The thermodynamic characteristics of ion exchange in a sulfonated polymer based on cis-tetraphenylcalix[4]resorcinarene

Article abstract of DOI:10.1134/S0036024407070011

The selectivity and thermodynamic characteristics of exchange of protons in SO₃H groups of a sulfonated network polymer based on cis-tetraphenylcalix[4]resorcinarene for Na⁺, Cu²⁺, and In³⁺ cations from aqueous solutions are considered. Semiempirical quantum-chemical calculations of molecular ensembles modeling the structure of the elementary polymer unit in the H and Na forms were performed. The experimental data on the equilibrium phase compositions and the heat of exchange were used to calculate the thermodynamic equilibrium constants, Gibbs energy, enthalpy, and entropy of ion exchange.

Full text of DOI:10.1134/S0036024407070011

ISSN 0036-0244, Russian Journal of Physical Chemistry A, 2007, Vol. 81, No. 7, pp. 1011–1015. © Pleiades Publishing, Ltd., 2007.
Original Russian Text © G.N. Al’tshuler, L.A. Sapozhnikova, E.V. Ostapova, O.G. Al’tshuler, 2007, published in Zhurnal Fizicheskoi Khimii, 2007, Vol. 81, No. 7, pp. 1159–1164.
CHEMICAL THERMODYNAMICS
AND THERMOCHEMISTRY
The Thermodynamic Characteristics of Ion Exchange
in a Sulfonated Polymer Based
on cis-Tetraphenylcalix[4]resorcinarene
G. N. Al’tshuler, L. A. Sapozhnikova, E. V. Ostapova, and O. G. Al’tshuler
Institute of Solid-State Chemistry and Mechanochemistry (Kemerovo Branch), Siberian Division,
Russian Academy of Sciences, Kemerovo, Russia
e-mail: sorbent@kemnet.ru
Received April 21, 2006
Abstract—The selectivity and thermodynamic characteristics of exchange of protons in SO H groups of a sul-
3
+
2+
3+
fonated network polymer based on cis-tetraphenylcalix[4]resorcinarene for Na , Cu , and In cations
from aqueous solutions are considered. Semiempirical quantum-chemical calculations of molecular ensembles
modeling the structure of the elementary polymer unit in the H and Na forms were performed. The experimental
data on the equilibrium phase compositions and the heat of exchange were used to calculate the thermodynamic
equilibrium constants, Gibbs energy, enthalpy, and entropy of ion exchange.
DOI: 10.1134/S0036024407070011
z+
+
z+
INTRODUCTION
tion phases involved in Cat –ç ion exchange (Cat =
+
2+
3+
Na , Cu , and In ), measured the heat effects of the
Network polymers based on cis-calix[4]resorcinare-
nes are new ion exchangers that can participate in cat-
ionic exchange reactions [1]. The purpose of this work
was to study the selectivity and thermodynamic charac-
+
+
2+
+
Na –H and Cu –H exchange processes, and
performed semiempirical quantum-chemical calcula-
tions of ensembles of the cis-(tetrasulfonatophe-
–
3
teristics of the exchange of protons of high-acidity nyl)calyx[4]resorcinarene anion L(SO
)
with the
4
SO H groups of a sulfonated network polymer based on
cis-tetraphenylcalix[4]resorcinarene,
+
+
3
H O and Na cations; these ensembles modeled the
structure of the elementary polymer unit in the H and
3
+
z+
z+
+
Na forms.
zH + Cat
Cat + zH ,
(1)
where bars label polymeric phase constituents.
The elementary unit of the sulfonated network poly-
mer based on cis-tetraphenylcalix[4]resorcinarene is
EXPERIMENTAL
The polymer was prepared by twice sulfonating the
cross- network polymer synthesized by the resol polyconden-
(
tetrasulfonatophenyl)calix[4]resorcinarene
linked with neighboring macrorings by methylene sation of cis-tetraphenylcalix[4]resorcinarene with
groups,
formaldehyde following the procedure described in [1].
The total ion-exchange capacity of the sulfonated poly-
mer with respect to 0.1 M NaOH was 5.65 equivalents
per kg dry polymer. Of these, 2.45 equivalents corre-
CH2
HO
OH
spond to the exchangeable SO H protons.
3
Solutions were prepared using HCl and NaCl of kh.
HO
HO
OH
OH
ch. (chemically pure) grade and CuCl · 2H O of ch.
R
R
R
2
2
(
pure) grade. InCl was obtained from indium metal of
3
R = Ph–SO H.
3
os. ch. (special purity) grade by dissolving it in hydro-
chloric acid [2]. The amount of cations sorbed and des-
orbed in ion exchange was calculated from changes in
R
+
ion concentrations in solution. The concentration of H
HO
OH
was determined by acid-base titration with methyl red
as an indicator. Cu and In were determined by com-
plexonometric titration, the indicator was 1-(2-pyridyl-
2
+
3+
CH2
p
3
+
To solve the problem formulated above, we determined azo)-2-naphthol [3, 4]. Low concentrations of In were
the equilibrium compositions of the polymer and solu- determined photometrically [4].
1
011

1
012
AL’TSHULER et al.
Table 1. Equilibrium phase compositions and ion exchange selectivity coefficients for sulfonated polymer based on cis-tet-
raphenylcalix[4]resorcinarene at 293 K
a
mCat
mH
xCat
kCat/H (2)
γ±CatClz
γ±HCl
k
(3)
Cat/H
Na+
1.49
0.92
0.78
0.67
0.60
0.28
0.275
Cu2+
1.64
1.66
1.84
1.82
1.81
1.53
In3+
0
0
0
0
0
0
0
.0100
.0401
.0504
.0605
.0752
.0900
.0920
0.0900
0.0599
0.0496
0.0395
0.0248
0.0100
0.0080
0.142
0.381
0.443
0.508
0.644
0.713
0.760
0.778
0.778
0.778
0.778
0.778
0.778
0.778
0.778
0.778
0.778
0.778
0.778
0.778
0.778
1.49
0.92
0.78
0.67
0.60
0.28
0.275
0
0
0
0
0
0
.00250
.00500
.0102
.0156
.0256
.0406
0.0965
0.0910
0.0820
0.0715
0.0511
0.0208
0.249
0.382
0.554
0.656
0.789
0.920
0.600
0.592
0.592
0.587
0.579
0.567
0.780
0.779
0.776
0.767
0.767
0.758
2.80
2.94
3.20
3.18
3.20
2.77
0
0
0
0
0
0
0
0
.00030
.00162
.00325
.00330
.00588
.00832
.0116
0.0990
0.0936
0.0887
0.0900
0.0820
0.0750
0.0650
0.0592
0.0559
0.160
0.292
0.263
0.505
0.584
0.727
0.777
0.22
0.14
0.18
0.14
0.40
0.41
0.84
1.14
0.504
0.502
0.496
0.495
0.489
0.482
0.474
0.474
0.780
0.780
0.779
0.777
0.773
0.769
0.764
0.763
0.75
0.49
0.65
0.53
1.45
1.57
3.31
4.47
.0127
The selectivity of ion exchange was studied by the orimeter was calibrated by dissolving chemically pure
dynamic method [5]. The polymer in the salt or H form cesium chloride in water; the reference value used in
was placed into a column, through which aqueous solu-
calculations was ∆ H° = 17205 ± 5 J/mol [6]. Mea-
aq CsCl
tions containing two electrolytes, HCl and NaCl, HCl
surements were performed in standard (control and
and CuCl , or HCl and InCl , were passed until the col-
2
3
measuring) stainless steel flasks of volume 6 ml. An
accurately weighed amount of swollen ionite was
immersed into an aqueous solution of an electrolyte
umn was equilibrated at 293 K. Equilibrium was con-
sidered established when the concentrations of electro-
lytes in the initial solution and several sequentially
taken filtrate samples coincided. The equilibrium ion
composition of the polymer phase was independent of
the initial polymer form. The equilibrium phase com-
positions and ion exchange selectivity coefficients are
listed in Table 1. The selectivity coefficients were cal-
culated by the equation
(
5.3 ml, measuring flask) and water (5.3 ml, control
flask) to determine the difference of the corresponding
heat effects. The weight of the swollen polymer was
0
.0100–0.0300 g. The polymer in the H form was
immersed into 0.001–0.005 M solutions of CuCl or
2
0
.01–0.1 M solutions of NaCl, and the polymer in the
salt form, into 0.001–0.006 M solutions of HCl. The
z
z
H
–
5
–4
kCat/H = (x /x )(m /m ),
(2) heat flux was 10 –10 W. The sensitivity of the calo-
Cat
H
Cat
rimeter was 0.04 V/W.
where x is the experimental cation fraction in the poly-
mer and m is the cation molality in solution.
i
i
The mean ionic molal activity coefficients of elec-
The heat effects of ion exchange were measured at trolytes in solutions were calculated by the Debye–
93 K on a DAK-1-1A microcalorimeter under isother- Hückel equation on the assumption that the closest
2
mal conditions with automatically balancing thermal approach distances were 4.5 Å for CuCl and 6 Å for
2
EMF at the expense of the Peltier effect. The microcal- InCl ions [7].
3
RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY A Vol. 81 No. 7 2007

THE THERMODYNAMIC CHARACTERISTICS OF ION EXCHANGE
1013
Quantum-chemical calculations were performed by
the MNDO semiempirical method with the PM3
Hamiltonian parametrization using the MOPAC 2000
program (the Chem 3D Ultra 9.0 CambridgeSoft Cor-
poration package).
C
O
S S
H
RESULTS AND DISCUSSION
Model Consideration
–
+
The calculated structure of L(SO ) (H é) mini-
3
4
3
4
mized with respect to the enthalpy of formation is
shown in Fig. 1. The sulfur atoms in this structure are
in the vertices of a distorted parallelogram. The calcu-
lated interatomic distances are listed in Table 2.
b
This table shows that all parallelogram edges
–
+
formed by sulfur atoms in L(SO ) (H é) are equal, of
a
S
S
3
4
3
4
5
–5.5 Å. The distance between sulfur atoms in
c
S
S
–
–
+
+
L(SO ) (Na ) and L(SO ) (Na ) · 4(H é) is as large as
3
4
4
3 4
4
2
d
8
.7 Å; in addition, the distances between cations and
between cations and sulfur atoms increase. It follows
+
that the replacement of hydroxonium cations with Na
or Na · ç é cations causes structure loosening.
+
2
–
3
+
4
Fig. 1. Structure of L(SO ) (H é) minimized with
4
3
respect to the enthalpy of formation in MNDO/PM3 calcu-
lations.
Corrected Ion Exchange Selectivity Coefficients
Corrected cation exchange selectivity coefficients
a
.95). For doubly charged Cu2+ cations, the corrected
0
k
[8] were calculated from the experimental data
Cat/H
selectivity coefficient remains virtually constant at all
on equilibrium solution and polymer compositions
a
3
+
(
Table 1) taking into account solution nonideality by x values, and, for triply charged In , the logk (x )
Cu In/H In
the equation
function is approximated by the polynomial
z
H
2z
±HCl
(z + 1)
γ
±CatClz
x
m
m
γ
a
In/H
3
2
a
Cat
z
H
logk
= – 4.75x + 8.31x – 2.77x – 0.015
In In In
k
= -------------- -- -------------- ,
(3)
Cat/H
x
Cat
at a 0.99 confidence level.
where γ is the mean ionic molal activity coefficient of
±
The corrected ion exchange selectivity coefficients
for the systems studied depend substantially on the
counterion composition of the polymer phase when cat-
the electrolyte in aqueous solution.
a
The dependences of logk
on the equivalent
Cat/H
+
3+
ions with odd charges (Na and In ) are sorbed. For
fraction of cations in the ionite x are shown in Fig. 2.
Cat
a
+
a
singly charged Na cations, a decrease in logk
as
Na/H
The dependence of logk
on xCat for singly charged
Cat/H
xNa increases is determined by the well-known energy
nonequivalence of exchange sites [9]. The suggestion
a
+
Na cations is described by the equation logk
=
Na/H
–
1.18xNa + 0.04 (the linear correlation coefficient is was made [10] that, for sorption of multiple-charge cat-
+
+
Table 2. Interatomic distances (Å) in cis-(tetrasulfonatophenyl)calix[4]resorcinarene anion compounds with the H O and Na
3
cations according to the MNDO/PM3 data
Sulfur–sulfur
Compound
Sulfur–cation
Cation–cation
a
b
c
d
–
3
–
+
4
L(SO ) (H O)
5.06
5.45
5.38
5.27
5.44
5.55
5.52
7.55
8.68
5.47
7.46
7.57
3.2; 3.5
3.8; 4.0
3.9; 4.0
4.0; 5.0
5.35; 7.62
5.2–9.1
4
3
+
L(SO ) (Na )
3
–
3
4
4
+
L(SO ) (Na ) · 4(H O)
4
4
2
RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY A Vol. 81 No. 7 2007

1
014
AL’TSHULER et al.
∆H, kJ/equiv
logka
Cat/H
0
0
0
0
.8
.6
.4
.2
0
3
4
0
4
8
2
2
–
0.2
0.4
0.6
0.8
–
–
1
–
–
–
1
0
0.2
0.4
0.6
0.8
1.0
Cat
x
0
0.2
0.4
0.6
0.8
1.0
x
Cat
Fig. 2. Dependences of corrected ion exchange selectivity
+
+
2+
+
3+
coefficients for the (1) Na –H , (2) Cu –ç , and (3) In
–
+
+
+
ç reactions on the equivalent fraction of cations in the sul-
fonated polymer based on cis-tetraphenylcalix[4]resor-
cinarene at 293 K.
Fig. 3. Differential enthalpy of exchange for the (1) Na –H
2
+
+
and (2) Cu –ç reactions in the sulfonated polymer based
on cis-tetraphenylcalix[4]resorcinarene at 293 K.
a
KCat/H, using the Gaines–Thomas equation [11]
ions, logk
(x ) increases as x grows because
Cat/H Cat
Cat
1
electrostatic interactions between multiple-charge cat-
ions and sulfo group anions from different polymer
chains draw neighboring polymer chains closer to each
other. Triply charged In cations can likely interact
with anions of neighboring polymer chains, which
a
lnKCat/H = (z
– zCat) + lnkCat/HdxCat
,
H
∫
0
3
+
where z is the charge of the cation. The KNa/H, KCu/H
,
i
and KIn/H values are 0.637, 1.042, and 0.206, respec-
results in an increase in the selectivity coefficient as xIn tively. The thermodynamic constant for ion exchange
with differently charged cations is likely influenced by
the statistical effect [12], which decreases KCat/H
grows.
The elementary polymer unit contains four SO
.
–
3
The differential enthalpies of exchange of protons
groups. According to model concepts, the smallest dis-
for sodium and copper cations, ∆H = (∂∆H/∂x ) , are
Cat T
–
tance between two SO groups is 5 Å (Table 2, Fig. 1).
3
shown in Fig. 3. The ∆H values correspond to xCat at
–
3
It is natural to suggest that the SO groups of one ele- the middle of the interval of changes in the counterion
polymer composition during measurements of the heat
2+
mentary unit and sorbed doubly charged Cu cations
make up supramolecular ensembles with fairly strict
geometry and stoichiometry. The form of the
a
effect of ion exchange. The ∆H (x ) dependences are
Cat
rectilinear (the linear correlation coefficients of the
∆
H (x ) and ∆H (x ) functions are 0.95 and 0.98,
Na Cu
logk
(x ) function is likely determined by the con-
Cu/H Cu
respectively). The integral enthalpies of ion exchange
stant Gibbs energy of formation of ensembles of doubly calculated by the equation
–
charged cations with an even number of SO group.
3
1
∆
H = (∂∆H/∂x )dx ,
Cat
Cat
∫
0
The Thermodynamic Functions of Ion Exchange
+
+
were –3.2 ± 0.7 and 1.4 ± 0.7 kJ/equiv for the Na –H
2
+
+
The data presented in Fig. 2 allowed us to calculate
the thermodynamic constants of ion exchange (1), values obtained are the standard enthalpies of ion
and Cu –H exchange processes, respectively. The ∆H
RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY A Vol. 81 No. 7 2007

THE THERMODYNAMIC CHARACTERISTICS OF ION EXCHANGE
1015
∆
S, J/(equiv K)
are shown in Fig. 4. We see that the entropy of the sys-
tem increases as the fraction of metal cations in the
polymer grows for both Na –H and Cu –H exchange
processes. This is in agreement with the model concept
of a decrease in polymer phase ordering as hydroxo-
nium ions are replaced by metal cations.
+
+
2+
+
2
0
0
0
2
1
To summarize, model considerations and the exper-
imental data obtained show that the type of the cation
sorbed and the structure and counterion polymer com-
position substantially influence the character and val-
ues of the thermodynamic functions of ion exchange
for the sulfonated polymer based on cis-tetraphenyl-
calix[4]resorcinarene.
1
–
–
10
20
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0
0.2
0.4
0.6
0.8
1.0
Cat
x
3
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+
+
Fig. 4. Differential entropy of exchange for the (1) Na –H
2
+
+
and (2) Cu –ç reactions in the sulfonated polymer based
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2
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1
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H
Cat
a
lnk
]. The behavior of the ∆G (xCat/H) functions was
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a
characterized by considering the logk
(x ) func-
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1
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(
∆S)T, xCat = ((∆H – ∆G)/T)T, xCat
(4)
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RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY A Vol. 81 No. 7 2007