Solvent isotope effects upon the kinetics of some simple electrode reactions

J. Electroanal. Chem., 114 (1980) 53--72

53

@) Elsevier Sequoia S.A., Lausanne -- Printed in The Netherlands

SOLVENT ISOTOPE EFFECTS UPON THE KINETICS OF SOME SIMPLE ELECTRODE REACTIONS

MICHAEL J. WEAVER *, PAUL D. TYMA and SCOTT M. NETTLES

Department of Chemistry Michigan State University, East Lansing, MI 48824 (U.S.A.) (Received 5th May 1980)

ABSTRACT The effects of replacing H20 with D20 solvent upon the electrochemical kinetics of simple transition-metal redox couples containing aquo, ammine or ethylenediamine ligands have been investigated at mercury electrodes as a means of exploring the possible contribution of ligand--aqueous solvent interactions to the activation barrier to outer-sphere electron transfer. The general interpretation of solvent isotope effects upon electrode kinetics is discussed; it is concluded that double-layer corrected isotopic rate ratios (kH/kD) E determined at a constant electrode potential vs. an aqueous reference electrode, as well as those determined at the respective standard potentials in H 2 0 and D20 (kH/kD), have particular significance since the solvent liquid-junction potential can be arranged to be essentially zero. For aquo redox couples, values of (kH/k D) were observed that are substantially greater than unity and appear to be at least partly due to a greater solvent-reorganization barrier in D20 arising from ligand--solvent hydrogen bonding. For ammine and ethylenediamine complexes values of (kH/kD) E substantially greater than, and smaller than, unity were observed upon the separate deuteration of the ligands and the surrounding solvent respectively. Comparison of isotope rate ratios for corresponding electrochemical and homogeneous outer-sphere reactions involving cationic ammine and aquo complexes yields values of (kH/k D) for the former processes that are typically markedly larger than those predicted by the Marcus model from the homogeneous rate ratios. These discrepancies appear to arise from differences in the solvent environments in the transition states for electrochemical and homogeneous reactions.

INTRODUCTION

It has been known for some time that sizable changes in the rate constants of homogeneous electron-transfer reactions between transition-metal complexes occur when heavy water (D20) is substituted for H20 [1--3]. These solvent isot o p e effects have been attributed to " s e c o n d a r y " isotope effects arising from differences in reactant--solvent interactions as well as to " p r i m a r y " isotope effects arising from the replacement of hydrogen b y deuterium in the coordination sphere of the reacting cations [2--4]. Studies of deuterium-isotope effects in electrode kinetics have largely been limited to the important but atypical cases of hydrogen and oxygen evolution [5,6], and no isotope effects upon the kinetics o f simple outer-sphere electrode reactions have apparently been reported. Nevertheless, .it is anticipated that such studies could shed light on * To whom correspondence should be addressed.

54 the role of the solvent in outer-sphere processes. In particular, the dielectric properties of H20 and D20 are almost identical; and yet the mass difference between H and D yields significantly different hydrogen-bonding properties, so that these measurements could, in principle, provide a means of assessing the importance of specific solute--solvent interactions to the kinetics of electron transfer. In some respects, electrode reactions are more suitable than homogeneous redox processes for such fundamental studies since the former type involves the thermal activation o f only a single redox center. Also, the comparison between the solvent isotope effects observed for corresponding homogeneous and electrochemical reactions involving transition-metal complexes could provide clues as to the similarities and differences between the reactant--solvent interactions in the bulk and interphasial redox environments. For this reason, we have examined the effect of replacing H20 solvent with D20 upon the electrode kinetics of a number of aquo and ammine complexes for which the solvent isotope effects u p o n outer-sphere homogeneous reactions involving these complexes have previously been scrutinized [2,4,7--9]. These reactions include Fe3~/2+ self-exchange [2,7] and the reduction of Co(III) ammines b y V~a~and Cr2a~ [8,9]. Although the sizable (factor of two) ratio of the rate constants in H20 and D20 ( k H / k D) for F e ~ n+ self-exchange was originally attributed to the presence of a hydrogen-atom transfer mechanism [7], similarly large values of kH/k D have been observed for cross-reactions involving aquo complexes for which this mechanism is ruled o u t [2,8,9]. We have recently measured the solvent isotope effect u p o n the formal electrode potentials E~ of a number of transition-metal redox couples [10]. For couples containing aquo or h y d r o x o ligands, large differences in Ef between H20 and D20 were observed that appear to be at least partly due to hydrogen bonding between these ligands and the surrounding solvent [10]. It is of interest to determine h o w these thermodynamic differences are reflected in the electrode kinetics of such complexes. Studies of isotope effects for substitutionally inert ammine and ethylenediamine complexes are also of particular interest since, in contrast to aquo complexes, the deuteration of the ligands and the solvent, i.e. the primary and secondary isotope effects, can be investigated separately [11,12]. The results of these experiments are reported in the present paper. EXPERIMENTAL

The Co(III) and Cr(III) complexes were synthesized as solid perchlorate salts using the procedures noted in refs. 13 and 14, respectively. Stock solutions of E u ~ were prepared b y dissolving Eu203 in a slight excess of perchloric acid, and those of Cra3~ as described in ref. 15. Solutions of Euaq ,2+ Craq2+and Vaq2+were 3+ obtained in the appropriate electrolytes b y electrolyzing solutions of EUaq, C r ~ and V(V), respec.tively, over a stirred mercury pool at --1100 mV vs. SCE; V ~ was formed b y reoxidizing V ~ at --300 mV vs. SCE. The source of F e ~ was Fe(C104)3 (G.F. Smith Co.). Potassium hexafluorophosphate (Alfa Ventron Corp.) was three times recrystallized from water. Sodium perchlorate was prepared from sodium carbonate and perchloric acid and recrystallized prior to use. Stock solutions of lanthanum perchlorate were prepared b y dissolving La203 in a slight excess of perchloric acid. The use of aqueous reagents such as

55

70% perchloric acid generally introduced only small (~1%) amounts o f water into the resulting D20 solutions. The Co(III) and Cr(III) ammine and ethylenediamine complexes were deuterated b y dissolving the protonated perchlorate salts in the minimum a m o u n t of D20 containing 1 mM hydroxide ions. The amine hydrogens are rapidly deuterated under these conditions [11 ]. These stock solutions were then added to the appropriate electrolyte in H20 or D20 acidified with sufficient perchloric acid (usually 5--10 mM) to suppress completely the exchange o f amine hydrogens on the time scale of the kinetics experiments. Water was purified either b y means o f a "MilliQ" purification system (Millipore Corp.) or by distillation from alkaline permanganate followed b y "pyrodistillation" [16], with identical results. Deuterium oxide (99.8%, Stohler Isotope Chemicals) was used either directly or following distillation from alkaline permanganate, again with identical results. All solutions for electrochemical scrutiny were deoxygenated by bubbling with prepurified nitrogen, from which residual traces of oxygen were removed by passing through a column packed with B.A.S.F. R3-11 catalyst heated to 140°C, and then humidified b y bubbling through either H 2 0 or D20 as appropriate. Kinetic parameters were obtained at a dropping mercury electrode (flow rate 1.8 mg s -1, mechanically controlled drop time 2 s.) b y means of normal pulse and dc polarography using a P.A.R. 174A polarographic analyzer coupled with a Hewlett--Packard 7045A X--Y recorder. The kinetic analyses of these irreversible polarograms employed the methods due to Oldham and Parry [17], which allowed rate constants in the range c a . 1 0 . 4 to 4 X 10 .2 cm s -1 to be evaluated reliably. The electrochemical cell used for the kinetic measurements consisted of a working c o m p a r t m e n t containing ca. 5 cm 3 o f the solution of interest in either H20 or D20, which was separated from the reference compartment by means of a glass frit ("very fine" grade, Corning, Inc.). For experiments where bulk electrolyses were performed, the platinum wire counter electrode was located in a third c o m p a r t m e n t which was also separated from the working c o m p a r t m e n t b y a glass frit. The reference compartment was filled with an aqueous solution of the same ionic composition as in the working compartment, in which was immersed a commercial saturated calomel electrode (SCE). When using strongly acidic electrolytes, the reference compartment was filled instead with saturated aqueous NH4C1 in order to minimize the liquidjunction potential [10]. The solvent liquid-junction potential b e t w e e n the H20 and D20 solutions is probably negligible (<1--2 mV.) using this cell arrangement, as shown b y the essentially identical formal potentials obtained in H20 and D20 for ferrocene/ferrocinium and Fe(bpy)~ ÷~2÷ (bpy = 2,2'-bipyridine) redox couples [10] (Both these couples are expected to exert only a small nonspecific influence u p o n the surrounding solvent.) Consequently, a given cell potential E measured in a given electrolyte in H20 and D20 will correspond to essentially the same, albeit unknown, value of the Galvani metal-solution potential difference Cm in both solvents. (See ref. 10 for a detailed discussion of this point.) All electrode potential are therefore quoted vs. an aqueous SCE using this cell arrangement, unless otherwise noted. All kinetic parameters were obtained at 25.0 + 0.1 ° C.

56 RESULTS

A q u o complexes Since large differences in the formal potential, AE D-H, are observed for redox couples containing aquo ligands when changing from H20 to D20 solvent [10], it is of particular interest to examine t h e corresponding differences in their electrode kinetics. Reactions that have been found to be suitable for 3+/2+ at cathodic overpotenscrutiny at the mercury--aqueous interface are _eaq tials * , and vraq ~ 3+/2+, --aq v3+/2 + and Euaq 3+n+at both cathodic and anodic overpotentials ( " a q " denotes OH2 or OD2 ligands in the appropriate solvents). When comparing electrochemical rate constants in H20 and D~O, it is desirable to correct the relative rates for differences in the ionic double-layer effect between these solvents. By assuming that this correction can be calculated using the simple electrostatic (Frumkin) model, we can express the ratio of the observed (apparent) rate constant for a given one-electron reaction in H20 to that in D20, ( k H / k D ) a p p , a s (cf. ref. 18) ,

l o g ( k H / k D ) a p p = log(kH/kD)cor r + (f/2.303)(Z + ~corr)AcDp-H

(1)

where ( k H / k D ) c o r r is the corresponding isotopic rate ratio corrected for ionic double-layer effects [18], A~bDpH the alteration in the average potential on the reaction plane in changing from H20 to D20, z the reactant charge, acorr the double layer-corrected transfer coefficient and f = F / R T . (The plus/minus sign in eqn. 1 refers to electrooxidation and electroreduction reactions respectively.) In order to estimate AODpH, plots of the excess electrode charge density qm against the electrode potential E are required in both H20 and D20. F!gure 1 consists of a pair of such plots for 1 M KF. These were obtained b y integrating the capacitance--electrode potential curves for these electrolytes [19,20] along with the following values of the potential of zero charge (pzc) that were determined b y t h e streaming potential method [ 21 ] : 1 M K F(H20), --434 mV; 1 M KF(D20), --440 mV vs. aqueous SCE. It is seen from Fig. 1 that the qm--E plots for H~O and D20 are quite similar, although it is interesting to note that the plot for D20 is displaced significantly relative to H20 at the most negative potentials. Since fluoride anions are not significantly specifically adsorbed within this potential range [22], these electrode charge displacements at fixed values of E, (Aqm)D-H, presumably arise from differences in the inner-layer structure b e t w e e n H20 and D20. For most of the reactions considered here, either 0.4 M KPF6 or 40 mM La(C104)3, rather than fluoride, supporting electrolytes were used in order to minimize the extent of ion-pairing and to enable acidic solutions to be used; there is extensive information available on the magnitude of the double-layer corrections for

* A l t h o u g h t h e f o r m a l p o t e n t i a l f o r _eaqF 3+/2+ [ 4 9 5 m V , p - 0.5 M ( H 2 0 ) ] is positive o f t h e p o t e n t i a l w h e r e m e r c u r y d i s s o l u t i o n o c c u r s in n o n - c o m p l e x i n g m e d i a (>~350 m V ) , we have f o u n d t h a t well-defined n o r m a l pulse a n d dc p o l a r o g r a m s c a n be o b t a i n e d f o r Fea3~ reduct i o n in acidified K P F 6 o r NaC104 over t h e p o t e n t i a l r a n g e ca. 300 t o - - 1 0 0 m V o n a c c o u n t o f a p p a r e n t l y very slow e x c h a n g e k i n e t i c s for F~ - - a3+/2+ q • T o o u r k n o w l e d g e , n o previous meas u r e m e n t s o f Fea3q/2+ k i n e t i c s at t h e m e r c u r y - - a q u e o u s i n t e r f a c e have b e e n r e p o r t e d .

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the present reactants in these electrolytes [13--15,18,23]. Although b o t h 0.4 M KPF6 and 40 mM La(C104)3 exhibit significant anion specific adsorption at positive electrode charges, the extent of adsorption is small at potentials more negative than ca. --500 mV and --650 mV respectively. Under these latter conditions, the relative qm--E curves for these electrolytes in H20 and D20 will be closely similar to those given in Fig. 1, so that the required double-layer cotrections to the observed rate ratios (kH/kD)Epp could be obtained to a reasonable approximation in the following manner. The value o f (Aqm)ED--H at the appropriate value of E was read from Fig. 1 and the corresponding difference in the diffuse-layer potentials ~bd between D20 and H20 in a given electrolyte, (ACO)ED-H, obtained using Gouy--Chapman theory. The corresponding values of (A~brp)~-H were obtained b y assuming that A~b~p = 0.7A~b d and A~brp = A~bd for 0.4 M KPF6 and 40 mM La(C104)3 respectively, as indicated from earlier studies [15,23]. These values of (ACrp)ED-H were then inserted into eqn. (1) to obtain the required values of (k H/k D)cor~. E (Fortunately the extent of these doublelayer corrections is small for most reactants.) Some reactions required scrutiny at positive electrode charges (corresponding to --E ~ 450 mV) where PF~ and particularly C10~ supporting electrolytes exhibit significant anion specific adsorption, so that ¢~p will be influenced b y t h e adsorbed anionic charge d e m sity q'. However, the use of 0.4 M KPF6 minimized the extent of the diffuselayer corrections since q ' ~ qm at potentials positive of the pzc in aqueous solution so that ¢~p ~ 0 [18,24]. A similar circumstance is expected in DE0, So that ACDp--H ~ 0 under these conditions.

58 TABLE 1 Solvent isotope effects upon the electroreduction kinetics of some transition-metal aquo c o m p l e x e s at t h e m e r c u r y - - a q u e o u s i n t e r f a c e Reactant

Solvent

Electrolyte a

E/mV vs. H 2 0

E p b/ kap c m s -1

0~app c

E d (k H/ k D )corr

SCE 3+ Feaq 3+ Feaq :3+ Craq 3+ Craq 3+ Craq 3+ Craq 3+ Vaq 3+ Vaq 3+ Euaq 3+ Euaq

H20 D20 H20 D20 H20 D20 H20 D20 H20 D20

0.4 M K P F 6 0.4 M K P F 6 40 m M La(C104)3 40 m M La(C104)3 0.4 M KPF6 0.4 M K P F 6 0.4 M KPF6 0.4 M KPF6 4 0 m M La(C104)3 40 m M La(C104)3

200 200 --850 --850 --850 --850 --500 --500 --750 --750

2.25 3.3 7.9 6.8 2.5 2.1 3.5 4.4 5.8 5.8

X X X X X X × X × X

10 -3 10 .3 10 -4 10 -4 10 -3 10 -3 10 -3 10 -3 10 -3 10 -3

0.48 0.48 0.57 0.57 0.63 0.63 0.67 0.67 0.57 0.57

~0.7 1.09 1.09 0.8 0.95

a Acidified w i t h 5 - - 1 0 m M HC104 t o s u p p r e s s h y d r o l y s i s o f a q u o r e a c t a n t s . b C a t h o d i c a p p a r e n t rate c o n s t a n t at s t a t e d e l e c t r o d e p o t e n t i a l , o b t a i n e d f r o m kap p = i / F c b, w h e r e i is t h e c u r r e n t d e n s i t y c o r r e c t e d for d i f f u s i o n p o l a r i z a t i o n a n d c b t h e b u l k r e a c t a n t concentration. c C a t h o d i c a p p a r e n t t r a n s f e r c o e f f i c i e n t , o b t a i n e d f r o m Otapp = - - ( f ] 2 . 3 0 3 ) ( ~ log kapp/~E)~. d R a t i o o f d o u b l e - l a y e r c o r r e c t e d r a t e c o n s t a n t kcorr m e a s u r e d in D 2 0 t o t h a t in H 2 0 a t f i x e d e l e c t r o d e p o t e n t i a l in same s u p p o r t i n g e l e c t r o l y t e ; o b t a i n e d f r o m c o r r e s p o n d i n g q u o t e d values o f kap p using eqn. (1) as o u t l i n e d in t h e t e x t .

Table 1 summarizes representative electrode kinetic parameters for the reduction of F e a3q+ , C r a3q+ , V a3q+ and E u a3q+ at the Hg/H20 and Hg/D20 interfaces. The rate parameters were all f o u n d to be independent o f pH below ca. pH 2.5 where hydrolysis of the aquo cations is suppressed. Essentially linear Tafel plots were obtained for each reaction over the observable span (200--300 mV) of cathodic overpotentials [15,23], so that the cathodic rate parameters can conveniently be expressed as a value of kap p at a selected electrode potential and an apparent cathodic transfer coefficient %pp, found from %pp = --(f/2.303)(~ log kapp/~E)tz The corresponding double-layer corrected rate ratios at a fixed electrode potential, (k H/k D)co~r, E are also given in Table 1. (Since essentially identical values o f %pp and hence ecor~ were measured for a given system in H20 and D20, these rate ratios will be approximately independent of the value of E chosen.) It is seen that the values of (k H/k D)oo~ E are comparable to, or somewhat less than, unity. However, a given electrode potential corresponds to larger cathodic overpotentials in D20 than in H20 since values of Ef for these couples are markedly less negative in the former solvent [10]. The cathodic Tafel plots were therefore extrapolated to the appropriate formal potentials for each couple measured in H20 and D20 [10] to obtain the " s t a n d a r d " apparent rate constants (ks)app listed in Table 2. These results are also presented as ratios of (ks)~pp for H D )app,. these rate ratios were cora given redox couple in H20 and D20 (ks/ks

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rected for the effect o f the ionic double layer as noted above, except that values of (Aqm) D-H and hence ACDpH between the respective formal potentials in D20 and H20 were inserted into eqn. (1) to obtain the values of (ksH/ksD)co~ given in Table 2. [For -Fo H~ksD)co~ was obtained - ~ a q 3+n+ the listed estimate of (ks by assuming that AOD-u = 0 in 0.4 M KPF6, and that aeor~ = 0.5.] It is seen that the values of (kH/kDs)eor, as well as (kHs/kD)app are substantially greater than unity, particularly for ~raqC 3+/2+ which also exhibits the largest value of

aE?-" [lO]. Ammine and ethylenediamine complexes The effects of separately deuterating the coordinated ligands and the solvent upon the irreversible electroreduction kinetics [13] of various Co(III) ammine and ethylenediamine complexes are summarized in Table 3. Some corresponding kinetic data for several Cr(III) ammine and ethylenediamine complexes are given in Table 4. Since essentially linear Tafel plots were obtained over the measurable overpotential range (ca. 300 mV) for each system, the kinetic parameters are again conveniently summarized as values of kap p at a selected electrode potential along with the corresponding values of 0~pp. The listed isotopic rate ratios {]~NH/]~ND~E and {kH20/J~D20~E resulting from deuter~,v /.v ]corr ~,v t.v /corr ating the ligands and the solvent respectively, were obtained from the appropriate pair of apparent rate constants. As before, the latter ratios were corrected for differences in double-layer structure between H20 and D20 using eqn. (1), assuming that Aq$~p = ACa [13,14]. Unfortunately, the values of E~ and hence ks for the ammine couples are u n k n o w n on account of the lability and thermodynamic instability of the reduced complexes. Inspection of Tables 3 and 4 reveals t h a t separate deuteration of the solvent and the reactant's coordination sphere can both have substantial influences upon the electroreduction rates measured at a fixed electrode potential. The latter effects are largest for the reduction of Co(NH3)36+ and Cr(NH3)63+, where deuteration of the ammine ligands produced isotopic rate ratios (kNH/kND)cEor r t h a t are around two in both H20 and D~O solvents. Values of (]~NH/I~ND~E \'~ / "~ Jcorr considerably greater than u n i t y are also seen for other Co(III) ammines and Co(en)~ + (Table 3). On the other hand, substitution of H20 by D20 solvent for a reactant with either pr'otonated or deuterated ligands generally resulted in noticeable rate decreases, so t h a t the listed values of t,~[bH20/bD20~E,,~ ,tort are uniformly less than u n i t y (Tables 3 and 4). Also listed in Tables 3 and 4 are the net isotopic rate ratios (k H/k D)co,r E resulting from deuterating both the ligands and the surrounding solvent. It is seen t h a t in every case (k H/k D)Ec o , , > l . Nearly all the reactions listed in Tables 3 and 4 are believed to occur via outer-sphere mechanisms [13,14]. The one exception is the reduction of Cr(NH3)sNCS 2÷, which probably occurs via a thiocyanate-bridged pathway [14]. It is interesting to note t h a t there were virtually no variations in aa, p observed for a given system as a result of deuteration of either the ligands or the solvent, at least within the experimental reproducibilityof aapp (-+0.01--0.02). The notable exception is Co(NH3)sOH 2÷ reduction, which exhibits significantly smaller values o f ~app in D20 t h a n in H2O. Unfortunately, basic solutions (pH ~> 9) were required for this reactant in order to suppress the protonation of the hy-

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63 droxo ligand; this prevented the separate study of primary and secondary effects since the ammine hydrogens are rapidly exchanged with the solvent under these conditions [11]. The diffusion coefficients D obtained from the polarographic limiting cur. rents were generally smaller for a given complex in D20 than in H20. The diffusion coefficient ratios DH2°/D D2° were typically 1.35 -+ 0.05 for M ~ complexes and 1.2--1.25 for Co(III) and Cr(III) ammine complexes. Deuterated ammine complexes also exhibited significantly (3--8%) smaller diffusion coefficients than the corresponding protonated complexes in both H20 and D20. The observed DH2°/D D20 ratios are roughtly consistent with the higher viscosity of D20 (1.107 cP) compared to H20 (0.8903 cP) [25] : inserting this viscosity ratio into the Stokes--Einstein equation [26] yields DH20/DD20 = 1.243. DISCUSSION

Interpretation o f observed isotopic rate ratios In order to interpret the substantial kinetic isotope effects presented in Tables 1--4, it is useful at the outset to consider the fundamental significance of the isotopic rate r a t i o s (kH/~D)cEorr and (ks/ks H D)corr. Consider the generalized electrochemical reaction ox + e-(¢m) ~ red

(2)

We can express the free energies of the thermodynamic states prior to, and following, electron transfer (labeled states I and II, respectively) as [27] G O= Go -0 x + p0_ _ F¢m

(3)

GoI = G~ed -o

(4)

where Gox ~0 and Gr -.ued are the partial molal free energies of the oxidized and reduced species, respectively, and p 0 is the chemical potential of the reacting electron. Since the overall free energy of reaction A G ° ( - G~I -- G[) for eqn. (2) will b y definition equal zero when 4m = 4 ° (the standard Galvani potential corresponding to the experimental formal potential for the redox couple), then, --0 0 Gred -- Gox = --F4 °

(5)

Although neither absolute nor even relative values of 4 ° in different solvents are strictly thermodynamically accessible quantities, as noted above the electrochemical cell arrangement used here allows the measured, differences in formal potentials in D20 and H20, AE D-H, to be equated to a v e r y good approximation (-+1 mV) with the corresponding difference in 4m, 0 (A40)D'-'H, between the two solvents. Therefore, from eqn. (5) we can evaluate the difference in (G°ed -- G°x) between D:O and H:O, A (G°ed -- G°x) D-H, using (eqn. 2 of ref.

10) A(G°ed - - ~ox]~0 ]D--H -- --F A E D-H

(6)

64

An analogous relationship for kinetic isotope effects can also be derived by noting t h a t the activation free energy corrected for double-layer effects AGcorr * [= Gco,r * -- GO)] can be separated into a potential-dependent ("electrical") part t t (Gcorr -- G°)e and a potential-independent ("chemical") part (Gcor, -- G°)c [27]. The former c o m p o n e n t is related [27] to the potential-dependent part of AG °, (6°i -- G°)e, by * $

(Geor, -- G°)e = 0~corr(V~i -- V~) e

(7)

Since from eqns. (3) and (4), (G~I -- G°)e = F¢ ° , then, t

(Gcorr -- V°)c = aco~FCm

(8)

The isotopic rate ratio (k H/k D)cor~ E can be expressed in terms of the corresponding activation free energies for the same reaction in DfO and H20 as R T ln(kH/kD)Ecorr

=

* D -- ( ~ G c4-o ~ ) S (AGco,r)

(9)

Since the condition o f constant E also essentially maintains constancy o f Cm, we can write: R T ln(kH/kD)Ecorr =

( G c o¢, ,

0 D -- GI)~

--

(Gc*o~r- -

G I0)cH =

• A(Vco~r -- (~0 - o x / c ]D--H

(10)

where the subscript " c " again refers to the potential-independent part of Gco~. The rate r a t i o (kH/]~D)cEor r [ o r the constituent ratio ~,o~(~H20/bD20~E/,~ ]eorr ] therefore provides a measure of the influence of solvent deuteration upon the relative stabilities of the reacting species within the reactant and activated states. The significance of the ra~e ratio (k~/k~ H D)co~ can be seen by noting that for cathodic reactions: In ~ CEO r

r

= ln(k~)¢o~r

acorrf(E--Ef)

(11)

so that ln(kH/kD)Ecorr = ln(kH/kD)cor r -- aco~ f A E f D - H

(12)

By combining eqns. (6), (10) and (12), we obtain: R T ln(kH/kD)corr = A(Gcorr * - - ~( o~ 0x),D¢ - - H --acor~ A(G~ed --0 __ N0 - o x :)D--H

(13)

The first and the second terms on the right-hand side of eqn. (11) constitute the so-called "intrinsic" and " t h e r m o d y n a m i c " contributions to the overall redox reactivity [28--30]. Thus (ks)cor~ is related to the intrinsic electrochemcal free energy of activation AGUe by - - R T ln[(k~)~o~/Z ~] = A G ~ (Z ~ is the electrochemical collision frequency). This intrinsic barrier AGi*e (labeled kel/4 in the Marcus treatment [31] ) is equal to the work-corrected free energy of activation w h e n t h e ground states immediately preceding and succeeding the transition state have equal free energies [28--31]. The rate ratio (k~/k~ H D)co~ * A l t h o u g h equivalent, eqn. (7) differs f r o m the corresponding relations given in ref. 27 in that the transition-state free energy used here is presumed to be c o r r e c t e d for the effect of the ionic double layer, so that the free energies o f the b u l k reactant and p r o d u c t ground states appear in eqn. (7), rather t h a n those for the corresponding states within the double layer [ 27 ].

65 therefore provides a measure of the change in the intrinsic barriers resulting from isotopic substitution, i.e.

RT ln(kS/kD)cor r

=

From the form of eqn. (13) it is seen that A(Gcor~

-ox,c

(14)

(AGi¢e) D - - ( A V : e ) n

= acor~

n D)co~r will equal unity when (ks/ks

-ox,

i.e. when the change in the potential-independent part of the transition-state free energy (AGco~) , D--H is equal to that expected for a (hypothetical) stable species having a structure and charge appropriately intermediate between ox and red. Therefore, values of (kn/k D) differing from unity result from changes in Gco~ * upon isotopic substitution that are not reflected in corresponding changes in G°x and G°ed, i.e. are unique ("intrinsic") to the transition state. The observation that (teH/k D)eo~ E ~ 1 for the aquo couples (Table 1) arises from an approximate compensation b e t w e e n the intrinsic and thermodynamic contributions (eqn. 12) inasmuch as (kH/kD)cor~ > 1 and AE D-H > 0 for each of these reactions (Table 2). The latter result indicates that A(G°~d -- G°x) D-H is negative (eqn. 6) [e.g. for c. _ _ ~0 v r a q9÷/2÷, A ( G r-0 ed - - o x , ~D--H = --5.4 kJ m o l - ' ] . This finding has been interpreted in terms of the relative destabilization of the oxi3+ dized species Maq in D20 resulting not only from deuteration of inner-shell water molecules b u t also from the greater "solvent-ordering" tendency [32] o f Ma3~ in D20 compared to H20 [10]. Evidence supporting this latter contention includes the especially large values of reaction entropies AS°~ for these M3+n+ couples [16] ; this result probably arises from hydrogen bonding between aq the M3~ aquo ligands which is partly dissipated when the cation is reduced to 2+ Maq. A significantly larger value of AS°c for Fea3~n+ is observed in D20 (190 J K -I m o l - ' , p = 0.2 M) than in H20 (181 J K -~ mo1-1) [10] which is consistent with the expected greater extent of hydrogen bonding in D20 than in H20 [10]. The observation that (ksHtiesD)~o~ > 1 for each of the four aquo couples given in Table 2 indicates that the intrinsic barriers for these reactions are significantly larger in D20 than in H20 (eqn. 14). In particular, for Cr 3÷n÷ [(AGi*~)D -- (AG~) H] = 2.9 kJ mol -~. The intrinsic barrier is usually separated into an "inner-shell" c o m p o n e n t (AGi*e)is arising from intramolecular reactant reorganization (particularly from changes in metal--ligand bond lengths), and an "outer-shell" c o m p o n e n t (AGi*e)os arising from reorganization of the surrounding solvent [31]. The observed values of (ksHtiesD)~or~ may arise from either or both of these contributions. Thus, the stretching of the metal-3+ oxygen bonds that is required in order for the tripositive aquo cations M~q to 2+ accept an electron to form the corresponding Maq species m a y well require significantly greater energy when the oxygen is bound to deuterium rather than to hydrogen as a result of coupling between the vibrations of the M--O and O--H (or O--D) bonds. By taking such inner-shell contributions into account, N e w t o n [33,34] has calculated that the ratio of the rate constants (kH/k D) for homogeneous Fea3~/2÷.self-exchange in H20 and D20 would be no greater than 1.15. Since the inner-shell contribution to the intrinsic barrier for homogeneous self-exchange is generally predicted to be twice that for the corresponding electrochemical exchange reaction [31] (see below), it follows that the correspond-

66 ing prediction for electrochemical Fe~qn÷ exchange is ( k sH/k sD)co~r ~ (1"15) 1/2 = 1.07. It therefore seems quite likely that the markedly larger observed value of (kH/k D) seen for Fea3qn+ (ca. 1.5, Table 2) is at least partly due to contributions from water molecules b e y o n d the primary coordination sphere. In view of the close similarity in the difference in metal--oxygen bond distances AN for Fea~ vs. F e ~ (A~ = 0.014 nm) and V ~ vs. Va3~ ( A ~ 0.015 nm) [35], together with the involvement of a t2g electron in both Fea3~/2÷and --aqV3÷n+exchange reactions, it seems likely that such a calculation for Va3~/2÷would also yield (ks/ks H D)cor~ ~ 1.0--1.1, in contrast to the observed value of 1.5. The simplest approach to the estimation of the outer-shell contribution (AGUe)o, involves treating the surrounding solvent as a dielectric continuum [31]. By inserting the k n o w n values [25] of the optical and static dielectric constants eop and es for liquid H20 [eop = (refractive index) 2 = 1.777, es = 78.3] and liquid D20 at 25°C (eop= 1.764, es = 77.95) into the relationship for (AGi*e)os derived by Marcus (eqn. 90 of ref. 31) leads via eqn. (14) to the prediction that (ks/ks H D)co~ = 1.06 (using the typical reactant radius of 0.35 nm and a reactant--electrode distance of 0.7 nm). Consequently, this dielectric-continuum model for the solvent is also unable to explain the observed values of (ks/ks H D)co~r- However, it seems feasible that the substantial differences in short-range solvent polarization between the oxidized and reduced forms of the ~'~aq M 3÷/2÷ couples could provide a much larger contribution to the increased intrinsic barriers in D20. Thus, the formation 2 + of the transition state in D20 is expected to involve a greater increase from Maq in the extent of solvent ordering induced b y hydrogen bonding compared with the corresponding process in H20. Similarly, the formation of the transition 3+ will require a greater dissipation of this hydrogen-bonded solstate from Maq vent in D20 than in H20. These differences will not affect the intrinsic barrier if *

A(G~o**

__ ¢~0

~D--H

-ox,c

~0

= acorr A(Gred

__ t,~0

)D--H

--ox,

(eqn. 13) i.e. when the isotope influence upon the transition-state stability is that expected for a cation with a structure identical to that of the transition state b u t having the charge (3-aco,r). However, in actuality the transition state is reached via the reorganization of nuclear coordinates while the reactant charge remains fixed, the electron transfer occurring rapidly (~10 -~6 s) once the transition state is formed [31]. The solvent reorientation required for transitionstate formation will therefore be unaided b y concomitant variations in the cation charge so that the required solvent structural changes should involve an additional c o m p o n e n t of the activation energy which will form part of the intrinsic barrier. Consequently, the larger structural differences between M ~ 2+ and Maq in D20 compared with those in H~O are also expected to yield larger intrinsic barriers in D20, in harmony with the experimental results. However, it is difficult to estimate quantitatively the magnitude of this contribution. It is interesting to note that the magnitude of ( k s H / k s D ) ~ o ~ for Craq3+/2÷(2.8) is substantially larger than for the other two hexacoordinate aquo couples Fea3~n÷ and --aqV3÷n*(~1.5, Table 2). This difference parallels the markedly larger values of both A S ~ and A E ~ -H observed for ~c~3+n÷ (209 J K -~ mo1-1, 55 mV, aq

67 p = 0.1 M) compared with F e ~ n÷ (181 J K -1 mo1-1, 43 mV) and -v- a q3÷/2÷ (155 J K -1 mo1-1, 33 mV) [10,16]. These correlations are compatible with the notion that an important c o m p o n e n t of the observed values of (kY/kD)co~ arises from specific solvent polarization. However, the intrinsic barrier to C r ~ n÷ exchange should also contain the largest inner-shell contribution since in this case the electron is transferred into an eg orbital; at least part of the especially large value of (ksH~ksD)co~ for this couple may arise from this source. It remains to rationalize the sizable isotope effects seen for the reduction of the Co(III) and Cr(III) amine complexes that are summarized in Tables 3 and 4. Since AE D-H values for these reactions are unknown (except for Co(en)~ ÷n÷ [10]), it is not possible to make a complete experimental separation of the observed values of (]¢NH/hND~E and k(hH20/hD20~E into intrinsic and thermo\'~ / '~ ]COr]¢ '~ / '~ Jcorr dynamic factors (eqn. 11). Nevertheless, approximate limits can be placed on AE~ - H which allow the intrinsic part to be estimated. The effects u p o n E~ of deuterating separately the ligands and the solvent have been examined [10] for Ru(III)/(II) amine couples that are structurally similar to the Co(III) and Cr(III) reactants considered here; the inertness of b o t h Ru(II) and Ru(III) to substitution allows E~ to be evaluated accurately using cyclic voltammetry [10]. Deuteration o f the ligands was found to have only a very small effect u p o n E~ (AE ND-NH G 2 mV [10]); deuteration of the solvent also yielded small positive shifts in Ef (AE D2°-H2° <~ 10 mV [!0]). The net effect of deuterating b o t h the ligands and the solvent, A E ~ -H ~< 10 mV, is therefore typically smaller than for "M - a q 3÷/2÷ couples. This behavioral difference is probably due to the apparently smaller solvent "structure-making" ability of tripositive ammine complexes compared with otherwise similar aquo species [14] presumably arising from the smaller tendency o f the less acidic ammine hydrogens to engage in hydrogen bonding with surrounding water molecules [16]. It is quite likely that the (experimentally inaccessible) behavior of the Co(III)/(II) and Cr(III)/(II) amine couples is not greatly different from that for the corresponding Ru(III)/(II) couples. A clue to the probable values of A E ND--NH for Co(III)/(II) ammines is given b y the observation [36] that the deuteration of the ammine ligands increase the equilibrium constant for the dissociation reaction Co(NH3)sOD~ + + D20 # Co(NH3)sOD 2÷ + D30 + in D20 b y a factor of 1.3. This finding can be rationalized b y the greater decrease in the zero-point vibrational energy [37] of the N--D bonds compared with the weaker [36] N--H bonds in the conjugate base resulting from its smaller cationic charge [38,39]. A similar charge effect upon the redox thermodynamics of Co(III)/(II) ammine complexes is therefore expected; a corresponding change in the relative stability of the oxidized and reduced forms leads to the estimate AE~ D--NH ~ 7 mV. In any event, it seems very likely that the values of AE~ D--NH for the Co(III)/(II) ammine and ethylenediamine couples and probably also the Cr(III)/(II) couples are small and positive. Therefore, from eqn. (5), the values of (kNn/kND)Eeor~greater than unity observed for these reactions are probably associated with still larger values of kt~ ' ~ S Nnt~ND~E I'~S /CO l'r • For example, if A E f N D - N H = 7 mV for Co(NH3)63+n+, then since ( ] z N H / k N D ) c E o r r ~,

68

2.0 in both H20 and D20 (Table 3) and aco~r = 0.5 [13], from eqn. (6) H D (ks/ks )tort ~ 2.3. It therefore appears that deuteration of amine ligands yields noticeable increases in the intrinsic electrochemical barrier f o r Co(III)/(II) and Cr(III)/(II). This effect is probably, at least in part, an inner-shell effect arising from coupling between the symmetrical M--N stretching vibration and the stretching and bending modes of the N--H (or N--D) bonds [34]. (Such coupling has been estimated theoretically to be much stronger than that between M--O and O--H bonds in aquo complexes [34] .) Additionally, there may be a contribution to H D (k~/k~ )co~r from the expected greater interaction between the ammine hydrogens and solvating water molecules when the former are deuterated (see below). However, this latter contribution is likely to be less significant than for aquo couples in view of the apparently weaker ligand--solvent interactions for the ammine complexes [10]. Since the effect of separate deuteration of the solvent upon the Co(III) and Cr(III) amine reduction rates yields values of x0~/hH20/hD20]E,,~ y c o r r that are less than unity (Tables 3 and 4), given that the values of A E D 2 ° - H 2 ° are probably small and positive it is quite possible that this thermodynamic factor could account partly or even entirely for the observed isotope effect (eqn. 5). Thus, since (kH20/kD20)Ecorr "~ 0.7 for Co(NH3)~ ÷ and Co(ND3)~ + reduction (Table 3), if ( b H 2 0 / b,~s D 2 0 ~ Jco~ ~ 1.0. for example AE D2°-H2° = 20 mV, then from eqn. (6) ,,o~ Although there are several factors that could produce larger intrinsic barriers in D20 compared with H20 solvent [(kS2°/kD20)cor r > 1], the opposite situation is unexpected and would be without an obvious explanation. It therefore seems most likely that the values of AE D2°-s2° for the Co(III)/(II) and Cr(III)/(II) amine couples are sufficiently large (ca. 10--20 mV) so to offset the observed values of/I~H20/hD20~E yielding (bH20/bD20~ ~ 1 (eqn. 5). In any case, the observation of non-unit values of (kS20/kD20 )co++ E is intriguing. Since the interactions between the ammine hydrogens and the oxygen of the solvating water molecules should be very similar in H20 and D20, this result suggests that there are significant differences in the long-range solvent polarization induced b y the ammine reactants in H20 and D20. These differences are likely due to "specific" (hydrogen-bonding) differences between these solvents;the Born model predicts only negligible (<0.5 mV) values of A E D 2 ° - H 2 ° since the dielectric constants of liquid H20 and D20 are almost identical (78.3 and 77.95 respectively, at 25°C [25]). The equal values of ¢~pv observed in H20 and D20 for each of the electrode reactions, except for Co(NH3)sOH 2+ reduction, indicates that the position of the reaction site in the interphase [ 14] is normally unaffected by isotopic substitution. The origin of the smaller value of a, pp observed for Co(NH3)sOH 2+ reduction in D20 compared to that in H20 (Table 3) may well be the same as that responsible for the anomalously small values of c~vp for this reaction in H20 which have been found to increase with increasing temperature. This latter result has been attributed to stabilizing hydrogen bonding between the oxygen of the h y d r o x o ligand and the inner-layer water molecules which diminishes as the electrode potential becomes more negative due to the tendency of the inner-layer water to become polarized with the hydrogens pointing towards the metal under these conditions [40]. This effect is expected to diminish with

69 increasing temperature since the extent of hydrogen bonding should then decrease. On the other hand, the substitution of D20 for HEO should increase the extent of hydrogen bonding at a given temperature, in harmony with the observed smaller value of a~pp in D20 at 25 ° C.

Comparison between isotope effects for corresponding electrochemical and homogeneous reactions The foregoing suggests that a substantial part of the rate changes observed upon replacing hydrogen with deuterium in the coordination sphere of the reactant as well as in the surrounding solvent can arise from the influence of water molecules b e y o n d the coordination sphere, i.e. from secondary as well as primary isotope effects. Additional evidence favoring such an interpretation is obtained b y comparing the isotope effects for corresponding electrochemical and homogeneous reactions. By assuming that the reorganizational barriers consist of independent, additive contributions from each reactant, it has been shown that [31,41] ( k e / Z e) = (~hox/Zh)l/2

(15)

where k~ and kohx are the (work-corrected) rate constants for the electrochemical and homogeneous exchange reactions involving a given redox couple, and Z h is the homogeneous collision frequency. We have recently shown [42,43] that eqn. (15) can be generalized to include heteronuclear (cross-) reactions, expressed b y ( k ~ / z °) = (k~2/z~) "~

(16)

where k~2 is the rate constant for the homogeneous cross-reaction, and where k[2 is the rate constant at the intersection o f the (double-layer corrected) cathodic and anodic Tafel plots for the t w o constituent electrochemical reactions. Equation (16) has been found to be in approximate accordance with experimental rate data for various ammine and aquo couples, although significant behavioral differences between these two reactant types were observed [43]. From eqn. (16), the following predicted relationship between the isotope effects for corresponding electrochemical and homogeneous reactions is obtained: H D e H D h 1/2 (k,2/k12)cor~ = [(kl~/kl~)co,,] (17) Table 5 contains comparisons between (k12/k12)co~ S D e D h and (k I-I 12/k12)~orr resulting from solvent deuteration for four redox reactions involving Co(III) ammines and aquo complexes. The electrochemical rate ratios were obtained from the rate constants at the intersection of the Tafel plots for the constituent halfreactions obtained in 0.4 M KPF6; the (small) double-layer corrections were applied as outlined above. The homogeneous rate ratios Were taken from the literature as indicated (note that the work terms are expected to cancel in such homogeneous rate ratios if the same supporting electrolyte is used in D20 and H20). Contributions to these rate ratios arise from differences in thermodynamic as well as intrinsic factors in H 2 0 a n d D20 [10]. In contrast to the prediction of eqn. (17), it is seen from Table 5 that (k~2/kl2)~o~H D e >~ (k12/k~2)cor~.H D h

70 TABLE 5 Comparison reactions

of solvent isotope effects for corresponding

H

Reactant pair

D

e a

(]z 12/k 12 )corr 2+

C o ( N H 3 ) ~ + - - Craq 3+ 2+ Co(NH3)6 -- Vaq

2+ C o ( N H 3 ) s O H ~ ÷ - - Vaq F eaq 3+ - - ~r e a2+ q

electrochemical and homogeneous

H

1.9

1.3 c

3.0

1.7 c

2.4 ~1.6

D

h b

(k 12/k 12 )corr

2.6 c ~2 d

a R a t i o o f r a t e c o n s t a n t s at t h e i n t e r s e c t i o n o f t h e ( c a t h o d i c a n d a n o d i c ) T a f e l p l o t s f o r t h e c o n s t i t u e n t e l e c t r o c h e m i c a l h a l f - r e a c t i o n s o b t a i n e d in H 2 0 a n d D 2 0 u s i n g a c i d i f i e d 0 . 4 M K P F 6 as s u p p o r t i n g e l e c t r o l y t e (see t e x t a n d r e f s . 4 2 a n d 4 3 ) , a f t e r c o r r e c t i o n f o r d o u b l e l a y e r e f f e c t s u s i n g e q ~ '7! ) as i n d i c a t e d in t h e t e x t . b R a t i o o f r a t e c o ~ s t a ~ : ~or l i s t e d h o m o g e n e o u s r e a c t i o n in H 2 0 t o t h a t in D 2 0 in s a m e suppo~:~g electrolyte, from literature source indicated. c R e L 9. "~ i~ef. 7.

It is expected that eqn. (17) would apply if the solvent isotope effect arises solely from changes in the inner-shell reorganization energy since this contribution should be insensitive to the surrounding environment. The unexpectedly larger electrochemical rate ratios implicate the involvement of surrounding (outer-shell) water molecules. Given that the cationic complexes in Table 5 u n d o u b t e d l y exert a substantial influence on the structure of the surrounding 2+ solvent, it would be expected that Vaq, for example, would experience a significantly different solvent environment when involved in a homogeneous electrontransfer reaction with Co(NH3)~ + compared with its environment at the merc u r y - a q u e o u s interface. This difference could account for the markedly larger value of (kx2/k12)cor~ H D e (3.0) compared with (k12/k12)corr H D h (1.7) for this reaction (Table 5) inasmuch as the surrounding solvent structure (the extent of hydrogen bonding, etc.) could be quite different in the two environments. It has been pointed out that no significant solvent isotope effect has been observed upon the rates o f homogeneous outer-sphere processes for reactants that do not contain coordinated water [2]. This finding has been used to support the contention that the o f t e n large isotope effects observed for reactions involving aquo complexes are chiefly or even entirely due to deuteration of the aquo ligands [2]. However, only two homogeneous reactions involving reactants not containing replaceable protons appear to have been studied: Co(NH3)~ ÷ + Cr(bpy)~ ÷, and Co(phen)~ ÷n÷ self-exchange [2]. The significant solvent isotope effects observed for the electrochemical kinetics of ammine and ethylenediamine complexes (Tables 3 and 4), illustrate the more general occurrence of this effect b e y o n d aquo complexes. It is interesting to note that deuteration of the ammine ligands yields sizable decreases in the rates of electrochemical and homogeneous processes involving Co(NH3)~ ÷ or Co(NH3)sOH~ ÷ in either H20 or D20. Thus Co(ND3)~+ reacts a factor of 2.3 times slower than Co(NH3)~ ÷ at a given electrode potential (Table 3) and a factor of 1.35 times slower for its homogeneous reduction b y Cr(bpy)~ ÷ [8]. However, again the relative electrochemical and homogeneous

71

isotope effects differ from expectations since equal rate decreases are predicted theoretically under these conditions [31 ]. This discrepancy between theory and experiment may again be due to an environmental solvent effect arising from the difference in the interactions b e t w e e n the NH3 and ND3 ligands and surrounding water molecules. CONCLUSIONS

Taken together, the foregoing results provide fairly convincing evidence that the deuteration of solvating water molecules can induce substantial changes in the electrochemical kinetics as well as thermodynamics of transition-metal aquo, ammine and ethylenediamine redox couples. As such, they furnish an illustration of the limitations o f the conventional dielectric-continuum model in describing the role of the surrounding solvent in the activation process leading to electron transfer, and suggest that an additional c o m p o n e n t of the activation barrier may arise from extensive changes in short-range solvent polarization associated with the formation and fission of hydrogen bonds. Since there is reason to believe that O...D hydrogen bonds in D20 are significantly (~1.0 kJ mol-1), stronger as well as more extensive than O...H bonds [44,45] in H20, larger intrinsic barriers in D20 would generally be expected for redox couples whenever the electron transfer entails an alteration in the hydrogenb o n d e d structure of the surrounding solvent. To explore this prediction further, it would be desirable to select chemically reversible redox couples which exhibit significant values of A E ~ -H and yet do not contain replaceable protons so that the secondary isotope effect upon the electrochemical kinetics would provide the sole contribution to (k~H/ksD)corr" The present approach of employing electrochemical cells where b o t h the kinetic and thermodynamic parameters in D20 and H20 can be compared at a constant Galvani potential (constant free energy of the reacting electron) provides additional experimental information b e y o n d that which is accessible to homogeneous redox systems, and illustrates the virtues of electrochemical systems in exploring the fundamental influences of the solvent upon redox processes. The utilization of this " e x t r a t h e r m o d y n a m i c " approach to unraveling solvent effects upon redox kinetics on a more general basis is the subject of a forthcoming paper [46]. ACKNOWLEDGEMENTS

Some additional experiments were performed by Ken Guyer. Drs. Marshall Newton and Roger Parsons kindly made available some unpublished results. This work is supported in part by the Air Force Office of Scientific Research (Grant No. A F O S R 77-3408) and the Office of Naval ReSearch. REFERENCES 1 J. H a l p e r n , Q u a r t . Rev., 15 ( 1 9 6 1 ) 207. 2 N. Sutin, J.K. R o w l y a n d R.W. D o d s o n , J. Phys. C h e m . , 65 ( 1 9 6 1 ) 1 2 4 8 . 3 H. T a u b e , E l e c t r o n T r a n s f e r R e a c t i o n s o f C o m p l e x Ions in S o l u t i o n , A c a d e m i c Press, New Y o r k , 1 9 7 0 , p p . 34, 37.

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