Interaction of Polyelectrolyte with Counterions (25) F. H. Field and M. S. 8. Munson, J. Am. Chem. Soc., 87, 3289 (1965). (26) S.Wexler, A. Lifshitz, and A. Quattrochi, Adv. Chem. Ser., No. 58, 193 (1966). (27) J. A. Burt, J. L. Dunn, M. J. McEwan, M. M. Sutton, A. E. Roche, and H. I. Schiff, J . Chem. Phys., 52, 6062 (1970). (28) P. Ausloos, R. E. Rebbert, and L. Wayne Sieck, J . Chem. fhys., 54, 2612 (1971). (29) S. E. Buttrill, Jr., J . Chem. fhys., 52, 6174 (1970).
1805 (30) W. T. Huntress, Jr., J . Chem. fhys., 56, 5111 (1972). (31) R. C. Dunbar, J. Shen, and G. A. Olah, J . Chem. Phys., 56, 3794 ( 1972). (32) K. Hiraoka and P. Kebarle, J . Chem. fhys., 63, 394 (1975). (33) B. H. Solka, A. Y-K. Lau, and A. G. Harrison, Can. J . Chem., 52, 1798 (1974). (34) S.K. Searles, L. Wayne Sieck, and P. Ausloos, J . Chem. Phys., 53, 849 (1970).
Polyelectrolyte Effects on Rates of Hydrated Electrons C. D. Jonah, M. S. Matheson, and D. Meisel" Chemistry Division, Argonne National Laboratory, Argonne, Illinois 60439 (Received April 25, 1977) Publication costs assisted by Argonne National Laboratory
The effect of polyvinylsulfate (PVS) on the rate of the reaction of ea; with several species highly reactive toward eaq-was investigated using the pulse-radiolysistechnique. The rate of ea< reactions with cations (CU", Cd2+, Ni2+,Zn2+,Ru(bpy)32+, F e ( ~ h e n ) ~Cr3+, ~ + ,Eu3+)is greatly inhibited by the presence of the polyelectrolyte. On the other hand, the reaction with negatively or uncharged species (NO3- and 0,) is hardly affected. It is shown that using this kinetic method the effective number of available sites on the polymer can be titrated. Furthermore, the specificity constants of cations, inert toward ea; (Mg2+,Ca2+,Ba2+,Li+, Na', K'), could be determined by measuring their effect on the rate of the reaction of ea; with a probe cation (Cu2+)"condensed' on the polymer. As expected from measurements of thermodynamic properties of similar polyelectrolytes, and from theoretical models, it was found that divalent ions are bound to the polymer much stronger than are univalent ions. For ions of similar valence the specificity constant is larger, the smaller is the hydrated ionic radius.
Introduction The interaction of polyelectrolytes with counterions has long been recognized to affect the thermodynamic properties (activity coefficients, osmotic coefficients, enthalpy of dilation, etc.) of the polyelectrolyte-counterions solution^.^-^ This same interaction is expected, and often is found, to affect rates of charged species with the counterions. Such kinetic effects have been summarized in several review articles.6-8 Most of these studies involve reactions in which a t least one of the reactants is a bulky organic compound where the interaction between that reactant and the polyelectrolyte is not necessarily a pure electrostatic interaction. Large enhancement coefficients can be obtained for such reactions in which the interaction is primarily electrostatic, as was shown by the work of Morawetz and co-workersgand Ise and co-workers'' on sensitized aquation of, and electron transfer to, Co(II1) complexes. In this study we explore the effect of small concentrations of polyvinylsulfate (PVS) on the rate of hydrated electrons, ea;, with simple ions, using the pulse radiolysis technique. Due to the simplicity of the reactants the interaction is expected to be purely electrostatic. As expected, the rate of the reaction of eaq- with various cations is strongly retarded when the cations reside in the potential field of the polyelectrolyte. This results from exclusion of the cations from the bulk of the solution, exclusion of ea; from the polymer field, and salt effect on the activity coefficient in the polymer d o r n a i n ~ . ~It, ~is expected that the kinetic effects would yield information relevant to the effective number of available sites in the polymer, the relative efficiency of fixation of the cations on the polyelectrolyte, and the occurrence of specific binding to macromolecules. The pulse radiolysis technique has been previously applied to studies of the interaction between several dyes and polyanions and rates of ea< and
OH radicals with the same polyanions were reported." Experimental Section The potassium salt of PVS was purified as described by Breslow and Kutner.12 The specific viscosity of 1%PVS in water was measured and from the correlation between this and the intrinsic viscosity in 0.1 M Na2S0412the average molecular weight was determined to be -250000. Concentrations for the polymer are given in equivalent equiv/L for 1%PVS) and so units of charge (6.17 X are the concentrations for the metal ions (n(M"+)equiv/L). Solutions for irradiations were prepared from 1%PVS stock solution a few hours before irradiation. All other chemicals were of reagent grade. Water used in this study was triply distilled. In order to avoid unnecessary effects of ions other than those studied no buffer was used in this study. However, the pH of the solutions was measured and found to be in the range of 6.5-5.5, except for those experiments where H+ was deliberately added. Thus the effect of [H'] ions on the rate of ea; decay is believed to occur only a t the slowest decay rates of eaq-. Unless otherwise stated all solutions were deaerated by bubbling prepurified argon for 10 min using the syringe technique. The same technique was used to obtain the desired concentration of oxygen when needed. The pulse radiolysis setup has already been described previ0us1y.l~ Electron pulses of -4 ns width produced (1-2) X M total concentration of radicals in 5-cm length cells. All solutions contained 10 mM of tert-butyl alcohol as OH scavenger. The tert-butyl alcohol radicals thus produced by hydrogen abstraction are known to be inert toward all scavengers used. The decay of eaq-((0.5-1) X M per pulse) was followed at 600 nm. The small yield (about 20% of the yield of eaq-)of hydrogen atoms cannot have any effect on the measured kinetics. The decay of ea; was found to follow a pseudo-first-order rate The Journal of Physical Chernlstry, Vol. 8 I, No. 19, 1977
C. D. Jonah, M. S. Matheson, and D. Meisel
1806 I
Y
I
' I
l
c5-
-,
3
0
2 [M"]
rneqil
Flgure 1. Dependence of the observed pseudo-first-order rate constant (corrected to p = 0) for the reaction of eaq- with divalent cations in the presence of 0.01 % PVS. Numbers above arrows indicate multiplication factors for the ordinate scale.
-
/( I 0.5 [ML?! meq /P
I
1.0
Figure 2. Dependence of the observed pseudo-first-order rate constant for the reaction of eaq- with metal chelates. Experimental conditions as in Figure 1.
law in all experiments. The risetime of the electronic setup was less than 20 ns and cannot affect any of our results.
Results and Discussion Effect of PVS on the Rate of ea; with Cations. The effect of 0.01 70PVS on the rate of the reaction of e,; with several highly reactive divalent cations was measured at different concentrations of the cations. Results are summarized in Figure 1,where the pseudo-first-order rate constant for the reaction Mn+ + eaq- -+ M(n-1)'
(1)
is plotted against the concentration of M2+(expressed in equiv/L). The range of hl for the free metal cations is from 6.4 X 1O'O M-I s- for Cd2+to 1.5 X lo9 M-l s-l for Zn2+.14 As can be seen in Figure 1,at low concentrations of M2+ the rate of reaction 1 is strongly inhibited. However, as soon as a certain value of [M2+]is reached the rate sharply increases, yielding from the slope nearly the same rate constant as in the absence of PVS. Obviously the interaction of the counter cations with the potential field of the negatively charged polyelectrolyte strongly inhibits its rate of the reaction with eaq-, In fact, with none of these metal ions could we measure hl for M"+, which is in the potential field of the polyion. When no more M"+ can be added to the polymer the rate is restored. The extremely sharp increase in the observed rate constants (Figures 1-3) is a clear demonstration of the condensation phenomenon in polyelectrolytes often predicted3J9but rarely observed with such distinction. In the absence of the metal cations the rate of the decay of eaq-hardly changes on addition of up to 0.1% PVS, which puts an upper limit for the rate constant of eaq-with polyvinylsulfate of 51.2 X lo6 L/(equiv X s). On addition of small concentrations of M2+some fluctuations, sometimes ranging up to an increase of -50% in; ,e decay rate, were noticed. However, when the rate of decay of ea< is that slow (tens of microseconds), even extremely low concentrations of impurities (most probably O2 or H+ at the level of M) would cause these random fluctuations. The rate of the reaction of e,; with M2+in the presence of PVS can be analyzed in terms of the rate of bound and free cations:
-
~
n
+ +eaq-~-+ +
~ ( n - 1 ) ~ ~
(la)
eaq--+ M ( ~ - I ) + ~
(Ib)
The Journal of Physical Chemistry, Vol. 81, No. 19, 1977
Flgure 3. Dependence of the observed pseudo-first-order rate constant for the reaction of eaq-with trivalent cations. Experimental conditions as in Figure 1.
where the indices b and f denote bound and free cations, respectively. The observed pseudo-first-order rate constant k,&d thus would be given by = kla[Mn+l f d- kzlb[Mn+1b
(1) From Figure 1, it is clear that k l b
