J. Phys. Chem. 1991,95,2595-2601 Conclusions All of the results to date are consistent with the fact that polymers of N O have not been observed. In view of the computed barriers to decomposition, however, it must be considered possible that such polymers could be realized a t extreme pressures and, because of the endothermicity of the polymerization, at high temperatures. It should of course be recalled that N O may decompose explosively a t elevated temperatures. (A referee has called attention to ref 53, in which it is reported that no polym(53) Swanson, B. 1.; Agnew, S. F.; Greiner, N. R. Proceedings of the Eighth Symposium (International) on Detonation; Naval Surface Weapons Center: White Oak, Silver Spring, MD, 1985; pp 715-724.
2595
erization of N O was seen in the diamond anvil cell at 80 K and at pressures up to 42 kbar. The referee suggests that kinking of the long (NO), chains at high pressures may rupture the weaker intermonomer bonds. The length and orientation of the chains might be significant, and perhaps relatively large specimens would be required in the diamond anvil cell to effect polymerization.)
Acknowledgment. This study was sponsored by SDIO/IST, and managed by the Naval Surface Warfare Center. The problem was proposed by Dr. Richard D. Bardo, to whom the writer is idebted for numerous useful discussions. He is also indebted to referees for helpful comments. Registry No. NO, 10102-43-9; S2N2,25474-92-4.
Association of Electroactive Counterions with Polyelectrolytes. 2. Comparison of Electrostatic and Coordinative Bonding to a Mixed Polycation-Polypyridine Junya Kobayasbit and Fred C. Anson* Arthur Amos Noyes Laboratories,$ Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125 (Received: August 10, 1990)
A soluble polysiloxane containing 4,4'-bipyridine as a singly quaternized pendant group was synthesized and allowed to interact with Fe(CN)64-, Fe(CN)S(OH2)s, and Ru(edta)OH2- as counterions. The electrochemical responses (formal potentials and mass-transfer-limited oxidation or reduction currents) of the electroactive counterions were utilized to evaluate diffusion coefficients and equilibrium binding constants. The latter were also measured by equilibrium dialysis. The moderate agreement between the equilibrium constants obtained by the two independent methods lent support to the general procedures employed in analyzing the electrochemical data, although some of the assumptions required for the data analysis may not be fully justified. The results obtained indicate that the polyelectrolytecounterionbinding equilibrium is static rather than dynamic on the electrochemical time scale of a few hundred milliseconds.
In recent reports from this laboratory, the electrochemical behavior of electroactive counterions added to solutions of a soluble polyelectrolyte was described and analyzed.ls*lb The system investigated consisted of a soluble polycation prepared by attaching quaternized pyridine groups to a polysiloxane chain. The electroactive counterion examined was Fe(CN)64- which is strongly associated with the polycationic chains in solution. The effects of this association on the electrochemical responses of the Fe(CN),& counterion were to shift the formal potential of the Fe(CN)6F-/C couple and to decrease the diffusion-limited currents for the oxidation of Fe(CN)6C because of the smaller diffusion coefficient of the polyelectrolyte with which it associates.Ib There were substantial effects from changes in the concentration of the KCI supporting electrolyte: a t sufficiently high concentrations, c\-replaced the Fe(CN)6e counterions and the limiting currents and formal potential were close to those obtained in the absence of the polyelectrolyte. The present study is an elaboration of the earlier work. By attaching 4,4'-bipyridine molecules to the polysiloxane polymer, a polyelectrolyte is obtained which contains both quaternary and unsubstituted pyridine nitrogen atoms. This polyelectrolyte differs from that employed in our previous study (Figure 1) in that both electrostatic bonding of counteranions and coordinative bonding of suitable metal complexes to the polyelectrolyte are possible. Both types of redox probes were attached to the polyelectrolyte and their electrochemical responses were compared to determine if structural information about the polyelectrolyte molecules deduced from the behavior of one type of probe was consistent *Corresponding author. 'Permanent address: Shimadzu Corp., Nishinokyo-Kuwabaracho. Nakagyo-ku, Kyoto 604, Japan. *ContributionNo. 8170.
0022-3654/9 1/2095-2595$02.50/0
with that indicated by the second type of redox probe. The intent was to test more extensively the previously advocatedIb application of counterion electrochemistry to learn about the structures and mobilities of soluble polymer molecules with which the counterions interact. Experiments related to those described here have been reported recently by Bard and co-workers for solutions in which DNA was the soluble polyelectrolyte and metal tris(che1ate) complexes were the electroactive probes bound to the polyelectrolyte chains.* Experimental Section Materials. Poly[ 3-[4-pyridyl-(N-pyridinium chloride)]propylmethylsiloxane] (PPS) (Figure 1A) was prepared by reacting poly( (3-chloropropyl)methy~iloxane)'8 with 4,4'-bipyridine according to a procedure employed previously with pyridine.'*vb The extent of reaction was determined by NMR to exceed 98%. Aqueous solutions of the product were dialyzed against pure water by using a cellulose membrane (Spectra/Por 3) with a molecular weight cutoff of 3500 to remove components of low molecular weight. Molecular weights of the products obtained were estimated from gel permeation chromatography of the poly((3chloropropy1)methylsiloxane) before it was reacted with the 4,4'-bipyridine. The molecular weight of the polyelectrolyte employed in this study was ca. 3 X IO4. Commercially available K2NH4Fe(CN), was recrystallyzed from a concentrated solution of NH40H. Dissolution of this salt (1) (a) Ohyanagi, M.; Anson, F. C. J. Eleclroonal. Chem. 1989,258,469. (b) Ohyanagi, M.; Anson, F. C. J . Phys. Chem. 1989, 93, 8377. (2) (a) Carter, M. T.;Bard, A. J. J. Am. Chem. Soc. 1987,109,7528. (b) Carter, M. T.;Rodriquez, M.; Bard, A. J. J . Am. Chem. Soc. 1989,111,8901. (c) Rodriquez, M.; Kodadek, T.;Torres,M.; Bard, A. J. Bioconjugate Chem. 1990, 2, 123.
0 199 1 American Chemical Society
2596 The Journal of Physical Chemistry, Vol. 95, No. 6, 1991
Kobayashi and Anson
LIM
L
120
A = @a-
B
0
1
2
3
4
5
[ POLYCATION I,
mM
@a-
@
G
Figure 1. (A) The polyelectrolyte employed in this study (PFS). (B) The polyelectrolyte employed in a previous study.Ib
in water provided the Fe(CN)5(OH2)h anion. Other reagent grade chemicals were used as received. Solutions of Fe(CN),(OH2)3and Fe(CN)6*- were freshly prepared just before they were to be used. Ru(Hedta)OH2 was prepared as previously de~cribed.~ Apparatus and Procedures. Conventional instrumentation and cells were employed as previously described.Ib The rotating glassy carbon disk electrode had an area of 0.32 cm2. Potentials were measured with respect to a standard saturated calomel electrode (SCE) or a sodium chloride saturated calomel electrode (SSCE). Equilibrium dialysis experiments were carried out by placing solutions of PPS inside a semipermeable dialysis bag prepared from Spectra/Por 3 Membrane (Spectrum Medical Industries) in a supporting electrolyte consisting of 0.1 M KCI 0.1 mM Fe(CN)64-. The dialysis was carried out against the same supporting electrolyte under argon until equilibrium was achieved as indicated by the lack of further changes in the quantity of Fe(CN)6e present inside the bag (20 h). The total concentration of Fe(CN),& inside the bag at the conclusion of the dialysis was determined by transferring aliquots of the solution to a 1 M KCI supporting electrolyte and measuring the plateau current for the oxidation of Fe(CN)64- a t a rotating disk electrode. It was demonstrated in separate experiments that the plateau currents measured in 1 M KCI were essentially independent of the presence of the polyelectrolyte.
L
140
0
1
2
PYRlMNlUM HYDROCHLORIDE I , M Figure 2. Formal potentials of the Fe(CN):-/& couple in various supporting electrolytes. (A) Supporting electrolyte: 0.1 M KC1 buffered at pH 5.5 with 20 mM acetate buffer to which was added PPS ( 0 )or polylysine (B). (B) Supporting electrolyte: pyridinium hydrochloride in 0.01 M HCI. Potentials are the average of anodic and cathodic peak potentials of cyclic voltammograms recorded with a glassy carbon electrode at a scan rate of 100 mV s-'. [Fe(CN)6e] = 0.1 mM.
+
Results and Discussion Three electroactive complexes that spontaneously associate with the polyelectrolyte shown in Figure 1A (PPS) were examined: Fe(CN)6C, Fe(CN),0Ht3-, and Ru(edta)OH2-. With the first two anions it was necessary to maintain a high ratio of PPS to added counteranion to avoid the formation of precipitates or excessive electrodeposition during electrochemical measurements.Ia For this reason most experiments were conducted with counteranion concentration of 0.05-0.1 mM. Behavior of Fe(cNa4-Counterions. Fe(CN)6e is an electroactive counterion that is bound to the PPS electrolyte only by electrostatic interaction. Its electrochemical behavior was very similar to that reported previously with an analogous polyelectrolyte which contained only quaternary pyridinium groups.Ib For example, the formal potential of the Fe(CN)63/*- couple is shifted to more negative values in the presence of PPS but becomes independent of the concentration of the polyelectrolyte above ca. 1 mM pyridinium sites (Figure 2A). This pattern has been interpreted as evidence that the Fe(CN)6e and Fe(CN)63- anions are both strongly bound to the polyelectrolyte chain which surrounds the multiply charged anions and essentially isolates them from the bulk of the solution. The formal potential for the Fe(3) Baar, R. B.; Anson, F. C. J . Electroanal. Chem. 1985, 187, 265.
I O 20 30 40 TEMPERATURE, 'C
50
Figure 3. Temperature dependence of the formal potential of the Fe(CN)63-/4-couple in 0.1 M KC1 in the absence (A) and in the presence (0)of 10 mmol/L of the polycation shown in Figure 1B.
(CN)64-/3- couple is thus controlled by the local concentration of pyridinium sites and is not influenced by the concentration of polyelectrolyte present in the bulk of the solution. The direction of the shift in formal potentials caused by the addition of PPS (Figure 2A) shows that the less highly charged Fe(CN)63- anion is more strongly bound by the polycationic electrolyte. This somewhat surprising behavior has been reported for a variety of cases4 in which pyridinium groups provide the positive sites for interaction of polyelectrolytes with multiply charged anions. It appears to result from the nature (solvation, polarizability, etc.) of the pyridinium sites of the polyelectrolyte because the formal potential shifts in the opposite direction in the presence of polylysine where the positively charged sites are ammonium ions (Figure 2A). The pyridinium sites need to be part of a polyelectrolyte to produce the negative shift in formal potential: Experiments in which pyridinium hydrochloride was used as the supporting electrolyte produced much smaller shifts in the formal potential of the Fe(CN)63-/e couple as the concentration of pyridinium cations was increased (Figure 2B). (4) (a) Oyama, M.; Shimomura, T.; Shigehara, K.; Anson, F. C. J . EleclroaMI. Chem. 1980, 112, 271. (b) Nan, J.; Murray, R. W. J . Electroanal. Chem. 1982, 131, 37. (c) Braun, H.; Storck, W.; Doblhofer, K. J . Electrochem. SOC.1983, 130, 807.
The Journal of Physical Chemistry, Vol. 95, No. 6, 1991 2597
Behavior of Electroactive Counterions
-
0 0
1
2 [ P P S ] ,
3
4
mM
Figure 4. Plateau currents for the oxidation of 0.05 m M Fe(CN)6C at a rotating glassy carbon disk electrode in solutions containing PPS. Supporting electrolyte as in Figure 2. Rotation rate: 3600 rpm.
Additional insight into the origin of the stronger binding of the less highly charged counterion was obtained from a measurement of the change in the entropy of the FC!(CN)~~-/~ redox couple produced by the presence of the monofunctional polycation shown in Figure 1 B. The temperature dependences of the formal potentials of the couple in the absence and the presence of the polycation are shown in Figure 3. The slopes of the two lines provide values of the difference in the entropies of the Fe(CN),+ and Fe(CN),’ anions.5a These entropy differences are -38 and -21 eu in the absence and presence of the polyelectrolyte, respectively. A simple thermodynamic cycle can be used to show that the 17 eu difference between the two values represents the difference between the entropies of association of Fe(CN),& and of Fe(CN)63-with the polyelectrolyte. Thus, the entropic factors favor the association of Fe(CN)64- over Fe(CN)63- and the observed stronger binding of Fe(cN)6* must reflect the dominance of enthalpic factors (e.g., solvation energies, hydrophobic interactions) which apparently favor the less highly charged counterion. A very recent paper presents clear evidence of much greater solvation of Fe(CN)6& than of Fe(CN)b3- anions by H 2 0 molec u l e ~ .Among ~ ~ the consequences of this difference in solvation is a significantly greater resistance of Fe(CN)6C anions toward extraction into nonaqueous media in phase-transfer e~periments.,~ The reported behavior provides a ready explanation for the preferential binding of Fe(CN)d- anions by hydrophobic polyelectrolytes. Plateau currents for the oxidation of Fe(CN)6& at rotating disk electrodes are depressed by the addition of PPS because the Fe(CN)6b anions that become counterions of the fixed charge sites on the PPS polyelectrolyte diffuse to the electrode at the lower rate corresponding to the smaller diffusion coefficient of the polyelectrolyte chainsIb (Figure 4). For cases where the plateau currents decrease to constant values that are independent of the concentration of polyelectrolyte, it follows that essentially all of the current results from the oxidation (or reduction) of the redox probe which is bound to the polyelectrolyte. If this situation is experimentally accessible with ratios of polyelectrolyte to redox probe high enough so that statistically only one or two redox probes are bound to each polyelectrolyte chain, the limiting value of the plateau current might provide an estimate of the diffusion coeficient of the macromolecule itself.lb Consant plateau currents were not quite obtained in the experiments used to construct Figure 4 so that an alternative route (described below) was used to obtain an estimate for the diffusion coefficient of the polyelectrolyte with Fe(CN)bb anions bound to it. Data such as those in Figure 4 can also be used to estimate the fractions of free and bound counterion present at each concentration of polyelectrolyte and, thereby, to estimate an equilibrium constant for the binding reaction.2b We will return to this possibility in what follows. The extent of the association between the PPS polyelectrolyte and Fe(CN)6C counterions is influenced strongly by changes in the ionic strength of the supporting electrolyte employed as is shown in Figure 5. Both the plateau currents at a rotating disk (5) (a) Ye,E. L.;Cave, R. J.; Guyer, K. L.;Tyma, P. D.;Weaver, M. J. J . Am. Chem. Soc. 1979, 101, 1131. (b) Noftle, R. E.;Pletcher. D.J . Elecmanal. Chem. 1990, 293. 273.
-
0
-0.8
-1.0
-06 -OA
ao
-a2
Log [KC11
Figure 5. (A) Formal potentials and (B) plateau currents as a function of the molar concentration of the KCI supporting electrolyte. [PPS] = 5 m M . (0)0.1 mM Fe(CN)6&; ( 0 )0.1 m M Fe(CN)50H23-;(B) valucs for 0.1 m M Fe(CN)6C in the absence of PPS.
u
0
’w
0
6
-
~
0
1
2
3
I P P S I ,
4
5
mM
Figure 6. (A) Formal potentials of the Fe(CN),Ls/z- couple (L = HzO, pyridine) in the presence of PPS. (B) Plateau currents for the oxidation of 0.1 mM Fe(CN),L3- in solutions containing PPS. Other conditions
as in Figure 2A.
and the formal potential of the Fe(CN)63/’ couple approach their values in solutions free of PPS as the concentration of KCI is increased and the Fe(CN)6e counterions associated with the polyelectrolyte are replaced by C1- anions. Similar behavior was observed in a previous study.lb Behavior of Fe( CiV),0H23- Counterions. The addition of Fe(CN),0H2’- counterions to solutions of PPS results in the coordination of Fe(CN),’ to the pendant pyridine groups of the polyelectrolyte. There is a tendency for precipitation of the resulting PPS-Fe(CN), complex unless the concentration of PPS is maintained high enough (e.g., at least 10-fold greater than that of Fe(CN),’-) to limit the number of anions coordinated to each polymer chain. Under these conditions the mixtures are wellbehaved. The electrochemical behavior of the mixtures is qualitatively similar but quantitatively quite different from that resulting from the addition of Fe(CN)64-: The formal potential of the Fe(CN)qOH23-/2-couple is ca. 0.1 V in the absence of PPS but shifts to 0.26 V in the presence of (excess) PPS and is independent of the concentration of PPS (Figure 6A). The direction of the shift in formal potential and its insensitivity to the concentration of PPS are the expected result of the essentially irreversible coordination of the Fe(CN)53- centers to the pendant pyridine groups on the PPS chains. Such coordinative binding is evidently much stronger than the electrostatic binding with the pyridinium groups that is also available and is used exclusively by the coordinatively saturated Fe(CN)64- anions.
2598 The Journal of Physical Chemistry. Vol. 95, No. 6, 1991
Kobayashi and Anson
3 0 0 4 0 0 5 0 0 6 0 0 7 0 0 WAVELENGTH,
+
nm
2
w
a 1.0 I
1
a
3
0
0
0.05
0.15
0.1
[ Fe(CN)s(OHd3-],
mM
Figure 7. (A) Absorption spectrum of solutions containing 10 mM of PPS in 0.1 M KCI to which increasing quantities of Fe(CN)50H23-were added. The concentrations of the anion were increased from 0.025 to 0.1 mM in equal increments. (B) The absorbance at 600 nm vs the con-
centration of the anion. The effect of added PPS on the plateau currents for the oxidation of Fe(CN),0H2' at rotating glassy carbon disk electrodes is shown in Figure 6B. The abrupt decrease in current is the expected result of the essentially quantitative attachment of the small, rapidly diffusing anion to the large, slowly diffusing polyelectrolyte. Each of the data points in Figure 6 was obtained with freshly prepared solutions so the lack of dependence of the current on the Concentration of polyelectrolyte shows that the diffusion coefficient of the metal-polyelectrolyte complex is not affected by an increase in the number of Fe(CN)53 centers bound to the polyelectrolyte chain (at least within the range of ca. 2-5 centers per chain covered in Figure 6). The behavior shown in Figure 6B is significantly different from that obtained with Fe(CN),& as the electroactive counterion where a more gradual current decrease is observed (Figure 4). If, as seems likely, the diffusion coefficient for the Fe(CN)6'+ polyelectrolyte complex is also independent of the number of Fe(CN)6e anions bound to the polyelectrolyte chain, the gradual decrease of the current in Figure 4 reflects only the increasing fraction of Fe(CN)6C anions associated with the polyelectrolyte as its concentration increases. The large spectral changes that occur in mixtures of PPS and Fe(CN)50H23-(Figure 7) confirm that the binding involves the formation of Fe(CN),pyPPS (pyPPS represents one of the pendant pyridine groups of the PPS polymer) complexes in the mixed solutions. The absorption maximum at 600 nm in Figure 7 resembles that at 520 nm for the well-characterized monomeric complex6 (1) in which the ligand has a structure similar to the
1
pendant group in the PPS polymer. The molar absorbance of this complex a t 520 nm is 5.62 X lo3 M-' cm-'.6 If the same value is assumed to apply to the Fe(CN),pyPPS complex, the data in Figure 7 indicate that the formation of the complex is quantitative with 10 mM PPS. The linear plot in Figure 7B was identical when the concentration of PPS was decreased to 2 mM so that it seems reasonable to assume that the coordination of Fe(CN)?- to PPS ( 6 ) Toma,
H.E.; Malin, J. M. Inorg.
Chem. 1973, 12, 1039.
1 1 1 1 1 -a2
OD
02
a4
OB
E vs S C E , V
Figure 8. Cyclic voltammetry of solutions containing 10 mM PPS and mixtures of Fe(CN)50H2- and Fe(CN)t-: (A) 0.15 mM Fe(CN)50H2-;supporting electrolyte 0.1 M KCI; (B) after addition of 0.1 mM Fe(CN)64-to the solution in (A); (C) repeat of B with 0.5 M KCI as supporting electrolyte. Scan rate: 20 mVs-'.
electrolyte is quantitative at all of the concentrations of PPS utilized in the experiments summarized in Figure 6. Additional evidence that the reaction of Fe(CN)64- and Fe(CN)50H23-anions with the PPS polyelectrolyte involves fundamentally different chemistry was provided by experiments in which the concentration of the KCI supporting electrolyte was changed (Figure 5). The electrostatic binding between Fe(CN)6e and PPS is largely eliminated in 1 M KCI as indicated by the return of both the plateau currents at the rotating disk electrode and the formal potentials of the Fe(CN)63-/4- couple to values close to those for polymer-free solutions. By contrast, the corresponding parameters for the solutions of the Fe(CN),pyPPS complex are much less sensitive to changes in the concentration of supporting electrolyte because neither potassium nor chloride ions compete with the Fe(CN)50H23-anions for coordination to the pyridine groups. Purely electrostatic binding of the Fe(CN),0H2)- anions to the PPS polyelectrolyte is apparently negligible under the experimental conditions employed. The small decrease in the formal potential for the Fe(CN)62-/3couple as the concentration of KC1 is increased is in the direction expected because chloride counterions are released from the polyelectrolyte when the Fe(CN)5Z-anions bound to the polyelectrolyte are reduced to Fe(CN)53-. The insensitivity of the plateau currents to changes in the concentration of KCI in the case of Fe(CN)5' centers coordinated to the polyelectrolyte (Figure 5B) is evidence against significant electrostatic intermolecular cross-linking via the multiply charged, coordinatively bound Fe(CN)53- centers. The anionic centers coordinated to the pendant pyridine groups in one PPS molecule doubtless do form electrostatic bonds to pyridinium groups in the same PPS chaini to produce intramolecular cross-links. However, links involving several different PPS chains are apparently uncommon because such multiple-chain adducts would be expected to diffuse more slowly than the non-cross-linked chains which the behavior of the Fe(CN)64- anions in Figure 5B indicates are predominate in the presence of high concentrations of KCI. The differences in the effects resulting from increases in the concentration of the KCI supporting electrolyte are particularly clear in comparisons of the cyclic voltammetric responses of
The Journal of Physical Chemistry, Vol. 95, No. 6, 1991 2599
Behavior of Electroactive Counterions 0
w
E
.-100
W
0 u)
9-200 c
W
- 300 4:
F
30
-n 20
10 0
1
2
3
4
C P P S I , mM
Figure 9. (A) Formal potentials of the Ru(edta)L-l2- (L = H20, pyridine) and Fe(edta)OH2-/2-couples in the presence of PPS. (B) Plateau currents for the reduction of 0.1 mM Ru(edta)L- and 0.1 mM Fe(edta)OH,- in solutions of PPS. (0) Ru(edta)L-; (B) Fe(edta)OH,-. Other conditions as in Figure 6.
Fe(CN),' and Fe(CN)50H2- in the presence of the PPS polyelectrolyte (Figure 8). The formal potentials of the Fe(CN)63/4and Fe(CN)SpyPPS3-/2- couples differ by ca. 135 mV in the presence of PPS so that mixtures of these two complexes yield two peaks in cyclic voltammetry (Figure 8B). However, the two peaks can be converted to a single composite peak by increasing the concentration of the KCl supporting electrolyte which eliminates the electrostatic, but not the coordinative binding so that the formal potential of the Fe(CN)6s/e couple is shifted to a more positive value which happens to lie very close to that for the Fe(CN)SpyPPS3-/2-couple (Figure 8C). Behavior of Ru1I1(edta)OH2-Counterions. Ru111(edta)OH2(edta = ethylenediaminetetraacetate) is an unusual complex of Ru(II1) in which the single coordinated water molecule is labile and can be rapidly replaced with more strongly bound ligands including ~ y r i d i n e . ~Addition of a stoichiometric excess of the PPS ligand to solutions of the Ru(edta)OHc complex produces an immediate positive shift in the formal potential of the redox couple to the value characteristic of the Ru(edta)py-l2- couple' (Figure 9A) and a corresponding decrease in the plateau current at a rotating disk electrode for the reduction of the Ru(II1) center (Figure 9B). The current is not affected by the addition of more PPS, probably because the coordinative bonding of the Ru(edta)OHy to the pendant pyridine ligands is already quantitative at millimolar pyridine concentrations. This strong binding would be consistent with the known association constant (K= 1 X lo5 M-I) for the reaction between the two monomeric reactant^.^ (The corresponding Fe(edta)OH,- complex, which has a negligible affinity for pyridine ligands, exhibits an electrochemical response that is unaffected by the addition of PPS (Figure 9)). The constant current of 16 PA in Figure 9B is larger than the 9-rA current that resulted when the same concentration of Fe(CN)?- centers were coordinated to the PPS molecules. If these constant currents that are obtained at high ratios of polyelectrolyte to metal complex are to provide a reliable measure of the diffusion coefficient of the polyelectrolyte itself, as proposed previously,Ib the constant current should be about the same for each type of metal center that is bound to the polyelectrolyte. The constant currents obtained for Fe(CN)s3 and Ru(edta)- clearly fail to meet this test. The singly charged Ru(edta)- complex bound to the pyridine groups in PPS interacts much more weakly with the positively charged sites in the polyelectrolyte chains than do bound Fe(CN)53- anions. The complexes of Ru(edta)- with PPS are much more soluble and remain in solution at all ratios of metal to polyelectrolyte. Thus, diffusion coefficients evaluated from (7) Matsukra, T.; Creutz, C. J. Am. Chem. Soc. 1978,100,6255;Inorg. Chrm. 1979. 18, 1956.
constant currents such as those in Figure 9B are likely to be more representative of those for the individual polyelectrolyte molecules. The complexes between Fe(CN)S3-and PPS are more prone to precipitate from solution and the smaller diffusion coefficients they exhibit may reflect a local condensation of the polyelectrolyte in the vicinity of the bound Fe(CN)s3- centers to yield a less hydrated portion of the chain that acts as a sort of anchor which slows down the diffusion of the complex and produces the smaller constant current obtained in Figure 6B. In support of this interpretation was the observation that the addition of Fe(CN)s0H23-to solutions of the Ru(edta)-PPS complex caused the diffusion coefficient of the latter to decrease to that obtained in mixtures of PPS and Fe(CN)sOH23-. This behavior indicates that weakly charged metal complexes such as Ru(edta)- are better choices than multiply charged counterions for electrochemical experiments directed at the estimation of polymer or polyelectrolyte diffusion coefficients from diffusion-limited currents. Estimates of the Equilibrium Constant for the Reaction between PPS and Fe(CiV),&. The values of ID in Figure 4 can be utilized to obtain an estimate of the equilibrium constant for the reaction governing the association of Fe(CN)6' anions with the PPS polyelectrolyte. The equilibrium of interest may be written as Fe(CN)t- + (py+), = Fe(CN)6"--(py+), (1) where m is the number of pyridinium groups on the PPS polyelectrolyte for which the Fe(CN)64-becomes the counterion. Unlm m = 4, the Fe(CN)64-anions associated with the PPS polyelectrolyte would also be serving as counterions for cations of the supporting electrolyte (e.g., potassium ions). It is convenient to express the equilibrium constant for reaction 1 in terms of the known total concentrations of pyridinium groups C,, and of ferrocyanide anions, C, (2)
where CBis the concentration of Fe(CN)6e associated with the PPS polyelectrolyte. The values of CBneeded to determine K can be obtained from the values of ID in Figure 4 if it is assumed that the currents result from the diffusion of both bound and unbound Fe(CN)6' anions to the electrode, that the diffusion coefficients of both species are independent of the concentration of the polyelectrolyte, and that the equilibrium expression defined in eq 2 is independent of the extent of the reaction. Bard and co-workers have employed a similar strategy in recent studies.2b.c One might well question the assumption that the diffusion coefficients of the PPS-( Fe( CN)t-), complexes remain independent of n (the number of Fe(CN)t- anions associated at each polyelectrolyte chain), because of the possibility of intramolecular electrostatic cross-linking when multiply charged counterions are employed. Polyelectrolytes such as PPS are likely to adopt more coiled structures to accommodate intrachain electrostatic bonds in the presence of multiply charged counterions and the resulting polyelectrolytes could diffuse at different rates. It is also doubtful that K would remain truly constant as multiply charged counterions replaced singly charged counterions and the possibilities for intermolecular cross-linking increased. Nevertheless, it was of interest to see if the ID values shown in Figure 4 could be accommodated in terms of the simple model of two types of diffusing reactants with differing but constant diffusion coefficients. To proceed, it is necessary to consider whether the bound and unbound Fe(CN)6@ anions diffuse independently or if there is coupling between the two by either place exchange or electron exchange between thems-I0 (on the electrochemical time scale of ( 8 ) Buttry, D. A.; Anson, F. C. J . Am. Chem. Soc. 1983, 105,685. ( 9 ) Buttry, D. A.; Savant, J.-M.; Anson, F. C. J . Phys. Chem. 1984,88, 3086. (10) Andrieux, C. P.; Hapiot, P.; Savant, J.-M. J . EircrrocrMi. Chem. 1984, 172, 49.
2600 The Journal of Physical Chemistry, Vol. 95, No. 6,I991
TABLE II: Evaluation of Equilibrium Constants for Reaction 1 by Equilibrium Dialysis“ conc of PPS,mM conc of Fe(CN),&, mM 10-’K,M-l 1.o 0.1 2.93 2.0 0.05 2.49 0.10 2.44 2.0 3 .O 0.05 2.93 5.0 0.10 2.27 av 2.6 f 0.3
TABLE I: Equilibrium Constants for Reaction 1 Evaluated from Plateau Currents at Rotating Disk E k e t ~ o d e s ~ ~ 1 0 - 3 ~M-1. mnc of PPS,mM static eq dynam eq 0.5 2.94 4.17 1.o 2.98 4.30 1.5 3.21 4.83 2.0 3.59 5.41 2.5 3.78 5.78 3.0 3.64 5.62 3.5 4.31 6.89 4.0 3.80 5.99 av 3.5 f 0.4 5.4 i 0.7
“Supporting electrolyte: as in Table I.
“Supporting electrolyte: 0.1 M KCI buffered at pH 5.5 with acetate buffer. bConcentration of Fe(CN),& = 0.05 mM.
a few hundred milliseconds a t rotation rates of a few thousand rpm). When the place exchange is rapid, the situation is equivalent to the ‘dynamic equilibrium” case analyzed by Evans” and discussed by Bard and co-workers.2b For this case it can be shown that the plateau currents at a rotating disk electrode are given by 11,= kCT(Dfif D f i ~ ) ’ / ’ (3)
+
where k = 0.20Aw1/Zu-1/6 and w is the electrode rotation rate (rpm), A is the electrode area, v is the kinematic viscosity, CT is the total concentration of ferrocyanide, and X f and xb are the fractions of free and bound ferrocyanide, respectively. When place exchange is slow (’static equilibrium”), the current is given by the simple sum of the contributions from each form Of Fe(CN)6e:12
+
11,= k c ~ ( D ? / ’ x f D B ~ / ~ X B )
(4)
The value of Xb is related to the equilibrium constant for reaction 1
* .=K
(5)
--xB Crn
Kobayashi and Anson
(1 -&)
The values of IDin Figure 4 were substituted in eq 3 or 4 to obtain values of XB which were, in turn, inserted into eq 5 to calculate values of K. The parameters utilized in the calculations were Df = 6.3 X 10” cm2 s-I l 3 and m = 4. The diffusion coefficient for the bound Fe(CN)6C, DB, was assumed to be the same as that of the Fe(CN)SpyPPScomplex as measured by the 1, value in Figure 6B that is independent of the concentration of PPS, DB = 5 X lo-’ cmz s-!, This assumption seems reasonable because of the essentially quantitative binding of Fe(CN)5s to the polymer so that the only electroactive diffusing species present is the Fe(CN)SpyPPS complex whose diffusion coefficient is measured by the constant set of currents in Figure 6B. The results of the calculations are shown in Table I. The lack of high precision in the values of K obtained is not surprising in view of the low reactant concentrations that had to be employed which resulted in correspondingly small currents. Despite the limited precision of the data, the values of K calculated for the static equilibrium model are somewhat more constant and give an average equilibrium constant of 3.5 X lo3 M-I but the differences between (11) Evans, D. H. J . Electroanal. Chem. 1989, 258, 451. (12) Equation 4 is not rigorously applicable to systems in which the oxidized and reduced forms of the two diffusants undergo rapid electron exchange but slow place exchange. Such systems belong to the class treated by Andrieux et aLiO We employed eq 4 in the present study in the absence of reliable estimates of the relevant electron-exchange rates but it may bc important in future work to recognize that eqs 3 and 4 do not apply to all of the case8 that can k encountered in studies of the association between polyelectrolytes and electroactive metal complexes. Cf.: Blauch, D. N.; Anson, F. C. J . Electroanal. Chem., in press. (1 3) von Stackelkerg, M.; Pilgram, M.; Toome, 2.Z. Elekrrochem. 1953, 57, 342.
the results for the two models are not large enough to provide a definitive distinction to be made. However, by evaluating K i n independent equilibrium dialysis experiments it was possible to identify the static equilibrium model as the more appropriate for this system. Equilibrium Dialysis. The equilibrium constant governing the association of Fe(CN)64-counterions with the PPS polyelectrolyte can be evaluated directly from equilibrium dialysis experiments without having to know if the equilibrium is static or dynamic. The only assumption is that true equilibrium is attained by the end of the dialysis period which was typically 20 h. A series of dialyses was carried out as described in the Experimental section from which values for the equilibrium constant of reaction 1 were calculated (Table 11). The values of K are reasonably constant and their average value, 2.6 X lo3 M-I, is closer to the value obtained from the electrochemical data for the case of a static equilibrium. Thus, the combination of the electrochemical and equilibrium dialysis experiments allowed the more likely equilibrium model to be identified. The 35% difference between the average values of K obtained from the electrochemical and the equilibrium dialysis experiments is probably a reflection of the limited accuracy of some of the assumptions mentioned earlier that were required in order to extract an equilibrium constant from the electrochemical data. We regard the binding constant obtained from the equilibrium dialysis experiments as more reliable. In principle, the equilibrium constant for the binding of Fe(CN),‘- counterions to PPS could be calculated from the Nernst equation by using the measured value of K for Fe(CN)6C binding and the shift in the formal potential of the Fe(CN)63-/e couple produced by the addition of PPS (Figure 2A). This tactic has been employed to estimate the relative affinities of oxidized and reduced metal chelates for DNAZbwhere hydrophobic factors appear to be more important than electrostatic interactions. However, in cases such as the present one, where electrostatic factors control the binding, the relationship between shifts in formal potentials in the presence and absence of polyelectrolyte, AE, and the ratio of binding constants is less clear. The simple relation given in eq 6 that has been used by Carter et a1.2bneglects AE = 0.059 log (Kd/KOx) (6) the change in the number of fmed charge sites for which the bound, redox active species serve as counterion when it is reduced or oxidized. For a one-electron redox couple, inclusion of this factor would add a term to eq 6 A E = 0.059 log ( K r d / K O x-) 0.059 log Cs (7) where C, is the concentration of fixed charge sites provided by the polyelectrolyte, pyridinium groups in the present instance. Equation 7 requires that the formal potential of electrostatically bound redox couples exhibit a dependence on the polyelectrolyte concentration. Quite the contrary behavior was observed for mixtures of Fe(CN)6t and PPS (Figure 2A). The likely insulation of redox couples bound to the interior of coiled polyelectrolyte chains from changes in the bulk concentration of polyelectrolyte has been offered as a possible explanation for the behavior of the formal potentials shown in Figure 2A. Whatever its origin, the behavior precludes the use of eq 7 to obtain a quantitative estimate of the equilibrium constant for the binding of Fe(CN)?- by PPS. This limitation on the use of electrochemical data to evaluate
J. Phys. Chem. 1991,95, 2601-2606 equilibrium constants for the association of electroactive complexes with polyelectrolytic hosts needs to be borne in mind whenever a lack of true dynamic equilibrium makes the detailed nature of the actual electrode half-reaction uncertain.
Concluding Remarks The use of the essentially irreversibly coordinated Fe(CN)53anion to obtain a value for the diffusion coefficient of a redox probe bound to a polyelectrolyte will not be possible in the more common cases where polyelectrolytes without functional coordination sites are studied. In such cases, the combination of electrochemical
2601
and equilibrium dialysis experiments, as exemplified in this study, offers a convenient and relatively straightforward general strategy for analyzing the binding equilibrium and mass transport behavior of mixtures of redox probes with soluble polyelectrolytes and polymers.
Acknowledgment. This work was supported in part by the National Science Foundation and the US.Army Research Office. J.K. received support from the Shimadzu Corp. (Kyoto). Discussions with Dr.Manshi Ohyanagi were helpful during the initial stages of this work.
Dissoclation Kinetics of Callxarene Ester-Na+ Complexes. Effect of Sodium Ion Exchange Reaction on *'Na Longitudinal Magnetization Recovery Curves and 'H NMR Spectra Takashi Jint and Kazuhiko Ichikawa* Department of Chemistry, Faculty of Science, Hokkaido University, Sapporo 060, Japan (Received: June 25, 1990; In Final Form November 2, 1990)
The effect of the sodium ion exchange reaction on 23Nalongitudinal magnetization recovery (LMR) curves and 'H NMR spectra has been investigated for p-tert-butylcalix[4]arene (BCA) and its ethyl acetate derivative (BCAD) in chloroform + methanol (2:l v/v) solutions. For BCA + NaSCN system, 23NaLMR curves and NMR spectra were almost identical with those of solvated sodium ion in the absence of BCA. In the case of the system BCAD + NaSCN, 23NaLMR curves at I < R < 1.2 (R= [NaSCN]/[BCAD]) showed non-single-exponentiaaldecays, and =Na NMR spectra showed non-lorentzian line shapes because of the presence of chemical exchange between solvated sodium ions and Na+-BCAD complexes. At R = 0.4 the sodium ion exchange reaction was confirmed by the temperature dependence of the 'HNMR spectra. The lifetimes of the Na+.BCAD complexes (A) and solvated sodium ions (B), 7, and 7g, for the first time have been determined between 23 and 60 OC by the simulations of 23NaLMR curves at R = 1 . 1 by using coupled expressions for the time evolution of the magnetization at sites A and B under the presence of chemical exchange: 7, = 1.0 X 10-2-1.5 X lo-' s and 78 = 1 . 1 X 10-'-2.6 X s. Since the lifetimes of sites A were independent of R,the predominant mechanism for the decomplexation of Na+-BCADcomplex is unimolecular and is characterized by the following activation parameters for dissociation path: AH'd = 56.3 f 6.6 kJ/mol, A s * d = -39 i 21 J K-'mol-', and AGld(298K) = 67.9 i 9.1 kJ/mol.
Introduction The calixarenes prepared by the condensation of p-alkylphenol and formaldehyde are a new class of host molecules, which are characteristic of cyclic oligomers having a cylindrical structure both in solid state and in solution.' Host-guest chemistry of the calixarenes is very interesting, since the calixarenes have unique complexing abilities toward both neutral molecules and ions. The calixarenes as well as cyclodextrins contain a hydrophobic cavity, which is made up by benzene units, so that they can include a small organic molecule.' Furthermore, the calixarenes also are able to exhibit ionophoric activities for alkali- or alkaline-earthmetal cations by means of functional group modification a t phenolic It is of particular interest that the tetraether or -ester ligand derived from p-tert-butylcalix[4]arene shows remarkable complexing abilities toward the sodium cation. Arduini et ala2found from ' H NMR titration experiments a 1:l stoichiometric complex of sodium ion with p-tert-butylcalix[4]arene ester derivative; the compound encapsulates a sodium cation into a hydrophilic cavity constructed with the tetraester (-OCH2C02-R) groups. Arimura et al.' determined the association constants of alkali picrates (M+Pic-) with p-tert-butylcalix[n]arene (n = 4, 6, 8) ester derivatives in tetrahydrofuran by using the electronic absorption 'Present address: Section of Physiology, Research Institute of Applied Electricity, Hokkaido University, Sapporo 060, Japan. *Author for correspondence; .
0022-3654/91/2095-2601$02.50/0
technique and indicated that a sodium ion was encapsulated leading to the solvent-separated ion pairs. The X-ray crystal structures of calix[4]arene tetraester and ketone derivatives showed that ethereal oxygen atoms were mutually separated by 3.03-3.28 A, enough to accommodate a sodium ion.s It has been found in extraction experiments that calix[4]arene tetraester and ketone derivatives show ionophoric activities.I4 The relationships between the structures and ion selectivities of calixarenes should be elucidated by the studies on the kinetics of ion exchange as well as the thermodynamic properties of complexing reaction. However, nobody has studied the kinetic properties of the sodium ion exchange reaction between the Na+.calixarene complex and solvated Na+ in the liquid state. In this work, we report the measurements of 23Nalongitudinal magnetization recovery (LMR) curves and 23Na/'H N M R spectra for p-tert-butylcalix[4]arene (BCA) Na+ and its ethyl acetate derivative (BCAD) + Na+ in chloroform
+
( 1 ) Gutsche, C. D. Prog. Mucrocycl. Chem. 1987, 3, 93. (2) Arduini, A.; Pochini, A.; Reverberi, S.;Ungaro, R. Terruhedron 1986, 42, 2089.
( 3 ) Chang, S. K.; Cho, I. J . Chem. Soc., Perkin Trans. 1 1986, 211. (4) Arimura, T.; Kubota, M.; Matsuda, T.; Manabe, 0.;Shinkai, S. Bull. Chem. Soc. Jpn. 1989,62, 1614. (S).Arnaud-Neu, F.; Collins, E. M.; Deasy, M.; Ferguson, G.; Harris, S. J.; Kaitner. B.; Lough, A. J.; MacKervey, M. A.; Marques, E.; Ruhl, B. L.; Schwing-Weill, M. J.; Seward, E. M. J . Am. Chem. Soc. 1989, 1 1 1 , 8681.
0 1991 American Chemical Society
