1502
RICHARD L. GUSTAFSON AND JOSEPH A. LIRIO
Binding of Divalent Metal Ions by Cross-Linked Polyacrylic Acid by Richard L. Gustafson and Joseph A. Lirio Rohm and Haas Company, Research Division, Philadelphia, Pennsylvania
19157
(Received July 31 1957)
The degrees of complexation of Ca2+, Ni2+,Cu2+, and Zn2+ ions by a polyacrylic acid (PAA)-divinylbenzene (DVB) copolymer have been measured potentiometrically at 4.4,25.0, and 49.4’ in 1.0 M NaN03. The equilibrium binding constants increased in the order CaZ+< Ni2+< Zn2+< Cu2+,demonstrating the unusual specificity of PAA for Zn2+over Ni2+that was observed previously in the case of polymethacrylic acid (PMA) complexes. The enthalpies of complex formation are positive and become less favorable as the extent of metal ion binding increases. The entropy changes upon complexation increase in the order Xi2+ < Ca2+< Cu2* < Znz+. The reaction Zn2+ H2A2 ZnAz 2H+ is favored by 15-18 cal/deg mol over the similar reaction involving Ni2+ions.
+
~
Introduction In a recent study’ of the binding of Ca2+,Ni2+,Cu2+, and Zn2+ ions by a polymethacrylic acid (PMA)-divinylbenzene (DVB) gel, it was shown that there was an unusual specificity for Zn over Xi. An examination of the literature has shown that the free energy of chelation of Xi2+ by monomeric, polydentate ligands is greater than that of zinc in nearly all cases. I n the case of complexation by the PMA gel, the entropy change upon binding of Zn2+ is approximately 20 cal/mol deg greater than that observed in the case of N2+. This more than compensates for a 4-5 lrcal/mol difference in AH” which favors the binding of nickel. This evidence suggests that the tetrahedral stereochemical configuration of the Zn2+ ion permits binding by the PMA gel with less steric strain than is encountered in the case of the Ni2+ ion. I n the case of the more flexible linear PRlA polymer, the formation of the Zn2+complex is still favored over that of Ni2+, although the difference is much less than that found in the case of the cross-linked PXA. It was considered desirable t o compare the degrees of complexation of Ni2+ and Zn2+ ions by a more flexible polycarboxylate structure in order to see if the order of binding followed the usual trend. Accordingly, the interaction of these ions, as well as Ca2+and Cu2+,with a polyacrylic acid (PAA) resin containing 7.5% divinylbenzene as a cross linker has been measured at 4.4,25.0, and 49.4’ in 1.0 M NaN03. Free energies, enthalpies, and entropies of complex formation have been calculated. A number of ~ o r k e r s have ~ - ~ investigated the interaction of Cu2+ions with linear or cross-linked polyacrylic that a maximum of two acid. It has been sh0wn~3~ carboxylate groups of PAA are bound per cupric ion, although datas concerning the binding of Cu2+by linear polymethacrylic acid are consistent with the assumption that four carboxylate groups are bound per metal ion. All available evidence suggests that, in the case of crosslinked PAA and PRIA, the cupric ion is bound by a maximum of two carboxylate groups. Such a condition The Journal of Physical Chemistry
+
has been assumed to be valid in the calculations described in this paper.
Experimental Section
Resin. A sample of a polyacrylic acid resin which contained 7.5% divinylbenzene was placed in a glass column and conditioned by treatment with three alternate washings each with 1 Ill NaOH and 1 M HCI. The acidified resin was washed with water until chloride free and oven dried a t 110”. The capacity of the resin was found to be 11.40 h 0.02 mequiv/g. Equilibmtions. The methods of equilibration of the resins with equivalent amounts of Ca2+, Ni2+, Cu2+, and Zn2+nitrates in a 1.0 M NaX03medium which contained varying amounts of standard NaOH were the same as those described previously. * Measurements of the pH’s of the solution phases in contact with the resin were made after equilibrium was attained at 4.4, 25.0, and 49.4’. I n addition, after the resin had been separated from the solution a t 25O, the bound metal ions were eluted from the resins with dilute HCl. The concentrations of the divalent ions were determined by complexometric titrations with EDTA.B These measurements permitted a comparison between the actual amount of metal bound and that calculated on the basis of potentiometric measurements of the hydrogen ion concentration in solution. (1) R. L. Gustafson and J. A. Lirio, J . Phys. Chem., 69, 2849 (1965). (2)F.T.Wall and S. J. Gill, ibid., 58, 1128 (1954). (3)H.1’. Gregor, L. B. Luttinger, and E. M, Loebl, ibid., 59, 34 (1955). (4) H.1’. Gregor, L. B. Luttinger, and E. M. Loebl, ibid., 59, 366 (1955). (5) E. M.Loebl, L. B. Luttinger, and H. 1’. Gregor, ibid., 59, 559 (1955). (6)A. M.Kotliar and H. Morawetz, J . Amer. Chem. Soc., 77, 3692 (1955). (7) H.Morawetz, J . Polym. Sci., 17, 442 (1955).
(8) G. Schwarzenbach, “Complexometric Titrations,” Interscience Publishers, Inc., New York, N. Y., 1957.
BINDING OF DIVALENT METALIONS BY CROSS-LINKED POLYACRYLIC ACID
Mathematical Treatment of Data Values of the binding constant, K3, for the reaction
M2+
+ HzA2
-
A
+ 2H+
MA2
(1)
1503
Table I: Values of Slope n and -Log [H+] a t Half-Xeutralization Points (pK,) of PAA-DVB Gel a t Various Temperatures in 1.0 M T\;aNOs
between metal ions and dicarboxylic acid chain segments were calculated by the use of the equations
[MA21[H+12
[H+I2 Ka = . [Mz+][HzAz] 1 - f i [HzAz]
(2)
a = - -T A - 2[HzAz] - 2[A2-] 2T x
(3)
2[HzAz] = T A ( ~
(4)
fi
CY)
- [H+]
Here, T A and T Mare the total molar concentrations of carboxylic groups and metal ions, respectively; fi is the average number of dicarboxylate groups bound per metal ion; a is the number of moles of hydroxide ion added per equivalent of metal ion; and K , is the dissociation constant of the polyacid. Values of AH" were calculated algebraically from K S values obtained a t the three temperatures employed. The entropies of reaction were calculated by the expression AS" = (AH' - A F ' ) / T , where AF" = -2.303RT log Ka.
Results and Discussion Dissociation Constant of PAA Gel. Plots of -log [H+]vs. log a / ( l - a) were linear in the range CY = 0.30.7 in accordance with the empirical equation
4.4 25.0 49.4
P Ka
5 . 3 1 rt 0.02 5 . 9 1 rt 0 . 0 1
n
1.80 1.87 1.92
Polyacrylate resin
Polymethacrylate resin -Log [H*] (a = 0.5) n
Metal
-Lo$ IH+]
ion
( a = 0.5)
n
Na Ca2+
5.29 4.79 4.42 4.08 3.28
1.87 1.50 1.31 1.12 1.30
Zn2f cue+
B .91 5.54 5.26 4.78 4.06
1.60 1.41 1.26 1.18 1.02
The order of selectivity (Ca2+ < Xi2+ < Zn2+ < Cu2+) is similar to that found by Gregor, et in the case of a linear polyacrylic acid. These workers found that values of -log B,, for the reaction
1.89 i 0.02 1 60i~0.00
The polyacrylic acid resin is more acidic than PMA by 0.6 pK unit. The higher value of the slope n in the former case indicates that the Coulombic interactions between neighboring functional groups are greater in the case of the polyacrylate resin. Binding of Divalent Metal Ions. The titration data obtained upon the interaction of partially neutralized PAA resin and metal ions are presented in the form of Henderson-Hasselbach plots in Figure 1. Values of -log [ H f ] a t the half-neutralization point ( a = 0.5) and n are presented in Table 11. Similar values ob-
5.29 5.29 5.34
Table 11: Values of Slope n and -Log [ H + ] a t CY = 0.5 for Interactions of Metal Ions with PAA and PMA Gels a t 25' in 1.0 M NaN03
Niz +
PAA PMA
n
tained prev'ously upon the interaction of the same metal ions with a P l I A gel are listed for comparison. In each case the difference between the -log [ H f ] value obtained at a = 0.5 in the presence of an equivalent amount of divalent metal ion and pK, for the resin is greater upon binding by PAA than by PMA; i.e., a greater pH drop is observed upon the addition of the metal ion in the former case. This indicates a greater binding tendency of PAA, which might be produced by the lower degree of steric strain which is encountered in this case in conforming to the geometrical requirements of the metal ion. The difference between the pH drop observed in the formation of the PAA complex and that of PMA is least in the case of zinc.
+
The values of pK, and n obtained in 1 M NaN03 at various temperatures are shown in Table I. As is the case for most carboxylic acids, including cross-linked polymethacrylic acid, the values of pKa and n are essentially constant in the temperature range of interest. The average values obtained for the PAA and PMA resins are
P Ka
hI2+
+ 2HA
MA2
+ 2H+
where
decreased in the order -i\Ig2+(3.8) > Ca2+ (3.7) > Go2+ (3.4) > Mn2+ (3.0) = Zn2+ (3.0) > Cu2+ (1.8) in 1 M KCl. The -log B,, values in the present case at 25" are as follows: Ca2+, 4.78; Xi2+, 3.50; 2n2+,3.06; (9) H. P. Gregor, L. B. Luttinger, and E. M. Loebl, J . Phys. Chem., 59, 990 (1955).
Volume 7 2 , Number 6
May 1968
RICHARD L. GUSTAFSON AND JOSEPH A. LIRIO
1504
same is true for A H " , although complexation by PMA is favored on an entropy basis. Although the unusual selectivity of Zn2+ over Yi2+ is observed in the case of
Table 111: Thermodynamic Functions for the Reaction of Divalent Metal Ions with a PAA-UVB Gel according to the Reaction M2 + HzAI e MAz + 2H+
+
-,I
Zn2 +
Ca2+
Ni2 +
0.1 0.2 0.3 0.4 0.5 0.6
8.03 8.71 9.39
...
...
7.37 7.71 8.05
6.65 6.78 6.98 7.22
0.1 0.2 0.3 0.4 0.5 0.6
10.96 11.89 12.82
0.1 0.2 0.3 0.4 0.5 0.6
6.6" 9.5"
0.1 0.2 0.3 0.4 0.5 0.6
- 14" - 8"
CU2+
-Log Kgj
k
I
I
-0.3
-0.2
I
I
-0.1
I
0.1
0
Log
I
0.2
I 0.3
I
.
.
... ...
I
Figure 1. Henderson-Hasselbach plots obtained upon the interaction of metal ions with cross-linked polyacrylic acid.
.
.
.
.
, . .
4.60 4.90 5.19 5.49
, . .
A.FoZ5, kcal/mol
(1
I-(1
I
...
I
1
.
.
...
...
...
10.06 10.52 10.99
9.08 9.25 9.52 9.85
...
... ... 6.27 6.68 7.08 7.49
... AH ', kcal/mol
Cu2+, 2.08. Gregor, et a l l 4previously obtained -log B,, values of 1.67 and 1.70 in 0.2 and 2.0 M NaN03 solutions, respectively, upon the binding of cupric ions by Amberlite XE-89, a cross-linked polyacrylic acid. Thus the polyacrylic acid resin used in the present study has a somewhat lower affinity for Cu2+than does XE89. The PAA-7.5% DVB resin binds Ca2+ and Cut+ less efficiently than did the linear PAA studied by Gregor, et al. This is expected because of the lower flexibility of the cross-linked resin. It is interesting to note that both the cross-linked and linear PAA have nearly identical affinities for Zn2+,however. Calculation of Thermodynamic Quantities. Values of log K 3 as well as A F " , A H " , and A S o for reaction 1 are shown in Table 111. As in the case of binding of divalent metal ions by a P J I A gel,' the free energies and enthalpies of binding become more positive with an increasing degree of complexation, whereas the entropy of binding becomes more favorable as + increases. i Similar results have been observed in cases of physical adsorption on activated carbon and synthetic polymeric adsorbents. It has been assumed in these studies that the adsorbent surfaces are heterogeneous and that the energetically preferred sites are occupied first. It is reasonable to assume that a similar effect takes place in the present case because of the supposed heterogeneity (which is the result of the different reactivity ratios of the acrylate and divinylbenzene) of the PAA gel. The free energies of the reaction
J12+
+ HZA2
MA2
+ 2H+
are more favorable for the binding by PAA than by P X A in every case as is illustrated in Table IV. The The Journal of Physical Chemistry
.
I
.
.
I
.
...
...
...
4 . 5 i0 . 6 5 , l f0.9 6 . 5 i0 . 5
7.9 f 1.0 8.9 f0.7 1 0 . 4 i:0 . 4 11.7 i 0 . 4
...
...
, . .
, . .
5.ozto 2 3 . 0 i:O . ; i 5 . 4 i0 . 4 6 . 0 i0 . 3
ASo, cal/mol deg
a
, . . , . .
, . .
...
...
...
-19 i:2 -18 i 3 - 1.5 i 2
-4 i 3 - 1 rt 2 +3i 1 +6i: 1
... ...
I
.
.
, . .
... -4 -6 -6 -5
i1 i2
It 1 f1
Calculated from 4.4 and 49.4" data only.
Table IV : Comparison of Thermodynamic Quantities Calculated a t k = 0.4 for Binding of Ni, Cu, and Zn Ions by PMA and PAA Gels at 2R" AHo, kcal/mol
AFO,
Ma+
kcal/mol
Ni cu Zn
10,99 6.68 9.52
Ni cu Zn
13.42 8.8,5 11.19
PAA
AS'. eu
6 .5 3 .0 10.4
- 1.5
10.6 8,9 14.2
-9 0 10
+
AHOI'IIA AH'PAA
AS"'PNA AS'PAA
-6 +3
PMA
AFOP~IA AFOPAA
Ni
cu Zn
2.4 2.2 1.7
4.1 3.9 3.8
6 6 7
1505
BINDING OF DIVALENT METALIONS BY CROSS-LINKED POLYACRYLIC ACID PAA, the da;ta of Table I V show that there is a somewhat smaller difference AFOPMA - AFOPAA in the case of Zn2+ than in the case of Ni2+. I n general, the differences in A F " , A H " , and AS" of metal ion binding by the two polymers are remarkably similar. Selectivities of PAA and P M A Gels f o r Divalent Ions. The quantities of metal ions bound by the various resin samples were determined by direct measurement. AS was found previously in the PMA gel binding studies, more metal ion is bound than is calculated on the basis of the pH determinations, The ratios of calculated to actual amounts of metal ions complexed by PAA and PIMA gels at a = 0.5 are shown in Table V. Here it may be seen that the discrepancy decreases as the binding affinity increases and that the agreement between the actual and calculated values is better upon binding by PAA, except in the case of Ca2+. Although the previously described calculations of K 8 do not permit accurate determinations of the species distributions in the resin phases, the K 3values give a relative measure of binding affinities. The enthalpy calculations, which demonstrate an increase in binding with increasing temperature, are independent of the inaccuracies produced by the fact that the presence of the metal ions apparently affects the dissociation relation (eq 5 ) of the polyacid.
I
'
I I
3
a
Figure 2. Plots of the fraction of bound carboxylate groups, 01'/01, us. the degree of neutralization for M2+-PAA and M2+P-MA gels in 1.0 M NaNOs a t 25": solid lines, PAA; dashed lines, PMA.
Table V : Ratios of Calculated t o Actual Amounts of Metal Ions Bound by Polyacrylate and Polymethacrylate Gels at (Y = 0.5
*vz+ Ca Ni Zn cu
PAA
PMA
0 .Lj65 0.810 0,915 0.978
0.587 0.761 0.904 0.938
I n Figure 2, the fraction of carboxylate groups bound to metal ions, a'/. (where CY' = milliequjvalents of AI2+ bound per milliequivalent of resin), has been plotted as a function of the degree of neutralization, a. Whereas the a'/. values tend t o level off at a values in excess of 0.5 in the case of the PhIA complexes, the plots for the PAA complexes continue to rise. Thus while the selectivity coefficients, K Nt Ma+ ~ (equal to inrhIz+(inSiva +)2/ m s ~ ~ , 1 2 + ( i nwhere r ~ a + )i2n , is the molality and r and s refer to resin and solution phases, respectively), of PMA are greater than those of PAA a t low degrees of neutralization, the selectivities of PAA for Ca2+? Xi2+, and Zn2+ions exceed those of PhIA for the same metal ions above a values of 0.34, 0.56, and 0.8, respectively. The over-all superiority of binding by the PAA gel is illustrated in Figure 3, in which the quantities of metal
0
I
0,2
I
I
0.4
0.6
I
0.8
5
a'
Figure 3. Plots of -log [H+]us. milliequivalent of divalent metal ion bound per milliequivalent of PAA or PMA gel: solid lines, PAA; dashed lines, PMA.
ion bound per milliequivalent of resin have been presented as a function of pH. At pH 5, over twice as much Ca2+ is bound by PAA as by PRIA. Similar relationships will be noted for the other systems studied. Naturally, as the pH of the solution phase increases, the percentage difference in the amount of metal ion bound by each resin will decrease.
Volume 72, Number 6 Mag 1968
