
generally increases as the cation becomes smaller and
as its valency increases, i.e. as the field of the cation a t
the anion increases. It is greater for the -SO3- than
for the -SeO,- ion, and hence increares with increasing
polarizability of the anion. The removal of the degeneracy is due to asymmetrical polarization of the
anions by the cations, i.e. to a disturbance of the mesomeric bond resonance in the anions. It is therefore
closely connected with the cation-anion ion-induced
dipole interaction.
Other types o f cation-anion interaction increase the splitting
of the bands if they change t h e structure of t h e anion e.g. t h e
covalent interaction. T h e splitting in t h e presence of transition
element ions is thus much greater t h a n o n e would expect
from the cation field. This is illustrated by comparison of t h e
Znz' ion with Mg*' ion in Fig. 3a. Finally. the splitting
with very small polyvalent cations is n o t so great a s it should
be o n the basis o f the cation field. This is due t o t h e influence
of the fields of the neighboring anionsrll.
2.2. Location of the Cations with Respect to the Anions
[ * ] For the preparation of the substances and methods of in-
vestigation, see [1-61.
[l] G. Zundel: Hydration and Intermolecular Interaction. Academic Press, New York 1969.
[ 2 ] G. Zundel, H . Noller, and G.-M. Schwab, Z . Naturforsch.
16b, 716 (1961).
[3] G. Zundel, Z . Naturforsch. 236, 119 (1968).
[4] G. Zundel, Kunststoff-Rdsch. I S , 166 (1968).
[S] G. Zundel, A . Murr, and G.-M. Scliwab, Z . Naturforsch. I7a,
The cation must be situated asymmetrically with respect to the 0 atoms of the -SO3- ion, since only then
can it disturb the C3" symmetry. It can also be deduced
[?] G . Zundel and A. Murr, Z . Naturforsch. 210, 1640 (1966).
1027 (1962).
[S] K . Nakamoro: Infrared Spectra of Inorganic and Coordination Compounds. Wiley, New York 1963, p. 87.
[*] A vibration of the benzene ring is superimposed at 1128 cm-1
[6] G. Zundel, Chemie-1ng.-Techn. 35, 306 (1963).
u1-
500
Angew. Chem. internat. Edit.
1 Vol. 8 (19691 J No. 7
0
a)
..
::
..
0
w
i
0
0
1
1
1lo
5
I
1
1200
00-
--T
1000
800
650
1200
1000
800
650
800
650
(cm-')
OC
ci
02 -
02
w
04
07
1.0
1.5
'
I
1200
--$
1000
I
I
800
650
15
(cm" )
00
-
1000
1(cm-')
Fig. 2. IR spectra of a) polystyrenesulfonic, b) polystyreneselenonic.
c) polystyrenethiophosphonic, d) polystyreneseleninic, and e) polystyrenephosphinic acids and of the corresponding Na+ salts.
_._. spectrum of the thoroughly dried acid 11.; -spectrum of the
acid after hydration at 98 % relative humidity [*I; . . . . spectrum of the
Na+ salt; ---- spectrum of the salt after hydration with DzO.
e)
..:
1200
[*] In 2c), 2d), and 2e), the bands of these acids are independent of the
degree of hydration in this range.
..__...
....'._
:
02
w
the removal of the degeneracy, and no band due to a
degenerate vibration at 1200 cm-1. It follows that a
cation must be present on every anion. The polyvalent
cations link their anions as shown in the formula. This
is presumably the reason for the membrane-tightening
action of Ca2+ in biological systems [91.
OL
07
10
15
[1711721
1200
-57
I
I
I
1000
800
650
(cm-')
that the cation must be associated with a certain one
atoms' in the direction Of One Of the so
Of the three
bonds. One finds only the two bands that result from
Angew. Chem. internat. Edit. / Vol. 8 (1969) J No. 7
[9] H. Schmidt and R. Staempfii, Helv. physiol. pharmacol. Acta
15,200 (1957).
501
Table 1. Bands of the anions in polystyrene derivatives and assignment of the bands (st
Substance
Na+ salt, bands
Polystyrenesulfonic
acid or Naf salt
=
stretching vibration).
A t high degree of hydration
After thorough drying
at -1200 cm-1, antisymm. s t [a];
1040 cm-1, symm. st of -SOj- (1,
-1200cm-’, antisymm. st [a];
1034 cm-1, symm. st
of -soj- ( I )
1350 and 1172 cm-1,
antisymm. and symm. st
of the double bonds;
907 cm-1, st of the single
bond of -S020H (6)
Polystyreneselenonic
acid or Naf salt
909 cm-1, antisymm. st;
860 cm-1, symm. st
of -SeO3- (2)
879 cm-1, antisymm. st;
847 cm-1, symm.st
of -SeO,- (2) [b]
965 and 911 cm-1, antisymm.
and symm. st of the double
bonds; 725 cm-1 st of the single
bond of -Se020H (7)
Polystyrenethiophosphonic acid or Na+ salt
1218 cm-1, antisymm. PO-st;
1037 cm-1, symm. PO-st
of -pso;- (3)
1170cm-1, st of the PO double bond of -POSHOH (S),
independent of degree of hydration Icl
Polystyreneseleninic
acid or Na+ salt
803 cm-1 [a], symm. st;
776 cm-1 [al, antisymm. st
of -SeOz- (41
839 cm-1, st of the SeO double bond, shifts slightly to higher
wavelengths on drying; 658 cm-1, st of the SeO single bond
of -SeOOH (9)independent of degree of hydration
Polystyrenephosphinic
acid or Na+ salt
1183 cm-1, antisymm. PO-st;
1056 cm-1, symm. PO-st
of -PHOz- ( 5 )
1170 cm-1, s t of the PO double bond; 965 cm-1, st of the PO
single bond of -PHOOH ( l o ) , independent of degree of
hydration
~
~
[a1 Doublet due to removal of degeneracy.
[bl Also (but only weakly) the bands observed o n thorough drying.
[d] Measured for high degree of hydration with D20.
[cl Position of the band of the single bond, see [l].
2.3. The Dissociation Process in Salts and the Nature
of the Ion Pairs 1101
The splitting of the bands decreases with increasing
degree of hydration [*I (see Fig. 3b) but is still present
at a degree of hydration > 5 , as is shown by comparison with the water adsorption isotherms of these substances [11-151. The bonds between the cations and
anions therefore become progressively weaker as the
degree of hydration increases; however, the cations
remain with their corresponding anions even at very
appreciable degrees of hydration. These processes in
the dissociation of the salts are illustrated in Graph 1.
The cations lie in a potential well at the 0 atom of
their corresponding anions. This potential well is influenced by the fields of the hydration water molecules
00
bl
02
w
I
07
10
m
jA70731
1200 1050
-V
Icm-’]
1200 1050
1200 101
Fig. 3. Band doublets of the antisymmetric stretching vibrations of
-SOj- ions a) in the presence of Rb+, Ba2+,Mgz+, AIj+, and Z++; spectra of dried membranes b) as a function of the degree of hydration;
1 to 4 in decreasing order of degree of hydration.
[lo] G. Zundel and A. Murr, Electrochirn. Acta (London) 12,
1147 (1967).
[*] The degree of hydration is defined as the number of water
in such a way as to favor the temporary release of a
cation from an anion. The strength of the bonding in
ion pairs is thus a function of the degree of solvation
and of the solvating medium. The temporary removal
of the ion is the source of the electric conductivity.
A cation ‘‘jumps” to the neighboring anion and forces
molecules per cation.
[ll]E. Glueckauf and G. P. Kirr, Proc. Roy. SOC.(London), Ser.
A 228, 322 (1955).
1121 G. Dickel, Chem. Techn. 1958, 449.
[13] G. Dickel, H. Degenhart, K. Haas, and J. W. Hartmann,
Z. physik. Chern. N.F. 20, 121 (1959).
[14] G. Dickel and J . W. Hartmann, Z . physik. Chem. N.F. 23,
1 (1960).
I151 D . Dolar, S.Lapanje, and S . Paljk, Z. physik. Chern. N.F.
34, 360 (1962).
I
X
U
Graph 1. Schematic representation of the potential well on dissociation
of the salts.
Angew. Chem. internat. Edit.
Vol. 8 (1969) / No. 7
the cation already there to execute a similar jump.
These jumping cations carry some of their water of
hydration with them.
2.4. Hydration at Low Degrees of Hydration
2.4.1. Consequences of t h e C a t i o n - W a t e r
Interaction
Table 2 gives the maxima of the wide bands of the OH
stretching vibration of the hydration water molecules
in salts of polystyrenesulfonic acid, as well as EKH
Table 2. Maximum of the OH stretching band of hydration water
molecules for salts of polystyrenesulfonic acid (low degree of hydration).
EKH
[electrostatically
L.E. cm-21 106
Ion
Li+
Na+
K+
Rb+
cs+
(CH&N+
(C2H5)4Nf
Be2+
Mg2+
Ca2+
Sr2'
Ba2+
AI~+
Ga3+
1n3+
TI,+
Sc3f
Y3+
La'+
Ce3+
Gd3+
zr4+
Hf4+
Mn2+
co=+
Ni2+
cu2+
Zn2+
Fe3+
.
3458 f 2
3459* 2
3460f 2
34621- 2
3459* 2
3449 f 5
3430f 5
3201 f 8
3394 i 5
3406f 10
3412f 10
3440f 10
3195 f 8
3315 i 6
3338 f 6
(3400% 10) [bl
33501 5
3364 f 6
3373 f 6
3369 f 6
3372 f 6
3285 f 8
3280 & 8
3406 i 6
3381 i 6
3373 f 6
3314h 8
3317 f 8
3310f 8
0.68
0.97
1.33
1.47
1.67
1.491
1.078
0.762
0.670
0.568
0.35
0.66
0.99
1.12
1.34
0.51
0.62
0.81
0.95
0.81
0.93
1.14
1.07
0.94 11 1
0.79
0.78
0.80
0.72
0.69
0.72
0.74
0.64
4.46
3.07
2.11
1.85
1.51
5.53
4.78
3.83
3.32
3.83
3.40
2.73
2.93
3.34
5.29
5.33
2.59
2.87
2.94
2.87
2.80
4.71
field. The monovalent cations and the ions of the
transition elements are exceptions to this rule. The
shift shows that the strength of the hydrogen bonds
linking the water molecules to neighboring groups
increases with increasing cation field, since the cation
field polarizes the OH groups of the water molecules.
The dipole moment becomes stronger and the H
atoms become more increasingly positively charged.
The hydrogen bond donor property of these groups
increases 1171. In addition the hydrogen bond acceptor
property of the 0 atoms of the neighboring anions
also becomes stronger with increasing cation field, since
these are also polarized by the cation. This polarization
involves rearrangement of the electrons in the anions
in such a way that two of the three 0 atoms become
stronger acceptors, as is shown by the findings with
acids. In the presence of transition element ions, the
bands show much larger shifts to lower wave numbers
than would be expected from the cation fields (comparison of values for transition element ions and Mg*+
in Table 2). Thus the water molecules are also polarized by covalent interaction of their lone electron pairs
with incompletely occupied d orbitals of the cations 1181.
2.4.2. A n i o n - W a t e r I n t e r a c t i o n
At low degrees of hydration the stretching vibrations
of the OH groups of the hydration water molecules in
the hydrogen bonds are shifted toward lower wave
numbers in the series of the Na+ salts with the anions
( I ) -(j) (Fig. 4).
[a] Maximum error estimated from: number of measurements, superposition of interferences, superposition with other bands, and width of
the bands in question.
[bl The membrane contains TI(OH)2+ as we11 as TI,+
[II.
" I
valuesrl71, which provide a relative measure of the
strength of the cation field at the H nuclei of the water
molecules. In the cation groups, this band moves
toward lower wave numbers with increasing cation
3600
3100
-7
3200
3000
2800
(cm-')
Fig. 4. IR spectra of the Na+ salt of -polystyrenesulfonic, ---- polystyreneselenonic, -. -. polystyreneseleninic. . . . . polystyrenephosphinic acids hydrated with HzO, all membranes at a relative humidity
of 1 1 % . [Anions ( I ) , (21, (41, and 1511.
The strength of the hydrogen bonds linking the OH
groups of the water molecules to the 0 atoms of these
anions thus increases in the same order. Since the
proton acceptor property of the anions also increases
in this order [191, it is not surprising that the hydrogen
bond acceptor property of the 0 atoms in the anions
shows a similar tendency [201.
[16] C. D . Hodgman: Handbook of Chemistry and Physics.
44th Edit.,Chemical Rubber Publishing Co., Cleveland/Ohio 1961.
1171 G. Zundeland A . Murr, Z . physik. Chem. N.F. 54,49 (1967).
Angew. Chem. internuf. Edit. J Vol. 8 (1969) 1 No. 7
[18] G. Zundel and A . Murr, Z. physik. Chem. N.F. 54,59 (1967).
1191 G. Zundel, 2. Naturforsch. 2Za, 199 (1967).
[20] G. Zundel, 2. strukturnoj Chim. 6, 384 (1965).
503
The magnitude of the dipole moment p of the water,
which is of fundamental importance to both the cationwater and the anion-water interactions, thus depends
not only on the dipole moment of the free water
molecule, but also contains a component due to the
interaction with the cation and the anions. The cationwater and anion-water interactions are accordingly not
independent at low degrees of hydration, but reinforce
each other.
ceptor property of the 0 atoms increases in this
order. This is not, however, in agreement with observations. The reason is that the number of free OH
groups of the water molecules depends not only on the
hydrogen bond acceptor property of the 0 atoms of
the anions, but also in particular on the number of 0
atoms available on the anions to act as acceptors [281.
2.5. Position of the Water Molecules with respect to the
Ions
At low degrees of hydration the water molecules are
located between the cation and the neighboring anions
as shown by the formula (this page). This is deduced
from the fact that the water molecules interact with
both the anions and the cation. It must, however, be
remembered in considering the pictures of the hydration structure obtained by TR investigation, that the
absorption of an IR quantum takes place extremely
rapidly. One obtains a picture of the temporary
equilibrium position, for, as is known, the hydration
structures undergo frequent rearrangements as a result
of thermal motion of the hydration water molecules C21-261. IR-spectroscopy of electrolyte solutions
thus affords data about structures which exist for
only a short time in dynamic equilibrium with analogous structures.
The stretching vibrations of the free OH groups (i.e.
those that are not involved in hydrogen bonding) of
the hydration water molecules can be observed for
some salts as a weak but sharp band a1 3615cm-1
(Fig. 4)I*]. Since this band is frequently absent, however, it must be concluded that disintegration of the
network of ion pairs and hydration water molecules is
only slight. The intensity of the shoulder increases
from the Sc3+ to the La3+ salt. The hydrogen bond
donor property of the OH groups of the hydration
water molecules decreases in the same order, i.e.
the number of free OH groups increases as the
hydrogen bond donor properly of the OH groups
of the hydration water molecules decreases [*8J.
The number of free OH groups in the series of
anions (1) to (5) investigated should decrease from
-SO3- to -PH02-, since the hydrogen bond ac[21] T. J . Swift and R . E. Connick, J. chem. Physics 37, 307
(1962).
[22] M. Eigen, Pure appl. Chem. 6 , 97 (1963).
[23] H . G. Hertz and M . D . Zeidler, Ber. Bunsenges. physik.
Chem. 67, 774 (1963).
[24] H . G . Hertz and M . D . Zeidler, Ber. Bunsenges. physik.
Chem. 68, 821 (1964).
[25] R . G . Pearson and M . M . Anderson, Angew. Chem. 77, 361
(1965); Angew. Chem. internat. Edit. 4, 281 (1965).
[26] D.G . Smirh and J . G. Powles, J. molecular Physics 10, 451
(1966).
[*] The overtone of the scissor vibration of the water molecules
gives rise to the shoulder observed at low degrees of hydration
on the wide OH stretching band at 3250 cm-1. Its intensity is increased by Fermi resonance with the stretching vibration [27].
[27] D. F. Hornig, J. chem. Physics 40, 3119 (1964).
[28] G . Zundel and A. Murr, Z . Naturforsch. 21a, 1391 (1966).
504
M@
There is thus a usually only slightly disintegrated network of hydration water molecules and ions. The
hydrogen bonds in this network are often strongly
bent, and vary slightly in their length[z91. As has been
shown by Luck 1301, bending can occur if it allows the
formation of more hydrogen bonds. The HzO molecules should give an antisymmetric and a symmetric
stretching vibration, i.e. a doublet; instead of this a
wide OH stretching band is observed. Due to the fact
that the hydrogen bonds are of different strengths, the
two OH groups of each water molecule have become
so different that they no longer vibrate together [**I.
This results from the differences in stretching and
bending of the hydrogen bonds.
2.6. Water Structure and Ions with Very Weak Fields
The shift of the wide OH stretching band behaves
anomalously in the presence of alkali metal ions
(Table 2), for which there is practically no change in
the position of the band with changing cation field 1331.
Now, the hydrogen bonds that link the water molecules to the 0 atoms of the -SO3- ions are weaker in
the presence of alkali metal ions than in liquid water;
this is indicated by the OH stretching vibration band
of the water molecules, which occurs at higher wave
numbers in the presence of alkali metal ions than in
pure liquid water [3420 cm-1 (25 "C)][I]. According to
the results obtained so far, the band should shift
toward lower wave numbers from Cs+ to Li+. Since
[29] T. T. Walland D . F. Hornig, J. chem. Physics43,2079(1965).
[30] W. Luck, Naturwissenschaften 52, 25, 51 (1965).
[**I T h e OD stretching band of the DzO molecules usually exhibits a doublet structure (see Fig. l a ) ; for a discussion of this
difference in the behavior of HzO and D20, see 11, 311.
[31] Th. Ackermann, G . Zundel, and K . Zwernemann, Ber. Bunsenges. physik. Chem., in press.
1321 G . Zundel and A. Murr, Z . Naturforsch. 246, 375 (1969).
[33] G . Zundel, A. Murr, and G.-M. Schwab, Naturwissenschaften
50, 17 (1963).
Angew. Chem. internat. Edit.
/ VoI. 8 (1969)1 No. 7
the cation-water interaction decreases from Li+ to CS+,
the bonding between the cations and the hydration
water molecules becomes weaker in this direction. The
OH groups of water molecules can displace the cations
from the lone electron pairs of their hydration water
molecules and form hydrogen bonds with the latter.
Thus from Li+ to Cs’, the association of the water
molecules with one another is increasingly favored in
relation to the insertion of water molecules between
the cation and the neighboring anions.
This discussion explains the anomalous behavior of
this band in the case of the alkali metal ions, since the
transition from Li+ to Csf is accompanied by increasing formation of a network of “pure” water structure.
The OH stretching vibration band of these water
molecules is situated, however, at lower wave numbers
than that of the water molecules inserted between the
cation and the neighboring -SO3- ions, and therefore
an opposing shift is superimposed. The two shifts
practically cancel each other out, with the result that
the position of the band is almost the same for all the
alkali metal ions.
The formation of the “pure” water structure is still
more noticeable in the case of the alkylammonium
ionsr321. The band is situated at 3449 cm-1 for the
( C H 3 ) 4 N + salt and even at 3430cm-1 for the ( C 2 H 5 ) 4 N +
salt. Thus, as expected, it has shifted much farther
toward the wave number for pure liquid water than in
the case of the Cs+salt. The position of the OH stretching vibration band is a measure of the water-structure
forming action of the apolar groups in these ions.
This water-structure formation is the cause of the
hydrophobic interaction 134-361. One should therefore
expect a stronger interaction of the alkylammonium
than of the alkali metal ions with the -SO3- ions, and
this is what is actually found, as is shown by the splitting of the antisymmetric SO stretching vibration band
of the -SO3- ion 1321.
2.7. Hydration with Increasing Degree of Hydration
of the OH groups in hydrogen bonds of the
hydration water consequently moves toward higher
wave numbers with increasing hydration. In other
words, the shift of the band toward smaller wave
numbers decreases with increasing hydration.
2. Two or more layers of water molecules are inserted between the cations and the neighboring
anions, i.e. a “second hydration shell” is formed [381.
It is possible to follow this in the presence of cations
having a very strong field, e.g. in the AP+ salt. The OH
stretching vibration band of the hydration water molecules of attachment type I1 appears at about 3430 cm-1
with increasing degree of hydration. In the case of
cations having strong fields, the band due to the OH
stretching vibration of the hydration water molecules
of attachment type I appears merely as a more or less
pronounced shoulder on the low wave number flank
of the hydration water band complex.
3. The Acids
When the acid proton is present on the anions, it rearranges the bonding electrons in such a way that the
groupings (6)-(10) are formed from the fixed ions
(1)-(5) (Fig. 2 and Table 1). The acid proton greatly
reduces the mesomeric bond resonance of its anion [191.
0
4
-S<O
OH
0
//
-se\=o
OH
SH
-60
OH
0
4
-sex
OH
H
-P<O
OH
As the number of water molecules increases, the bond-
ing between the cations and the anions becomes looser;
this leads to two changes in the bands of the hydration
water molecules.
1. If more water molecules are inserted between the
cation and the anions, the polarizing effect of the
cation is distributed over these water molecules, with
the result that the hydrogen bonds formed by the OH
groups of these water molecules become weaker 1371.
The acceptor property of the 0 aioms of the anions
also decreases somewhat, since the polarization of the
anions by the cations decreases as the cation-anion
bond becomes weaker. The stretching vibration band
[34] H. G. Hertz and M . D . Zeidler, Ber. Bunsenges. physik.
Chem. 68, 821 (1964).
[35] H. G. Hertz, Ber. Bunsenges. physik. Chem. 68, 907 (1964).
[36] G. Nemethy, Angew. Chem. 79, 260 (1967); Angew. Chem.
internat. Edit. 6, 195 (1967).
[37] G. Zundel and A . Murr, J. Chim. et Physique, 66,246, (1969).
Angew. Chem. internat. Edit.
1 Vol. 8 (1969) No. 7
3.1. Dissociation
The anion vibration bands of polystyrenephosphinic
and polystyreneseleninic acids do not change with increasing degree of hydration. In polystyrenesulfonic
and polystyreneselenonic acids, on the other hand, the
rearrangement of the bonding electrons due to the acid
proton disappears with increasing degree of hydration
(Fig. 2). The integral extinction of these bands can be
used as a measure of the removal of the proton from
the anion, i.e. as a measure of the true degree of dissociation. According to this, the true degree of dissociation decreases from polystyrenesulfonic to polystyrenephosphinic acid in the series of acids investigat[38] G. Zundel and A . Murr, Z . physik. Chem. 233, 415 (1966).
505
ed. It is understandable that the true degree of dissociation should be much lower for the -SeOOH (9) and
-PHOOH (10) groups, since on dissociation of these
groups the charge has only two instead of three XO
bonds over which it can be distributed 119,441.
3.2. Association of the Acid Groups
After thorough drying all these acids exhibit a pair of
bands (Fig. 5), which is due to the OH o r OD group
of the acid. When this pair of bands occurs, the acid
3800
3LOO
3000
-T
2600
2200
1800
(cm')
Fig. 5. IR spectra of polystyrenesulfonic acid hydrated with H 2 0 (two
membranes superimposed on each other). The membranes were kept in
the sample cell at a fixed relative humidity for about 6 hours before the
spectra were recorded. The drying steps were carried out successively
without interruption. 1 % crosslinked [*I, 1.50 acid groups/benzene ring
1 + 6 decreasing relative humidity, 7 thoroughly dried membranes;
pair of bands at 2950 and 2405 cm-1 (OH) or at 2240 and 1805 cm-1
(OD) (not shown here).
[*I
Crosslinking with divinylbenzene added during the polymerizatiou.
groups are linked as shown in ( I I ) 1391, though not
always in pairs.
According to Hadii et a!. [40,411, the pair of bands is
due to the stretching vibration and the overtone of the
bending vibration of the acid OH or OD groups, these
two vibrations being coupled by Fermi resonance I*].
Such strong coupling of bands situated so far apart is
possible only if a very anharmonic, i.e. asymmetrical,
potential well exists in the hydrogen bonds formed by
these groups.
These hydrogen bonds are very strong, as is shown by the
position of the bands and the strong anharmonicity of the
potential well. I t seems at first surprising that the strong poly[39]
22b,
[40]
1411
439.
G. Zundel, H . Mefzger, and I . Scheuing, Z . Naturforsch.
127 (1967).
D . Hudti, Pure appl. Chem. 11, 435 (1965).
D . Hudti and N . Kobilarow, J. chem. SOC.(London) 1966,
[*] The appearance of the two vibrations was earlier explained
by an asymmetrical double potential minimum in these hydrogen
bonds [42], on the basis of work by Somorjui and Hornig 1431.
However, Hudfi et al. 140,411 studied this pair of bands for hydrogen bonds whose acceptors differ appreciably in their strength.
They concluded that the pair of bands cannot be explained by an
asymmetrical double potential minimum.
[42] G. Zundel and H. Metzger, Spectrochim. Acta, Part A 23,
759 (1967).
[43] R . L. Somorjui and D . F. Hornig, J . chem. Physics 36, 1980
(1 962).
styrenesulfonic acid is associated via hydrogen bonds as
strong as those formed in the weak polystyreneseleninic acid.
An IR-spectroscopic and a n ebullioscopic study of anhydrous
p-toluenesulfonic acid in chlorinated hydrocarbons showed
that this acid is dimeric and gives the same pair of bands [391.
How can the relatively strong polystyrenesulfonic acid form
such strong hydrogen bonds? We have seen that the acid
proton rearranges the electrons in these anions in such a way
as to give -S020H groups ( 6 ) . Since the doubly bonded 0
atoms are much stronger acceptors for hydrogen bonds than
the 0 atoms in the 4 0 3 - ions, the strong polystyrenesulfonic
acid can form hydrogen bonds as strong as those formed by
the weak polystyreneseleninic acid.
These bands are a measure of the association of the
acid groups 1**I. In the case of polystyrenesulfonic
acid, the band at 2405cm-1 appears only with increasing drying, whereas in the case of polystyreneselenonic acid the corresponding band is already
faintly visible even when the membrane has been
hydrated at a relative humidity of 98 %; it too intensifies with increasing drying. For polystyrenethiophosphonic acid, polystyreneseleninic acid, and polystyrenephasphinic acid, the band is as intense after hydration of the membrane at 98 % relative humidity as
after intensive drying. The tendency to associate increases from the -S020H (6) to the -PHOOH
(10) groups. It thus shows the opposite course from
the true degree of dissociation [44J.
3.3. Excess Proton, IR Continuum, and
Proton Dispersion Forces
In the ion exchangers, the degree of hydration can be
reduced to any desired extent without modification of
the amorphous structure of the liquid state by crystallization. These substances have therefore proved
particularly suitable for the investigation of the nature
of the excess proton, which is hydrated with only a
few water molecules [45-47 583.
Curves on the right-hand side of Figure 6 show a plot
of the number of water molecules available to the
excess proton against the true degree of dissociation
mt of the polystyrenesulfonic acid. mt was determined
from the integral extinction of the bands of the
-S02OH groups (6). The acid proton in polystyrenesulfonic acid is released from the anion when it has two
water molecules available (extrapolation of the curves
on the right hand side in Fig. 6).
Polystyrenesulfonic acid gives an intense absorption
continuum extending from the O H or OD stretching
vibration bands toward lower wave numbers (see
Figs. l a , lb). The extinction of this absorption continuum increases in proportion to the true degree of
dissociation at low excess proton densities (curves on
left-hand side in Fig. 6). Since the dissociation of poly-
[**I However, the band at the higher wave number cannot be
used as a measure of the degree of association, since another
band becomes superimposed on it with increasing hydration [l].
144) G. Zundel and A . Mefzger, Z . physik. Chem., 240,50 (1969).
[45] G. Zundel and H. Metzger, Z . physik. Chem., N.F. 58, 225
(1968).
1461 G. Znndeland H . Metzger, Z . Naturforsch. 22u,1412 (1967).
[47] G. Zundel and H. Metzger, Z . physik. Chem., N.F. 59, 225
(1968).
Angew. Chem. internut. Edit,
1 Vol. 8 (1969)
No. 7
35
-t
+=
OL
l2
10
O3
t
OZW
01
I
Fig. 61'1. a) Number (n') of water molecules available to theexcess proton
as a function of the true degree of dissociation at of polystyrenesulfonic
acids (three curves on the right-hand side of the Figure; left ordinate).
b) Extinction of the absorption continuum (at 2000 cm-1) as a function
of the true degree of dissociation at of polystyrenesulfonic acids (three
straight lines o n left-hand side of the Figure; right ordinate).
Each of the sets of three curves shows curves for membranes having
different degrees of crosslinking and sulfonation.
styrenesulfonic acid occurs when there are two water
molecules available to the acid proton, this result
shows that the continuum arises when H502+ groupings are formed.
In crystals containing the grouping H3O+,the symmetric bending vibration of this grouping is observed at
about 1200 cm-1[48-501. When the spectrum contains
a symmetric bending vibration of the grouping H3O+,
the band of this vibration at about 1200 cm-1 should
disappear on transition from H20 to DzO hydration,
and should be replaced by the D3O+ band at about
890 cm-1. However, no appreciable change is observed
on transition from H20 to DzO hydration. The grouping H30+ accordingly does not execute any vibrations
as an entity in the non-crystalline medium. This can be
explained only if the life-time of the H3O+ grouping is
very short under these conditicns.
The excess proton thus moves extremely rapidly between the two water molecules in H5O2+. This grouping can therefore be represented by the two boundary
structures [511. The absorption continuum is closely
connected with this mobility of the excess proton
in HsOzf.
The absorption continuum is not temperaturedependent between 292 and 85 OKI521. Thus no activation energy is required for the movement of the excess
proton in H5O2+. The proton tunnels accordingly in
the hydrogen bond of this grouping. A potential well
is present, as is shown in Fig. 7.
1481 D . E. Bethell and N . Sheppard, J. Chim. physique PhysicoChim. biol. 50, C 72 (1953).
[49]C. C.FerrisoandD.F.Hornig, J.chem.Physics23,1464(1955).
1501 R . D. Gillard and G. Wilkinson, J. chem. SOC.(London)
1964, 1640.
[511 G. Zundel, H. NoNer, and G.-M. Schwab, Z . Elektrochem.,
Ber. Bunsenges. physik. Chem. 66, 129 (1962).
1521 C . Zundeland G.-M.Schwab, J.physic. Chem. 67, 771 (1963).
Angew. Chem. internat. Edit.
Vol. 8 (1969) j No. 7
X+
Fig. 7. Symmetrical double minimum potential well in a symmetrical
hydrogen bond (spatial coordinate x in arbitrary units).
Do the two water molecules of the H5O2+ retain their
individuality as vibrating groups while the excess
proton is tunneling between them? At low degrees of
hydration, i.e. when the H5O2+ groupings are being
formed, the extinction of the absorption continuum
increases linearly with the integral extinction of the
scissor vibration. This is possible oniy if the water
molecules in H5O2+ vibrate as individuals (451.
Many authors have studied and discussed the special
stability of the H904+ grouping. (For reviews
see [ I , 53,541.) The integral extinction of the scissor
vibration increases strongly while the first four water
molecules are adding to the proton that has been
removed from the anion. Hence the extinction COefficient of the scissor vibration of the outer water molecules in the grouping H904+ is very much higher than
that of the water molecules in pure liquid water 11,461.
All this shows the special position of this grouping in
the network of the hydration structure. The extinction
of the continuum does not change on transition from
HsOz+ to H904+. Owing to the symmetry of the
grouping H904+, however, none of the three hydrogen
bonds can be favored, i.e. they must all have a potential well with a low barrier, the potential being so symmetrical that the protons can tunnel. Thus the three
inner protons in H904+ act as the excess proton.
The continuum is due to the tunneling excess protons,
which have a continuous energy distribution, i.e. are
in energy bands. How do these energy bands arise?
The tunneling of a particle in a potential well, as shown
in Figure 7, always causes splitting of the energy levels,
but never broadening. The continuum must therefore
be due to some other factor. The transition of an
excess proton from one boundary position to the other
is associated with a fluctuation of the electromagnetic
field in the neighborhood. This field fluctuation changes
the potential at the position of a neighboring excess
proton. It is very large, since the center of the charge is
displaced much more on tunneling of a proton than
the tunneling H nucleus itself. This is because the
transition of the H nucleus causes a considerable displacement of the electrons, i.e. of the negative charge,
in the opposite direction, and the field fluctuation depends on the amount of displacement, not of the H
nucleus alone, but of the center of the charge. Neighboring tunneling protons are coupled via this fluctuating field, and this coupling leads to a shift of the energy
levels. Estimation of the shift of the levels by these
coupling forces for pairs of tunneling protons with the
[53]M. Eigen, Angew. Chem. 75, 489 (1963); Angew. Chem.
internat. Edit. 3, 1 (1964).
1541 H. L. Clever, J. chem. Educat. 40, 637 (1963).
507
I
,
I
ff
II
M
1;
X(W)
-
'\\
.\
I
x(H)-
Fig. 8. Shift and splitting A E of the energy terms of the tunneling protons as a function of the distance from the center of the hydrogen bonds.
perturbation calculation for nearly degenerate states [551
gives the energy terms of the tunneling protons as a
function of the distance between the centers of the two
hydrogen bonds Fig. 8 1561.
The shift of the lowest level by the fluctuating fields
associated with the tunneling of the proton is
where vo is the tunneling frequency in the ground
state, p is the dipole moment of the grouping H5O2+
when the proton is in one of the boundary positions,
E is the dielectric constant of the medium between
the tunneling protons, and g is a factor that takes
into account the orientation of the two hydrogen
bonds with respect to each other. It passes through
values from -2 to +2. R is the distance between the
hydrogen bonds with the tunneling protons. Similar
relations exist for the shifts of the other levels.
If we consider many pairs of tunneling excess protons
in a liquid, the orientation factor g and the distance R
pass through a random statistical multiplicity of
values. The shifts of the energy levels consequently
pass through a continuous range of values. This is the
cause of the energy bands of the tunneling protons,
and hence of the absorption continuum.
The lowest energy level, which is preferentially occupied by the tunneling protons, is lowered. The tunneling protons thus attract one another. The term
"proton dispersion forces" is suggested by the processes involved in their occurrence. These forces are as
strong as the other intermolecular forces.
When the concentration of tunneling protons in polystyrenesulfonic acid exceeds 1.5 mequiv. of H+/g, the
[ 5 5 ] A . Dalgarno in D . R . Bates: Quantum Theory. Academic
Press, New York 1961, Vol. 1, p. 202ff.
[56] E. G. Weidemann and G . Zundel, Z. Physik 198, 288 (1967).
508
extinction of the continuum no longer increases appreciably with increasing concentration [*I. The extinction of the continuum per tunneling proton thus
decreases at approximately the same rate as the concentration is being increased at high concentrations of
tunneling protons. The extinction of the continuum
shows a saturation effect, which presumably corresponds to the transition from coupling in pairs to
coupling of all the tunneling protons 1581.
This absorption continuum is not confined to dissociated polystyrenesulfonic acid. It was observed by
Suhrmann and Breyerrsgl as early as 1933 in the investigation of aqueous acid and base solutions in the
overtone region, and later by Ackermann [60,611 in the
fundamental vibration region. It occurs with all polyelectrolytes having dissociated acidic and basic (Fig.
9a) groups[II. It is observed when an excess proton
100
80
60
LO
20
3800 3100 3000 2600 2200 1800 1600 1000 650
----T(cm-')
Fig. 9. IR spectra. a) -poly;p-trimethylammoniumstyrene hydroxide 131,621, hydrated; . . . . poly-p-trimethylammoniumstyreneiodide
[31,62], hydrated; b) - saturated solution of p-toluenesulfonic acid
monohydrate in CHjOH; . . . . CH3OH.
tunnels between molecules such as methanol (Fig. 9b)
and dimethyl sulfoxidetll, and has recently also been
discovered in biopolymers [*I. Energy bands of tunneling
protons and proton dispersion forces thus play a part
in many systems.
The rate-determining step in the anomalous conductivity of protons is the structure migration (or structure diffusion), as discussed in particular by Eigen
et al. [63J; the structure migration of a grouping of the
size H5O2f is sufficient. Tn this process, the H nucleus
can tunnel and so migrate in the field direction if the
bridges formed by the outer water molecules in H5O2+
or H904+ are linearized during thermal motion [I]. This
H nucleus then assumes the role of the excess proton.
['I The concentration of the tunneling protons cannot be varied
directly via the concentration of fixed ions incorporated, since
the latter are no longer uniformly distributed in the membrane at
low concentrations, as is shown by the kinetics of the sulfonation
reaction 1571.
1571 G. Zundel and H. Metzger, Z. physik. Chem., 240,90 (1969).
[58] G. Zundel and If. Metzger, Z. physik. Chem. 235, 33 (1967).
[59] R . Suhrmann and F. Breyer, Z. physik. Chem., Abt. €3 23,
193 (1933).
1601 Th. Ackermann, Z . physik. Chem. N.F. 27, 253 (1961).
I611 Th. Ackermann, Z . physik. Chern. N.F. 41, 113 (1964).
1621 Th. Ackermann, G. Zundei, and K . Zwernemann, Z. physik.
Chem. N.F. 49, 331 (1966).
[63] M . Eigen and L. DeMaeyer, Proc. Roy. SOC.(London),
Ser. A 247, 505 (1958).
Angew. Chem. internat. Edit.
Vol. 8 (1969) No. 7
3.4. The Hydration Structure of the Acids
3.4.1. Pol y s t y ren e s u 1f o n i c A c i d 1471
The -S020H groups of polystyrenesulfonic acid
dissociate only when two water molecules are available
per acid group. If this acid is slowly dried, the last water
molecule per acid group is attached as shown in (a).
This water molecule is presumably often bound, not
merely to one acid OH group, but to two, i.e. by one
on each lone electron pair. The OH stretching vibration bands of the OH groups in the two different
hydrogen bonds are found at 3210 and 3050 cm-1. If
two water molecules are present, the acid proton is
removed from the anion. However, the number of
water molecules on the excess proton increases only
slowly at first with increasing degree of dissociation
(curves on right-hand side in Fig. 6). This situation
changes only when most of the -S02OH groups have
dissociated.
If no further water molecules are available, the H502+
or H904+ groupings formed are linked to the 0 atoms
of the -SO3- ions ( I ) via hydrogen bonds, as is shown
by the following findings: 1. A stretching vibration
band due to free OH groups at about 3600 cm-1 is at
best indistinct. 2. The degeneracy of the antisymmetric
stretching vibration band at about 1200 cm-1 is
removed (cf. the doublet in Fig. la). The stretching
vibration band of the OH groups in the hydrogen
bonds formed by the outer water moIecules of H502+
or H904+ is very broad and is situated at about
2900cm-1, while that of the OD groups occurs at
2100 cm-1. The stretching vibration band of the OH
groups of the water molecules attached to the H904+
grouping appears at about 3400 (H20) or 2500cm-1
(DzO) with increasing degree of hydration. The
Angew. Chem. internat. Edit. J Vol. 8 (I969)J No. 7
resulting network of the hydration structure is shown
schematically in (b). For the sake of clarity only one
excess proton is shown.
3.4.2. P o 1y s t y r enesel en on i c A c i d
The hydration structure of polystyreneselenonic acid
does not differ very greatly from that of polystyrenesulfonic acid, except that the true degree of dissociation
of the -Se020H groups (7) is smaller than that of the
-S020H groups (6). Thus the -Se020H groups are
mostly not yet dissociated when they have two water
molecules available. Moreover, the groupings (12) are
not yet all dissociated even when the membranes have
been hydrated at 98 % relative humidity. Therefore,
hydrated -Se020H groups, which are probably mostly
still associated even at relativelyhigh degrees of hydration, are situated between the hydration structures
around the dissociated acid proton 1443.
3.4.3. Polyatyreneseleninic a n d
Polystyrenephosphinic Acids
Quite different hydration is found in polystyreneseleninic and polystyrenephosphinic acids [441. The
-SeOOH ( 9 ) and -PHOOH (10) groups dissociate
only to an extremely small extent, and they remain
associated even when these membranes are considerably hydrated. The band that arises at 3390 (H20) or
2490 cm-1 (D20) with increasing hydration thus corresponds to &hestretching vibration of the OH or OD
groups in the hydrogen bonds of the water molecules
by which the latter are linked to 0 atoms of the acid
groups or to one another. Finally, the shoulder at
about 3640 (H2O) or 2680cm-1 (D2O) shows that
there are a considerable number of free OH or OD
groups in the network of the hydration structure,
which consequently shows appreciable disintegration,
particularly in polystyrenephosphinic acid. This is
understandable in view of the strong hydrogen bonds
between the associated acid groups, which strain the
structure. A hydration structure is thus present in
these two acids, as is shown schematically in (c).
Received: January 25, 1968
[A 707 IEI
Revised: September 23, 1968
German version: Angew. Chem. 8 / , 507 (1969)
Translated by Express Translation Service, London
509
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