Influence of temperature on ion-exchange equilibrium accompanied by complex formation in resins

Reactive & Functional Polymers 38 (1998) 205–218

Influence of temperature on ion-exchange equilibrium accompanied by complex formation in resins V.A. Ivanov*, V.I. Gorshkov, V.D. Timofeevskaja, N.V. Drozdova Department of Chemistry, Lomonosov Moscow State University, Moscow 119899, Russia Accepted 15 July 1997

Abstract The paper deals with finding the correlation between the influence of temperature on the ionic selectivity of ion-exchange resins studied experimentally and their chemical structures. The effects of temperature on selectivity of resins are compared with the data for the soluble complexing reagents. The physicochemical basis of the influence of temperature on ion-exchange selectivity is considered.  1998 Elsevier Science B.V. All rights reserved. Keywords: Ion exchange; Equilibrium properties; Selectivity; Influence of temperature; Enthalpy

1. Introduction Looking at the history of ion exchange we have to recognize that in the 1940s and 1950s the generation of physical chemists, to whom ¨ Professor E. Hogfeldt belonged, studied the phenomenon of ion exchange exceptionally comprehensively. Most aspects of thermodynamics and of equilibrium were reflected in the works of that time. The influence of temperature on the equilibrium properties of ion-exchange resins was studied in the pioneering works of many researchers [1–11] mainly using newly discovered resins with the strongly acidic sulfonic and strongly basic active groups synthesized from functionalized copolymers of styrene

*Corresponding author.

and divinylbenzene. It was shown that the selectivity of cation-exchange resins usually decreased insignificantly with temperature in the case of exchange of the equally charged cations, and increased in case of exchange of monovalent and divalent cations. Based on those results, the influence of temperature on equilibrium of most ion-exchange systems is regarded as insignificant [12], p. 166; [13], Ch. 3). This opinion was predominant up to the present time, despite the fact that a significant influence of temperature on carboxylic resins for the Ca 21 – Na 1 and Mg 21 –NH 1 exchanges was noted 4 [14,15]. However, these results were underestimated and not further developed. Until recently, the influence of temperature on the cation-exchange equilibrium of numerous nonsulfonic ion-exchange and complexing resins was less studied than the strong acidic sulfonic resins. Since the 1980s we investigated

1381-5148 / 98 / $ – see front matter  1998 Elsevier Science B.V. All rights reserved. PII: S1381-5148( 97 )00162-4

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the exchange of mono- and divalent cations of elements of the first, and of the second, and of the transition groups on resins with carboxylic, amino carboxylic and phosphonic active groups. These results have been partially published [16– 19]. For some resins a significant temperature effect was demonstrated. The same effect was repeated in later works [20,21] for the exchange of calcium and magnesium ions on sodium ionic form of carboxylic resins of the polymethacrylic type from solution imitating sea water. A strong influence of temperature on the exchange of Ca 21 and Mg 21 ions was also found for the polymethacrylic cation-exchange resin and for the chelating resin with iminodiacetic active groups [22]. For these resins the selectivity changed with temperature. Later [23–25] for both types of resin, effects of temperature on selectivity in ionic systems containing Cu 21 , Zn 21 , and Al 31 ions were discovered. The influence of temperature on complexing of metal cations on weak basic anion-exchange resins has not so far been studied. This paper deals with the correlation between the influence of temperature on ionic selectivity and the nature of intermolecular interactions. We present mainly new experimental results, which enable conclusions to be drawn regarding the relationship between the temperature and the chemical structure of resins, and to compare the effects of temperature on selectivity with the thermochemically determined data and with the data for the soluble complexing reagents, and to consider the physicochemical basis of the influence of temperature on ion-exchange selectivity.

2. Experimental The ion-exchangers under study were polyacrylic resin (KB-2 3 10) crosslinked with 10% divinylbenzene (DVB), polymethacrylic resins with 2.5% DVB (KB-4P2), 6% DVB (KB-4) and 16% DVB (KB-4 3 16), polymethacrylic

resin SG-1 crosslinked with triethyleneglycoldimethacrylate, polystyrene resins (crosslinked with DVB) with carboxylic (KMD) and phosphonic (KRPh-8P) groups, two chelating resins: polystyrene with iminodiacetic groups (ANKB50) and polyvinylpyridine with carboxylic groups in the a-position (VPK), and the weakly acidic polyvinylpyridine anion exchanger (AN40) crosslinked with DVB. The experimental method of determining the equilibrium parameters was almost the same as that in [12] (p. 229). The only peculiarity consisted in a consecutive dynamic and batch treatment of resin with the same solution in order to equilibrate the phases. After equilibration the solution was separated from the resin by suction and both phases were analyzed. The coincidence of the results obtained for different initial ionic forms of resins was picked as the principal criterion of equilibrium having been attained. The experimental method allowed determination of the overall volume of resins beads and the concentrations of the exchangeable ions in the resin. In order to use the maximum ion-exchange groups of the resin and at the same time to prevent the precipitation of the divalent metal hydroxides, in experiments with the cation-exchange and chelating resins the pH values in solutions containing the mixture of the alkali and alkaline earth metals were | 8–9, and in solutions containing the mixture of the alkali and transition metals ions were | 5. In experiments with the cation-exchange and chelating resins for the ion-exchange reaction 1 1 1 1 ] AR ZA 1 ]BXZ B ⇔] AXZA 1 ]BR Z B zA zB zA zB

(1)

where R is the polymeric matrix of resin; A and B are the counterions with the charges zA and z B ; X is the monovalent co-ion); the next equilibrium parameters were determined:equilibrium coefficient: 1 /zB

1 / zA

B mB cA K˜˜ A 5 ]] 1 / zA ? ]] mA c 1B/ z B

(2)

V. A. Ivanov et al. / Reactive & Functional Polymers 38 (1998) 205 – 218

207

selectivity coefficient: y 1B/ z B x 1A/ zA Kx, y 5 ]] ? ]] y A1 / zA x B1 / z B

(3)

separation factor: y B xA a AB 5 ] ? ] yA x B

(4)

were m and c are the concentrations of ions in resin and in the external solution in equivalents per litre; y and x are the equivalent fractions of counterions in resin and in the external solution. In this paper for systems with the alkaline earth B metals only the K˜˜ values are presented; and all ¯B A

A

values K ,Kx, y and a are presented for systems with Co 21 , Ni 21 and Zn 21 ions. The experimental date are presented completely in [26,27]. The B relative errors of determination of K˜˜ A ,Kx, y and a did not exceed 15%, as well as the discrepancies between experimental values for each solution did not exceed the maximum errors. Because the capacity of metal sorption on weak basic anion-exchange resins depends on pH [28], in experiments with complexing of Ni 21 ion on anion-exchange resin AN-40 both pH values and temperature were varied.

Fig. 1. Plots of the equilibrium coefficient K˜˜ vs. temperature for the polymethacrylic resin KB-4 for M 21 –Na 1 exchange from 2.5 M solution containing NaCl and 0.08 equiv. / l CaCl 2 (1); 0.02 equiv / l CaCl 2 (2); 0.005 equiv. / l CaCl 2 (3); 0.081 equiv. / l MgCl 2 (4) and 0.01 equiv. / l SrCl 2 (5). Initial ionic form of resin: Na 1 5black points; M 21 5empty points.

3. Results Experimental data in Figs. 1–3 and in Table 1 together with the literary data on sulfonic resins [1–13] demonstrated that the temperature dependencies of the equilibrium characteristics of the di- and monovalent ion exchange correlated with the chemical structures of resins. For all cation exchangers (sulfonic, carboxylic, phosphonic) without the donor nitrogen containing groups the selectivity towards divalent ions increased with temperature. In the case of polyacrylic and polymethacrylic resins the temperature effects were found to be significantly stronger than that for resins with polystyrene

Fig. 2. Plots of the equilibrium coefficient K˜˜ vs. temperature for Ca 21 –Na 1 exchange from solution 2.5 equiv. / l NaCl50.08 equiv. / l CaCl 2 . Resins: 1–355 polymethacrylic KB-4, KB-4P2, KB-4x16 SG-1; 45polyacrylic KB-2; 65carboxylic polystyrene KMD; 75iminodiacetic chelating; 85polyvinylpyridine carboxylic chelating. Initial ionic form of resin: Na 1 5black points; Ca 21 5empty points.

208

V. A. Ivanov et al. / Reactive & Functional Polymers 38 (1998) 205 – 218

Fig. 3. Plots of the equilibrium coefficient K˜˜ vs. the ionic composition of resin for Ca 21 –Na 1 exchange from 2.5 M solution at 208C (1) and 828C (2). Resins: A5polymethacrylic KB-4; B5phosphonic polystyrene KRPh; C5polyvinylpyridine carboxylic chelating; D5iminidiacetic chelating.

matrix (the equilibrium coefficients’ increase was up to quadruple due to the increase of temperature from 108C to 958C). For all cation-exchange resins the optimal compositions of phases can be selected (Fig. 4) which corresponds to the maximal temperature shifts of the resin ionic composition s y(908C) 2 y(208C)d. The optimal compositions of different resins have been found to be close to the mean equal contents of both exchangeable ions in resin ([y(908C) 2 y(208C))] / 2 ¯ 0.5. The equilibrium coefficients for chelating polyampholytic resins did not significantly depend on temperature in the case of exchange of alkali-earth and alkali-metals ions (Figs. 2 and 3) and decreased with temperature in the case of

transition and alkali metals ions exchange (Table 1). Due to the nonuniform effects of temperature on selectivity of cation exchangers and of chelating resins, for some solution compositions at high temperature the former became more selective than the chelating resins (Figs. 2 and 3). This fact corrodes to some extent the opinion that chelating resins are more suitable than cation exchangers for separation of divalent ions due to their higher selectivity. For all of theB studied ion-exchange systems, the values of K˜˜ A ,Kx, y and a increased with the decrease of the divalent ion in resin and in solution (Fig. 3). The most significant increase of selectivity took place in cases of the complexing phosphonic cation exchanger KRPh-8p and of the chelating resins VPK and ANKB-50. Most likely, this could be due to the difference of the complexes compositions in resin at different ratios of ions. At low concentrations of divalent ion in the resin more of the ligand groups of the resins were coordinated by the metal ion. From the point of view of the separation processes in columns, the volumetric capacity (per 1 ml of resin bed or per 1 ml of the volume proper of resin) is important. Fig. 5 shows the experimental values of capacities of some resins at two temperatures. The polymethacrylic cation-exchange resin has significantly higher volumetric capacity than the chelating resins. Also, its capacity at the fixed ionic composition of resin depended on temperature in contrast to chelating and phosphonic resins. At high temperature in the region y Ca $ 0.4 polymethacrylic resin had about 18–20% higher volumetric capacity than at room temperature. It could be because the divalent ions affected the conformation of the polymeric chains more strongly at high temperature when the mobility of the polymeric chains was increased. Fig. 6 shows that the temperature did not affect the capacity of the Ni 21 sorption on the weak basic anion exchanger AN-40 at the fixed pH value in contrast to the data of [29,30]

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209

Table 1 Equilibrium characteristics M 21 –Na 1 (M5Zn, Co, Ni) for solution 2.5 equiv. / l NaCl–0.01 equiv. / l MCl 2 on polymethacrylic resin KB-4 and chelating resin ANKB-50 Ionic system KB-4 Zn 21 –Na 1

T (8C)

Initial ionic form of resin

y M 21

M K˜˜ Na

M Kx, y Na

M a Na

90

Na 1 Zn 21 Na 1 Zn 21

0.58 0.62 0.47 0.50

17.8 20.5 13.3 15.0

29.2 33.2 20.5 22.7

354 416 221 256

Na 1 Co 21 Na 1 Co 21

0.67 0.68 0.31 0.34

23.3 24.2 8.5 9.5

38.4 39.3 12.4 13.6

488 503 107 122

Na 1 Ni 21 Na 1 Ni 21

0.61 0.56 0.33 0.32

21.3 20.4 9.3 9.6

32.0 27.6 13.5 13.9

400 331 125 122

Na 1 Zn 21 Na 1 Zn 21

0.55 0.57 0.61 0.62

25.3 27.6 30.0 30.0

26.5 28.0 32.6 32.2

311 334 405 407

Na 1 Co 21 Na 1 Co 21

0.56 0.56 0.57 0.59

26.0 26.4 26.4 28.0

26.4 26.4 27.2 29.0

307 307 317 345

Na 1 Ni 21 Na 1 Ni 21

0.54 0.50 0.58 0.56

24.2 22.4 27.6 27.9

25.5 22.6 28.4 27.6

300 256 348 331

20 Co 21 –Na 1

90 20

Ni 21 –Na 1

90 20

ANKB-50 Zn 21 –Na 1

90 20

Co 21 –Na 1

90 20

Ni 21 –Na 1

90 20

Fig. 4. Plots of the temperature stimulated shifts of resins compositions vs. the mean composition of resins. Resins: 1, 2, 35polymethacrylic KB-4 (Ca 21 –Na 1 ; Ca 21 –K 1 and Mg 21 –Na 1 exchange); 45phosphonic KRPh-8P (Ca 21 –Na 1 ).

which demonstrated calorimetrically significant negative enthalpy of the transition metals sorption on the vinylpyridine resins. This effect was investigated in the dynamic experiment (Fig. 7). About 2 g (air dried) of the anion exchanger was equilibrated at 908C with 1.0 equiv. / l NaCl10.01 equiv. / l NiCl 2 , pH 3.4. Then, this sample was placed in the column (diameter 0.6 cm); the equilibrium solution was separated from resin by suction at 908C; the temperature was decreased to 208C and the same solution was passed through the column. Breakthrough curve (Fig. 7) showed that the sorption capacity of resin at low temperature was some higher than at 908C. However, this difference was

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V. A. Ivanov et al. / Reactive & Functional Polymers 38 (1998) 205 – 218

Fig. 6. Plots of the Ni 21 sorption vs. pH for weakly basic anion exchanger AN-40 in solutions 1.0 equiv. / l NaCl50.01 equiv. / l NiCl 2 (1) and 0.01 equiv / l NiCl 2 (2). Temperature: 208C5empty points; 908C5black points.

S

D

≠ln K BA ]]] ≠T

Fig. 5. Volumetric capacity of resins (per 1 ml of resin) vs. the ionic composition of resin for Ca 21 –Na 1 exchange in 2.5 M solution. Resins: 1510-polymethacrylic KB-4; 25 polyvinylpyridine carboxylic chelating VPK; 35iminidiacetic chelating; 45phosphonic KRPh-8P. Temperature: 208C5empty points; 908C5black points.

about 13% of the maximal sorption of Ni 21 by this resin Fig. 4.

4. Enthalpy 0 Enthalpy DH of ion exchange Reaction (1) can be calculated from the temperature dependence of the equilibrium constant:

/zB 1 / zA a 21 a AX B ]] K BA 5 ]] ? a A21 / zA a B1 / z B

using the van’t Hoff equation

DH 0 ]] 5 (6) 2 p RT where ]aA and ]a B are the activity of components and in resin; aA and a B are the activity of components and in solution. The integral value DH 0 characterizes the complete substitution of one equivalent of ion A in resin phase by the ion B from the solution when ions A and B in both phases are in the standard conditions [31]. Although the principal way of finding the thermodynamic constant from the experimental data is known since the early work of Professor ¨ Hogfeldt [32] this problem remains under discussion. Sometimes, in the van’t Hoff equation instead of thermodynamic equilibrium constant some other experimental equilibrium characteristics are used, whether the corrected equilibrium coefficient m B1 / z B a A1 / zA B ˜ K A 5 ]] ? ]] m 1A/ z B a 1B/ z B

(7)

(5) or the equilibrium coefficient Eq. (2), or some other. The differential values of enthalpy calculated in this way require some additional inter-

V. A. Ivanov et al. / Reactive & Functional Polymers 38 (1998) 205 – 218

211

Fig. 7. Elution curve by passing the solution 1.0 equiv. / l NaCl50.01 equiv. / l NiCl 2 at 208C through the anion exchanger AN-40 equilibrated preliminary with the same solution at 908C.

pretation in order to be compared with the calorimetrically determined values of the enthalpies. Let us write the relation between the thermodynamic equilibrium constant and the corrected equilibrium coefficient as 1 1 ] B B ln K˜ A 5 ln K A 1 ]ln ] gA 2 ]ln g B zA zB

(8)

where ] g are the activity coefficients in the resin phase. The right part can be rearranged through the chemical potentials of components B

ln K˜ A 5

S

0 0 mB 1 1 mA 1 mB 1 ] 2] ] ]2] ]1] ] R zA T zB T zB T mA 1 ] 1 1 2 ] ] 1 ]ln m B 2 ]ln mA zA T zB zA

D

(9)

where ] mi are the chemical potentials of components in resin with concentrations mA and m B ; m i0 are the standard chemical potentials of components in solution. After differentiation the last equation with respect to temperature at the constant resin composition and with the use the expression for the partial molar enthalpy h i [33] ≠( m /T ) 1 F]]] G 5 2h ?] ≠T T i

p

we obtain

i

2

(10)

S

B ≠ln K˜ A ]]] ≠T

D

p,m

S

1 1 1 1] 5 ]]2 ]h A0 2 ]h B0 1 ]h B zB zB RT zA DH˜ m 1] 2 ]hA 5 ]] (11) 2 zA RT

D

The middle part of Eq. (11) shows that the value DH˜ m characterizes the complete substitution of one equivalent of ion B in solution by one equivalent of ion A from the infinite big volume of resin of the fixed concentrations of components mA and m B ; when ions A and B in solution are in the standard states. It is important to emphasise that Eq. (11) is valid when the ionic composition of resin remains constant with temperature. This is possible only if the resin swelling at the fixed ratio of ions in resin remains constant with temperature. For most of the ion-exchange resins this condition is valid (see Fig. 5) but for the polymethacrylic resin. In the latter case, the concentrations of both components mA and m B cannot be fixed simultaneously. Also, at the fixed equivalent fractions of components in resin, yA and y B , the molar concentrations change with temperature. Then, Eq. (9) can be rearranged as B ln K˜ A 5

S

0 0 m *B 1 1 mA 1 mB 1 ] 2] ] ]2] ]1] ] R zA T zB T zB T m *A 1 ] 1 1 2 ] ] 1 ]ln y B 2 ]ln yA zA T zB zA

D

(12)

V. A. Ivanov et al. / Reactive & Functional Polymers 38 (1998) 205 – 218

212

and consequently after differentiation with respect to temperature at the constant values yA and y B it follows

S

≠ln K˜ BA ]]] ≠T

D

p,y

S

1 1 1 1] 5 ]]2 ]h 0A 2 ]h 0B 1 ]h B* zB zB RT zA DH˜ y 1] 2 ]h *A 5 ]]2 (13) zA RT

D

] 0 1 RT ln y 1 where the values ] m *A ;m A A 0 ] 1 RT ln y 1 RT ln ] gA , ] m B* ;m gB and RT ln ] B B ] ] h *A ,h *B correspond to the gipothetic state of ionexchanger with the unit summer concentration m 0 5 mA 1 m B 5 1 and with the same activity coefficients ] gA and ] gB as in the real ion exchanger with the definite concentrations of components. To use the values with such complicated interpretation is rather difficult. It is more useful to estimate quantitatively the role of the temperature dependence of the resin swelling. After differentiation with respect to temperature at the constant equivalent fractions of components in resin yA and y B , Eq. (9) can be rearranged to

S

≠ln K˜ A ]]] ≠T B

D

p,y

S

1 1 1 1] 5 ]]2 ]h 0A 2 ]h 0B 1 ]h B z z z RT A B B 1] 1 2 ]hA 1 ] zA zB ≠ln m D D S]] ≠T 0

1 1 ] 1 ˜B ln K˜ A 5 ln K BA 1 ]ln ] gA 2 ]ln g ln gA B 2] zA zB zA 1 1 ]ln gB zB

(15)

we obtain B ln K˜˜ A 5

] 1 1 mA 1 mB 1 m B ] ] ] ] ] ] ] 2 2 1 R zA T zB T zB T mA 1 ] 1 1 2 ] ] 1 ]ln cA 2 ]ln c B zA T zA zB

S

D

1 1 1 ]ln m B 2 ]ln mA zB zA

(16)

After differentiation the last equation with respect to temperature at the constant concentrations of components in both phases and using the expression for the partial molar enthalpy in Eq. (10) we obtain:

S

≠ln K˜ BA ]]] ≠T

D

p,m,c

S

1 1 1 1] 5 ]]2 ]hA 2 ]h B 1 ]h B z z z RT A B B ˜ DH˜ m,c 1] 2 ]hA 5 ]] (17) 2 zA RT

D

D S

1 2] zA

dynamic equilibrium constant and the equilibrium coefficient

DH˜ y ]] 5 2 p,y RT (14)

Experimental data presented in Fig. 5 shows that in case of the Ca 21 –Na 1 exchange the value of the last member in the middle part of Eq. (14) does not exceed 0.002. If the enthalpy has the value of about 5–15 kJ / equiv., then DH˜ y /RT 2 has the value of about 0.007–0.021. This estimation shows that the temperature dependence of the polymethacrylic resin swelling is relatively small. Analogously with the described transformations, from the relation between the thermo-

The differential characteristic DH˜˜ m,c could characterize the substitution of one equivalent of ion B in a infinitely big volume of solution with the fixed ionic composition (with the concentrations of components cA and c B ) by one equivalent of ion A from the infinitely big volume of resin with the fixed equilibrium ionic composition (with the concentrations of components mA and m B ). The problem is that the compositions of both phases remain constant with temperature only in the case when both the resin swelling and the selectivity remain constant with temperature, i.e. when DH˜˜ m,c 50. Sometimes, in order to compare different ionexchange systems from the experimental temB perature dependencies of K˜˜ A at the fixed total

V. A. Ivanov et al. / Reactive & Functional Polymers 38 (1998) 205 – 218

solution concentration c 0 the values DH˜˜ y,c 0 and DH˜˜ x,c 0 are determined which relate to the fixed ratios of ions whether in resin or in solution:

S S

˜B ≠ln K˜ A ]]] ≠T ≠ln K˜˜ BA ]]] ≠T

D D

DH˜˜ y,c 0 5 ]] p, y,c 0 RT 2

(18)

DH˜˜ x,c 0 5 ]] p,x,c 0 RT 2

(19)

Strictly speaking both these values can be also interpreted as has been done for DH˜ y . However, to use the values with such complicated interpretation is also very difficult. More useful is to estimate quantitatively its deviation from H˜ m or B B H˜ y using the relation between K˜ A and K˜˜ A . It follows from this relation

DH˜˜ y,c 0 DH˜ y ≠ln sg 1B/ z B /g A1 / zAd ]] ]] ]]]]] 5 1 ≠T RT 2 RT 2

S

D

213

The temperature dependencies of the mean activity coefficients g6,CaCl 2 and g6,NaCl in the mixed solutions with concentrations up to 6 M were measured in [35]. This data shows that for solution of 4.8 M NaCl–0.4 M CaCl 2 the ratio 3/2 2 g 1Ca/ 2 /gNa 5 g 6,CaCl /g 6,NaCl decreases 1.4 times 2 with a temperature increase from 258C to 1108C ≠ln sg 1B/ z B /g 1A/ zAd and ]]]]] p, y is the value about ≠T 20.004. That means that in case of polymethacrylic resin when the enthalpy is the value about 5–15 kJ / equiv. and the first member in the right part of Eq. (18) (about 0.007–0.021) exceeds the second member. Fig. 8 shows the experimental values DH˜˜ x,c 0 vs. the equivalent fraction of divalent ion in resin determined on the integral mode of the van’t Hoff equation under supposition that the value DH˜˜ x,c 0 do not depend on temperature

S

D

p, y,c 0

(20) In the ion-exchange system with a fixed ratio of ions in the resin, the ratio of the activity coefficients in solution changes with temperature both due to its change with temperature at the fixed solution composition and due to the change of the solution composition with temperature (below we omit the subscript c 0 )

S

D

≠ln sg 1B/ z B /g 1A/ zAd ]]]]] p, y ≠T 1 /zB 1 / zA ≠ln sg B /g A d 5 ]]]]] p, y,x ≠T ≠ln sg 1B/ z B /g 1A/ zAd ≠x B ]]]]] 1 ? ]] ≠x B ≠T p, y

S

D

S

D

(21)

It is known, [34], that in the concentrated solution NaCl with admixture of CaCl 2 the activity coefficients of both components change with the concentration of admixture extremely slightly. That means that the last term in Eq. (21) also has an extremely low value and can be neglected for solutions studied in the present paper.

Fig. 8. Plots of the enthalpy changes LH˜˜ y,c 0 vs. the ionic composition of resin. Resins: 1, 2, 35polymethacrylic (Ca 21 – Na 1 ; Ca 21 –K 1 and Mg 21 –Na 1 exchange); 45phosphonic (Ca 21 –Na 1 ).

214

V. A. Ivanov et al. / Reactive & Functional Polymers 38 (1998) 205 – 218

˜˜ 2 ) 2 ln K(T ˜˜ 1 ) G RT 1 T 2 Fln K(T DH˜˜ y,c 0 5 ]]]]]]]]] T2 2 T1

(22)

While in fact the enthalpy can depend on temperature, according to Eq. (22) some mean values of enthalpy for the given temperature interval were determined. For the investigated complexing resins (both carboxylic and phosphonic) the calculated values changed with the equivalent fraction of divalent ion in resin: in most cases DH˜˜ y,c 0 decreased with the divalent ion fraction. The maximal values of DH˜˜ y,c 0 were 5–14 kJ / equiv. depending on the fixed group of resin and on the exchangeable ions. These values coincided with the calorimetrically determined integral values of enthalpies [36]. From the experimental data in Fig. 2 for the polymethacrylic resin KB-4P2 for three temperature intervals 5–208C, 20–508C and 50– 958C the values of DH˜˜ x,c 0 were calculated using the Eq. (20). These values presented in Fig. 9 showed that the reaction of exchange of divalent and monovalent ions became more endothermic with temperature. The influence of temperature on selectivity of the ion-exchange resins can be predicted in some cases on the basis of the data for the soluble low molecular complexing reagents [22,23]. Our experimental results allowed us to compare the data for resins with the data for the low molecular reagents with different active groups summarized in [37,38]. These data show

that the complexing of the divalent ions with the carbonic acids are the endothermic reactions (1–5 kJ / equiv.) as well as the ion exchange of the divalent and monovalent ions on carboxylic cation-exchange resins. In case of amino-carboxylic chelating reagents complexing with the divalent ions was accompanied with the significant exothermic effects (22.5–20 kJ / equiv.) in contrast to chelating resins for which very weak influence of temperature was observed. So, in case of complexing of Ca 21 and Ni 21 ions with the succinic acid the changes of enthalpy were 1.90 and 4.75 kJ / equiv. while in case of complexing of the same ions with the ethylendiaminotetraacetic acid the changes of enthalpy were 213.7 and 217.25 kJ / equiv. Most significant difference was observed between the data for the soluble amines and the weakly basic anion exchanger. In case of complexing of heavy metals with the soluble amines the changes of enthalpy were significant negative values (210– 230 kJ / equiv.). In contrast, our results presented in Figs. 6 and 7 showed extremely weak influence of temperature on complexing of nickel on vinylpyridine resin. The comparison discussed shows that there is significant differences in the physicochemical ‘pictures’ of interaction of ions with the soluble complexing reagents and with the complexing ion-exchange resins.

5. Physicochemical basis of influence of temperature on ion-exchange selectivity The influence of temperature on ion exchange of divalent and monovalent ions on resins is sometimes explained [39] using the Gerny-Anderegg approach which is very usual in the theory of the coordination chemistry in solutions [40,41]. It is based on dividing the Gibbs energy in two parts

DG 0 5 DGel 1 DGnel Fig. 9. Plot of the enthalpy change LH˜˜ x,c 0 vs. temperature for polymethacrylic resin KB-4P2 and solution 2.5 equiv. / l NaCl5 0.08 equiv /.l CaCl 2 .

(23)

The authors of the approach explained the first part as the electrostatic interactions term, and

V. A. Ivanov et al. / Reactive & Functional Polymers 38 (1998) 205 – 218

the second one as the nonelectrostatic interactions term (Gerny named these interactions the covalent ones). According to Gerny the electrostatic term depends on temperature due to the temperature dependence of the dielectric constant of solvent as

S D

T e 5 e0 exp 2 ] u

(24)

where u is the characteristic temperature of solvent (219 K for water); e0 is the constant (305.7 for water). When T . u, the value of e decreases with temperature, and the electrostatic term:

SD

T DGel 5 2 Aexp ] u

(25)

increases (here A is the positive coefficient which does not depend on temperature). Taking into account DG 0 5 2 RT lnbn , (where bn is the stability constant of the complex compound) the authors of [40,41] obtained

S S

D

≠ln b 1 T ]]n 5 ]]2 Ae T / u ] 2 1 1 DGne ≠T u RT

D

(26)

This relation showed that the temperature dependence of the stability constant was determined by ratio between two terms of enthalpy: the electrostatic term which was positive and became more positive with temperature and the nonelectrostatic term. As for ion-exchange processes on the crosslinked polyelectrolytes, more detailed explanations are required due to some reasons discussed below. Ion-exchange resin can be considered as the concentrated solution of the crosslinked polyelectrolytes in a definite volume of water. It has 21 1 been shown [42] that in Ca and NH 4 ionic forms of the polymethacrylic carboxylic and in polystyrene sulfonic resins 4–8 molecules of water only (depending on the solution concentration) were connected with the fixed groups. It is also important that the fixed groups in form of the divalent ion were connected with some lesser number of the water molecules as

215

compared with the same fixed groups in form of the monovalent ions while in the aqueous solutions the divalent ions are more hydrated than the monovalent. This could be due to the fixed groups of resins substituted the water molecules in the close coordination spheres of ions. Chemical bonds between the fixed groups of resins and counterions of alkaline earth and transition metals in their close coordination spheres were confirmed earlier by a number of different methods for different types of resins — for carboxylic and phosphonic cation exchangers, for chelating and weak base anionexchange resins (see, for example, [43]). Even for the noncomplexing sulfonic resins the en2 trance of oxygen of the fixed SO 3 groups in the close coordination sphere of copper has been found [43,44]. These facts mean that in the ion-exchange reaction the partial dehydration of ion B transferring from the external aqueous solution in to the resin phase and the partial dehydration of ion A transferring from the resin phase in to the external aqueous solution take place: R f A(H 2 O) ]nA g 1 1 / 2 f B(H 2 O) 2n B g 21 D H ⇔1 / 2R B(H O) ] 1 A(H O) 1 (n 2n] 2 2

f

2

2n B

g f

2

nA

g

B

B

nA 1n]A )H 2 O

(27)

This ion-exchange reaction can be divided into four partial reactions with the individual changes of enthalpies R f A(H 2 O) n]A g → R 2 1 f A(H 2 O) n]A g 1 ;

Dbond?(R A)

2 (28a)

f A(H 2 O) n] g 1 1 (nA 2 n]A )H 2 O → f A(H 2 O) ]n g 1 ; A

A

DHh(A1 )

(28b)

1 / 2 F B(H 2 O) 2n g G 21 → F B(H 2 O) 2n] g G 21 1 (28c) (n 2n] )H O; 2 DH 21 B

B

2

h(1 / 2B

)

1 / 2 f B(H 2 O) 2n] B g 21 1 R 2 → 1 / 2R 2 f B(H 2 O) 2n] B g ; DHbond?(1 / 2R 2 B )

(28d)

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V. A. Ivanov et al. / Reactive & Functional Polymers 38 (1998) 205 – 218

where nA and n B are the numbers of molecules of water hydrating the ions A and B in the solution; ]nA and ]n B are the numbers of molecules of water hydrating the ions A and B in the resin; DHh is the change of hydration enthalpy in process of metal ion transfer from resin phase in to solution (kJ / equiv.); DHbond is the change of enthalpy in process of formation of chemical bonds between the fixed ionic groups and the counterions (kJ / equiv.). It is supposed that the fixed ionic groups of resin do not change their hydration in the ion-exchange process. Now, the change of enthalpy of Eq. (27) can be represented as

DH 5 f DHh(A1 ) 2 DHh(1 / 2B 21 ) g 1 f DHbond(1 / 2R 2 B ) 2 DHbond(R A) g 5 DHh, S 1 DHbond, S

(29)

In a manner analogous to the Gerny approach DHbond could be divided into terms corresponding to the electrostatic and to some other types of interactions (donor–acceptor in the first place). In some electrostatic models of ion-exchange equilibrium [12,45–48] the macroscopic dielectric constant of fully swollen resin is used. Its values are higher than that for the organic matrix without fixed ionic groups (e ¯ 2) and significantly lower than the dielectric constant of pure water. The data on the influence of temperature on the macroscopic dielectric constant of ion-exchange resins are not known to authors. At the same time such influence seems to be weaker than that for water and could not explain the influence of temperature on selectivity of cation exchangers observed. The changes of hydration of ions in ion-exchange reaction and formation of donor–acceptor bonds seem to be more significant here. It is known that the values of enthalpy of hydration of divalent cations (2700– 21000 kJ / equiv.) differ significantly from that for the monovalent ions of alkali metals (from 2500 kJ / equiv. for Li 1 to 2280 kJ / equiv. for Cs 1 ) [49,50]. Also, the enthalpies of hydration of

complex divalent cations [M(H 2 O) n ] 21 are higher than that for the monovalent ions 1 [M(H 2 O) n ] (here n changes from 1 to 6) (Fig. 10) [51]. That means that the value of DHh, S in Eq. (29) has the positive sign both for ions of second group and for the transition metals ions. The displacement of this term in more positive region can be also promoted by higher dehydration of divalent ions sorbed by resin as compared with monovalent ions which has been found in [42]. The process of hydration of ions is often considered as the complexing one with formation of donor–acceptor bonds between these ions and molecules of water. That means that the process of formation of donor–acceptor bonds between the fixed ionic groups of resin and counterion can be considered as a competitive process to hydration of this ion. Also, it follows from the above consideration that the term DHbond, S in Eq. (29) must be of the opposite sign to the hydration term DHh, S .

Fig. 10. Enthalpies of hydration of complex cations [(H 2 O) n ] 1 (where M: Na51 and Li52) and [M(H 2 O) n ] 21 (where M: Mg5 3; Ca54; Sr55; Ba56; Co57; Zn58; Ni59; Cu510) vs. the number n.

V. A. Ivanov et al. / Reactive & Functional Polymers 38 (1998) 205 – 218

The direction of influence of temperature on the equilibrium constant depends on values of DHbond,S and DHh, S terms of the opposite signs. For all of the studied cation exchangers the positive hydration term DHh, S prevails over the comparatively low donor–acceptor term DHbond, S and determines the increase of selectivity with temperature. In the case of exchange of alkaline-earth and alkali-metal ions on chelating resins the hydration term is compensated for almost completely by the exothermic term DHbond, S . As a result the selectivity depends on temperature very weakly. In the case of exchange of transition metals and zinc on chelating resins the exothermic term DHbond, S prevails over the hydration term leading to a weak decrease of selectivity to divalent ions with temperature (see also Table 1). The prevailing role of the hydration term in increasing the selectivity of cation-exchange resins with temperature allows estimation of the direction of the enthalpy changes as was done in [50] for complex compounds formation in solution. According to Eq. (27) the exchange of 1 equiv. of ion B 21 in solution by 1 equiv. of ion A1 from the resin is accompanied by release of (n B 2n] B ) mol of water connected with the divalent ion and by association of (nA 2n]A ) mol of water connected with the monovalent ion. If we neglect the change of hydration of the polyanion and by dilution of external solution in the ion-exchange process, then the change of the specific heat of the ion-exchange system can be represented as

Dr Cp 5 Dr Cp,bond 1 Dr Cp,h ?sn B 2n] B 2 nA 1n]Ad (30) where Dr Cp,bond is the change of the specific heat of the ion-exchange system due to the change of its ionic form; Dr Cp,h is the change of the specific heat of water. Following [50], the change of the specific enthalpy by the ice fusion (37.7 kJ / mol) can be chosen as the most close analog of Dr Cp,h . It is known [50] that in complexing reactions the first term which is

217

analogous to is always small as compared with the hydration term. Most likely, in ion-exchange reactions it is also valid D C ¯ D C ?sn 2n] 2 n 1n] d (31) r

p

r

p,h

B

B

A

A

Following the above, in ion-exchange reaction Eq. (27) the coefficient is always positive and the change of the specific enthalpy of the ionexchange system is also positive. Then, this ion-exchange reaction must become either more endothermic or less exothermic with temperature as has been found from the experimental data in one of the ion-exchange systems (Fig. 7). Acknowledgements This work was supported by Russian Fund for Basic Researches, Program ‘Universities of Russia’ (grant UNI-021-95). References [1] G.E. Boyd, J. Schubert, A.W. Adamson, J. Am. Chem. Soc. 69 (1947) 2818. [2] J.F. Duncan, B.A.J. Lister, Disc. Faraday Soc. 7 (1949) 104. [3] J.D. Cosgrove, J.D.N. Strickland, J. Chem. Soc. 7 (1950) 1845. [4] P. Gregor, J. Bregman, J. Colloid. Sci. 6 (1951) 323. [5] N.T. Coleman, Soil Sci. 74 (1952) 115. [6] O.D. Bonner, L.L. Smith, J. Phys. Chem. 61 (1957) 1614. [7] V.I. Gorshkov, G.M. Panchenkov, Dokl. AN SSSR (in Russian) 114 (1957) 575. [8] N.N. Matorina, A.N. Popov, Zh. Fiz. Khim. (in Russian) 32 (1958) 2772. [9] O.D. Bonner, R.R. Pruett, J. Phys. Chem. 63 (1959) 1417. [10] O.D. Bonner, R.R. Pruett, J. Phys. Chem. 63 (1959) 1420. [11] K.A. Kraus, R.J. Raridon, J. Phys. Chem. 63 (1959) 1901. [12] F. Helfferich, Ion Exchange, McGraw-Hill, New York, NY, 1962. [13] W. Rieman, H. Walton, Ion Exchange in Analytical Chemistry, Pergamon, New York, NY, 1970. [14] G. Klein, M. Villena-Blanco, T. Vermeulen, Ind. Eng. Chem. Process Des. Develop. 3 (1964) 280. [15] V.S. Soldatov, L.P. Novitskaya, M.S. Bespalko, Z.I. Kogan, in: K.V. Chmutov (Ed.), Synthesis and Properties of Ion Exchange Materials, Nauka, Moscow, 1968, p. 216 (in Russian). [16] V.D. Timofeevskaya, V.A. Ivanov, V.I. Gorshkov, Zh. Fiz. Khim. 62 (1988) 2531 (in Russian), English translation in Russ. J. Phys. Chem., 62 (1988) 1314.

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[33] I.R. Krichevsky, The Ideas and Fundamentals of Thermodynamic. Kimija, Moscow, 1970, p. 319 (in Russian). [34] F.Y. Reznik, N.N. Orlova, L.N. Viteeva, in: G.I. Mikulin (Ed.), The Problems of Physical Chemistry of the Electolytes Solutions. Khimija, Leningrad, 1968 (in Russian). [35] H.F. Holmes, C.F. Baes, R.E. Mesmor, J. Chem. Thermod. 13 (1981) 101. [36] Z.A. Samchenko, E.F. Nekrjach, O.D. Kurilenko, Khim. Zh. 41 (1975) 1042 (in Russian). [37] L.G. Sillen, A.E. Martell, Stability Constants of Metal–Ion Complexes, Section 2. Organic Ligands, London, 1964. [38] R.M. Smith, A.E. Martell, Critical Stability Constants. Plenum, New York, London, 1977. [39] L.K. Shataeva, N.N. Kuznetsova, G.E.El‘kin, Carboxylic Cation Exchangers in Biology. Nauka, 1979 (in Russian). [40] R.W. Gurney, Ionic Processes in Solution, New York, NY, 1953. [41] G. Anderegg, Helv. Chim. Acta 51 (1968) 1856. [42] N.B. Ferapontov, V.I. Gorshkov, Kh.T. Trobov, L.R. Parbuzina, Zh. Fiz. Khim., 68 (1994) 1109 (in Russian). [43] G.P. Vishnevskaja, L.S. Molochnikov, PMR in Ion Exchangers. Nauka, Moscow, 1992 (in Russian). [44] G.P. Vishnevskaja, I.N. Lipunov, E.N. Kazantsev, Dokl. AN SSSR, 213 (1973) 618 (in Russian). [45] E.M. Kuznetsova, Zh. Fiz. Khim., 45 (1971) 2581 (in Russian). [46] N.A. Izmailov, Khimija, Moscow, 1976 (in Russian). [47] G. Eisenman, in: L. Liberti, F.G. Hellferich (Eds.), Mass Transfer and Kinetics of Ion Exchange. Martinus Nijhoff, The Hague, 1983, p. 121. [48] E.M. Kuznetsova, Zh. Fiz. Khim. (in Russian) 66 (1992) 2688. [49] R.A. Robinson, R.H. Stokes, Electrolyte solutions. Butterworths, London, 1957. [50] V.P. Vasiliev, Thermodynamic Properties of the Electrolytes Solutions. Visshaja Shlola, Moscow, 1982 (in Russian). [51] K.B. Yatsimirskii, Thermochemistry of complex compounds. AN SSSR, Moscow, 1951 (in Russian).