2496
B. J. FELBER, E. M. HODNETT, AND N. PURDIE
Divalent Transition Metal Complexes of Hydrolyzed Ethylene-Maleic Anhydride Copolymer** by Betty J. Felber, Ernest M. Hodnett, and Neil Purdie’b Chemistry Department, Oklahoma State University, Stillwater, Oklahoma
74074 (Received December 26, 1967)
In the alternating 1: 1 copolymer of ethylene and maleic acid with molecular weight of 20,000-30,000, the two carboxyl groups have very different pk values; both are larger than those of succinic acid. Formation constants have been measured potentiometrically for the complexes between this copolymer and manganese(II), cobalt(II), nickel(II), copper(II), zinc(II), and cadmium(I1) ions. The interionic attraction theory of electrolytes was useful in treatment of the data. The values are much larger than those previously reported for analogous systems in media of high ionic strength, where complexation occurs with the cation of the added electrolyte. A comparison is made with the corresponding metal-monosuccinate complexes; the differences in stabilities are discussed in terms of the enthalpy and entropy of complex formation.
Introduction The binding of counterions to polymeric ions has been well established. The mechanism for binding may be2 (1) electrostatic in character and therefore dependent upon the charge of the counterion or (2) site binding and therefore dependent upon complex formation. This distinction is analogous to the one made between ion pairs and complexes for metals with monomeric ligands. Results from kinetic studies of complex formation by relaxation techniques3 suggest that ion pairs and complexes exist in equilibrium with each other and with the free aquated ions. Consequently, both mechanisms may operate, to a greater or lesser extent, depending upon the structure of the polymer. For example, alkali metal ions are poor participants in ion association unless the ligand is highly charged. The high degree of association in sodium polyacrylate is perhaps principally electrostatic in origin and the predominant interaction is ion pair formation in which the solvation spheres of the interacting ions remain intact. Preferential site binding can be expected to be really important when the same effect manifests itself a t least to some degree in the low molecular weight or monomeric units of the polymer. Coulombic forces bring the metal ions into the sphere of influence of the polymer, as in ion pair formation, but the liberation of coordinated solvent molecules causes the equilibrium to lie predominantly in favor of a contact ion pair or metal chelate at the active site. As an illustration, hydrolyzed substituted ethylene-maleic anhydride copolymers4 would be considered to form complexes by the site-binding mechanism, since the monomer succinic acid5 forms stable complexes. Previous reported studies of ion binding are restricted to the interactions of alkaline earth ions, especially copper(I1) with polyacrylic acide and analogs, with substituted ethylene-maleic anhydride copolymers and T h e Journal of Physical Chemistry
with amino acids and proteins.’ Most of the data available are for media of high ionic strength. Any quantitative study of ion binding between metal ion and polymer is complicated by several properties of the polymer. Polyelectrolytes ionize considerably less than their monomeric counterparts. The act)ualdegree of ionization depends upon concentration, the precise degree of neutralization (which may involve a configuration transition),* the molecular weight, and the ionic strength of the environment. If the analytical method is potentiometry, as in the present case, an additional complication may arise from competitive ion binding by the cation of the base used in titration It was our belief that the magnitude of the reported stability constants4 (in the order of 100) seemed inconsistent with the extreme preference a polyelectrolyte or an ion-exchange resin might have for a divalent ion over a univalent ion. Rloreover, we wanted to test the degree of applicability of the interionic-attraction theory of electrolytes to polyelectrolytes. It is relevant, for example, that the theory has been applied with some success to ion binding with micelles in aqueous solution.9 Our preference was for a model syn(1) .(a) Presented a t the 154th Meeting of the American Chemica Society, Chicago, Ill., Sept 1967; (b) to whom communications should be directed. (2) F. T. Wall, J . P h y s . Chem., 61, 1344 (1957). (3) M. Eigen and K. Tamm, 2. Eiektrochem., 66, 93, 107 (1962). (4) H. Morawetr, A. M.Kotliar, and H. Mark, J . Phya. Chem., 58, 619 (1954). (5) A. McAuley, G . H. Nancollas, and K. Torrance, Inorg. Chem., 6, 136 (1967). (6) M. Mandel and J. C. Leyte, J . P o l y m . Sei., A2, 2883, 3771 (1964). (7) H. iMorawetz, “High Polymers,” Vol. 21, Interscience Publishers, New York, N. Y., 1965, p 369 ff. (8) M. Mandel, J. C. Leyte, and M. G. Stadhouder, J . P h y s . Chem., 71, 603 (1967). (9) C. W. Davies, “Ion Association,” Butterworth and Co. Ltd., London, 1962, p 122.
bIETAL
2497
COMPLEXES O F HYDROLYZED ETHYLENE-RIALEIC ANHYDRIDE COPOLYMER 12
Figure 1. HEMA neutralization curves: (a) with quaternary ammonium hydroxide; (b) with potassium hydroxide; (c) with quaternary ammonium hydroxide and [HEMA]/[Cu(II)] = 2.
AglAgC1, 0.2 M HCllglass
potassium hydroxide and tetramethylammonium hydroxide, the absence of a large inflection at the second equivalence point when the latter base is used as titrant might indicate that potassium is bound to the polymer in some way, Figure 1. This is not uncommon for univalent ions with carboxylic acid groups. Lithium and sodium ions are known to complex with acetic acid" when they are present in relatively high concentrations. I n polyacrylic acid, low concentrations of lithium, sodium, and potassium ions have been observed to depress the pH titration curve compared to that of the symmetrical quaternary ammonium ions. This has been attributed to cation-polyion interactions rather than to specific salt effects.12 HEMA is a substituted polymeric succinic acid, but, unlike succinic acid, the buffer regions are quite distinct. The data were treated as the dissociation of two separate monobasic acids; the Iiatchalskyl3 form of the empirical Henderson equation corrected for activity coefficients was used pH = pkl
+ n log [a/(l - a)]- 0.5091'/z
(1)
for the first dissociation and pH = pic,
+ n log [a/(l - a)] - 1.5271"'
(2) for the second dissociation step. Here a is the degree of ionization. Plots of pH against log [ a / ( l - a)]for both buffer regions are linear with slopes n = 1.5 and n = 2.2, respectively. For substituted ethylene(IO) S. rMachi, T. Sakai, IM. Gotoda, and T. Kagiya, J . Polym. Sci., A4, 821 (1966). (11) H. S. Harned and B. B. Owen, "Physical Chemistry of Electrolytic Solutions," Reinhold Publishing Corp., New York, N. Y., 1943, p 316. (12) H. P. Gregor and M. Frederick, J . P o l m . Sci., 23, 451 (1957). (13) A. Katchalsky and P . Spitnik, ibid., 2 , 4 3 2 (1947). Volume 78, Number 7
July 1968
B. J. FELBER, E. M. HODNETT, AND Tu’. PURDIE
2498 5.5
Table I Vol of base, ml
1.80 2.00 2.20 2.40 2.60
0:4
06
pkl,appa
42.5 47.2 52.0 56.7 61.4
4.847 4.913 4.971 4.998 5.044
5.80 6.00 6.20 6.40 6.60
maleic anhydride copolymers, as a rule n is approximately 1for the widely spaced first carboxyl groups and is greater than 2 for the ionization of the second carboxyl groups.14 The pk values from eq 1 and 2 relate to the ionization constants at the midpoints of the respective buffer regions. The manner in which the dissociation constant, pkl, apparently varies with a is illustrated in Figure 2a, where a = 1 corresponds to the half-neutralization point. The apparent dissociation constant, pk1,,,,, is related to pH by the equation
+ log [ ~ l / (-l a)] - 0.5091”a
(3)
The smooth curve is an indication that the elongation of the polyion on neutralization is not complicated by an additional configuration transition; consequently the treatment of the data is simplified. For comparison, curve b is included. This curve is typical of the dependence of pkl ,app on a when a compact coil to random coil transition is induced by i0nizati0n.l~ The curves are for analogous copolymers differing only in the side-chain substituents and should coincide at values of a greater than 0.7. They do not because activity coefficient corrections have been made only for HEMA. The apparent dissociation constants and the pk values are given in Table I. The carboxylic oxygen atoms are more basic in HEMA than in succinic acid, owing in part to the inductive effect of the ethylene moiety of the polymer. No information is available in the literature for the dissociation of 2,3-dimethylsuccinic acid, which is structurally more comparable to the polymer. However in the series of dicarboxylic acids, (CH2),(COOH)2, the basicity is observed to increase with increasing x . ~ For the second dissociation in particular, the large differencein basicity also reflects the increased dificulty in removing a proton from the highly charged polyion. T h e Journal of Phgsical Chemistry
ionization,
36.8 41.6 46.3 51.0 55.7
%
Pk2,WPh
9.119 9.234 9.318 9.415 9.515
Mean pkglaPP=
0:8
Figure 2. The dependence of the first dissociation constant on the degree of ionization for (a) HEMA and (b) the alternating 1: 1 copolymer of hydrolyzed n-butyl vinyl ether and maleic anhydride: P. Dubin and U. P. Strauss, J. Phys. Chem., 71, 2757 (1967).
pH =
%
Vol of base, ml
a Mean pkl,,,, = 4.956; mean pkl = 4.965. 9.320; mean pka = 9.602.
4 . g 0:2
2nd
1st ionization,
Metal Complexes. The counterions studied were the divalent ions of the transition metals manganese, cobalt, nickel, copper, zinc, and cadmium. I n Figure 1, a typical potentiometric curve is shown with the copper(I1) ion present. By analogy with the divalent transition metal succ i n a t e ~at~ similar analytical concentrations of reagents, one might anticipate the two complex species MHA+ and RIA to exist in solution for at least some of the metal ions RI2+
+ HA-
= nIHA+
J42+
+ A2- = MA
HA- and A2- correspond to monomeric residues at different stages of ionization. However, analysis of the emf data from experiments in which the ratio of the analytical concentrations of metal and polymer were approximately 2 : 1, 1: 1, and 1:2, which indicated that the system could be satisfactorily interpreted in all cases by the consideration of only one complex
M2+ + A’- = MA
(4)
for which the thermodynamic stability constant expression is
K M A= [RIA]/ [JIZ+] [A2-] X 1/fi2
(5)
and f2 is the mean activity coefficient of the divalent ions. The concentration of ionic species may be calculated from equations for total metal ion concentration m = [hI2+]
+ [MA]
(6)
for total polymer concentration in terms of moles of monomer
u = [HzA]
+ [HA-] + [A2-] + [MA]
(7)
for electroneutrality b
+ [H+] + 2[R!P+] = [HA-] + 2[A2-] + 2m
(8)
(14) ~ J. D.Ferry, D. C. Udy, F. C. Wu, G. F. Heeder, and D. B. Fordyce, J . Colloid Sci., 6,429 (1951). (15) P. Dubin and U. P. Strauss, J . Phys. Chem., 71, 2757 (1967). (16) A. E.Martell and L. G. Sillen, “Stability Constants,” Special Publication No. 17, The Chemical Society, London, 1964.
2499
METALCOMPLEXES OF HYDROLYZED ETHYLENE-MALEIC ANHYDRIDE COPOLYMER where b is the concentration of tetramethylammonium hydroxide, and for the thermodynamic dissociation constants for the ligand
hi0 = [H+l[HA-l(fi2/[HzAI)
(10) The required stability constant is given by eq 5 and the ionic strength is given by
+ h + 3[i\i12+]+ [A2-]
+
-1ogft = 0.509~~~[1'/*/(1Ba)1'/2- C I ] (12) where Ba = 1 and C = 0.3. Because the acid dissociation constants are known to be concentration dependentj2 the initial analytical concentration of polymer was kept constant in all titrations with metal ion present. At higher concentrations of A2-, as would be obtained in the second buffer region, higher complexation is possible
+ A'-
= RIA%'-
Analysis of the data was not always possible because of precipitation especially when the metal ion was in excess. The results of this calculation are not yet conclusive and are not reported. It has been proposed7 that the concept of ionic strength has meaning in polymer solutions only if the product e$,1 in the extended Henderson-Hasselbalch equation is less than kT. pH = pko
+ log [a/(l - a ) ] + 0.434e$,l/kT
9,364 9.364 8.860 8.860
(11)
Activity coefficients were calculated using the Daviess equation
MA
10% M
(9)
kzo = [H+][A"](fi/ [HA])
I =b
Table 11: Measurements at Z 4 0
I n the present case the maximum value of e$el calculated from the last point used in the first buffer region is 0.7kT. We therefore have some confidence in applying the interionic-attraction theory, and it is encouraging that even in its present form, without elaborating on the solution model, constant values for stabilities of metal complexes can be approached. Furthermore, when no activity corrections are made, the "stabilities" calculated are not by any means constant. It should be possible to vary the model by examining the dependence of K M Aon changing the parameters Ba and C in the Davies equation,g but this has not been attempted in the light of the more serious approximations made-for example, the use of the macroscopic dielectric constant for water in the vicinity of the polymer. Equations 9 and 10 are really only applicable when the dibasic acid is monomeric and when k1° and kZoare true thermodynamic constants. Dissociation constants k1 and k~ derived from eq 1 and 2 were used to , this presumes that their dependence calculate K M Abut on a is determined by only a change in ionic strength, which is not the case. A considerable improvement was
M
~O-KMA
Manganese-HEMA 5.277 6.45 5.277 6.46 9.988 6.63 9.988 6.10
Mean ~O-~KMA
6.41 f 0.2
9.382 9.382 9.364 8.880 8.880 8.262 8.287 8.287 8 272
Cobalt-HEMA 4.782 4.19 4.782 4.28 4.782 4.54 9,052 4.21 9.052 4.15 9.052 4.73 14.08 3.98 14.08 3.81 14.08 4.69
4.29 f 0 . 3
9.382 9.382 9.361 9.361 8.880 8.880 8.860 8.860 8.287 8.287
Nickel-HEMA 4.973 3.38 4.973 3.65 4.973 3.45 4.973 3.71 9.412 4.08 9.412 4.07 9.412 3.77 9.412 3.63 14.64 4.02 14.64 3.86
3.76 f 0.2
9.382 9.382 9 364 9.364 8.880 8.880 8.860 8.860 8.287 8 287 8.269 8.269 8.272
Copper-HEMA 4.975 422 4.975 432 4.975 499 4.975 476 9.417 453 9.417 486 9.417 391 9.417 377 14.65 486 14.65 475 14.65 399 14.65 372 14.65 512
445 f 42
9.361 9.361 8.860 8.860 8.860 8.269 8.269 8.269
5.024 5.024 9.056 9 056 9.056 14.80 14.80 14.80
Zinc-HEMA 5.23 5.33 5.07 5.08 5.07 4.67 4.24 5.07
4.97 f 0 . 3
9.361 9.361 9.364 8.860 8.860 8.862 8.269
Cadmium-HEMA 4.966 19.4 19.8 4 966 4 966 20.5 9.396 22.4 9.396 22.5 9.396 23.0 14.71 PPt.
21.3 f 1 . 4
I
I
(13)
loam,
I
I
I
I
Volume 78, Number 7 July 1068
2500
obtained if instead kl,appfrom eq 3 was used. I n this way a correction was made for the dependence of the first dissociation constant on cy in the complex-formation reaction. This was done by selecting data points from the first buffer region when metal was present to correspond with the points used in determining the apparent dissociation constant. A similar correction could not be made for k2 in this part of the titration curve, and the average k2,&ppvalue was used: This probably contributes to the relatively large error in K M Acompared to the very precise succinate data of Kancollas, et aL6 Stability constants are given in Table 11. Compared to the corresponding divalent metal monosuccinates, the stabilities of the mono-HEMA complexes are greater by a t least six orders of magnitude. With the exception of manganese and cobalt the association constants for all the dicarboxylate complexes follow the Irving-Williams order of stability.” This result is consistent with the metal monosuccinate data. Copper-mono-HEMA as expected is again considerably more stable than the others, which is attributed to the contribution to the crystal field-stabilization energy from tetragonal distortion of the octahedral symmetry as a result of the Jahn-Teller effect. The increase in stability in going to HEMA complexes is in part a result of the increased basicity of the coordinating oxygen atoms. This is directly related to the heat of formation of the complexes and indirectly, through AG, to the entropy of formation. It is difficult to predict what effect an increase in basicity will have upon the heat term. For example, the metal-dicarboxylate complexes are formed with an unfavorable positive enthalpy.’* The complexes are therefore stabilized by a relatively large positive entropy, reflecting the liberation of coordinated water molecules from the interacting ions. As the basicity increases in going from oxalate to succinate, the enthalpy becomes progressively more positive. If this trend were to continue to HEXA, the entropy contribution would be considerable. On the other hand for the corresponding metal-glycinate complexes, where the nitrogen atom
The Journal of Physical Chemistry
B. J. FELBER, E. M. HODNETT, AND N. PURDIE has a basicity almost equal to the second oxygen in HEMA, the enthalpy is negativels and reinforces a smaller entropy term to produce much more stable complexes. It becomes necessary, therefore, to consider both possibilities. Compare as an example copper-succinate ( K M A= 1.82 X lo3) and copper-HEMA (KMA= 4.45 X 10’O). The literature values for the formation of copper-succinate are AH = 4.56 kcal mol-’ and AS = 30.1 eu a t 25”. A similar AH for copper-HEMA would mean an entropy contribution of 64 eu/monomer. If, however, it is assumed that the entropy is unchanged (the chelate effect is small for a seven-membered ring), the calculated AH for copperHEMA is -5.5 kcal mol-’. The real situation is perhaps intermediate between these two extremes. Some credence to this conclusion is vindicated by the observed heat of formation of CuPAA,lg AH = 1.6 kcal mol-l. A change in enthalpy would not explain exclusively the increase in stability over the succinates, and it is better to think of it in terms of an additional favorable entropy factor. This might indicate an additional configuration transition in going from an ordered hydrogen-bonded ligand species to a complex. As expected, the stability constants are indeed much larger than any others previously reported for analogous systems. This is in part due to the difference in ionic strength, but perhaps more so to the fact that previously competitive ion binding by the added salt has been ignored. Acknowledgments. We wish to thank The Research Foundation, Oklahoma State University, for financial support, the Marathon Oil Go. for partial support of B. J. F., and D. Litchinsky for help in compiling computer programs. We are also indebted to Dr. John H. Johnson, Monsanto, St. Louis, Mo., for supplying the polymer samples. (17) H. Irving and R. J. P. Williams, J . Chem. Soc., 3192 (1953). (18) G. H. Nancollas, “Interactions in Electrolyte Solutions,” Elsevier Publishing Co., Ne-# York, N. Y . , 1966, p 185. (19) E. M. Loebl, L. M. Luttinger, and H. P. Gregor, J . Phys. Chem., 59, 559 (1955).
