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Investigation into the kinetics of ion-exchange processes accompanied by complex formation
J inorg, nucl. Chem. Vo[. 43, pp. 787-789, 1981 Printed in Great Britain
0022-1902/81/040787-03502.00]0 Pergamon Press lad,
INVESTIGATION INTO THE KINETICS OF ION-EXCHANGE PROCESSES ACCOMPANIED BY COMPLEX FORMATION A. 1. KALINICHEV*, T. D. SEMENOVSKAYA, E. V. KOLOT1NSKAYA, A. YA. PRONIN and K. V. CHMUTOV Institute of physical Chemistry,U.S.S.R. Academy of Sciences. Moscow, U.S.S.R. (Received 24 April 1979; received for publication 3 July 1980) Abstract--A theoretical and experimental study of the diffusion processes in complex-formation in ion exchangers has been made. The study is based on diffusion-type equations expressing the laws of material balance for the counterions and a co-ion. These equations are complemented by the conditions of electroneutrality and absence of any electric current. In particular, the approximate solutions of the equations suggest that during the initial stages of particle conversion, the degree of conversion depends on the input concentration and is proportional to \/(t), the effective diffusion being controlled by the individual diffusion coefficients for the counterions. The exact solution of the problem, for varying relations between the individual diffusion coefficient has been obtained numerically by using computers. The principles thus found have been verified experimentally for the Me-H exchange in a carboxylic cation exchanger and for Me-Me exchange in a complex formation vinylpyridine cation exchanger, respectively. The experimental data agree with the theoretical deductions. INTRODUCTION The mechanism of ion exchange accompanied by complexformation of a counterion with a fixed exchange group of an ion exchanger has been considered qualitatively by Helfferich[1]. Participation of the co-ion Y in the diffusion processes in the ion exchanger phase has been noted as a distinguishing feature of such an exchange process. If, in the displacement of the ions A, the ion exchanger passes from a dissociated form to that of a stable RB complex then the well-defined B[A boundary, as the exchange process develops, is moving toward the particle centre. The electrolyte B Y from the solution diffuses through the complexed layer to the moving exchange boundary whose velocity depends on the ion B concentration gradient in the layer and the diffusion coefficients of the ions A and B. Thus in the complexformation reaction with the functional groups, even in the case of intraparticle kinetics, the exchange rate depends on the solution concentration, as distinct from the model of an ordinary exchange process when there is no co-ion in the ion exchanger phase.
ZAa~ + c~) = ao
13~
i~A,B.Y
where c~ is the ion concentration in the layer, a~ is the concentration of the ion associated with the fixed groups (ay = 0), Z~ are the charges, ao is the total ion exchanger capicity, the ion fluxes being governed by the NernstPlanck relations: Y .~ = @~(grad C + z~C~--~grad ¢~), i = ,4, B. Y (4/ where ~ are the individual diffusion coefficients. ¢ is the electric potential. In case when reaction rate does not limit the process and the stability constant of the RB complex is large, the relation between as and C8 can be described by a "rectangular" isotherm: a R : a o , if Cn#O;
THEORETICAL CONSIDERATION If we neglect swelling effects, consider the system as being isothermal, and take into account the fluxes of all three ions, as distinct from a work[2] where the co-ion flux is ignored, it will be possible to write down the main quations describing the process under study, as follows: The law of a meterial balance:
a~=O, if C . : O .
The equation system (1)-(5) can be solved approximately by the method of integral relations. Under the physically justified assumption of the constancy of the co-ion Y concentration at the moving boundary, which has been supported experimentally[3], the following equations have been obtained for a fractiional conversion F~< 0.6[4, 5]:
F(t)= 3x/ (2D¢ C~°t~], D~=(zB- zv)~A~R O(a~+c~)_ Ot
div.~
i=A,B,
K
(11
Condition for the absence of electric current: Z,L = O.
(2)
i-A.B.Y
Condition for electroneutrality: 787
15)
'~ ~
ao~o /
ZB~B
I6)
-- Z y ~ A
where t is time, D e is the effective diffision coefficient ro is the particle radius, Co is the solution concentration at the particle boundary, in the present case being equal to the concentration of the surrounding solution. For the exact solution of the problem, eqns (I)-(4) are complemented by the equilibrium condition of reaction that accompanies the ion-exchange process. For singly
A.I. KALINICHEV et al.
788 charged ions [6, 7].
Ki = C ( a o -
i (IA --
aa)/ai,
i = A, B
(7)
where KA, Ks are the instability constants of the RA, RB complexes, by expressing aA, as and Cr in terms of CA and Ca, eqns (1)-.(4), (7) can be reduced to a system of two non-linear equations in partial derivatives with respect to CA and Ca, this is complemented by the initial conditions, condition in the centre of the particle and condition of concentration constancy at the boundary of the particle. This system has been solved by numerical methods using computers [8]. Shown in Figs. 1 and 2 are the distributions of the concentrations aa, Ca and Cv in the particle for certain diffusion coefficients and constants K , which, among other things, show, a well-defined moving concentration boundary. The fractional conversion F (Fig. 3), for small values at the initial stages, is proportional to V'(t) and does not depend on Dy, which fits eqns (6).
4O~C
1.0
• 3c
,~oo 0.5
0
0.5
LO
x
Fig. I. Distribution of as(curves la-4a) and Ca (curves 1c-4c) concentrations, X=l-d~'o for D,~=0.IDs; Dr=0.0l Ds; K,dco =0.1, Ks~Co= 0.001 for various values of the parameter ¢=X/[~s(Cotlao~o2)] 1-¢=0.1; 2-¢=0.5; 3 - r = 0 . 9 : 4-~'= 1.0.
F 0.5
O
f I.O
0.5
r
Fig. 3. Dependence of fractional conversion F on 1" for KA/CO=
Ks/Co=O.OOl; l, DA =O.l DR; Dr =0,1DB; 2, DA = 0 . [ Ds; Dy=O.O1D~; 3, DA =0.01DB; Dr =0.1Ds; 4, Da =0.01D~; D, = 0.0l DB.
0.1,
EXPERIMENTAL Experimental verification of eqns (6) was carried out by a study of the Me-H kinetics on a carboxylic cation exchanger KB-4 and Me-Me exchange on a complex-formingvinylpyridine ampholyte VPC. The aqueous solutions of HCI or one of the following salts: NiCI2, NiSO4,Sr(NO3h, ZnSO4,containing a displacing ion, were filter (at a rate of 100ml/min for a specified period of time) through a thin (0.2 cm) cylindrical sorbent bed with a base area of 0.63 cm2, The bed consisted of the spherical ion exchanger particles in the form of the displaced ion. The rate used ensured a constant value of Co in the process of exchange and excluded the influence of external diffusion factors[4]. The fractional conversion of ampholyte VPC was determined by the desorption of the sorbed ions with a 3 M HNO3 solution, and the fractional conversion of cation exchanger KB-4--by the titration of the sorbent layer with NaOH solution. The concentration of the metal ions in the solution was found by complexometrictitration and spectrophotometry. The vinylpyridine ampholyte used by the authors consists of an oxymethylated copolymer of 2-methyl-5-vinylpyridinewith divinylbenzene (DVB), containing a grouping of a-picolinic acid as the functional group, and a cation exchanger KB-4 consists of a copolymer of methyl methacrylate and DVB with a carboxyl functional group. RESULTS AND DISCUSSION Shown in Figs. 4 and 5 are the kinetic dependencies of the displacement of the Na + ions by H + ions from the weakly acid carboxylic cation exchanger KB-4 and of
0.4
I
2
0.3
~1o°
2
0.2
0.1 O
05
I.O
v
O
2
4
6
8
secl'2
Fig. 2. Distribution of Cy concentration for DA = 0.1 Ds; Dy = 0.01Ds; KA/Co=O.I; Ks/Co=O.O01; 1, ~-=0.1; 2, ¢=0.2; 3
Fig. 4. Effect of HCI solution concentration on the exchange rate H÷-Na ÷ in cation exchanger KB-4, T=293°K 7o=0.02cm; 1,
r = 0.5; 4, r = 0.9; 5, ~"= 1.0.
Co=0.2 M; 2, Co = 0.1 M; 3, Co = 0.03 M.
Investigation into the kinetics of ion-exchangeprocesses accompanied by complex formation
./. F°2~
o o
Ol o
IO
20 secl/2
Fig. 5. Effect of Nd(NO3h solution concentration on the exchange rate Nd3+-Na+ in ampholtye VPC, T = 363°K, T0= 0.05 cm. pH =4.5; l, Co:0.1 M; 2, Co=0.03 M; 3, Co =0.01M. Na ~ ions by Nd 3. ions from the complex forming vinylpyridine ampholyte VPC. In the two cases the exchange process is accompanied by the formation of weakly dissociating compounds of the displacing ions with the fixed exchange groups of the ion exchanger, the isotherm for the process being close to a rectangular configuration. As can be seen from Figs. 4 and 5, the dependence F(X/(t)) in the region F < 0 . 5 is linear and the value of F/V(t) is proportional to ~/(Co). The results shown in Fig. 6 demonstrate the effect of the exchanging ion diffusion coefficients on the rate of the process. In the displacement of the Na ÷ ions from ampholyte VPC by Sr:÷, Ni 2÷ and Zn 2+ ions the formation of a stable Me-ion exchanger complex will take place. The sorption rate of Me 2+, other experimental conditions being equal, is controlled by the value DM~2+, since it is possible to assume, approximately DN,*>> DMe2 +. 1.0
I
789
The diffusion coefficients, as estimated from eqns (6), on the basis of the experimental kinetic dependencies (Fig. 6, curves 1, 2, 3), are: Dsr = (3.2 ± 0.3). 10-7 cm2/s, DNi = (2.0±0.2t " 10-7 cm2/s, Dz, =(1.9±0.2). 10 7 cm2/s. In the exchange process Ni 2÷- Sr2+ and Ni 2+- Zn 2+ (Fig. 6, curves 4, 5) there is a displacement of the less stable strontium and zinc complexes by the more stable complex of nickel with the fixed ion exchanger groups. The relation between the stability constants of these complexes is such that the sorption isotherm has a prominently concave shape, and well-defined Ni/Sr and Ni/Zn boundaries make their appearance in the ion exchanger particle in the process of exchange. The reason for the diminishing rates of exchange (to a lesser extent for the exchange Ni2+-Sr2~ and to a greater extent for the exchange Ni2+-Zn2+) lies in the Sr2+ and Zn z* ions which have smaller diffusion coefficients compared with the Na ÷ ion, being involved in the interdiffusion process. It is possible, by using eqns (6), to calculate the effective interdiffusion coefficient for the experimental conditions corresponding to those shown in Fig. 6 (curves 4, 5), based on the above found individual diffusion coefficients for the SP ÷, Zn 2+ and Ni 2~ ions. The interdiffusion coefficients calculated and found experimentally from the exchange Ni2+-Sr2. and Ni2~-Zn2~, are close to each other, being: DNi-z,~c,lc~ = (I.9 ± 0.2)' DN~-Z,~e,o,-- (1.5 ±0.1)' DN,_sr(calc) = (2.7 ± 0.3)' DNi-s,~x~, -- (3.3 : 0.3)"
10 7 cm2/s. 10 7 cm2/s, 10-7 cm2/s, 10 7 cm2/s.
It is to be concluded that the dependence of the exchange rate, as found by the present authors, on the concentration of the surrounding solution should be taken into account in the estimation of the width of the chromatographic zone in the columns with complexformation ion exchangers.
2
3 4 REFERENCES (
I. F. Helfferich, J. Phys. Chem. 69, 1178(1%5). 2. M. Nativ, S. Goldstein and G. Schmukler, J. lnorg. NucL Chem. 37(9L 1951 (1975). 3. T. D. Semenovskaya, A. I. Kalinichev and K. V. Chmutov, Zh, Fiz. Khim. 52, 2943 (1978).
F 015
4. A. I. Kalinichev, T. D. Semenovskaya and K. V. Chtmutov,
5.
0
I
I
I
t
2
4
6
8
6.
.~cI/2
Fig. 6. Effect of individual diffusion coefficients on the ion exchange rate in ampholyte VPC at Co = 0.025 M, T = 293°K. ro = 0.005cm; I, Sr2+-Na~; 2, Ni2+-Na+; 3, Zn2+-Na+;4, Ni2*Sr2~; 5, Ni2+-Znz+.
7. 8.
In Sorption and Chromatography, p. 144. Nauka, Moscow (1979). K. V. Chmutov, A. I. Kalinichev and T. D. Semenovskava, DokL AN SSSR 239, 650 (1978). F. Helfferich, Ion Exchangers. lnostrannaya Literatura, Moscow (1%2). I. Turkova, In Liquid Column Chromatography (Edited by Z. Deyl, K. Macek and J. Janak), Vol. I, p. 120 Mir, Moscow t19781. A. 1. Kalinichev, E. V. Kolotinskaya and A. Ya. Pronin, Zn. Fiz. Khim. 53, 506 (1979).
0022-1902/81/040787-03502.00]0 Pergamon Press lad,
INVESTIGATION INTO THE KINETICS OF ION-EXCHANGE PROCESSES ACCOMPANIED BY COMPLEX FORMATION A. 1. KALINICHEV*, T. D. SEMENOVSKAYA, E. V. KOLOT1NSKAYA, A. YA. PRONIN and K. V. CHMUTOV Institute of physical Chemistry,U.S.S.R. Academy of Sciences. Moscow, U.S.S.R. (Received 24 April 1979; received for publication 3 July 1980) Abstract--A theoretical and experimental study of the diffusion processes in complex-formation in ion exchangers has been made. The study is based on diffusion-type equations expressing the laws of material balance for the counterions and a co-ion. These equations are complemented by the conditions of electroneutrality and absence of any electric current. In particular, the approximate solutions of the equations suggest that during the initial stages of particle conversion, the degree of conversion depends on the input concentration and is proportional to \/(t), the effective diffusion being controlled by the individual diffusion coefficients for the counterions. The exact solution of the problem, for varying relations between the individual diffusion coefficient has been obtained numerically by using computers. The principles thus found have been verified experimentally for the Me-H exchange in a carboxylic cation exchanger and for Me-Me exchange in a complex formation vinylpyridine cation exchanger, respectively. The experimental data agree with the theoretical deductions. INTRODUCTION The mechanism of ion exchange accompanied by complexformation of a counterion with a fixed exchange group of an ion exchanger has been considered qualitatively by Helfferich[1]. Participation of the co-ion Y in the diffusion processes in the ion exchanger phase has been noted as a distinguishing feature of such an exchange process. If, in the displacement of the ions A, the ion exchanger passes from a dissociated form to that of a stable RB complex then the well-defined B[A boundary, as the exchange process develops, is moving toward the particle centre. The electrolyte B Y from the solution diffuses through the complexed layer to the moving exchange boundary whose velocity depends on the ion B concentration gradient in the layer and the diffusion coefficients of the ions A and B. Thus in the complexformation reaction with the functional groups, even in the case of intraparticle kinetics, the exchange rate depends on the solution concentration, as distinct from the model of an ordinary exchange process when there is no co-ion in the ion exchanger phase.
ZAa~ + c~) = ao
13~
i~A,B.Y
where c~ is the ion concentration in the layer, a~ is the concentration of the ion associated with the fixed groups (ay = 0), Z~ are the charges, ao is the total ion exchanger capicity, the ion fluxes being governed by the NernstPlanck relations: Y .~ = @~(grad C + z~C~--~grad ¢~), i = ,4, B. Y (4/ where ~ are the individual diffusion coefficients. ¢ is the electric potential. In case when reaction rate does not limit the process and the stability constant of the RB complex is large, the relation between as and C8 can be described by a "rectangular" isotherm: a R : a o , if Cn#O;
THEORETICAL CONSIDERATION If we neglect swelling effects, consider the system as being isothermal, and take into account the fluxes of all three ions, as distinct from a work[2] where the co-ion flux is ignored, it will be possible to write down the main quations describing the process under study, as follows: The law of a meterial balance:
a~=O, if C . : O .
The equation system (1)-(5) can be solved approximately by the method of integral relations. Under the physically justified assumption of the constancy of the co-ion Y concentration at the moving boundary, which has been supported experimentally[3], the following equations have been obtained for a fractiional conversion F~< 0.6[4, 5]:
F(t)= 3x/ (2D¢ C~°t~], D~=(zB- zv)~A~R O(a~+c~)_ Ot
div.~
i=A,B,
K
(11
Condition for the absence of electric current: Z,L = O.
(2)
i-A.B.Y
Condition for electroneutrality: 787
15)
'~ ~
ao~o /
ZB~B
I6)
-- Z y ~ A
where t is time, D e is the effective diffision coefficient ro is the particle radius, Co is the solution concentration at the particle boundary, in the present case being equal to the concentration of the surrounding solution. For the exact solution of the problem, eqns (I)-(4) are complemented by the equilibrium condition of reaction that accompanies the ion-exchange process. For singly
A.I. KALINICHEV et al.
788 charged ions [6, 7].
Ki = C ( a o -
i (IA --
aa)/ai,
i = A, B
(7)
where KA, Ks are the instability constants of the RA, RB complexes, by expressing aA, as and Cr in terms of CA and Ca, eqns (1)-.(4), (7) can be reduced to a system of two non-linear equations in partial derivatives with respect to CA and Ca, this is complemented by the initial conditions, condition in the centre of the particle and condition of concentration constancy at the boundary of the particle. This system has been solved by numerical methods using computers [8]. Shown in Figs. 1 and 2 are the distributions of the concentrations aa, Ca and Cv in the particle for certain diffusion coefficients and constants K , which, among other things, show, a well-defined moving concentration boundary. The fractional conversion F (Fig. 3), for small values at the initial stages, is proportional to V'(t) and does not depend on Dy, which fits eqns (6).
4O~C
1.0
• 3c
,~oo 0.5
0
0.5
LO
x
Fig. I. Distribution of as(curves la-4a) and Ca (curves 1c-4c) concentrations, X=l-d~'o for D,~=0.IDs; Dr=0.0l Ds; K,dco =0.1, Ks~Co= 0.001 for various values of the parameter ¢=X/[~s(Cotlao~o2)] 1-¢=0.1; 2-¢=0.5; 3 - r = 0 . 9 : 4-~'= 1.0.
F 0.5
O
f I.O
0.5
r
Fig. 3. Dependence of fractional conversion F on 1" for KA/CO=
Ks/Co=O.OOl; l, DA =O.l DR; Dr =0,1DB; 2, DA = 0 . [ Ds; Dy=O.O1D~; 3, DA =0.01DB; Dr =0.1Ds; 4, Da =0.01D~; D, = 0.0l DB.
0.1,
EXPERIMENTAL Experimental verification of eqns (6) was carried out by a study of the Me-H kinetics on a carboxylic cation exchanger KB-4 and Me-Me exchange on a complex-formingvinylpyridine ampholyte VPC. The aqueous solutions of HCI or one of the following salts: NiCI2, NiSO4,Sr(NO3h, ZnSO4,containing a displacing ion, were filter (at a rate of 100ml/min for a specified period of time) through a thin (0.2 cm) cylindrical sorbent bed with a base area of 0.63 cm2, The bed consisted of the spherical ion exchanger particles in the form of the displaced ion. The rate used ensured a constant value of Co in the process of exchange and excluded the influence of external diffusion factors[4]. The fractional conversion of ampholyte VPC was determined by the desorption of the sorbed ions with a 3 M HNO3 solution, and the fractional conversion of cation exchanger KB-4--by the titration of the sorbent layer with NaOH solution. The concentration of the metal ions in the solution was found by complexometrictitration and spectrophotometry. The vinylpyridine ampholyte used by the authors consists of an oxymethylated copolymer of 2-methyl-5-vinylpyridinewith divinylbenzene (DVB), containing a grouping of a-picolinic acid as the functional group, and a cation exchanger KB-4 consists of a copolymer of methyl methacrylate and DVB with a carboxyl functional group. RESULTS AND DISCUSSION Shown in Figs. 4 and 5 are the kinetic dependencies of the displacement of the Na + ions by H + ions from the weakly acid carboxylic cation exchanger KB-4 and of
0.4
I
2
0.3
~1o°
2
0.2
0.1 O
05
I.O
v
O
2
4
6
8
secl'2
Fig. 2. Distribution of Cy concentration for DA = 0.1 Ds; Dy = 0.01Ds; KA/Co=O.I; Ks/Co=O.O01; 1, ~-=0.1; 2, ¢=0.2; 3
Fig. 4. Effect of HCI solution concentration on the exchange rate H÷-Na ÷ in cation exchanger KB-4, T=293°K 7o=0.02cm; 1,
r = 0.5; 4, r = 0.9; 5, ~"= 1.0.
Co=0.2 M; 2, Co = 0.1 M; 3, Co = 0.03 M.
Investigation into the kinetics of ion-exchangeprocesses accompanied by complex formation
./. F°2~
o o
Ol o
IO
20 secl/2
Fig. 5. Effect of Nd(NO3h solution concentration on the exchange rate Nd3+-Na+ in ampholtye VPC, T = 363°K, T0= 0.05 cm. pH =4.5; l, Co:0.1 M; 2, Co=0.03 M; 3, Co =0.01M. Na ~ ions by Nd 3. ions from the complex forming vinylpyridine ampholyte VPC. In the two cases the exchange process is accompanied by the formation of weakly dissociating compounds of the displacing ions with the fixed exchange groups of the ion exchanger, the isotherm for the process being close to a rectangular configuration. As can be seen from Figs. 4 and 5, the dependence F(X/(t)) in the region F < 0 . 5 is linear and the value of F/V(t) is proportional to ~/(Co). The results shown in Fig. 6 demonstrate the effect of the exchanging ion diffusion coefficients on the rate of the process. In the displacement of the Na ÷ ions from ampholyte VPC by Sr:÷, Ni 2÷ and Zn 2+ ions the formation of a stable Me-ion exchanger complex will take place. The sorption rate of Me 2+, other experimental conditions being equal, is controlled by the value DM~2+, since it is possible to assume, approximately DN,*>> DMe2 +. 1.0
I
789
The diffusion coefficients, as estimated from eqns (6), on the basis of the experimental kinetic dependencies (Fig. 6, curves 1, 2, 3), are: Dsr = (3.2 ± 0.3). 10-7 cm2/s, DNi = (2.0±0.2t " 10-7 cm2/s, Dz, =(1.9±0.2). 10 7 cm2/s. In the exchange process Ni 2÷- Sr2+ and Ni 2+- Zn 2+ (Fig. 6, curves 4, 5) there is a displacement of the less stable strontium and zinc complexes by the more stable complex of nickel with the fixed ion exchanger groups. The relation between the stability constants of these complexes is such that the sorption isotherm has a prominently concave shape, and well-defined Ni/Sr and Ni/Zn boundaries make their appearance in the ion exchanger particle in the process of exchange. The reason for the diminishing rates of exchange (to a lesser extent for the exchange Ni2+-Sr2~ and to a greater extent for the exchange Ni2+-Zn2+) lies in the Sr2+ and Zn z* ions which have smaller diffusion coefficients compared with the Na ÷ ion, being involved in the interdiffusion process. It is possible, by using eqns (6), to calculate the effective interdiffusion coefficient for the experimental conditions corresponding to those shown in Fig. 6 (curves 4, 5), based on the above found individual diffusion coefficients for the SP ÷, Zn 2+ and Ni 2~ ions. The interdiffusion coefficients calculated and found experimentally from the exchange Ni2+-Sr2. and Ni2~-Zn2~, are close to each other, being: DNi-z,~c,lc~ = (I.9 ± 0.2)' DN~-Z,~e,o,-- (1.5 ±0.1)' DN,_sr(calc) = (2.7 ± 0.3)' DNi-s,~x~, -- (3.3 : 0.3)"
10 7 cm2/s. 10 7 cm2/s, 10-7 cm2/s, 10 7 cm2/s.
It is to be concluded that the dependence of the exchange rate, as found by the present authors, on the concentration of the surrounding solution should be taken into account in the estimation of the width of the chromatographic zone in the columns with complexformation ion exchangers.
2
3 4 REFERENCES (
I. F. Helfferich, J. Phys. Chem. 69, 1178(1%5). 2. M. Nativ, S. Goldstein and G. Schmukler, J. lnorg. NucL Chem. 37(9L 1951 (1975). 3. T. D. Semenovskaya, A. I. Kalinichev and K. V. Chmutov, Zh, Fiz. Khim. 52, 2943 (1978).
F 015
4. A. I. Kalinichev, T. D. Semenovskaya and K. V. Chtmutov,
5.
0
I
I
I
t
2
4
6
8
6.
.~cI/2
Fig. 6. Effect of individual diffusion coefficients on the ion exchange rate in ampholyte VPC at Co = 0.025 M, T = 293°K. ro = 0.005cm; I, Sr2+-Na~; 2, Ni2+-Na+; 3, Zn2+-Na+;4, Ni2*Sr2~; 5, Ni2+-Znz+.
7. 8.
In Sorption and Chromatography, p. 144. Nauka, Moscow (1979). K. V. Chmutov, A. I. Kalinichev and T. D. Semenovskava, DokL AN SSSR 239, 650 (1978). F. Helfferich, Ion Exchangers. lnostrannaya Literatura, Moscow (1%2). I. Turkova, In Liquid Column Chromatography (Edited by Z. Deyl, K. Macek and J. Janak), Vol. I, p. 120 Mir, Moscow t19781. A. 1. Kalinichev, E. V. Kolotinskaya and A. Ya. Pronin, Zn. Fiz. Khim. 53, 506 (1979).