1513
Binding of Counterions to the Polyacrylate Anion
Binding of Counterions to the Polyacrylate Anion at Varying Charge Densities R. J. Eldridge and F. E. Tretoar" Department of Physical Chemistv, University of Melbourne, Parkville, Victoria 3052, Australia (Received May 7, 1973: Revised Manuscript Received December 29, 1975)
Ultraviolet spectrophotometric measurements were used to investigate ion association in solutions containing hexaamminecobalt( 111)perchlorate, supporting electrolyte, and either partially neutralized poly(acry1ic acid) or acrylic acid-methyl acrylate copolymer with all the carboxylic acid groups neutralized. Several detailed models of the binding site are considered, and all but one rejected. It is concluded that the binding site is composed of adjacent carboxylate groups. When the polyion carries only short sequences of charged groups, the triply charged counterion is associated with fewer than three such groups. In contrast to Cu2+, it is unable to force a redistribution of charged and uncharged groups to create binding sites. The association of di- and trivalent cations with polyanions has been widely regarded as chelation of the cation by neighboringld or widely ~ e p a r a t e danionic ~ ? ~ groups. However, Begala and Strauss7 have presented evidence against the chelation of Mg2+ and Ba2+ by polyacrylate (PA). The structure of the polyion-counterion adduct is thus uncertain. Optical studies of the binding of nonlabile complexes can help clarify the nature of the binding site. We have previously reporteds the results of a spectrophotometric study of the association of the hexaamminecobalt(II1) cation (M) with PA in the presence of added NaC104 or LiC104. The ratio of bound to unbound M varies as the first power of the carboxylate concentration, and inversely as the cube of the concentration of added salt. From these observations we concluded that M is site-bound by three carboxylate groups on a single polymer chain. We further concluded tentatively that the carboxylate groups composing a binding site are close together. This model can be tested by examining the effect of interrupting the sequence of carboxylate groups. We now report the results of an extension of this work to samples of polyacrylic acid (PAA) in which the numbers of binding sites (carboxylate anions) have been limited either by partial neutralization or by partial esterification followed by complete neutralization of the remaining carboxylic acid groups. In the former case the "partitions" between sequences of carboxylate groups are free to move; in the latter case they are not. A comparison of the amounts of M bound by these substances should reveal the local requirements for the binding of a trivalent cation and thus provide a test of our model.
tration of aliquots with acidified KMn04 showed that a negligible proportion of ester groups hydrolyzed over a period of several months. PAA solutions at different degrees of neutralization a were made by addition of aliquots of standard NaOH or LiOH solution. Sequence Length of Carboxylate Groups in the Copolymers. These are calculated from standard copolymer theory.1° The fraction of all monomer units occurring in a sequence of n successive acid units is
PnA= PAA,(1 - PAA) where PAA
rA/(rA
+fE/fA)
(2)
= k A A / k A E the ratio of rate constants for addition of acid and ester to a growing chain ending in acid. f E and f A are the fractions of ester and acid in the reaction mixture. The values of r A and T-Eused are 1.44 and 1.0, respectively.ll The fraction of acid groups occurring in a sequence of n is rA
m
P,' = P , A /
P,A
PAAn-1(
n=l
1- P A A )
(3)
Another quantity of interest is the mean length of acid sequences, given by12 f
i
=~ 1/(1- PAA)
(4)
Results and Discussion The spectrophotometric results for the binding equilibrium
M3+
Experimental Section The preparation of PAA ((M,) = 710 000) and hexaamminecobalt(II1) perchlorate, and the spectrophotometric technique have been described previously.8 Absorbance measurements were made a t 235.8 nm and 30.0 "C in 1-cm cells using a Hilger and Watts Uvispek fitted with a circulating water thermostat. The concentration of M was 5 X M in all cases. Mandel and Stadhouderg have partially methylated polymethacrylic acid (PMAA) using dimethyl sulfate, but in this work we prepared the analogous PAA derivative by copolymerizing acrylic acid (AA) with methyl acrylate (MA). Copolymers containing 62.2 and 77.24 mol 96 acid (calculated on total monomer units) were dissolved in an equivalent quantity of aqueous NaOH for the ion-binding study. The pH of these stock solutions (CCOO-= 0.1-0.2 M) was 7-8, and ti-
(1)
+ nCOO-
MS
where M3+ represents a free, and MS a site bound hexaamminecobalt(II1) ion, are plotted in terms of the dimensionless absorbance increment
+
A = [MS]~MS [ M 3 + ] € ~ 3 + [COO-]€,
+
- CM3+€M3+- c p € p
(5)
where the E are molar absorbances, C the stoichiometric molar concentrations, and the subscript p indicates polymer. Figures 1-3 show the absorbance increment A as a function of the stoichiometric carboxylate concentration Ccoo- for eight series of solutions containing 5 X M M(C104)3 and varying concentrations of polyelectrolyte and added perchlorate. Curves for fully neutralized PA ( a = 1)are included for comparison. It can be seen that decreasing the charge The Journal of Physical Chemistry, Vol. 80,No. 13, 1976
1514
tA
* 5
1
0
i
5
2
0
e
S
S
O
r lo
ccoo-
Absorbance increment A vs. stoichiometric carboxylate concentration (M)in NaPA-NaC104 solutions, [Na+] = 0.41 M: NaPA 100% (+), 75% (A), and 50% (V)neutralized; 23% (A)and 38% (V) methylated. Figure 1.
lA I -0-
5
-A-
1
I
I
I
I
10
15
20
25
30
1
3 lo ccoo-
Absorbance increment A vs. stoichiometric carboxylate concentration in LiPA-LiC104 solutions: [Li+] = 0.41 M,LiPA 100% (+)and 50% (V)neutralized; [L?] = 0.51 M, LiPA 100% (0)and 50% (A) neutralized. Figure 2.
R. J. Eldridge and F. E. Treloar
(b) the redistribution of carboxyl and carboxylate groups with the creation of binding sites consisting of three adjacent carboxylate groups; (c) the bringing of three carboxylate groups close to a trivalent cation by changes in the conformation of the polyion; or (d) binding to fewer than three carboxylate groups when triads are not available. Models (b) and (c) predict for the effective concentration C* of binding sites C* = %Ccoo-.Thus A should depend only on CCOO-(and C N ~ C ~ O ~ ) . However, the spectrophotometric data in Figure 1 show 3 at any Ccoo- to depend on the linear charge density of the polyion. The similarity of the partly esterified and the incompletely neutralized polyacrylates is further evidence against model (b). The order of binding ability is a = 1> 23% esterif > a = 0.75 > 38% esterif > CY = 0.50 showing that esterification does not block binding more effectively than does incomplete neutralization. The available intrinsic viscosity molecular weight data suggest that the unperturbed dimensions of PAA and poly(methy1 acrylate) are not very different.l3 Because of the high electrolyte concentration used in this work, the polyelectrolyte will not be expanded greatly above its unperturbed dimensions. Thus the free energy gain from forming electrically neutral M(COO)3units is insufficient to alter either the polyion conformation or the distribution of -COOH and -COO- groups. The binding of M to PA is therefore qualitatively different from the binding of Cu2+to carboxylic polyacids. The observations of Morawetz3 suggest that binding of Cu2+ to PA involves a redistribution of charged and uncharged monomer units as postulated in model (b). A further difference between M and Cu2+ is seen in the dependence of the extent of binding of M on ionic strength (Figure 2). Mandel and Leyte14 have shown the association constant in the Cu(I1)-PMA system to be independent of ionic strength up to 0.1 M. The difference in binding behavior between M and Cu2+ may presumably be attributed to the exceptionally strong covalent bonding between Cu(I1) and polycarboxylic acids. Leyte et al.15J6 have demonstrated the existence of metal-to-metal bonds in the Cu(I1)-PMA adduct at low degrees of neutralization showing that Cu2+ions are able to bind on adjacent sites. This would almost certainly require a forced redistribution of -COOH and -COO- groups. For type (a) binding, the hypothetical extent of association can be calculated from the absorbance data. In ref 8, we assumed the limiting value (0.942) of A at high CCOO-to correspond to complete binding of M. Model (a) thus predicts for the fraction f of M bound to three -COO- groups,
, lO'C,-
Figure 3. Absorbance increment A vs. stoichiometric carboxylate concentration (M)in NaPA-NaC104 solutions, [Na+] = 0.26 M:NaPA 100% neutralized (0):23% (V)and 38% (V)methylated.
density on the polyion reduces the absorbance increment, but even a t the lowest charge density studied (a = 0.5), h is sufficiently large to indicate the occurrence of site binding. The binding ability of the sodium polysalts is greater than that of the lithium at all charge densities, showing that binding must still be regarded as a competition between trivalent and univalent counterions for binding sites as was previously seen for fully neutralized polymer. The structure of the binding site can be elucidated by considering the following possible types of site binding to a polyion with short sequences of charged monomer units: (a) attachment of M only to three adjacent carboxylate groups; The Journal of Physical Chemistry, Vol. 80, No. 13, 1976
f = 1110.942
(6)
Equation 6 assumes that the M-PA adduct has the same molar absorbance a t all charge densities as it does a t a = 1. The work of Mathewsl7v's provides some support for this assumption. This work showed sites for the binding of M to anionic polysacchafides to consist of three or more charged groups, not all of which were able to approach very closely to the bound cation. Mathews found the adducts of M with chitosan derivatives having both one and two sulfate groups per saccharide unit to show the same absorbance increment, equal to 0.40 at 235 nm, under his experimental conditions. Chondroitin sulfates, which have -OSOS- and -COO- units on alternate saccharide units, also showed A = 0.40 at 235 nm. However, different binding behavior was observed with heparin, which has a greater number of anionic substituents per monomer unit. Several heparin samples yielded more strongly absorbing adducts than did either the chondroitin sulfates or the chitosan derivatives. and further sulfation increased still
1515
Binding of Counterions to the Polyacrylate Anion TABLE I: Distribution of Carboxylate Groups in Copolymers Mole fraction
coo0.622 0.772
Fraction of these occurring
-
Singly (PI’)
In pairs (Pz’)
0.378 0.228
In triads
0.235 0.176
(P3’)
Mean COOsequence length
Concn of binding sites from eq 7, c*/ccoo-
2.64 4.38
0.111 0.171
0.146 0.136
further the absorbance of the heparin-[Co(NH&] adduct. These observations suggest that the association of M with three anionic groups results in the same increase in absorbance at several charge densities. Only when more than three anionic groups are close to a trivalent ion, as in the case of heparin, does the absorbance become even greater. For model (a), the stoichiometric concentration C* of binding sites in the copolymer solutions can be calculated from eq 4.If we assume that a sequence of three to five adjacent charged groups provides one binding site, a sequence of six to eight provides two, and so on, then
y77
n
v
I
I
io3
This series converges rapidly for the values of PAAcharacterizing the copolymers used in this work, and the values of C* obtained are shown in Table I. It is apparent that most acrylate monomer units occur in short sequences, and C*/ CCOO-is small. The distribution of sequence lengths in the partly neutralized polyacids cannot be calculated in this way, but C* must be smaller than %Ccoo-. For the case of NaPA ( a = 1 ) in NaC104 solution, plots of f / ( l - f ) against [COO-] are linear,8 with slope given by K / 3[Na+] where K is the equilibrium constant for the association of M with a triad of -COO-Na+ units. Figure 4 shows f / ( l - f ) plotted against the hypothetical concentration of binding sites C* - f c M , where CM is the stoichiometric concentration of M. For the partly neutralized polyacrylates C* was approximated by %CCOO-. The picture is similar when the neutralizing ion is Li+. Clearly interpreting the data according to model (a) leads to the conclusion that more binding occurs to the copolymers than to PA ( a = 1)at a given concentration of carboxylate triads (at least at low carboxylate concentrations). Thus model (a) may be rejected, leaving only model (d). The curvature of the plots in Figure 4 is further proof that the absorbance increase is not due to the formation of a single adduct, as is the fact that the gradients of the linear portions of these curves at low Cp depend on some power smaller than the third of the salt concentration. Our conclusion that the binding is type (d) can be tested by deriving an expression for the absorbance of a system containing M associated with one, two, and three carboxylate ligands, in the presence of extraneous Na+ ions. The model to be used is essentially that of ref 8, the only change being a generalization to enable n to vary from one to three. Using A to represent the -COO- ligands, and denoting the stepwise association constants by k , we have
I
I
I
(c*-rcj
Figure 4. Test of model (a): f / ( 1 - vs. hypothetical concentration of binding sites, [Na+] = 0.41 M; NaPA 100% (+), 75% (A) and 50%
(V)neutralized; 23% (A)and 38% (V)methylated.
A-‘ 4-
* 100
200
300
(ccoo,-
400
3fCJ
500
600
700
800
-‘
Figure 5. General model of the binding equilibrium: reciprocal of the absorbance increment vs. reciprocal of the concentration of free ligands: [Na’] = 0.26M, NaPA 100% neutralized (0):23% (V) and 38% (‘I methylated; ) [Na+] = 0.41 M NaPA, A 38% methylated.
It must be recognized that hz and k3 (or K ) incorporate “effective” carboxylate concentrations3J4 and may therefore depend on the charge fraction [A]/C,, decreasing as [A]/C, decreases. Activity coefficients are also incorporated in the association constants. This procedure should be quite satisfactory a t constant ionic strength. The activity coefficient of M may vary significantly between 0.26 and 0.58 M although this is unlikely at the low concentration of M used in this work. The absorbance increment then becomes
The Journal of Physical Chemistry, VoL 80, No. 13, 1976
1516
Communications to the Editor
where the E are molar absorbances. However
i.e.
f,
[MI = C M / ( + ~ [A] n = l h i . . . kn/[Na+]n)
(12)
and
therefore
- z A 2,3=1 n k l . . . k ,
-1
+
3 k l . . . kn (14) [Na+]" - e M ? z l [ N B + l " CMMIAl 3 k1 . . . k, 3 kl . . . k , n = i [Nasln [AI
Zl[Na+1n
x =&
(EMA,
- ntA - CM)
(15)
(16)
+
1 B[A] l / A = l/A[A]
+ B/A
(17)
The model reduces to that of ref 8 if the first and second terms of the series in the numerator and denominator of the right-hand side of eq 16 are much smaller than the third. A plot of A-l against [A]-' would be linear under these conditions, with the gradient at any value of [A] increasing as the concentration of 1:l electrolyte increases. In fact the second and third association constants are not negligible. They should diminish as the fraction of carboxylate groups on the polymer which are charged decreases, since the effective concentration of ligands about a -COO-M3+ group will be smaller. (This would not be so if charges were able to move freely along the polyion.) Thus the gradient of the A-l vs. [A]-' plots would be expected to increase with decreasing charge density. [A]-1 is not known, but Figure 5 shows A-l plotted against (CCOO- 3fcM-l). This quantity approaches [A]-1 a t high polymer concentrations and is a better approx-
-
imation to [A]-l than is Ccoo--l. The curvature of these plots shows that the effective ligand concentration is dependent on [AI/CIJ. The gradient A-l of each curve decreases as [A]-l decreases, that is, as the polyion becomes less densely covered with trivalent ions. Also, the gradients of the various curves are least for the most highly charged polyions, showing that the second and third association constants indeed diminish as [A]/C, diminishes. Finally, it is seen that increasing the concentration of added salt increases the steepness of the curves, as expected. However Figure 5 and Figures 1-3 show that a t low charge densities A remains small even when the polyion is greatly in excess. Thus binding to fewer than three carboxylate groups persists even when sufficient triads are available to accommodate all the trivalent cations present so that binding depends on the overall charge density of the polyion.
Acknowledgments. We are indebted to Mr. J. Charlesworth, who collaborated in the development of the copolymerization procedure and prepared some of the samples. One of us (R.E.) gratefully acknowledges financial support from the Commonwealth Department of Education and Science. This work has been supported by the Australian Research Grants Committee. References and Notes (1) F. T. WallandS. J. Gill, J. Phys. Chem., 58, 1128(1954). (2) H. P. Gregor, L. B. Luttinger, and E. M. Loebl, J. phys. Chem., 59,990 (1955). (3) H.Morawetz, J. Polym. Sci., 23, 247 (1957). (4) J. J. O'Nelll, E. M. Loebl, A. Y. Kandanian, and H. Morawetz, J. Polym. Sci. A, 3, 4201 (1965). (5) S. A. Rice and M. Nagasawa, "Polyelectrolyte Solutions", Academic Press, New York, N.Y., 1961, p 443. (6) V. Crescenzi, F. Quadrifoglio, and B.Pispisa, J. Chem. Soc. A, 2175 (1968). (7) A. J. Begala and U. P. Strauss, J. Phys. Chem., 76, 254 (1972). (8) R. J. Eldridge and F. E. Treloar, J. Phys, Chem., 74, 1446 (1970). (9) M. Mandel and M. G. Stadhouder, Makromol. Chem., 80, 141 (1964). (10) G. E. Ham, "Copolymerization", High Polymers Series, Vol. XVIII, Interscience, New York, N.Y., 1964, Chapter 1. (11) R.J. Eldridge and F. E. Treloar, J. Polym. Sci., Polym. Chem. Ed., in press. (12) G. Goldfinger and T. Kane. J. Polym. Sci., 3, 462 (1948). (13) J. Brandrup and E. H. Irnmergut, Ed., "Polymer Handbook", Interscience, New York, N.Y., 1966, pp lV21-22. 14) M. Mandel and J. C. Leyte, J. Polym. Sci., 56, S23 (1962); J. folym. Sci. A, 2, 2883, 3771 (1964). 15) J. C. Leyte, Kolloid-Z., 212, 168 (1966). 16) J. C. Leyte, L. H. Zuiderweg, and M. van Reisen, J. Phys. Chem., 72, 1127 (1968). 17) M. E. Mathews, Blochim. Biophys. Acta, 37, 288 (1960). 18) M. E. Mathews, Arch. Blochem. Biophys., 104, 394 (1964). (In ref 8 we pointed out that eq 6 of ref 17 is incorrect. The correct form of this equation was given by Mathews In ref 18.)
COMMUNICATIONS TO THE EDITm
Vibrational Assignment and Force Constants of the Tetrasulfide Ion, S4*-
Sir: Recently Daly and Brown1 investigated the Raman spectra of solid Na2S4 and its aqueous solution. They observed six frequencies and assigned these to the six'fundamentals of The Journal of Physical Chemistry, Vol. SO3No. 13, 1976
Sd2- assuming the molecular symmetry C2. They also made a normal-coordinate treatment using a valence force field with six force constants @f,,frl.', fa, f r a , and f 7 ) and assuming reasonable values for the geometrical parameters. However, these parameters do not agree with the values found by x-ray crystal structure analysis of Na2S4,2and some of the force constants
