CATION DIFFUSION IN BIFUNCTIONAL POLYMERS
BASED ON CIS-TETRAPHENYLCALIX[4]RESORCINARENE
H. N. Altshuler, O. H. Altshuler
Kemerovo division of Institute of Solid State Chemistry and Mechanochemistry SB
RAS, Kemerovo, Russia
Abstract. The kinetics of ion exchange in network bifunctionalized polymers
containing sulfonate and phenol hydroxyl as ionogens has been studied. It is shown
that interaction of the investigated polymers with water solutions of electrolytes is
controlled by diffusion of ions in a polymeric phase. For non-steady state the solution
of the fundamental differential equation of cation diffusion in functionalized polymers
by means of the model of a spherical layer is obtained for a variety of initial and
boundary conditions provided the diffusion coefficient is constant. The nanoreactor
effect consisting in great rate increase cation diffusion flux in bifunctionalized
polymers containing sulfonate and phenol hydroxyl groups as ionogen was found. The
proposed mathematical model explains the nanoreactor effect in bifunctional
polymers.
INTRODUCTION
Recently, the chemistry of novel hybrid functional materials is aimed at creating the
closed nanoreactors.
Calixarene having the hydrophobic cavity surrounded by hydrophilic groups is a
typical nanoreactor [1]. Earlier [2-5], we synthesized new network functionalized
polymers by the catalytic resol polycondensation of calix[4]resorcinarene deriva-tives
with formaldehyde. In works [6, 7] network polymers based on ciscalix[4]resorcinarene for the first time are used as matrixes to create solid space
nanoreactors for catalytic hydrogenation. The thermodynamics of an ion exchange in
calixarenecontaining polymers was investigated [8].
The purpose of this work was to determine the limiting stage of an ion exchange and
to make the mathematical description of non-stationary transport of cation flux in
solid space nanoreactors based on immobilized tetraphenylcalix[4]-resorcinarene,
functionalized by sulfonate and phenol hydroxyl groups. Polymers 1 and 2 containing
the following formula of the repeating unit:
CH2
CH2
HO
HO
HO
OH
R'
R
R
R'
HO
OH
OH
R
R
OH
CH2
HO
HO
OH
OH
CH2
CH2
p
polymer 1: R=Ph;
OH
HO
OH
HO
R
R
s
polymer 2: R=Ph-SO3H.
are selected as objects of research.
9-10
RESULTS AND DISCUSSION
Bifunctional polymers based on immobilized calix[4]resorcinarenes participate in the
following processes of an ion exchange with single charged cations:
on sulfonate groups
OH
OH
+ Cat+
L
+ H+ ,
L
Aer
- +
+
SO3 Cat
SO3 H
ogel
Pow
der
on phenol hydroxyl groups
L OH + Cat+ + OH-
L
OH
SO3-Cat+
+ Cat
+
L O- Cat+ + H2O ,
-
L
+ OH
(II)
RnSi
X4n
O-Cat+
SO3-Cat+
+ H2O,
80
(III)
where L - a fragment of calix[4]resorcinarene immobilized in a polymer; Cat+ –
Li+, Na+, Ag+, N(CH 3 ) 4 .
The kinetic dependences of the degree of transformation F on time t1/2 for processes
(I) - (III) are resulted in Fig. 1.
F
0.8
(I)
(III)
0.6
1
2
3
0.4
4
5
6
(II)
0.2
0
0
10
20
30
40
t 1/2, s1/2
Fig. 1. Kinetic dependences of processes (I), (II), (III) of sorption of metal cations at
polymers based on cis- tetraphenylcalix[4]resorcinarene from aqueous solutions: 1NaCl, 2 – NaOH, 3 – LiCl, 4 – LiOH, 5 – AgNO3, 6 – (CH3)4NOH. (I) - H+ – Cat+
ion - exchange on sulfonate groups of polymer 2 on the data [9]; (II) - Cat+ sorption
from alkaline solutions with participation of hydroxyl groups of polymer 1 on the
data [10]; (III) - Cat+ sorption from alkaline solutions with participation of hydroxyl
groups of sulfonated polymer 2.
9-11
Degree of transformation calculated as F  М t / М  , where Мt - the amount of
cations sorbed to the time t; M - equilibrium ion - exchange capacity. It is seen from
Fig.1 that ion - exchange H+– Cat+ for sulfonate groups of polymer 2 has the
highest rate (fig. 1, (I)), sorption process of cations Cat+ from alkaline solutions with
participation phenol hydroxyl groups of polymer 1 has a minimal rate (fig. 1, (II)).
Rectilinearity of dependences of the degree of transformation F from t1/2 at F  0.5
(factors of linear correlation exceed 0.99) and passage of lines through the beginning
of coordinates(Fig. 1) according to the criteria [11] testify that the interaction of
polymers based on cis-tetraphenylcalix[4]resorcinarene with aqueous solutions of
electrolytes is controlled by diffusion of substance in polymer. Thus, a particlediffusion ion-exchange kinetics takes place.
The particle-diffusion ion-exchange kinetics at spherical symmetry in case of constant
diffusion coefficient is described [11] by differential equation
  2C 2 C 
С
.
 D 2 
t

r
r

r


(1)
Where D – diffusion coefficient of species; С – the current concentration of species in
a polymer; r – radius -vector.
Process (I). Cation-exchange on sulfonate groups at polymer 2
The expression [12]
Mt
6  1
2
 1  2  2 exp  Dw n 2 2 t / r0 .
M
 n 1 n


(2)
for the degree of transformation of a monofunctional ionexchanger describes
experimental data in all the researched range of concentrations for exchange of
protons from SO3H - groups at sulfonated network polymer 2 by metal cations
from solution (Fig. 1, (I)). Here, Dw - effective diffusion coefficient in polymer, r0average radius of spherical particle of polymer. Values of an effective diffusion
coefficient of cations in a sulfonated polymer based on cis-tetraphenylcalix[4]resorcinarene, calculated with probability 0,9 by equation (2), are in the
interval (1.9 ÷ 2.1)10-11 m2/s.
Process (II). Cation-exchange on phenol hydroxyl groups at polymer 1
The rate of the process (II) is controlled by diffusion of ОН– anions in a polymer.
The known [13] equation (3)
3


D C 0 t  1 
 1

  
F  1  sin  arcsin 1  12 OH OH
2
Cr r0  2 


 3

(3)
describes experimental data of ion-exchange rates in polymer 1 (Fig. 1, (II)) in all the
researched range of concentrations. Here DOH - diffusion coefficient of ОН– anions in
0
polymer, COH
- concentration of ОН– anions on the surface of a spherical particle of
9-12
a polymer, Cr - general concentration of fixed ionogens (ionized and not ionized
hydroxyl groups) in a polymer.
Process (III). Cation-exchange on phenol hydroxyl groups at polymer 2
Here, initial sulfonated polymer 2 already contains Cat+ cations whose concentration
is equal to that of SO3 -groups. In process (III) the ion- exchange of hydroxyl group
protons by a Cat+ cation from an alkaline solution takes place. Concentration of coions (free ОН– anions) introduced from the diluted solution in to the ionexchanger
containing a significant amount of ionized sulfonate groups is very small because of
Donnan effect. The rates of process (III) at sulfonated polymer based on
calix[4]resorcinarenes are controlled by H+ and Cat+ interdiffusion in a spherical
particle of a polymer.
According to diffusion mechanism for process (III) at constant diffusion coefficient
DH of free protons the flux equation [13]
J Сat   Dw grad CСat .
(4)
is obtained.
Ka
DH , at CСat  Cr (Ка - dissociation constant of fixed hydroxyl
Cr  K a
groups in a polymer).
Since swelling and hydration of researched polymer 2 upon conversion (III) remain
constant (30 mol H2O on 1 g-equ. of full capacity of polymer), it is possible to
assume, that the effective diffusion coefficient in polymer Dw in equation (4) is
constant. Let us calculate its magnitude. DH =10-9 m2/s [13], Сr  1103 mol/m3.
Potentiometric titration of sulfonated calixarenecontaining polymers [4] gives the
magnitude Ka 10-5 mol/m3. Thus, the effective diffusion coefficient Dw, calculated
by the equation (5), is equal 10-17 m2 /s.
Here, Dw 
Model
As the rate of delivery of Cat+ cations from solution to SO3 - groups is high, the flux
of Cat+ cation diffusion during process (III) determined by the differential equation
(4), will be actually directed from sulfonate-groups to hydroxyl groups of
bifunctional polymer 2 (Fig. 2).
9-13
C1
C2
C0
a
b
r
L-OH
L  SO3 Cat 
J Cat
Fig. 2. The diffusion flux of Cat+ throughout a spherical layer in bifunctional
polymer 2.
We assume that the spherical particle of polymer consist of a set of spherical layers.
Sulfonate-groups are located on the external surface of each spherical layer and
hydroxyl groups are on its internal surface (Fig. 2). The surface r = a is maintained at
C1, and r = b at C2, and the region a  r  b is initially at C0. For non-steady state the
solution of the diffusion equation (1) can be obtained by Laplace transformation
method or method of separation of variables [14] provided the diffusion coefficient is
constant. It results in function C(r,t), after its integration [14] the total amount of
Cat+, which accumulates in the spherical layer after time t, is M t'
M t' 


6

2
4
b  a  a 2  ab C1   b2  ab C2  (a 2  ab  b2 )C0 
3
2 
2 




 a C
n 1
2
1
 C  C2

 (a 2  b 2 )C0  b 2C2  2ab cos n  1
 C0  
 2


exp  D n 2 2 t /(b  a)2
n2
(6)
.


When С0 = 0, С1 = 0, С2 = Cr
M t' 

4
ab 
6  
 C 
(b  a) b2  Cr  2  b2Cr  2ab cos n  r  
3
2
 n 1 
 2 


exp  Dn 2 2t /(b  a)2
n2
4 3

M '  Cr
b  a 3 .
3

(7)
,


(8)
Degree of transformation in time t is
9-14
 
 2 ab  6  2
exp  D n 2 2t /(b  a) 2
b


b

ab
cos
n





2   2 n 1
n2
M'

F  't  
M
a 2  ab  b 2



.
(9)
In special case, if а = 0; b = r0, we obtain equation (2).
Graphs of F against Dt /(b  a) 2  are shown in Fig. 3 for different values of b/a.
The top curve corresponds to solid sphere (a = 0), bottom - to plane sheet (r>> (b a)). In the 0  F  0.5 range the experimental values correspond to the chosen model
at small values b - a. According to equation (9), the rates of process (III) do not
depend on the concentration of a solution, and concentration of polymer (at Cr  0),
probably, neither on the form and size of a spherical particle of a polymer. Actually,
experimental values F(t1/2) for exchanges Н+ – Li+, Н+ – Na+ at various values of
solution concentration are described by the same functional dependence (Fig. 1, (III)).
1/ 2
F
a = 0, solid sphere
b/a = 4
b/a = 2
b/a = 1,1
b/a = 4, plane sheet
Dt/(b  a) 
2 1/2
Fig. 3. Dependence F on Dt /(b  a) 2  . Curves - calculation; dots - experiment: 1 cation sorption from 0.1 mol/dm3 NaOH solutions; 2 - cation sorption from 0.03
mol/dm3 NaOH solutions; 3 -cation sorption from 0.05 mol/dm3 LiOH solutions by
sulfonated polymer 2 (process (III)).
1/ 2
Nanoreactor effect
In the case of constant diffusion coefficient, according to equation (4), the diffusion
flux depends only from concentration gradient. At monofunctional polymer 1 the
magnitude of concentration gradient is determined by changing the concentration of
diffusion species at a macroscopical distance from an external surface of an
ionexchanger particle to its center. At bifunctional polymer 2 the cation diffusion
flux overcomes the distance between SO3 Cat  and ОН – groups (Fig. 2) which is the
value of molecular size and essentially less than the dimension of an ionexhanger
particle. In the repeating unit of polymer 2 the distance is 1-2 nanometers. This
9-15
results in essential increase in the rate of process (III). At the same time the rate of
process (III) should be less than that of process (II) which provides for the delivery
of cations from a solution to sulfonate-groups of polymer. Half-transformation times
(t at F = 0.5), calculated from the experimental data (Fig. 1), are equal: for process (I)
16 s, for process (II)  9500 s, for process (III)  50 s. Comparing the rates of ionexchange with participation of weakly dissociated ionogen at mono and bifunctional
polymer, we find out the nanoreactor effect, consisting in hundredfold increase of
ion- exchange rate.
ACKNOWLEDGEMENTS
The authors would like to thank the Russian Foundation for Basic Research for
financial supporting of this work (project № 07-03-96030).
REFERENCES
Buchachenko A.: Chemistry on the border of two centuries — achievements and
prospects. Russian Chemical Reviews 1999 68 (2) 85-102.
2. Altshuler H., Ostapova E., Fedyaeva O., Sapozhnikova L., Altshuler O.:Novel
network polymers based on calixresorcinarene. Macromol. Symp. 2002 181
1-5.
3. Altshuler H., Sapozhnikova L., Ostapova E., Fedyaeva O., Altshuler O.:
Cationites based on calix[4]resorcinarene derivates. Solvent Extraction and Ion
Exchange 2002 20 (2) 263-271.
4. Al’tshuler O., Sapozhnikova L. Al’tshuler H.: New sulfonate-containing
network
polymers
based
on
immobilized
cis
-metacyclophane3,5,10,12,17,19,24,26-octols Polymer Science Series A 2007 45 (7) 1198-1206.
5. Altshuler H., Abramova L., Altshuler O.: The Production Way of Polymeric
Cationits (Variants), Russian Federation patent, Pat № 2291171, January 2007.
6. Al’tshuler H., Sapozhnikova L.:Synthesis of ultradisperse transitive metals in
immobilized microreactors Journal of structural chemistry 2004 45
Supplement 178-182.
7. Al’tshuler H., Sapozhnikova L.: Preparation of ultradispersed transition metals
in immobilized microreactors Russian Journal of Applied Chemistry 2004 77
(11) 1896-1898.
8. Al’tshuler H., Sapozhnikova L., Ostapova E., Al’tshuler O.: The thermodynamic
characteristics of ion exchange in a sulfonated polymer based on cis tetraphenylcalix[4]resorcinarene. Russian Journal of Physical Chemistry A.
2007 81 (7) 1011-1015.
9. Al’tshuler H., Malyshenko N., Shkurenko G.: Kinetics of cation exchange on
sulfonic polymer based on immobilized cis -tetraphenylcalix[4]resorcinolarene.
Russian Journal of Applied Chemistry 2007 80 (10) 1737-1740.
10. Al’tshuler H., Fedyaeva O.: Kinetics of cation exchange on calixarenecontaining
polymer. Russian Journal of Physical Chemistry 2001 75 (11) 2088-2089.
11. Helfferich F.: Ionenaustauscher. Weinheim, Verlag Chemie, 1959.
1.
9-16
12. Boyd G., Adamson A., Myers L., jr.: The echange adsorption of ions from
aqueous solutions by organic zeolites. II. Kinetics. J. Am. Chem. Soc. 1947 69
2836.
13. Helfferich F.: Ion-exchange kinetics. V. Ion exchange accomponied by
reactions. J. Phys. Chem. 1965 69 (4) 1178-1187.
14. Crank J.: The matematics of diffusion. Oxford, Calendon Press, 1975.
9-17