摘要:

Effect of Solvent and Temperature on Proton TransferReactions of Excited MoleculesBY H. BEENS, K. H. GRELLMANN, M. GURR AND A. H. WELLERChemisch Laboratorium der Vrije Universiteit, Amsterdam, NetherlandsLaboratorium fur physikalische Chemie der Techn. Hochschule, Stuttgart, GermanyReceived 12th February, 1965The spectral difference in fluorescence emitted from the forms (I), (11) and (III) has been usedto study proton transfer reactions of electronically excited molecules :* * *o 0(I) (10 (111)AH+B+AH.. . B-tA . . . HE3by fluorescence measurements. With intermolecular hydrogen bonds, pronounced effects ofsolvent and of temperature have been observed which indicate that in this case proton transferis strongly facilitated by an increase in polarity of the surrounding medium.In polar solventsconsiderable changes in solvent orientation are required and can become rate-determining, par-ticularly at low temperatures. With intramolecular proton transfer equilibria the solvent effect isweaker and in the opposite direction. This is attributed to compensation by intramolecular elec-tron migration of the dipole moment of form (111). An upper limit of 0.12 kcal/mole has beenobtained for the activation energy of the intramolecular proton transfer.Proton transfer in solution from an acid AH to a base B, to yield the conjugatebase A- and the conjugate acid HB+, quite generally, can be considered to occurin three steps :diffiusion reaction diffusion AH+B 4 A H . . . B --, A - . . . HB+ + A-+HB+.The rates of the first and third step, both being diffusional, depend upon the diffusioncoefficients of the species involved, and on the dielectric constant of the mediumwhen both partners are ions.The second step is the actual proton transfer reactionin which solvent molecules may participate as transferring agent and/or becauseof the reorganization of the solvation spheres involved. The investigation describedbelow was undertaken as part of a programme having the aim to elucidate themechanism of the internal proton transfer process in a number of typical cases.In the first part of this series 1 the rate of protolysis of ammonium derivatives ofpyrene (cf. table 1) in the excited state was examined in alcoholic solvents betweenroom temperature and 100°K.It was found that the reaction velocity and itstemperature coefficient depended on the nature of the solvent, but not on the strengthof the acid which varied from 102 to 106 moIe/l. This could be explained by theassumption that the rearrangement of surrounding solvent molecules, prior to theproton transfer is rate-determining, which implies proton-tunnelling between Franck-Condon states.The fluorescence method which is also applied in this study makes use of theinformation, which can be obtained from fluorescence spectra and fluorescenceintensities, about the kind and relative amount, respectively, of any particular(1) (11) (IV)181 84 PROTON TRANSFER REACTIONS OF EXCITED MOLECULESspecies occurring in the excited (fluorescent) state.The experimental methods havebeen described.1-3 With few exceptions the concentration of the fluorescing substancenever exceeded 2 x 10-4 mole/l.1.0I 30.5020 25 30v (103 cm-1)FIG. 1 .-Fluorescence spectra of ,%naphthol in various solvents : methylcyclohexane, - ;dioxane, - - . --f triethylamine, ---a ; alkaline alcohol, . . . . . . . . ; n-butylamine, ---aI I I1.0-4' 0.50175 20 2 2.5 25 2 75v (103 m-1)FIG. 2.-Fluorescence spectra of 3-hydroxypyrene in various solvents : methylcyclohexane, - ;dioxane, - - ; triethylamine, -.-a ; alkaline alcohol, . . . . . . . . ; n-butylamine,- - aThe fluorescence spectra of P-naphthol and 3-hydroxypyrene in a number ofdifferent solvents are shown in fig. 1 and 2. The absorption spectra of these com-pounds show little variation in these solvents ( < 700 cm-1 with /?-naphthol anH .BEENS, K . H . GRELLMANN, M. GURR AND A. H . WELLER 185< 500 cm-1 with 3-hydroxypyrene) except in alkaline alcohol, where the absorption(and also the fluorescence) is due to the ionized form, which can be described asthe hydrogen bond complex ArO- . . . HOR. On the other hand, in methyl-cyclohexane, the free hydroxycompound ArOH is present, so that the spectra ofTABLE l.--CHANGE OF pK ON EXCITATION (ROOM TEMP.)/3-napht hol3 -hydr oxyp yrene4-ammoniumpyrene (in ethanol)3-ammoniumpyrene-5,8,1O-trisulphonatebenzoic acid cationacetophenoncationPK PK-~"K9.5 6.78.7 5.03.5 5.52.6 9.7- 7.2 - 6.0- 6.0 - 9.0fig. 1 and 2 can be ascribed to the following excited species, with the wavelength offluorescence decreasing from left to right :* ocC2 ">; A o H*o H *o *o 0ArO .. .HN; ArO . . .HOR; ArO . . . HNR3; ArOH.. .a c2 lH4The gradual red shift in this series is a direct consequence of the gradual changeof the whole substituent,? whose ionization potential decreases in going from -OH0 Ht o - 0 . . . HN.RThis assignment, together with the negligible change in absorption, implies thatin amines as solvents the ionization of the hydroxy-compound occurs only in theexcited state. This is due to the well-known 3-5 change on excitation of acid-baseproperties of substituted aromatic compounds. In many cases the pK (pK valuein the excited state) differs substantially from the ground-state pK.An estimateof the difference, pK-pK, can be obtained on the basis of eqn. (1)***AH -AH (kcal/mole) = 2.86 x Av (cm- '), (1)which relates the reaction enthalpies of the acid-base equilibria in the ground andexcited states to the frequency shift Av of the fluorescence or long wavelength ab-sorption band in going from the conjugate base to the acid. With the assumptionthat the corresponding entropy changes are equal (AS = AS), one obtains**pK-pK = (0*625/T)Av (cm-l);some values relevant to this study are given in table 1.INTERMOLECULAR PROTON TRANSFERIn inert solvents a hydrogen-bond complex is formed between acid and base:KassAH+Br=tAH.. . B. (3)Nagakura and Baba 6 have shown that the absorption spectra of 1 : 1 hydrogen-bond complexes of phenols with suitable bases are shifted to longer wavelengthsi including base (or acid) attached to it by hydrogen bonds186 PROTON TRANSFER REACTIONS OF EXCITED MOLECULEScompared with the absorption spectra of the unbonded species.The shift Avass istypically about 500 cm-l and indicates a stronger hydrogen bond in the excited state.Thus additional complex formation according to* kiz *AH+B+AH.. . B (4)can occur in the excited state. The rate constant klz (or, rather, the relative rateconstant klzz, where z is the lifetime of the excited acid AH) can be obtained fromfluorescence measurements at different concentrations of B making use of the spectraland intensity differences of the fluorescence of complexed and uncomplexed acid.The method has been outlined 3 ~ 7 for hydrogen-bond complexes with pyridine anda-chloropyridine, where, on account of the hydrogen-bond complexes being non-fluorescent, the procedure is particularly simple.As the fluorescence behaviourof the hydrogen-bond complexes, considered here, was more complicated, as canbe seen, for example, from fig. 3 and 6, a modified method had to be applied, detailsof which will be given elsewhere.8 In any case, knowledge of Kass (the associationconstant in the ground state) as well of &I/&, the ratio of the extinction coefficientsat the excitation wavelength of AH . . . B and AH, respectively, is required, inorder to calculate the fraction*of directly excited complexes. Fluorescence measurements yield the quantity &the degree of association that eventually, during the lifetime of the excited acid,will be reached and which according to eqn.(6),also depends on the rate of hydrogen bond formation in the excited state. Eqn. (6)has been derived 3 with the assumption that dissociation of the excited hydrogen-bond complex is negligible.? Corresponding values of k12~ (cf. table 2) of P-naphtholTABLE L-DATA ON HYDROGEN-BOND FORMATION IN GROUND AND EXCITED STATESAT 22"acid base Avms (cm-1)cB (M), wherea% 0.99in methylcyclohexane (q = 0.712 cpoise)/I-naphthol triethylamine 120 700 110 0.078n-butylamine 170 680 (> 50) 0.0963-hydroxypyrene triethylamine 180 360 205 0.05 1n-butylamine 230 320 (> 100) 0.07 1(0.010) 0in toluene (q = 0.572 cpoise)fl-naphthol t riethylamine 42 670 45 0.2073-hydroxypyrene triethylamine 60 350 115 0,113in o-chlorotoluene (q = 1.02 cpoise)3-hydroxypyrene triethylamine 1 10 350 145 0.0750 estimate for 230°K.t An estimate with the aid of eqn.(2) using data of table 2 gives k217'<@0511. REENS, K . H . GRELLMANN, M . GURR AND A . H . WELLER 187and 3-hydroxypyrene, respectively, differ by about a factor of two. This is due toa similar difference in lifetime.From the data of table 2, a-values at room temperature can be obtained. Inthe last column, base concentrations have been calculated at which practically allacid molecules are present as hydrogen-bond complexes in the excited state.The change of fluorescence spectra of P-naphthol in methylcyclohexane at roomtemperature on addition of triethylamine is shown in fig.3. Up to about 0.1 h4*F i I I30.5020 25 30FIG. 3 .-Fluorescence spectra of j?-naphthol in methylcyclohexane at different concentrations of trie-thylamine 1,O.OOO M ; 2,0-002 M ; 3,0404 M ; 4,0408 M ; 5,O-020 M ; 6,0*10 and 0.1 5 M ; 7, assolvent.triethylamine the change undoubtedly is due to hydrogen-bond formation. How-ever, the broadness of the spectrum observed at and above 0.1 M triethylamine,when practically all excited naphthol molecules are complexed, indicates that thisspectrum is due to more than one emitting species only. Comparison with thefluorescence spectrum in pure triethylamine suggests the contact ion-pair (In) tobe the other component.Fluorescence quenching experiments with oxygen showthat both components are equally quenched. This indicates that the proton-transferequilibrium (eqn. (7)) :between the forms (II) and (111) is fully established within a time which is shorterthan the mean lifetime of the excited molecules.Lowering of the temperature, however, changes the fluorescence spectrum ofthe hydrogen-bond complex in favour of the ion-pair (111), as shown in fig. 4. Theintensity ratio at two sufficiently separated frequencies (22,500 cm-1 and 28,000 cm-1)can be used as a relative measure of the equilibrium constant K23. Values of188 PROTON TRANSFER REACTIONS OF EXCITED MOLECULES*log K23 obtained in this way from the spectra of fig. 4 (and from others at intermediatetemperatures) yield AH23 = -0.9 kcal/mole when plotted against T-1. Thisexothermicity is further evidence for a proton-transfer equilibrium (7) which ispractically established.Fig.4 also shows the fluorescence spectrum in toluene of the hydrogen-bondcomplex P-naphthol-triethylamine. Again, the amine concentration is high enough*1.00.5 301 I IToluene Met h y L c yc lohexa n e20 25 30v (103 cm-1)FIG. 4.-Fluorescence spectra of 8-naphthol in methylcyclohexane+ 0-14 M tritthylamine at differenttemperatures, and in toluene+ 0.20 M triethylamine.to prevent fluorescence of uncomplexed P-naphthol to be observed. The same istrue in pure triethylamine (cf. fig. 3). In both solvents, the long wavelength com-ponent due to the ion-pair (III) is much more pronounced than in methylcyclo-hexane.Relative values of the equilibrium constant K23 in these three solvents,obtained from the intensity ratio of the two components, are given in table 3.*TABLE 3.-RELATIVE EQUILIBRIUM CONSTANTS FOR INTER- AND INTRA-MOLECULAR PROTON TRANSFER M THE EXCITED STATE.(relative to toluene, for which all equilibrium constants arbitrarily were put equal to 10)solvent*K intranu nOH 0OH 0 I II II C*K23 with triethylamineconstant diel. % 20 k:Etrol f-hydroxy- ArOH = ((AoR (>'\ORpyreneOGHSmethylcyclohexane 2.02 1.4241 1.5 t l 18 12toluene 2.38 1.4968 10 10 10 10triethylamine 2.42 1.4003 7.7 7.6o-chlorotoluene 4.45 1.5255 90acetonitrile 37.4 1.3441 4.5 H. BEENS, K.H. GRELLMANN, M. GURR AND A . H. WELLER 189The fluorescence spectra in methylcyclohexane and toluene of the hydrogen-bond complex 3-hydroxypyrene-triethylamine are shown in fig. 5. The changecaused by lowering the temperature is much less significant than with /3-naphtholFIG. 5.-F1MethylcyctohexaneI 20.5020 25 30v (103 m-1)uorescence spectra of 3-hydroxypyrene in methylcyclohexane+ 0.14 M triethylaminein toluene+ 0.126 M triethylamine.and- 0.5 4n 0020 24 28v (103 cm-1)FIG. 6.-Fluorescence spectra of 3-hydroxypyrene in o-chlorotoluene at different concentrationsof triethylamine.1, 000 M ; 2, OOOO9 M; 3, 0.0036 M ; 4, 0.0113 M ; 5, 0.21 190 PROTON TRANSFER REACTIONS OF EXCITED MOLECULES*and can be interpreted as a slight sharpening of the structure. Thus, AH23 is eitheraround zero or strongly positive.The latter assumption implies that the spectrumin methylcyclohexane is solely due to the form (11). In toluene, evidently, the ion-pair (111) is favoured over form (II) and the same is true in pure triethylamine (cf.fig. 2). This effect is still more pronounced in o-chlorotoluene, as shown in fig. 6,where at triethylamine concentrations high enough for complete association in theexcited state, almost exclusively the emission due to the ion-pair is observed.Relative values of the equilibrium constants K23 in these solvents, calculated fromthe intensity ratio at 21,000 cm-1 and 25,600 cm-1, are given in table 3. Resultsvery similar to these with triethylamine have also been obtained with N-dimethyl-benzylamine.9 Whenever tertiary amine was added, the changing fluorescencespectra had at least one isosbestic point in common, the spectra in fig. 3 and 6 beingtypical examples.*17.5 22-5v (103 cm-1)27.5FIG.7.-Fluorescence spectra of 3-hydroxypyrene in methylcyclohexane+ n-butylamine at 230°K.1, 0.01 M ; 2, 0.20 MDifferent results, however, were obtained with primary amines. Since the effectcan be demonstrated more clearly at low temperatures, fluorescence spectra obtainedat 230°K are shown in fig. 7. At this temperature the viscosity of methylcyclo-hexane is 2-27 cpoise, i.e., only about three times larger than at room temperaturewhereas the association constant Kass is increased by more than a factor of 30.Thus at a concentration of 0.01 M n-butylamine practically all 3-hydroxypyrenemolecules are present in the complexed form (11).This is borne out by the fluor-escence spectrum showing a red shift of some 400 cm-1 from that in pure methyl-cyclohexaiie (cf. fig. 2). Increase of the butylamine concentration causes the gradualappearance of a new fluorescence component at longer wavelength at the expenseof the original one. The close similarity of this long wavelength emission with thaH . BEENS, K . H. GRELLMANN, M. GURR AND A . H. WELLER 191obtained in pure n-butylamine, combined with the failure of tertiary amines to bringabout this same effect, suggests an interpretation according to reaction (8) :* H k24 * @ €3 @HArOH.. . NHi-RNH,-+ArO .. . H N . . . HNH (8)R R R(11) W’>From the fluorescence spectra of fig. 7 and others at intermediate base con-centrations, k24~11=30 M-1 could be obtained, where ZII is the lifetime of the com-plexed form (11) which probably does not differ very much from that of the excitedmolecule in pure methylcyclohexane. This result is compatible with a diffusion-controlled reaction rate in methylcyclohexane at 230°K.INTRAMOLECULAR PROTON TRANSFERThe fluorescence spectra of compounds with intramolecular hydrogen bonds,like those given in fig. 8 have been explained previously 3 9 10 by the assumption ofthe protomeric isomerization equilibrium (9)Q OOH 0 0 HOI II * I IImet hy Icy clohexanen-butylchloride --toluene __ .-acetonit rileethanol _-- .... -VOH 01 M inmet h y lc yclo hexanen-butylchloride - - -toluene - -_acetonitrile __ . -OC2H5-__FIG. 8.-Fluorescence spectra of salicylic ester and 5-ethoxysalicylic ester in diserent solvents atroom temperature192 PROTON TRANSFER REACTIONS OF EXCITED MOLECULESwhich is established during the lifetime of the excited state. The intramolecularproton transfer is made possible by the mutually opposite effect of excitation on theacid-base properties of the two substituents. As indicated in table 1, the hydroxy-group becomes more acidic and the carbonyl group more basic on excitation.The fluorescence spectra shown in fig. 8 consist of two components. The shortwavelength component, whose spectral position is very similar to that of the cor-responding o-methoxy derivative, is evidently due to form (V), whereas the othercomponent can be ascribed to the form (VI).Relative values of the equilibriumconstant in various solvents or at different temperatures can be obtained from theintensity ratio of the two fluorescence components. Intensities measured at21,800 and 27,500cm-1 have beenusedfor salicylic ester and at 20,000 and 25,300 cm-1for the ethoxy derivative. Relative Kintra-values in some solvents at room temper-ature as obtained from the fluorescence spectra in fig. 8 are given in table 3 . Valuesof AHinka, obtained through van't Hoff-plots from fluorescence measurements be-tween 300 and 200°K in methylcyclohexane are :***AHintra = -0.7 kcal/mole for salicylic ester,AHintra = + 0.9 kcal/mole for 5-ethoxy-salicylic esterThus, lowering of the temperature shifts equilibrium (9) to the right-hand side forsalicylic ester and in the opposite direction with the 5-ethoxy derivative.Fluorescence measurements with salicylic ester in methylcyclohexane have beenextended 'f to still lower temperatures.It has been found that the spectra at liquid-nitrogen and at liquid-helium temperatures were identical within the precision limitsof the measurement. The almost complete absence in these spectra of the shortwavelength component is of particular interest in view of the activation energy involvedwith proton transfer across hydrogen bonds.*DISCUSSION AND CONCLUSIONS*According to the data in table 1, the pK value of 3-hydroxypyrene is about3.7 compared with 2.8 for P-naphthol. The latter pK has also been obtained frommore exact kinetic measurements.2, 3 In view of the close structural similarityof the two compounds it seems safe to assume that this, for the greatest part, isan intrinsic difference in acid strength, which also exists in solvents other than water.In other words, excited 3-hydroxypyrene may be considered in any solvent as anacid weaker than excited /I-naphthol by some (1.35(3.7 - 2-8) =) 1-2 kcal/mole.This, in fact, is borne out by the results in methylcyclohexane which show thatAH23, the enthalpy difference between ion-pair (111) and hydrogen-bond complex(11) with triethylamine, for 3-hydroxypyrene is at least 0.9 kcal/mole more positivethan for /I-naphthol.Unfortunately, owing to uncertainties in pK-pK, the pK value of 3-hydroxy-pyrene is not known accurately enough to allow mutual comparison of K23 valuesin column 4 and 5 of table 3.Comparison of K23 values is thus confined to withineach column.t The measurements have been carried out in the laboratory of Prof. Dr. H. C. Wolf, whoseco-operation is gratefully acknowledged.*** **H. BEENS, K . H. GRELLMANN, M. GURR AND A . H. WELLER 193This comparison clearly shows that the equilibrium constants for intermolecularproton transfer strongly increase with solvent polarity. This is evidently due tothe considerable increase of the dipole moment when the ion-pair is formed.The presence of hydrogen atoms, available for additional, although weak,hydrogen bonding in primary (and possibly secondary) amines seems to be a relevantfactor as shown by reaction (8).Evidently, the base-shared ion-pair (IV’) is morestable in this case than the contact ion-pair (III’),* @ @H EHArO . . . HNH . . . NHR R(m’)from which a fluorescence spectrum at shorter wavelengths, similar to that in tri-ethylamine would be expected. Actually, fluorescence spectra of this type areobtained from rigid solutions of both P-naphthol and 3-hydroxypyrene in glassyn-butylamine at temperatures below 150°K. It seems that in these rigid solutionsthe dielectric relaxation time, being longer than the lifetime of the excited state,prevents the proton from further migration.With intramolecular proton transfer equilibria a solvent effect opposite in direc-tion to that with intermolecular hydrogen bonds is observed (cf. table 3), indicatinga decrease in dipole moment when the proton is transferred. This strongly suggestsconsiderable intramolecular charge transfer in the excited state of these salicylicesters, SO that the following structures are possibly a more realistic representation :0 0OH 0 0 HO(V‘)As must be concluded from the fluorescence spectra, there is practically completeproton transfer in salicylic ester (dissolved in methylcyclohexane) even at 4~2°Kwithin lo-gsec, the lifetime of the excited state. Thus the transfer rate constantat this temperaturemust be larger than 108 sec-1. With VOH = lO14sec-1 (frequency of the OHstretching vibration) one obtains E I 0-12 kcal/moIe, a result which strongly suggestsproton-tunnelling as the actual transfer mechanism.k = vOH exp (- E/R .4*2) (10)1 Urban and Weffer, Z. Elektrochem., 1963, 67, 787.2 Weller, 2. pliysik. Chem., 1955, 3, 238.3 Weller, Progress in Reaction Kinetics, ed. Porter (Pergamon Press Ltd., London, 1961), vol. I,4 Forster, Z. Elektrochem., 1950, 54, 42, 531.5 Weller, 2. Elektrochem., 1957, 61, 956.6 Nagakura and Baba, J. Amer. Chem. SOC., 1952,74, 5693.7 Grellmann and Weller, 2. Elektrochem., 1960,64, 145.8 Grellmann, Gurr and Weller, in preparation.9 Grellmann, Diss. (Stuttgart, 1960). Gum, Diss. (Stuttgart, 1962).G187.10 Weller, Naturwiss., 1955, 42, 175 ; Z. Elektrochem., 1956, 60, 1144

ISSN:0366-9033    

DOI:10.1039/DF9653900183

出版商:RSC    

年代:1965

数据来源: RSC

摘要:

Proton Transfer during Reactions in the Excited StateBY T. S. GODFREY, G. PORTER AND P. SUPPANDept. of Chemistry, The University of SheffieldReceiced 15th April, 1965An understanding of the mechanism of a photochemical reaction may involve a knowledge ofprotolytic reactions, not only of the ground-state molecule, but also of excited states, free radicalsand other intermediates involved. In molecules, such as ketones and quinones, having hydroxyand amino substituents, protonation raises the quantum yield of reaction from near zero to nearunity and our interpretation of this observation involves a consideration of protolytic reactions inthe ground and upper singlet states and in two types of triplet state. Protolytic equilibrium is main-tained only between states of similar electron configuration.The relationship between proton,electron and hydrogen atom transfer is briefly discussed.Forster,l Weller 2 and their collaborators have shown that proton transfer ratesand the related acidity constants of many molecules in their lowest singlet excitedstates may differ widely from those in the ground state. Two experimental methodswere used for this purpose : a direct method involving study of the fluorescence yieldof the acidic and basic forms as a function of pH, and an indirect method based onthe energy levels of the excited states of the two forms. In general, good agreementwas obtained between the two methods.This phenomenon is of particular importance in the application of flash photolysistechniques to proton transfer reactions.After flash excitation, the acid-base equili-brium is shifted in the excited singlet state ; the molecule then returns to the groundstate in a time of approximately 10-8 sec and the relaxation of the ground state to theoriginal acid-base equilibrium is then studied by the usual absorption spectroscopicmethods. Proton transfer rates in the ground state can, therefore, be measureddirectly and the method is complementary to the fluorescence method which providesinformation about the first excited singlet level only. For example, when certainphenols are flashed in aqueous solution, transient absorption spectra are observed,even in the presence of oxygen, which are readily shown to be due to the correspondingphenolate anions.From the rate of disappearance of the transient in a bufferedsolution, the protonation rate constant in the ground state is determined. Forp-hydroxybenzophenone, a molecule of special interest in connection with the laterdiscussion, the rate constant of protonation of the phenolate anion is found to be6 x 1010 1. mole-1 sec-1.Other methods, such as those developed by Eigen 3 and his colleagues, are availablefor the study of protolytic reactions of stable molecules in this ground state and theparticular value of flash photolysis methods is that they allow study of protolyticchanges in unstable species such as free radicals and in metastable electronicallyexcited states.Jackson and Porter 4 measured the acidity constants of naphthols, naphthylamines,naphthoic acids, quinoline and acridine in their lowest triplet states and found thatthe acidity constants of the triplet states of these molecules were intermediate betweenthose of the lowest excited singlet and the ground states, and much nearer to the latter.Again two methods were used; first, direct observation of the absorption spectrum19T .S . GODFREY, G . PORTER AND P . SUPPAN 195of the triplet states as a function of pH and, secondly, the method of Weller, basedon energy levels derived in this case from phosphorescence spectra in rigid media.Again, agreement between the two methods was satisfactory.The acidity constants of the three states are readily understood 5 in terms of thedifferent contributions of charge transfer configurations such as the following :The energy of these charge transfer states is considerably higher than the energyof the lowest excited singlet and triplet but the degree of mixing-in of the chargetransfer configurations will have a profound effect on the proton affinity of a state.Singlet-triplet splitting of charge transfer states is small whereas that of the lowest(principally -71 - -71) singlet and triplet states is large.Hence the lowest excited singlethas more charge transfer character than the triplet, and this accounts well for theobservations (table 1).TABLE 1molecule pK (ground state) pK* (singlet) pK* (triplet)P-naphthol 9.46 2.8 8.1P-naphthylamine 4.1 -2 3.3P-naphthoic acid 4-2 10-12 4-0a-naphthoic acid 3.7 10-12 4.1acridine 5-5 10.6 5.6quinoline 5.1 - 6.0Proton transfer rates and equilibria in excited states may be of prime importancein determining the course and yield of a photochemical or radiation-chemical change.This is obvious if the chemical reaction involves the proton itself or the hydrogenatom which contains this proton, or if these play a part in a hydrogen-bonded structurewhich undergoes some change, as in the photo-denaturation of proteins for example.The state of protonation may, however, have more subtle but equally profoundindirect effects on the course of a reaction and protolytic reactions involving a seriesof different electronic states may be involved.An interesting example of this closeassociation between proton transfer rates and overall photochemical mechanism isafforded by recent investigation on the photochemistry of substituted aromaticketones.PROTON TRANSFER IN EXCITED AROMATIC KETONESThe general reaction of photo-excited carbonyl compounds in alcohol, paraffin orsimilar solvents is abstraction of a hydrogen atom from the solvent RH,* 0 >C=O + RH = >C-OH + R,to yield a ketyl radical from ketones or a semiquinone from quinones. The reactionhas been extensively investigated for aromatic ketones 6 and quinones 7 and it hasbeen shown that conversion to the triplet manifold occurs with unit efficiency andthat all subsequent changes arise from the lowest triplet level.Furthermore, it isknown that in benzoquinones and benzophenones this excited lowest level is of1z-n type and, since the transition involves a net movement of electronic charge fromthe oxygen into the n system, the oxygen is positive relative to the ground state.I196 PROTON TRANSFER I N EXCITED STATEis this new electron distribution which makes the oxygen of excited n--71 triplets anefficient abstractor of electrons or hydrogen atoms.In substituted ketones and quinones three types of electron configuration areimportant ; these are designated as n-n, -71--71 and CT (charge-transfer) states.The change in electron distribution, referred to the ground state, may be representedas follows for the specific example of p-aminobenzophenone :\ d - 6+4c=o4\C=O4\ 8- C-0n--71 7r--71 CTIn so far as reactivity is determined by an increased positive charge at the oxygenatom we might expect that the n--n state would be highly reactive, the CT stateunreactive and the -71--71 state intermediate between the two.This prediction hasbeen fully confirmed in the following way.Radiationless conversion between excited states is very rapid compared withchemical reaction and reaction therefore occurs only from the lowest excited tripletlevel; the electron configuration of this level is therefore of unique importance.For p-aminobenzophenone in alcohol the lowest level is of CT type and the quantumyield of reaction is 0.00. In paraffinic solvents the two lowest triplet levels areinverted, the lowest is now n-n, and the quantum yield of hydrogen abstractionfrom the paraffin is 20 %. Photochemical investigations of related molecules andspectroscopic data are in excellent accord with this interpretation.8When we come to study the analogous hydroxy- and methoxy-substituted benzo-phenones the situation appears to be anomalous, since p-methoxybenzophenonereacts with isopropanol with a quantum yield of unity whereas p-hydroxybenzophenoneis almost unreactive.The spectra are nearly identical and show that in both casesthe lowest triplet level is of F Z - ~ type although the charge transfer level is onlyslightly higher. It is, therefore, the OH substituted compound which is anomaloussince both would be expected to be reactive.Since the only difference between the two molecules lies in the replacement of aCH3 group by a hydrogen atom we must examine carefully the protolytic equilibriumin the hydroxy derivative.The acidity constant in the ground state for the equilibriumC==O\4c=o \4gives the value KG = 6.5. In alkaline solution there is a profound change in spec-trum resulting in an inversion of states so that the lowest triplet is now of CT typeand therefore unreactive. This explains the lack of reactivity of p-hydroxybenzo-phenone in alkaline solution but further investigation shows that the molecule is alsounreactive in acid solutions down to a pH less than 1. We must, therefore, nowconsider proton transfer processes in the excited states.Approximate values for the acidity constants in the first excited singlet and tripletstates were determined from spectroscopically measured energy levels as follows T .S. GODFREY, G . PORTER AND P . SUPPAN 197The levels used were the CT absorption bands for singlets and the phosphorescentstates for triplets. The increased charge-transfer character of the excited singletstate compared with the ground state, and the intermediate position of the tripletstate are similar to the cases studied by Jackson and Porter. The pK of the equili-brium between the lowest triplet states of acid and base suggests, however, that atpH 1 most of the ketone would be protonated and hence reactive, which is not inaccordance with the very low quantum yield which is observed under these conditions.Consider the following general scheme of reactions :productsground \k2 statewhere K is the equilibrium constant between acid and base in their triplet states,kl is the rate constant of reaction of the protonated triplet with solvent and k2 is therate constant of deactivation, by all processes, of the deprotonated triplet to the groundstate.In accordance with what has been found for aromatic ketones in general letus assume that (i) the quantum yield of formation of triplet (BH+B-) is unity and(ii) acid-base equilibrium is established in the triplet state. Then* *-- - l+- k2K (1)1Y , = quantum yield of product = kl P H I *k,[B-]*+k,[BH]*' Yp kl[H+]'An approximate estimate of the ratio kzlkl can be made as follows : for benzo-phenone itself 6 in pure isopropanol kl = 2 x 107 sec-1 so that in 50 % isopropanol+water used in the above experiments kl = lO7sec-1.The rate constant of decay oftriplet benzophenone 9 in the absence of reaction (benzene) is 105 sec-1. This leadsto a ratio of k2/kl of 10-2 and further evidence that this is the correct order ofmagnitude is provided by the fact that the measured quantum yield in isopropanol iswithin a few per cent of unity. In the absence of other information we shall assumethat the ratio is similar in the hydroxy derivative. Then from eqn. (1) we find that,at pH 1, the quantum yield of product formation equals 99.9 % (using PKtriplet = 3.0)which is to be compared with an observed value of quantum yield of 0.02 %.In order to account for this discrepancy we must re-examine our assumption thatequilibrium is established between the lowest triplet levels of acid and base.Thesestates have different electronic configurations, the lowest triplet of the acid beingn--7t type and the lowest triplet of the base being a charge-transfer state. There is noreason why conversion between electronic states should occur during the process ofproton transfer at a rate any greater than that in the fully protonated or deprotonatedmolecules. In the range of pH and pK which we are considering the establishmentof acid-base equilibria will be extremely rapid (T< 10-10 sec) but this applies onlyto the protolytic processes themselves and not to the establishment of acid-baseequilibria between species having different electronic configurations. The valuepK = 3 which we used, therefore, refers to an equilibrium which is probably notestablished in the time available.The energy of the charge-transfer triplet state of the protonated molecule cannotbe directly measured since, as usual, phosphorescence only occurs from the lowest(n--n> state. An approximate estimate can be made by assuming that the singlet-triplet splitting of charge-transfer states is the same as in the deprotonated molecul198 PROTON TRANSFER I N EXCITED STATEwhich leads to the value of pK = -4 for the acid-base equilibrium between tripletcharge-transfer states.A very low value is in accordance with the electron distributionin the state. The scheme is now that shown in fig. 1.We shall further assume that (i) the triplet is originally formed in a charge-transferstate, and (ii) acid-base equilibrium is maintained between charge-transfer states butnot between n--x and CT states so that the only route from triplet charge-transfer30,000-20,000ObPRODUCTSBid---------p K t 6 - 5FIG.1 .-Protolytic equilibria in the triplet states of p-hydroxybenzophenone. Equilibriumbetween BH (n--.IT) and B- (CT) states (pK = 3) is not established.E(cm-')ACTandn-ll- 1 Chcrnica! rmcti!n Jproduct 5S T S Tn -ACT4 - OH Qa CO 4 -O-Q&O + HtFIG. 2.-Processes following photoexcitation of p-hydroxybenzophenone.base to triplet n--71 acid involves protonation to form charge-transfer acid followed bythe radiationless conversion process with rate constant k3. The value of k3 is unknownbut a reasonable estimate for a symmetry forbidden conversion of this kind would bein the range 108- 109 sec-1.Then, as before,where K' now refers to the acid-base equilibrium between charge-transfer tripletsonly. At pH 1, taking kz = 105 sec-1 as before, this leads to a value of quantumyield of product of 1-10 % compared with the observed yield of 2 %.In this argument we made the assumption that all the triplet was originally formedin the CT state and this is readily accounted for in terms of proton transfer processesin the singlet states.The pK of the lowest excited singlet states is - 4 so that de-protonation of the acid in this state will occur in a time less than 10-10 sec beforeradiationless conversion to the triplet is possible. All the triplets will, therefore,first be formed in the unprotonated form, the lowest state of which is a CT state.The whole scheme is shown in fig. 2 from which will be seen that between excitationand reaction each molecule must undergo at least two proton transfer reactionsT .S . GODFREY, G . PORTER AND P . SUPPAN 199RELATION BETWEEN ELECTRON, PROTON AND HYDROGEN ATOM TRANSFERIn alkaline solution the overall reaction of the excited states of carbonyl compoundswith alcohols is the following :> C=6 + RCHzOH-, > k-0- + ReHOH + H+ (solvent) ; (1)whilst in acid or in hydrocarbon solution the final product is the protonated ketylor semiquinone radical. The final product depends, not on the mechanism of theprimary reduction, but on the pK of the equilibrium> C-OH = > c-0- + Hf (solvent)which, for this type of radical, is usually near 7.For duroseniiquinone, for example,direct observation in flash photolysis experiments shows that pK = 6.The interesting question now arises in connexion with reaction (1) as to the coursefollowed by the proton during the primary reaction. Two mechanisms may beconsidered :(a) primary electron transfer :> C=O + RH+ > L O - + RH++R* + H+where RH is the reactive solvent or solute and H+, in all cases, represents the solvatedproton.(b) primary hydrogen atom transfer :>C=O+RH = >&-oH+R.>LO-+H+5-It is possible to give an unequivocal answer to this question since the acidic andbasic radicals have quite distinct spectra, both of which are observed after flashphotolysis.That mechanism (b) is followed was first shown by Bridge and Porter 7for the photoreduction of duroquinone in ethanol water. Under conditions wherethe overall reaction is reaction (l), i.e., the final product is durosemiquinone radicalion, the radical initially formed is fully protonated and the deprotonation reaction (2)which follows is directly observed.At first it may seem unusual that the proton should be transferred along with theelectron to the excited quinone molecule when the equilibrium form is the deprotonatedone. However, two different protolytic equilibria are involved, first the equilibriumin the transition complex during electron transfer,and, secondly, the equilibrium between the protonated semiquinone and the solvent,> e-OH + S+ > d-0- + SH+.The former equilibrium lies, as would be expected, to the left and the latter to theright. The proton transfer to solvent is slow enough to enable the products of thefirst reaction to be observed before the second equilibrium has been established.0 + *>C-OH.. . R+>C-O-. . .HR,1 Forster, 2. Elektrochein., 1950, 54, 42, 531.2 Weller, Prog. Reactions Kinetics, 1961, 1, 189.3 Eigen, Kruse, Maass and De Maeyer, Prog. Reaction Kinetics, 1964.2,285.4 Jackson and Porter, Proc. Roy. SOC. A , 1951,260, 13.5 Godfrey and Murrell, Proc. Roy. SOC. A , 1963, 278, 71.6 Beckett and Porter, Trans. Faraday Soc., 1963, 59,2038.7 Bridge and Porter, Proc. Roy. SOC. A , 1957,244,259,276.8 Porter and Suppan, Pure Appl. Chem., 1964,9,499.9 Linschitz and Bell, J. Arner. Chem. SOC., 1963, 85, 528

ISSN:0366-9033    

DOI:10.1039/DF9653900194

出版商:RSC    

年代:1965

数据来源: RSC

摘要:

Proton Mobility in Water at High Temperatures and PressuresBY E. U. FRANCK, D. HARTMANN AND F. NENSELInstitut fur Physikalische Chemie, Technische Hochschule, Karlsruhe, GermanyReceived 15th January, 1965The electrolytic conductance of aqueous solutions of KCl, HC1 and &SO4 has been determinedbetween 45 and 220°C and up to 8000 bars. The conductivity of hydrogen ions has been derivedand the abnormal proton mobility is discussed as a function of temperature, pressure and waterdensity. The second dissociation constant of sulphuric acid is given up to 190°C for 4000 and8000 bars.The abnormal high values of the mobility of Hf and OH- ions in water havereceived extensive study. Recently, the theoretical interpretation has made con-siderable progress. Major contributions and critical reviews have been given amongothers by Gierer and Wirtz,l Conway, Bockris and Linton2 and Eigen and DeMaeyer.3 The most probable concept is that of a rapid fluctuation of the protoniccharge within HgO; complexes and structural diffusion of such complexes byformation and dissociation of hydrogen bonds.The structure diffusion determinesthe observable mobility of the positive charge in liquid water. An analogousmechanism is conceived for the migration of OH- ions. It is assumed that theobserved increase of the proton mobility with increasing temperature under satura-tion pressures 1 up to 160°C, as well as the mobility increase with rising pressure,is a consequence of an enhanced structure diffusion of the H90: complex.Electrolytic conductances of acids in water under elevated pressure have beenmeasured by several authors.4 The measurements of Zisman 5 and of Hamann andStraws6 have been extended to about 12,000 bars at temperatures between 30 and75°C. In order to discuss separately the mobility variation with temperature aswell as with pressure or density, it is desirable to have high pressure conductancedata over a wider range of temperature.For that purpose an apparatus has beenconstructed which permitted conductance measurements with dilute aqueous solu-tions of HCl and &SO4 and of various salts between 45 and 220°C up to 8000 bars.EXPERIMENTALThe main part of the apparatus is a conductance cell which is immersed in a kerosene-filled high-pressure autoclave (fig.1 a). A conventional pressure generating system isconnected with the autoclave which has a Bridgman-type unsupported area-seal with a copperpacking. The kerosene transmitted the pressure to the cell. The electrical lead from theinner electrode is extended out of the autoclave through a thick-walled tube and an in-sulated seal for connection to the conductance bridge. The autoclave is made of a Co-Cr-Ni-Fe-alloy (DEW-ATS 105). Its internal diameter and volume are 1-65cm and17 cm3. It has four deep thermocouple wells drilled into the wall at different positionsOne additional sheathed thermocouple is introduced into the autoclave with its junctionin the kerosene close to the cell.Fig. l b shows the conductance cell in detail. The container for the aqueous solutionis a bellows which has been gold-soldered to the main body of the cell.The bellows andbody are of a palladium-gold alloy (80 % Pd, 20 % Au). The body is connected to the20E . U. FRANCK, D. HARTMANN AND F . HENSEL 201autoclave and is at ground potential. Its inner surface is one of the electrodes. The secondelectrode is a platinum cylinder on a platinum wire insulated from the body by means ofa non-porous tube of very pure sintered aluminium oxide. Small changes of length ofthe platinum wire or of the insulating tube, which may be caused by temperature or pressurevariations, cannot affect the cell constant. The design of the seal using a Teflon packing isevident from fig. 16. It separates the fluid effectively from the pressure-transmitting fluid.Because of the low rigidity of the bellows the pressure differences between the solution andkerosene are negligible.The solution is introduced into the cell using a syringe beforeinserting the central electrode and closing the seal. After filling, the cell is suspended byits electrical lead in the autoclave cavity. The cell constant is about 0.3 cm-1.FIG. 1.-High pressure autoclave (a) and conductance cell (b).The conductance of the solutions was measured with an impedance bridge (WayneKerr Universal Bridge B221 and Low Impedance Adaptor Q 221) in conjunction withfrequency generator (Audio Signal Generator S 221) and tunable indicator (Rhode andSchwarz, type UBM BN 12121/2). The solutions were prepared from water with a specificconductance below 2 x 10-6 cm-1 ohm-1 at 25°C and from chemicals of guaranteed purity.Conductance data were determined at constant temperatui es while the pressure was in-creased and decreased stepwise with intervals of 1000 bars from somewhat beyond satura-tion pressure up to 8000 bals.The pressure was measured by Bourdon gauges (Dreyer,Rosenkranz and Droop, Hannover) which were repeatedly calibrated up to 3000 barsby a dead-weight gauge. At each run the frequency dependence of the conductance waschecked. Variations at frequencies greater than 10 kc/sec were always negligible. Solutionsof KCI, HC1 and H2SO4 were investigated at 45, 75, 100,130, 160, 190 and 220°C. Theinolarity of the initial solutions was always 0.01 or 0.005 (for H2SO4).Additional meas-urements with solutions of lower concentration were considered unnecessary, since only thetemperature and pressure dependence of the conductance was to be examined.RESULTSThe reproducibility of the data obtained for subsequent runs with increasingand decreasing pressure was better than 0.4 % for KCl and HCI solutions and bette202 PROTON MOBILITYthan 0.8 % for HzS04 solutions. Considering all possible sources of error theprobable inaccuracy of the specific conductances should not exceed 1 %. Thecalculated maximum error is & 1.0 % at 45"C, & 1.5 % at 130°C and 1.9 % at220°C. The new data for the specific conductance can be compared with thoseof Zisman 5 for HCl solutions at 75°C and with those of Hamann and Strauss 6I 2000 4000 6000 0000p in barof solutions at 25°C and 1 bar = 0.01.FIG.2.-Equivalent conductivity of KCl in water. Ap at pressure p , A p=l at p = 1 bar ; molarityfor KCl solutions at 45°C. In some parts of the total pressure range the new dataare lower than the previous results by 1-2 %. Preference is given to the new data,since the new cell design is probably better suited to exclude small contaminationsof the solution and to prevent minor variations of the cell constant.The specific conductance IC has been converted into equivalent conductanceA according toA(p,T) = IC(~,T)U(~,T) x 1000~-1.Instead of the specific volume of the solutions v(p,T), the specific volume of purewater has been used. c is the concentration of the solutions in equiv./l.at 25°CTABLE EQUIVALENT CONDUCTANCE h OF KCl, HCI AND H2S04 IN WATER(concentration : 0.01 equiv./l.) in cm2 ohm1 equiv.-1Tin O C 45 75 100 131 160 190 220KC1 200 295 379 484 578 670 74 5HCl 508 678 826 947 1037 1109 1160H2S04 395 435 452 465 482 490 500and 1 bar. The specific volume of water was obtained from the experimental valuesof Bridgman 7 and Kennedy.8 Some of the data had to be evaluated by extrapolationfrom the shock-wave results of Rice and Walsh.E . U . FRANCK, D. HARTMANN AND F . HENSEL 203I I II 2000 4000 6000 8000p in barFIG. 3.-Equivalent conductivity A of HCl in water, A, at pressure p, Ap=l at p = 1 bar ; molarityof solutions at 25°C and 1 bar = 0.01.p in barFIG. 4.-Equivalent conductivity A of H2S04 in water A, at pressurep, Ap-l at p = 1 bar, moIarityof solutions at 25°C and 1 bar=O.005204 PROTON MOBILITYIn fig.2, 3 and 4 the experimental results are presented as functions of pressurefor constant temperatures. The data are the ratios of the equivalent conductanceA, at pressure p over the equivalent conductance at atmospheric pressure.At all temperatures up to 220°C the conductance at saturation pressure could beused for ApSl. These ratios can be converted into absolute values of A, by multi-plication by the equivalent conductances at the saturation pressure given in table 1.DISCUSSIONCONDUCTANCE OF KCl, HCl AND H2S04The behaviour of A (KCl) as demonstrated in fig. 2 is typical for other normalsalts of strong acids and bases.1094 The decrease of the conductance is primarilythe consequence of the increase of viscosity with rising pressure.Since Walden’srule requires that A-q-1 the decrease of Ap/Ap=,l should be identical with thedecrease of ylp=l/ylp with increasing pressure. At least below 100°C, where viscositydata are available, the decrease of the conductance is less steep than that of 17-1,which suggests that the effective diameter of the hydrated ions is reduced at higherpressures. The conductance of HCl solutions behaves differently (fig. 3). Thedecrease with increasing pressure is much less pronounced than that of A (KCl),and below 130°C there is even an initial increase of A(HC1) with pressure. Thisbehaviour is ascribed to the abnormal proton mobility and will be discussed below.As is shown by fig.4, the conductance of dilute sulphuric acid is generally increasedwith rising pressure. There are considerable differences in slope, however, atdifferent temperatures. This behaviour is the result of the combined pressuredependences of viscosity of water, abnormal proton mobility and dissociation ofHSO; ions.PROTON MOBILITYIn order to demonstrate the contribution of the protons to the conductance ofthe HC1 solutions, either the “ proton conductivity ” I.(H+), or the “ excess con-ductivity ” of the protons AE(H+) can be used :A(H+) eA(HC1)- t-A(KCl),&(H+) A(HC1) - A(KC1).t- is the transport number for C1- ions in KCl solutions, which is here taken asequal to 0.5 for all temperatures and pressures. A(H+> and AE(H+) have been plottedin fig.5 . When AE(H+) is used, one assumes that there is a “ normal ” contributionto the mobility of the positive charge which is at all temperatures and pressuresequal to the mobility of the potassium ion. Although this assumption is certainlyquestionable, I&€+) will be discussed in accordance with previous usage.1It appears reasonable to look at AE(H+) not as a function of pressure but as afunction of the density of water, p . Thus AE(H+) =f(p,T) is plotted in fig. 6, andtwo conclusions are drawn.THE DENSITY DEPENDENCE OF AE(H+) is positive in whole temperaturerange. The increase with density is almost linear and not too different at all tem-peratures. With increasing density the number of water molecules in the immediatevicinity of the H90 ;t -complexes increases, which should facilitate the structuraldiffusion of these complexes.At lower temperatures, high pressures may dis-integrate water clusters producing unbonded molecules which could be the reasonfor slightly higher values of d&/dp at lower temperatures, as derived from theslopes of the isotherms of fig. 6E. U. FRANCK, D . HARTMANN AND F . HENSEL800700600500300 2000 4OOO 6000I 1'0° ZOm 4OW 6000 8000p in barFIG. 5.-" Proton conductivity ", A(H+) = A(HC1) - r-A(KCl), and " excess conductivity " ofprotons, AE(H+) = A(HC1)- A(KC1) as a function of pressure and temperature.p in g/cm3 Tin "CFIG. 6.-" Excess conductivity ", AE(H+), of protons as a function of water density p and of tem-perature ; - - - coexistence line of liquid and vapour.THE TEMPERATURE DEPENDENCE of &(H+) is very similar for all densitiesinvestigated. It is positive and very pronounced from 45 to 130°C.The temper-ature dependence is almost zero between 130 and 220°C. There may be a flatmaximum of AE(H+) at the highest temperatures206 PROTON MOBILITYFrom the slope of the AE against T curves between 45 and 130°C, " activationenergies " between 1300 and 1800 cal/mole can be formally derived at the differentconstant densities. This increase of AE with temperature at constant densities maybe due to the disintegration of water clusters and also due to an accelerated additionof unbonded water molecules to the HgOi-complexes.A decision may be possibleif recent infra-red determinations of the percentage of unbonded molecules in purewater can be extended to higher pressures.ll.12 The flat maxima of AE beyond150°C may be caused by dissociation of the weakly bonded water molecules in thehydration sphere of the H90i complexes. It is improbable that these complexesthemselves begin to decompose at such temperatures. Previous conductancemeasurements seem to indicate that no observable contributions of AE(H+) remainat 600°C and water densities below 0.7 g/cm3.13DISSOCIATION OF HSO,The second dissociation constant K2 of sulphuric acid has been derived. Thedetails are discussed elsewhere.14 Additional measurements of A(K2S04) wereused for this purpose,14 together with several assumptions : (i) the conductivity ofthe hydrogen ion can be taken from the investigations discussed above; (ii) theactivity coefficients fH+, f&o; and fs0:- can be derived from the Debye-Hiickeltheory; (iii) the relation A(HS0,) = 0.65 A(SOi-) is sufficiently valid in the wholeregion of temperatures and pressures.15TABLE 2.-sECOND DISSOCIATION CONSTANT K2 OF SULPHURIC ACIDin mole 1.-1 x 103pressure, bar 45°C 100°C 160°C 190°C4000 55.93 10.19 1-97 0.728000 7 9 14 47-59 10.36 4-*701 6-840 0.821 0.161 0.086Using the degree a of dissociation of the HSO, ion, and the molarity rn of thesulphuric acid solution, the constant K2 in mole 1.-1 for the reaction HSO;+H++SOi- follows fromThe &-values obtained for saturation pressure agree within about 15 % with thedata derived from the silver sulphate solubility results of Lietzke, Stoughton andYoung.161 Gierer and Wirtz, Ann.Physik, 1949, 6, 258.2 Conway, Bockris and Linton, J. Chem. Physics, 1956,24, 834.3 Eigen and De Maeyer, Proc. Roy. SOC. A , 1958,247,505.4 Hamann, Physico-Chemical Efects of Pressure (Butterworths Sci. Publ., London, 1957).5 Zisman, Physic. Rev., 1932, 39, 151.6 Hamann and Straws, Trans. Faraday SOC., 1955,51, 1684.7 Bridgman, The Physics of High Pressure (G. Bell and Sons, London, 1952).8 Kennedy, Amer. J. Sci., 1950, 248, 540 ; 1954, 252, 225.9 Rice and Walsh, J. Chem. Physics, 1957, 26, 815.10 Franck and Hensel, 2. Naturforsch., 1964, 19a, 127.11 Nemethy and Scheraga, J. Chem. Physics, 1962, 36, 3382.12 Luck, Ber. der BEnsengeseIlschaft 1965, in press.13 Franck, Z. physik. Chem., 1956, 8, 192.14 Hartmann, Diplomarbeit (Karlsruhe, 1964), to be published in Ber der BiinsengeselZschafi 1964.15 Shtrill and Noyes, J. Amer. Chem. SOC., 1926, 48, 1861.16 Lietzke, Stoughton and Young, J. Physic. Chem., 1961, 65, 2247

ISSN:0366-9033    

DOI:10.1039/DF9653900200

出版商:RSC    

年代:1965

数据来源: RSC

摘要:

Proton Migration in Aqueous SolutionBY G . J. HILLS, P. J. OVENDEN AND D. R. WHITEHOUSEChemistry Dept., The University, SouthamptonReceiued 25th January, 1965Consideration is given to the temperature and pressure coefficients of ionic translation andproton migration. Both processes may be regarded as controlled by a single activated step, involvingthe rotation of water molecules, and the activation parameters are defined and discussed. Dataare presented for the pressure and temperature dependence of the equivalent conductance of HCI,the corresponding transference numbers and for the single-ion conductances. These support theproposals that proton migration occurs principally by charge-transfer to and reorientation of freewater molecules, and that the rate-determining step is the reorientation of a water molecule sothat it can receive a proton from an adjacent hydronium ion.This paper is concerned with the study and interpretation of the high mobilityof the hydrogen ion in aqueous solution.Particular emphasis is laid upon thetemperature- and pressure-derivatives of the mobility, which circumscribe themodel to a greater extent than do the absolute values at arbitrary temperaturesand pressures.It has been evident from the earliest considerations of the problem that somespecial mechanism obtains whereby the transfer of protonic charge can occur ina manner which is a consequence of the peculiar properties of water. The explanationcannot be found in the small size of the proton, especially since the mobilities ofthe alkali metal ions show that small size is generally an impediment, because ofelectrostatic effects leading to primary solvation and dielectric drag.1There is little doubt that the high mobility stems from the ability of the protonto interact with one of the lone pairs of electrons of a water molecule to form thehydronium ion H3O+ in which the single proton loses its identity.At the sametime a proton can transfer from the hydronium ion to an adjacent water moleculewhich is favourably oriented. The exchange takes place within a hydrogen bondand the actual distance an individual proton moves is quite small although thecentre of charge moves through an 0-0 distance.Since the formation of hydrogen bonds plays an important role in these processesthe structure of the water itself is particularly relevant to the problem. The struc-tural features of water have been a subject of controversy and the effort to describethese and to relate them to the known properties of water has lately intensified.The available concepts and terminology of the solid state invariably lead to exaggera-tion of the solid-like features of water and the " flickering cluster " notion of Frankand Wen2 is as far as we need to commit ourselves for the present purpose.Theidea of co-operative hydrogen bond formation leads to the possibility of a chainof proton transfers taking place ; whether these contribute significantly to the highmobility will be further considered in the final section of this paper.Having outlined the likely processes involved it is now necessary to considerwhich of them is rate determining.Two important steps in the elucidation of thisproblem are contained in the papers of Conway, Bockris and Linton 3 and thoseof Eigen and his co-workers.420208 PROTON MIGRATIONConway, Bockris and Linton by using a simple electrostatic model for waterconcluded that the rate-determining step is the re-orientation of the water moleculesin the field of the hydronium ion. The conclusion reached by Eigen and his co-workers is essentially simiIar although they considered that the rate-determiningstep is likely to be the rotation of a water molecule on the periphery of the H90,+complex, the existence of which was proposed in an earlier paper.5 Any aggregatesof water molecules which are present would be a hindrance to the rotations postulated,and it should therefore be possible to test these proposals by observing the dependenceof the hydrogen ion mobility on factors, such as temperature and pressure, whichalter the degree of structure.The fast few years have seen a considerably increased interest in temperatureand, especially, pressure coefficients of translational processes.The formal analysisof the results for normal ionic migration, in which charge transfer is accompaniedby mass-transfer, has been considered in terms of the isochoric temperature derivativeof the limiting equivalent conductance,E , = RT2(d In A"/dT), (1)and the isothermal pressure derivative, RT(d In Ao/8P)~.In terms of rate-processtheory, Ev is an internal energy of activation and is an average quantity related tothe corresponding individual ionic temperature derivatives by the equation 6E V = tYET,+ + tZEV,-, (2)where t; and t: are the corresponding transference numbers, also at infinite dilution.The temperature and pressure derivatives of the individual ionic conductances havebeen interpreted in terms of the theory of absolute reaction rates in which ionicmigration is visualized as biased Brownian motion and is described by the relationzieO F AG: ;zp = - L~ exp --6h RT (3)AG; is the standard molar free energy of activation and L is the length of an activ-ated jump. Ev,~ was thus identified with AUZ,i, the standard internal energy ofactivation of the ith species and the pressure coefficient related to the volume ofactivation, A V:, i.e.,where p is the coefficient of isothermal compressibility.It follows that Ep, the" normal " isobaric enthalpy of activation is given bywhere cc is the coefficient of cubical expansion.These re-statements of the temperature and pressure coefficients of ionic con-ductance depend on the validity of eqn. (3) only in so far as the model supposes acharacteristic jump distance. The derivatives of this quantity appear as minorterms in (4) and (5) and AV: and AH;,f will be slightly different for other models.Although the internal energy of activation has appeared from other studies ofionic migration to be a characteristic property of each solvent system, it is as wellto realize that isochoric coefficients are not as simple in their significance as iG .J . HILLS, P. J. OVENDBN AND D. R. WHITEHOUSE 209For example, Williams 7 has drawn attention to the fact that sometimes supposed.constant total volume invariably refers to the unactivated state. Allowingprocess of activation A-+A*, to proceed in two successive stages,AV* ( q f )v *A(T,V)-4A~~,V*)--fA*(~,v*),it is evident that the enthalpy of activation is given byV*AH$ = (AU& + (aTIP) dV, V Jor, if a and P are equated to those of the solvent, byAH: z(AU,f),+ +(aT/fl)AV*.However, equally well, one could carry out the process in the reverse order,(ACT of )V AV*A( T , V ) - - + A ~ , V ) - + A ( T . V *),wherebyV*AH; = (AU:),+S (aT/fl) dV~ ( A u , ~ ) , + ( c x T / ~ ) A v * .VWhether (AU& and (AU:)v* are significantly different, it is not yet possible tosay.They depend for their evaluation on the values attributed to aT/P whichlocally may vary considerably from the bulk value. Clearly the experimental quan-tity Ev is some average of the two and in what follows no distinction will be madebetween Ev, (AU$)v and (AU*)v*.The justification for this assumption may be found in the constant, temperature-independent values of Ev which characterizes conductance in non-aqueous solutions butwhich is only usefully related to the corresponding values for the individual ions whenEv + =Ev,- (eqn. (2)). In these systems, the isochoric quantities are solely a functionof solution density and constant volume is probably the most useful restriction.However, with aqueous solutions, radically different behaviour is observed.Atroom temperature and pressure, the effect of increasing the temperature or pressureis to increase the fluidity of the solvent and therefore to break down intermolecularbonding, clusters or whatever structures are postulated. This leads to negativevolumes of activation, whereas for other solvents at all temperatures and pressuresAY* is positive. Moreover, since the structural features of the solvent are likelyto vary with temperature even at constant volume, then Ev is no longer temperature-independent and increases as the density of the system decreases which is also oppositeto all other systems.This long but still cursory discussion of the temperature and pressure coefficientsof ionic mobilities is given because in this respect also the hydrogen ion is anomalous.We may anticipate the results by noting that the transference number of the hydrogenion is both temperature- and pressure-dependent and therefore, as eqn.(2) shows,Ev is not readily related to the values for the individual ions unless Ev, +z Ev, -which is unlikely when the hydrogen ion is involved. Unfortunately, conductancesare both more easily and more accurately measured than are transference numbers,especially at high temperatures and pressures, and we shall be forced to rely on thewide body of conductance data as well as the small range of transference numbers210 PROTON MIGRATIONPRESSURE TRANSMITO SOLUTIONBY MERCURYFIG.1.10 cm I I I I5 0 0 lo00 1500 2(pressure, P (atm)FIG. 3.30FIG. 1 .-Pressurized concentration cell.FIG. 3.-Isothermal pressure dependence of the limiting transference number of the hydrogen ionTHIS W O R K 0 $WALL*GILL II , , I I , ,0 . 0 2 0.04 0 . 0 6 0.00 0'10 0-0.820; ' ' ' 'concentration, m (mole kg-1)2FIG. 2.-Isobaric concentration-dependence of the transference number of the hydrogen ion at25°CG . J. HILLS, P . J . OVENDEN AND D . R. WHITEHOUSE 21 1EXPERIMENTAL AND RESULTSThe determination of equivalent conductance and of transference numbers as a functionof temperature presents no new problems, except that the stability of the systems and theprecision of the measurements decrease with rising temperature.Their determination asa function of pressure is more difficult, although the techniques of measuring conductanceover a wide range of pressures are well established and are described elsewhere2 It isthe transference numbers which present the greatest difficulty. The moving boundarymethod has been successfully adapted to high pressures and a limited range of values foraqueous solutions at 25°C has been reported by Wall and Gill.10 We have preferred thee.m.f. method because it is a continuous procedure and, with reproducible electrodes, anaccurate one.Pt, HI, I H2, PtHCl (ml) [ HCl (m2)AgIAgC1 I AgIAgC1Measurements have been made on the multi-compartment cellat 25 and 45°C over a range of pressures from 1 to 2000atm.An example of the typeof apparatus used is shown in fig. 1. The full details of the experimental techniques andof the evaluation of fH+ from the e.m.f. data will be given elsewhere and only the h a l resultsare given here, in fig. 2 and 3. They are seen to be in good accord with those of Wall andGill at 25°C.lG+ was evaluated using the conductance for HC1 determined by Wall and Gill 12 andby Ellis.13 There is an assortment of conductance data for aqueous HC1 at various tem-peratures and pressures; 12-17 the concordance is not good but the general trend is notin dispute. The pressure dependence of A;+ at 25 and 45"C, as shown in fig. 4 and 5,displays the essential characteristics of the results.DISCUSSIONThe qualitative features of proton migration may be summarized as follows-(i) The conductance of the hydrogen ion increases with increasing temperature andincreasing pressure.(ii) The pressure dependence is even more marked than withother univalent cations, i.e., AVG+ is more negative than AVZ+ (cf. fig. 6). (iii) Theinternal energy AU: of activation is lower and less density-dependent than corres-ponding values for other univalent cations (cf. fig. 7).The broad conclusion to be drawn from this is that proton migration in aqueoussolution bears many similarities to that for other ions and is similarly related, forexample, to the peculiar variation with temperature and pressure of the fluidity ofwater.Since the excess mobility of the proton increases monotonicly with temperature,it is clear that the presence of " flickering clusters " is not essential to the high mobilityof the proton since it is unlikely that such structures persist in water at the highertemperatures.Chains of proton transfers no doubt do occur, particularly at thelower temperatures, but they do not appear to contribute significantly to the highmobility. In fact, the reverse is probably true because the same interactions whichresult in cluster formation will also hinder the rotation of water molecules. Theexperimental evidence given here brings us close to the various models proposedby Conway, Bockris and Linton,3 by Eigen and his co-workers,4 and later by Horneand Axelrod; 16 i.e., one in which the rate-determining step is the reorientationof a water molecule in the path and in the field of a proton.The need to free a water molecule so that it can reorient may require the breakingof one or more hydrogen bonds with the surrounding water structure.If Frankand Wen's notion of co-operative hydrogen bond formation and disruption isaccepted, it is reasonable to suppose that, under conditions in which the propose212 PROTON MIGRATIONA-3 3451 I I 1 .* 5 0 0 1000 1500 20004pressure, P (atm)FIG. 4.-Variation of limiting hydrogen ion conductance with pressure at 25°C.00pressure, P (atm)FIG. 5.-Variation of limiting hydrogen ion conductance with pressure at 45'CG . J . HILLS, P. J . OVENDEN AND D . R. WHITEHOUSE 2130.92 8-94 0.96 0.98 1*00relative solvent volume, ui5FIG.6.-Activation volume of conductance process., y3s0, 60Q$./KCl + - +tic1 - 1 I I I92 0-94 0*96 6.98 1.30relative solvent volume, uisFIG. 7.-Activation energy of conductance process at constant volume214 PROTON MIGRATIONclusters are present, the process of re-orientation of a water molecule will result inthe local collapse of the water structure to a more close-packed variety. This willpressure, p (atm x 10-2)FIG. 8.-Relative conductance of hydrogenand potassium chloride (0.01 M).lead to a negative volume of activation whichwill become less negative as the temperatureand pressure are increased and the degree ofstructure is reduced. Both of these trendsare clearly seen in the data (cf. fig. 8).The smaller values for AV* for othercations is also in accord with this hypothesis.The common value of AV*, Ev, etc., forionic translation in a particular solventrequires a common rate-determining step,namely, the rearrangement of the solventcage in the path of the ion.The electrostaticfield of the ion is, however, not localized butdestructive of hydrogen bonded order. Theorder and hence the “ volume ” of the initialstate will be less than the bulk value. Bysimilar argument, it is evident that the internalenergy of activation for ionic translation willbe greater than that for proton migration,since the centro-symmetric electric field willretard reorientation of neighbouring watermolecules. Ionic size will clearly be a factordetermining the intensity of the field and thenumber of water molecules involved in thecage.Eqn.(3) on which AV* and AU* arebased is not strictly applicable to protonmigration which occurs by a different processto that assumed in the derivation of theequation. However, a derivation based on anequally simple model for proton migration isunlikely to alter the main features of theequation and will probably result only in a small modification of the pre-exponentialterm. Certainly AU* will be unchanged and only the minor terms in the calculationof A V 4 will be affected, so that the main conclusions already drawn will still be valid.CONCLUSIONSThe anomalous pressure dependence of the fluidity of water is explicable interms of the variation of the degree of directed order.The effects of this orderingis observed even at high pressures (in excess of 2500 atm) but they rapidly disappearwith increasing temperature. Ionic translation is accompanied by a decrease inthis particular form of order. It is sensitive to increase in solvent disorder and ismore pressure-accelerated than is the fluidity itself.Proton-migration is even more sensitive to pressure and is therefore even moredependent on the free rotation of water molecules. This it may accelerate and thisit certainly uses, in a sequence of rotations, couplings and charge transfers, toaugment the processes of normal migration by mass transfer. The idea of a transitoryGrotthuss chain may be retained but such a mechanism functions in spite of thehydrogen-bonded intramolecular structure of water rather than because of itG . J . HILLS, P . J . OVENDEN AND D . R . WHITEHOUSE 215The authors acknowledge the continuing interest of the Central ElectricityGenerating Board in electrochemistry at high temperatures and pressures and fortheir support of this particular research.1 FUOSS, Proc. Nat. Acad. Sci., 1959,45,807. Boyd, J. Chem. Physics, 1961,35, 1281.2 Frank and Wen, Disc. Faraday SOC., 1957,24, 133.3 Conway, Bockris and Linton, J. Chem. Physics, 1956, 24, 834.4 Eigen and Maeyer, Proc. Roy. SOC. A, 1958,247, 505.5 Wicke, Eigen and Ackerman, 2. physik. Chem. 1954,1,340.6 Howard, B., Thesis (London, 1963).7 Williams, Trans. Faraaky SOC., 1964,60, 1548.8 Brummer and Hills, Trans. Faraday SOC., 1961 57, 1823.9 Ovenden, P. J., Thesis (Southampton, 1965).10 Wall and Gill, J. Physic. Chem., 1955,59,278.11 Whitehouse, D. R., Thesis (London, 1965).12 Wall and Gill, J. Physic. Chem., 1954,58, 740.13 Ellis, J. Chem. SOC., 1959, 3689.14 Hensel and Franck, Z. Naturforsch., 1964, 19a, 127.15 Zisman, Physic. Reu., 1932, 39, 151.16 Hamann, Physico-Chemical Efects of Pressure (Butterworths, London, 1957).17 Horne, Myers and Frysinger, J. Chem. Physics, 1963, 39, 2666.18 Horne and Axelrod, J. Chem. Physics, 1964, 6, 1518.ZwanzigJ. Chem. Physics, 1963, 38, 1603, 1605

ISSN:0366-9033    

DOI:10.1039/DF9653900207

出版商:RSC    

年代:1965

数据来源: RSC

摘要:

GENERAL DISCUSSIONProf. M. C. R. Symons (University ofLeicester) said: In addition to the use offlash photolysis for the study of protolytic reactions of unstable species as discussedby Godfrey, Porter and Suppan, useful information can often be obtained fromline-widths in electron spin resonance spectra. The situation is comparable withthat discussed extensively in this meeting for n.m.r. but the time scale is ratherdifferent. Although there are many known examples representing the two extremesof slow transfer (radicals Re- and eRH detectable simultaneously) and rapid transfer(one averaged spectrum for Re- and -RH), we know of no explicit study in whichactual rate data for proton transfer have been derived from line-broadening.We have found that in such solvents as methanol, low concentrations of duro-semiquinone and its conjugate acid exchange protons, either directly or via solventmolecules, at a rate which is sufficiently slow that both radicals give rise to spectrahaving very narrow lines, hyperfine splitting from the acid proton being well resolved.1Radicals R@H, formed by extraction of a-hydrogen from monohydric alcohols,give rise to spectra which generally show no hydroxyl proton hyperfine splitting,the radical cH2QH which gives rise to a splitting of 0.9 being exceptional. Absenceof splitting is probably due to exchange since these radicals are expected to havevery similar electron distributors.Similarly, radicals R&O, which give rise tocharacteristic spectra show no a-proton hyperfine coupling when R = H.Thishas been ascribed to a rapid exchange with solvent protons.2 Few of these situationshave been studied from the view-point of proton-transfer : they might well constitutea useful approach to the problem.Prof. B. E. Conway (Ottawa) said: Prof. Hills remarked that his observationsof a negative volume of activation in the electrochemical proton discharge reactioncould only reasonably be interpreted in terms of the formation of free H atomsas transient species. This raises the difficulty, discussed by Butler,3 that a highenergy of activation for the process would then be expected if the final state (theH atom) of the discharge step were not chemisorbed. An alternative possibilitymay be suggested. In water, the H30f ion has relatively an unexpectedly largepartial g ionic volume 4 probably owing to the ordered, hydrogen-bonded W90,+structure which will characterize the equilibrium double-layer capacitance at theelectrode in acid solutions.However, in the kinetic process of discharge, the protonwill tend statistically to be displaced out of the €190; equilibrium configurationand reside more at a particular water molecule nearer the electrode; this displace-ment may be associated with a negative volume change, which would be seen asan apparent contribution to the volume of activation as measured by the effect ofhigh pressures on the kinetics at constant electrode potential.Prof. R. M. Noyes (University of Oregon) said: As the data of Franck et 01.show, the conductance of KCl solutions invariably decreases as the pressure isincreased, but the authors point out that the percentage change in conductance isless than in reciprocal viscosity.To the extent that Walden’s rule is obeyed, thisobservation does imply a changing diameter of the hydrated ions with changing1 T. E. Gough, unpublished result ; cf. Bridge and Porter, Proc. Roy. SOC. A, 1957,244,259,276.2 Baird-Thomas, J. Chem. Physics, 1961, 35, 1504.3 Butler, Proc. Roy. SOC. A, 1936, 157, 423, and Horiuti and Polanyi, Acta physicochim., 1935,4 Noyes, J. Amer. Chem. SOC., 1964, 86, 971.8, 505.21GENERAL DISCUSSION 217pressure. However, Hammond and Stokes 1 reported that diffusion coefficientsof a number of neutral molecules changed less than the viscosity when the samemolecule was examined in different solvents.Similarly, Rosman and Noyes 2found that the rate of the diffusion-controlled recombination of iodine atoms variedless than the viscosity when solvent was changed. In view of this evidence thatdiffusion coefficients are generally less sensitive than viscosities to changing solventconditions, it seems risky to interpret these conductance data as reflecting anysignificant change with pressure in the nature of the migrating species.Prof. M. Eigen (Gottingen) said: The model of structural diffusion as the rate-limiting step of proton migration in aqueous media is strongly supported by thefinding that in ice the mobility is appreciably higher than in water. Also the largeisotope effect in ice suggests that here the proton jump is the rate-limiting step.Thus, we may conclude that the proton transfer in the H-bond is faster than theorientation of H20 molecules necessary for the formation of new H-bonds.One would expect that the proton stays close to the centre of hydration becauseof the orientation of the negative ends of the water dipoles towards the centre.Asthe number of H20 molecules in the hydration complex (at high temperatures)is reduced, so also is the multiplicity of H-bond connections at the periphery ofthe complex. Thus the initial increase of mobility due to liberation of water mole-cules from water structure (as found by pressure and temperature increase) willnot only level off but also be slightly inverted as the hydration complex finally de-composes.Dr. K.E. Johnson (Sir John Cass College, London) said: With reference to thepapers of Franck et al. and Hills et al., there is another property of the proton whichdoes not distinguish it markedly from several other ions. If one compares thestandard potentials of ions in water at 25°C 3 with their standard potentials in anon-hydrogen-bonded solvent, viz., fused LiCl+ KC1 eutectic at 450°C,4 then atotal of 27 couples divides conveniently into four groups: (a) where the oxidantis relatively more stable in water : Al3+/Al, Cu2+/Cu+, Cr3+/Cr2+, Mgz+/Mg, Li+/Liand V2+/V ; (b) where the oxidant is relatively more stable in the chloride melt :Ag+/Ag and Cu+/Cu ; (c) where solvent differences are significant but not great :In3+/Tn, V3+/V2+, Ni2+/Ni, Pt2+/Pt and Tl+/T1 ; ( d ) where solvent differences arenot manifest : K+/K, Mn2+/Mn, Fe3+/Fe2+, Co2+/Co, Fe2+/Fe, Zn2+/Zn, CrZ+/Cr,Cd2+/Cd, Sn2f/Sn, Pb2+/Pb, 12/1-, Br2/Br-, C12/Cl-, and H+/H2.Typical standardpotential values in H20 and LiCl +KCl respectively are : for Li+/Li, -2.27 and- 1.74 V ; for H+/H, 0.76 and 0.87 V taking ZnZ+/Zn as reference at 0 V in eachsolvent.The absence of the proton from group (a) which includes the most stronglyhydrated ions confirms that its bonding to water differs from that of other cationswhile its presence in group ( d ) suggests comparable values of the solution energyof the proton in the two liquids. Might a comparison of translational propertiesof ions between two such solvents not also be fruitful?Dr.G. Kohnstam (University of Durham) said : HilIs prefers to discuss his resultsin terms of the isochoric temperature coefficients but there is no a priori reasonfor believing that for chemical reactions these parameters are simpler to interpretthan the isobaric coefficients; this has been pointed out by Whalley and his co-1 Hammond and Stokes, Trans. Furuday SOC., 1955, 51, 1641.2 Rosman and Noyes, J. Amer. Chem. Soc., 1958, 80,2410.3 recommended values of I.U.P.A.C.Laitinen and Liu, J. Amer. Chem. SOC., 1958, 80, 1015. Laitinen and Pankey, J. Amer. Chem.SOC., 1959, 81, 1053. Laitinen and Plambeck, J. Amer. Chern. Soc., 1965, 87, 1202218 GENERAL DISCUSSIONworkers.1 Although it has been shown that for ion migration Ep is temperature-dependent while Ev is not,2 this need not necessarily apply to all chemical processessince factors other than the variations of the solvent structure and density maycontribute to the temperature coefficient of Ep.3 The interpretation of reactionsin solution will be greatly aided when Ep and Ev for the same process can be com-pared at a number of different temperatures, but such a comparison requires aknowledge of the compressibility and the coefficient of thermal expansion (and oftheir derivatives) at the appropriate temperatures and pressures.Unfortunately,all the necessary information is not yet available.Dr. Henryk Eisenberg ( Weizmann Institute of Science, Rehovot) said : Prof.Hills and Franck have emphasized in their contributions the significance of protonmobility measurements, at high temperatures and pressures and at constant volume,in relation to the structure of water.We find that an equationf ( n ) = ApB exp (- Ct),closely describes the refractive index n of water over a wide range of pressures andtemperatures ; f(n) is the Lorenz-Lorentz function (n2- l)/(n2+2), p is the density,and A , B and C are constants. By differentiation of eqn. (1) one obtains(a 111 flap), = PB,- (a In f/aT), = aB + C,and-(a In f/aT), = C , (4)where a = -(a Inp/aT)p is the cubical expansion coefficient and /3 = (d lnp/dP)Tthe isothermal compressibility.Eqn. (l), with A = 0.2062523, B = 0.88823 and C = 5.8303 x for thesodium D line, describes the experimental results relative to air of Tilton andTaylor4 to within a few digits in the seventh decimal place, in the temperaturerange 0-60°C.The differential coefficient (an/aP)T at low pressures has been measuredby Roentgen and Zehnder 5 from 0-23°C; an analysis of their data shows that Bis indeed constant and in close agreement with the value obtained from the workof Tilton and Taylor. Eqn. (3) shows, as first observed by Jamin,6 that (an/aT)p#Ofor water at 4"C, where a = 0 ; the temperature (0.12"C) at which (dn/aT)p vanishesis obtained by setting the 1.h.s. of eqn. (3) equal to zero and evaluating the tem-perature for which a = -C/B.For most liquids (an/aT)v, and therefore C, are equal to zero and n is a functionof density only. On the other hand, C for water does not vanish with moderate in-crease in temperature and pressure. An analysis of recent data of Waxler, Weirand Schamp,7 who measured the refractive index of water from 1.6 to 54.3"C andatmospheric pressure to 1100 bars, shows that (a lnf/dT)v and therefore C (eqn.(4))is constant over this whole range. The data of Franck, Hartmann and Hensel(this Discussion, fig. 6) show that the temperature coefficients (iX/aT)v of theproton mobility are constant up to close to 100°C at densities p up to 1.15 g/cm3,and diminish rapidly at higher temperatures. It thus appears reasonable to assume1 Baliga, Withey, Poulton and Whalley, Trans. Faraday Soc., 1965, 61, 517.2 Brummer and Hills, Trans. Faraday Soc., 1961, 57, 1823.3 Caldin and Kasparian, this Discussion.Hulett, Quart. Reu., 1964, 18, 227. Kohnstarn,4 Tilton and Taylor, J. Res. Nat. Bur. Stand., 1938, 20, 419.5 Roentgen and Zehnder, Ann. Physik Chem., 1891, 44, 24.sJamin, Compt. rend., 1856, 43, 1193.7 Waxler, Weir and Schamp, J. Res. Nat. Bur. Stand., A , 1964, 68, 489.The Transition State (Chem. SOC. Special Publ.), 1962, 16, 179GENERAL DISCUSSION 219that a similar behaviour may be observed in refractive index (or dielectric) measure-ments of water at very high pressures and temperatures; valuable information onthe structure of water may thus be obtained in the region in which C is expected tovanish, and the transition to a “ structureless ” liquid occurs.Prof. E. C. Baughan (Shivenham) said: I would make three points on abnormalmobility : (a) On Wynne-Jones’ comments, abnormal proton mobility requiresfavourable rates and equilibria for proton transfer from a molecule A to a moleculeB. A and B may be identical (OH: mobility in H20) or they may differ.Theirdifference may prevent abnormal mobility even where structure seems favourable ;thus NH,f is not abnormally mobile in H20 ; in methanol CH30Hi is abnormallymobile but OH; is not. Such effects are to be expected in mixed solvents. (b) Hills,Overton and Whitmore’s view 1 is that the rate-determining step for OH; in wateris the rotation of a soluent molecule. This might explain why the mobilities ofH3SO,f and HSO; are so nearly the same in anhydrous HzS04 although both areenormously faster than other ions.( c ) Hydrogen-bonding is not a necessary con-dition for abnormal mobility; thus, Cl- is abnormally mobile in anhydrous SbC13and AsC13.2Prof. B. E. Conway (Ottawa) said: With regard to Hills’ paper, it would beuseful to have available information on the effect of pressure on the dielectric re-laxation time z of water at various temperatures. If local rotation of elements ofthe water structure is involved as the rate-determining step in proton conductance,3there should be a close relation between the pressure effects on z and on the excessor anomalous conductance.Prof. Hills remarked that it will be the free or non-bonded water moleculesrather than those in structured groups that will participate predominantly in therotation-controlled proton conductance.While this view follows the concepts ofwater structure discussed by Frank4 and by NemCthy and Scheraga,s I wonderif water molecules in the condensed structure can ever be regarded as at all free inthe sense of being steam-like. The hydrogen bond between two water moleculescan suffer an appreciable degree of bending before a local positive interaction energyarises6 and local dipole-dipole interaction energies (of which the H-bond is to alarge extent a special case) will be expected always to be appreciable in the liquidphase. In our own theoretical work, we have regarded the local field provided bythe proton as it arrives at a given site in the water “ lattice ” as providing the drivingforce necessary for reorientation of water molecules out of structural elementsrather than causing reorientation of “ free ” water molecules.In this connection, Prof.Baughan remarked that the proton must tend to leavethe acid centre (H3Of) and then rotate a neighbouring water molecule. While thisis essentially the process involved, we believe that the process must be more of aco-operative or coupled one in so far as the act of proton transfer presumably cannottake place until a suitable (hybrid?) orbital (an unshared pair) is presented by therotating water molecule to the acid site from which proton transfers can then occurwith a favourable activation energy. A distribution of orientations and associatedtransfer events will probably be involved.1 cf. Eigen and de Maeyer, Pruc. Roy. SOC.A , 1958, 247, 505.2 Davies and Baughan, J. Chem. Soc., 1961, 1711.3 cf. Bernal and Fowler, J. Clzem. Physics, 1933, 1, 515. Conway, Bockris and Linton, J.Chem. Physics, 1956, 24, 834.Frank, Pruc. Roy. Suc. A , London, 1958,247,481 ; Disc. Faraday Suc., 1957,24, 133.5 Nemkthy and Scheraga, J. Chem. Physics, 1962, 36, 3382, 3401.6Conway, Can. J. Chem., 1959, 37, 613. Cohan, Cotti, Iribane and Weissmann, Trans.Faraahy Suc., 1962,58,490. Magat, Trans. Faraday Suc., 1937, 33, 114220 GENERAL DISCUSSIONProf. Dr. M. Mandel (Rijksuniversiteit, Leiden) said : Prof. Hills has emphasizedthe fact that reorientation of a water molecule in the path and the field of a protonis the determining factor of proton migration in water. He has stated that theparticular Grotthus mechanism for such a proton migration occurs in spite of thehydrogen-bonded intermolecular structure of water rather than because of it asthis structure hinders the rotation of water molecules.Two things should, how-ever, be distinguished: (a) the possibility to establish a Grotthus chain; (b) themechanism by which this chain is extended through the solution. Prof. Hills' argu-ment only refers to the latter. The same factors, however, which determine theintermolecular structure of water make the occurrence of the Grotthus chainpossible.This may be illustrated with results obtained in another proton-transferringsolvent where the intramolecular structure is found definitely to oppose protonmobility rather than to enhance it.Dawson and workers 192 have found that informamide the ionic conductance of the proton is of similar magnitude and evenslightly smaller than that of K+, which itself is much smaller than in water. Al-though not much is known about the structure of liquid formamide, its particularhigh dielectric constant ( E = 109.5 at 25°C compared to 78.5 for water) suggeststhe existence of long chains of strongly bonded molecules.H H H H H HRupture of hydrogen bonds followed by reorientation of solvent molecules informamide will therefore be particularly difficult. This explains the low mobilityof both K+ and H+ in this solvent. The absence of any particular mechanism forthe mobility of the proton is due, however, to the impossibility of establishing aGrotthus chain in formamide.This is a result of its molecular asymmetry. Tnthe protonized molecule the additional proton is probably fixed on the oxygenatom 3-5 whereas the exact location of the positive charge has not been establishedyet.. . . H-N-C-0 . . . H-N-C-0.. . H-N-C-0 . . .A plausible representation of the solvated proton in formamide would beH H H H H H H H. . . H-N-C-0 . . . H-N--C-OH . . .O=C-N-H . . . O=C-N-H . . . +The additional proton can jump backwards and forwards between two adjacentmolecules but no real transferring chain can be established even over short inter-molecular distances. Thus proton migration will be of the same type as for any othermonovalent cation.Prof. G. J. Hills, Mr. P. J. Ovenden and Mr. Whitehouse (University of South-ampton) (partly communicated) : Prof.Mandel has raised an interesting point, fromwhich it is clear that intermolecular hydrogen bonding is not of itself sufficient forabnormal proton migration. Hydrogen bonding in certain solvents (perhaps form-amide) can give rise to rapid tunnel transfer of the proton between solvent molecules.This is seriously interfered with by the presence of other solvent molecules and mix-tures of solvents (each individually able to augment the migration of the proton) donot generally give rise to abnormal protonic mobilities. In formamide the extension1 Dawson, Newel1 and McCreary, J. Amer. Chem. Sac., 1954, 76, 6024.2 Dawson, Wilhoit and Sears, J. Amer. Chem. SOC., 1957,79, 5906.3 Stewart and Muenster, Can.J. Chem., 1961,39,401.4 Janssen, Spectrochim. Acta, 1961, 17,475.5 Katritzky:and Jones,jlChem. and Ind., 1961, 722GENERAL DISCUSSION 221of this intermolecular charge transfer through the solution apparently requiresthe reorientation of the protonated solvent molecule (cf. the mechanism proposed byHuckel for proton migration in water) followed by reorientation of a neighbouringneutral solvent molecule.In aqueous solution, the first of these steps is not required since rapid intramole-cular charge transfer can take place. The second, which is accelerated by the fieldof the proton, is believed to be rate-determining 1 and the activation energy for protonmigration is approximately 2 AGZ - NpF,, where AGof is the activation energy forrotation of a water molecule in the absence of the field of the proton F,, p is thedipole moment of a water molecule and N i s the Avogadro number.Proton-accelerated reorientation of solvent molecules is presumably presentin other solvents. The extent to which the lowering of the activation energy of thisstep offsets other, electrical relaxation effects will depend on the size and the chargedistribution of both the protonated and neutral solvent molecules.The data forformamide solutions suggest that in this case it is the reorientation of the protonatedsolvent molecule which is difficult and results in a complete absence of an abnormalproton mobility.Dr. P. A. H. Wyatt (Shefleld) said: The range of anomalous proton mobilityeffects has probably been extended in pure sulphuric acid.Whatever may be theprecise mechanism, the general explanation of anomalous mobility is well established.In a reaction likeH30+ + HzO-,H20 + H,O+,which is proceeding in all directions all the time throughout the solution, theapplication of an electric field slightly favours jumps in the field direction, and theresultant current contribution is proportional to the field strength and sufficientto explain the anomalous mobility observed. I suggested 3 that a similar effectmight even be detectable in proton jumps between neutral molecules, such as occurin the autoprotolysis of sulphuric acid :H2SO4+H2SO4-+H3S0~ +HSO,.Proton jumps of this kind are also taking place continuously in all directions and,assuming a reasonable value for the diffusion-controlled recombination rate ofthe ions, I calculated that the expected drift in the direction of an applied fieldcould account for 30-40 % of the conductance of the pure acid.Experimentalconfirmation was found in the appearance of an intercept of the expected magnitudeon plotting the conductance data of Prof. Gillespie and his co-workers 4 againstthe effective HSO, concentration.This is an ordinary low-field conductance contribution and different from thedissociation field effect: there is no overall increase in the extent of ionizationin the solution. Many reactions involving the redistribution of charges could beinfluenced in this way by the presence of a field, but normally the conductancecontribution would be too small to measure, and even in favourable cases the effectis difficult to separate experimentally from ordinary conductance.This com-plicates the search for further examples, but another case does seem to have arisenin the sulphuric acid system. Dr. G. A. Mountford and I now believe that thereis evidence for a high mobility, of about 10-15 % of that of HSO,, for the HS2071 Conway, Bockris and Linton, J. Chem. Physics, 1963,39, 2666.2 Whitehouse, D. R., Thesis (London, 1965).3 Wyatt, Trans. Faraday Soc., 1961, 57, 773.4 Gillespie, Oubridge and Solomons, J. Chem. Sac., 1957, 1804222 GENERAL DlSCUSSlONion in this solvent. If this is the case, there must be at least four proton exchangereactions in the solvent H2SO4 which give rise to abnormal mobility:H,SOZ + H2S04-+H2S04 + H,SOzH2SO4+HS0i+HS0; +H2S04H2SO4+H,SO4+HSO, +H,SOZ.These reactions all involve the transfer of protons between oxygens attached tosulphur atoms and form an interesting series with proton transfer rates governedby the factors considered earlier in this discussion.Prof.R. J. Gillesgie (McMaster University), said: We have obtained consider-able new experimental data that support Dr. Wyatt’s suggestion 1 that there is acontribution to the conductance of sulphuric acid from asymmetric autoprotolysisin the applied field.In connection with the papers presented by Prof. Hills and Dr. Franck, we maybe able to learn a good deal about the mechanism of the proton migration processthat gives rise to the abnormal mobilities of the H3O+ and OH- ions in water bystudying the similar abnormal mobilities of the autoprotolysis ions of other hydrogen-bonded solvents such as H2S04, HS03F and HF. For example, a large numberof cations and several non-electrolytes all decrease the mobility of the hydrogensulphate ion in sulphuric acid.2 For the alkali metal cations their effect is greaterthe greater the extent of their interaction with the solvent, i.e., the greater their degreeof solvation. This was interpreted as an effect of the cation or non-electrolytein breaking-up the structure of the solvent and thereby reducing the mobility ofthe HSO; ion. However, in view of Prof. Hills’ remark that proton migrationoccurs in spite of the structure of the solvent rather than because ofthe structureof the solvent, a new interpretation of these results may be needed.1 Wyatt, Trans. Faraday SOC., 1961,57,773.2 Flowers, Gillespie, Robinson and Solomons, J. Chem. SOC., 1960, 4327.3 Gillespie and Solomons, J. Chem. SOC., 1957, 1796

ISSN:0366-9033    

DOI:10.1039/DF9653900216

出版商:RSC    

年代:1965

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Classical and Quantum-Mechanical Effects in ElectrochemicalProton Discharge, and the Kinetics at Low TemperaturesBY M. SALOMON" AND B. E. CONWAYDept. of Chemistry, University of OttawaReceived 18th January, 1965In previous studies of the kinetics of electrocheniical proton discharge, it has been implicitlyassumed that an " adiabatic " electron transfer mechanism is involved, i.e., the reaction involvesan activated complex which is partially (or totally) neutralized. In a previous treatment of theactivated complex in rate-determining proton discharge, it was shown that the H/D separationfactor SD could be expected to be related to the ratio of exchange current densities R only on theassumption that the activated complex retains its full charge in the activation process.In thepresent paper, SD and R are shown to be related by reference to experimental and theoretical con-siderations for an assumed fully charged transition state, and on the basis that proton tunnellingcontributions to the rate are not appreciable. Experimental evidence in support of the latter con-tention is given by low-temperature kinetic studies down to - 125 and - 150°C in supercooledalcoholic solutions. A model of the activated complex in proton discharge is considered andinvolves a " non-adiabatic " electron transfer process. In these terms, the activated complex(particularly that for H+ transfer into Pd) is analogous to that in acid-base proton transfer pro-cesses ; the electrode plays the role of a base with variable base strength ; the theoretical treatmentof Bader based on Platt's calculations of force constants can be applied, giving an account of thepotential dependence of SD.The electrochemical hydrogen evolution reaction proceeds by the followingpossible steps :H30& + M + e-+MH + H,O, (I!with the alternative succeeding desorption processes,MH+HM-+H2or MH+H30&+ e+M+H, +H20.(111)Other possible steps have been considered by Horiuti and co-workers 1 but are notwell supported by experiment? In the present paper we shall concentrate attentionon reaction (I) which experimental evidence indicates is rate-determining at mercuryand possibly several other metals. It will be the purpose to discuss : (a) how (I) isrelated to acid-base proton transfer reactions in general: (b) how the activationprocess and the activated complex may be discussed in the light of electrochemicalisotope effects; (c) how the field at the interface enters into these considerationsand finally ( d ) the role of non-classical proton transfer processes.3-7In previous papers,8-13 we have examined how the steps (I) and (Ill) may bedistinguished in terms of the H/D separation factor SD and shown 8, 9 that step (1)can be associated with SD + 3 while step (111) can give SD = 6-7.Correspondingratios R 10 of exchange currents for €32 and D2 production in pure HzO and D20solutions can be similarly diagnositic of mechanism and proton-tunnelling effects canbe indicated by anomalous Tafel slopes and potential dependence of SD.~, 7 Moredetailed calculations,9, 14 following our earlier quasi-thermodynamic examination of* present address : Frick Chemical Laboratory, Princeton University, Princeton, N. J.22224 ELECTROCHEMICAL PROTON DISCHARGEzero-point energy differences, confirm that SD can approach 3 for mechanism (I) atHg but indicate that considerable uncertainties in the calculation of SD can arise fromdifficulties in the evaluation of transition-state force constants.Johnston 15 haspointed out that the semi-empirical London-Eyring-Polanyi (L.E.P.) potential energysurface calculation is totally unsatisfactory and misleading and more empiricalprocedures 16 are to be preferred, as we have used previously,g or the Sat0 potentialmay be used.15MECHANISMS OF PROTON TRANSFERIn terms of absolute rate theory,l7 the discharge of a proton from a lyonium ionL30+ (i.e., H30+, H2DO+, HD20+ and D3O+) can be writtenL30' + M + e&X'+ML,,,+ L,O,where X# is the activated complex.It is evident that the electrochemical protontransfer can, in the general sense, be regarded as an acid-base transfer occurring betweenthe acid L3O+ and the metal M acting as a base of variable " base strength " on accountof the fact that the electrode surface charge density & can be varied appreciably(approx. from positive, through zero to -25 pc cm-2 at the Hg cathode) as the potentialis made more cathodic with respect to the potential of zero charge (P.z.c.). Thisvariation of qM corresponds effectively to a variation from zero at the P.Z.C.to ca. 0.15excess electrons per atom at the metal surface at high cathodic potentials, viz., at 1 Vhydrogen overpotential.The strength of the analogy to acid-base reactions depends on the model consideredfor the activation process and the reaction in the electrochemical proton transfer case.If the H entity is transferred as a proton interstitially to surface sites (e.g., at Pt 9)or into the metal (Pd, Ni, Fe) containing formally one excess electron per ion trans-ferred, the analogy to acid-base reactions of the kindAH+ + B-+A + BHis close. However, if electron transfer occurs '' adiabatically " 18 or " non-adiabatic-ally " by tunnelling 199 20 to an activated complex, (e.g., see ref. (20)) the analogy toacid-base proton transfer as conventionally considered is less close.In either case,however, the un-neutralized activated complexes H20 . . . Hf . . . M (-) (acidicsolutions) or H-O- . . . Hf . . . M (-) (basic solutions) will be analogous to thosein corresponding acid-base transfers of the type (2), orHA + B--+A- + BHrespectively. The following cases may be formally distinguished.CASE (a) : In previous treatments of the electrochemical proton transfer problem,los 21-24it has been implicitly assumed that the activated complex is partially neutralized.18In Gurney's treatment,lg no activated complex in the conventional sense is involved,and electron transfer to levels in the initial state was regarded as occurring by atunnelling process, leaving a free H atom.22 The first type of representation en-counters difficulties since if the activated complexes statistically carry less than theunit charge and also occur part way across the electrode potential gradient, thesymmetry factor p should not necessarily have the value 0-5 which is normally found.In fact, it will have the general valuewhere 6 is the fraction of the metal-solution potential difference, measured from theinitial state, at which the activated state occurs, and 1 - y is the fractional charge held(2)(3)p = a+ y(l-26), (4M.SALOMON AND B. B. CONWAY 225on the average by the activated complex, e.g., as considered by Hush.18 Nevertheless,B will still be 0.5 when y = 0-5 or 6 = 0.5. While a value of 6 = 0.5 is reasonable,y need not necessarily be 0.5 but then p = 6 irrespective of the value of y.CASE (b) : A more realistic picture of the situation may be as follows (cf.ref. (22) :partial proton abstraction occurs out of the acids H3Q+ or H20 and electron transfertakes place by a non-adiabatic or tunnelling process to the resulting activated complexwhen the latter exists in a favourable conformation with respect to stretching of theOH bond and local solvent structure reorganization. The resulting entity H thenbecomes adsorbed as “ MH ”, and the conjugate base, H20 or OH-, relaxes into anormal statistical configuration in the double-layer.CASE (c) : Proton activation may occur adjacent to the negatively charged electrodesurface and proton transfer continues from this state into the surface layer (or insome cases, e.g., at Pd, into the bulk phase) of the metal, the proton then becomingeffectively a surface or bulk phase alloy by interaction with electrons of the metallicphase which have not been ‘‘ transferred ” in quite the same sense as in case (a);this case is thus more analogous to the process of metal ion deposition consideredelsewhere,25 and also to conventional acid-base transfers.CASE ( d ) : Finally, proton tunnelling may occur direct to the negatively chargedelectrode surface as treated by Bawn and Ogden,s by Conway6 as a function ofpotential, and by Christov.7 The various possibilities are shown schematically infig.1. Case (d) could be recognized 6 by low-temperature kinetic studies, and protonye(1-YY)O(a) H20+-H+MOSH20.. .H . . . M(l-y)@.activated complex-tH20+HM(b) H20+-H+M@+H20 . . . H + aactivated complexnu -[-+H2O. . . H . . . M]+€&O+HMwater relaxation H adsorption+n(c) H20+-H+M@+H20 . . . H . . . M@+H20+HM.activated complex(d) HzO+-H+M@ +H2O+HM.QFIG. 1 .-Models for electrochemical proton transfer.tunnelling, if appreciable, would be indicated by (i) a temperature dependent apparent 26activation energy ; (ii) isotopic dependence of the Tafel slope dq/d In i,6 and (iii) anappreciable variation of SD with potential. Distinction between the other cases ismore difficult but examination of isotope effects (separation factors S and the ratio R)in regard to reaction mechanism and dependence of S and R on electrode potentialhas been treated in several previous papers by the present authors 6, 8-11 andothers.1, 79 149 239 24 These matters will now be further discussed.226 ELECTROCHEMICAL PROTON DISCHARGEISOTOPE EFFECTSKINETIC FORMULATION AND RATIO R OF EXCHANGE CURRENTS FOR CLASSICALH2 AND D2 PRODUCTIONIn terms of partition functions, the rate of proton discharge in I in A cm-2 is 9 9 27exp [ .kT @1F f# z = zF-(1 - OH)CL30+ exp - - _____h RT ~M&,O+In this equation, O and C are the fractional coverage by H (or D) and the bulk con-centration, respectively ; f is the molecular partition function and Q is the molecularpartition function per unit volume (i.e., Q = f/V) ; 4~ is the inner potential of themetal and @I the potential at the outer Helmholtz plane ; /3 is the so-called symmetryfactor and other terms have their usual significance.If the activated complex isneutralized during the activation process, then the unreacting 0-L bonds in L30fwould suffer an increase in frequency10 towards those for OL bonds in L20. Ifthe mechanism of proton discharge can be regarded as simply a proton transfer stepas in acid-base reactions, then the frequencies of the unreacting 0-L bonds in theinitial and activated states are, to a first approximation, identical (cf. the modelconsidered by Westheimer,z*) and SD and R will be simply related. This model cansuccessfully predict reasonable values of SD and R, and can also be shown to beconsistent with an activation mechanism classical with respect to the proton transfer.The ratio R of exchange currents is defined as the ratio of rates of H2 and D2production at the respective reversible potentials in the respective pure solvents.An electrochemical rate constant k” at zero overpotential may be defined aio/(C~~o:>( 1 -O), where io is the exchange current density so thatFor the condition CH,O+ = CD,O+ and (1-811) = (1-OD) (e.g., as at Hg cathodeswhere 8H,6D’0),29 it follows that R = k&/db and the # r , ~ - + r , ~ term can be replacedby #:,D-+;,H, the difference of the standard reversible potentials.In eqn. (6),isotopic differences of $1 have been neglected? The terms in f; are primed becausethey contain contributions from two unreacting O-H or O-D bonds. If a fullycharged activated complex is considered, these unreacting O-H and O-D bonds canbe regarded as being identical to those in the initial state,2* so that to a first approxi-mationwhere f+ ,H/’# ,D now refers to internal motions directly involving the reacting H andD entities.From eqn. (6) and (7),SEPARATION FACTOR SD AND ITS RELATION TO RThe separation factor SD is defined (cf. ref. (8)) aM. SALOMON AND B . E. CONWAY 227where (CD/C& is the atomic D and H ratio in the bulk, and Ci terms are the rates ofproduction of H or D from various solution species, expressed as current densities.Then SD is given by(10)f% H f$ HfH2DO+ fHD20++ C H ~ D O + P H ~ + CHD~O + P H ~+ CH~DO + PD- + CHD~O+PD- f $ , D f;".DfH2DO+ fHD20+In eqn. (lo), all terms i n f ~ , 4 and 0 cancel t since they refer to the same electrode.The terms p~ and p~ are the statistical factors which correspond to the multiplicityof reaction paths 30, 31 and have been removed from f~~o+.It is to be noted that pis used instead of the symmetry number since use of the latter, in general, leads todifficulties, e.g., in relation to the calculation of relative discharge rates for protonsfrom ions such as H2DOf and HDzOf which have no elements of rotational sym-metry. Dividing through eqn. (10) by ( ~ D C D , O + ) ~ ~ ,D/~D,o+ gives-___-(11)'H30+ fDsO+ f;,H 'HzDO+ +---- fDsO+ f $ , H CHD20+ +---- f D 3 0 + f $ , H'D3O+ f H 3 0 + >>,I) 'D30+ fH2DO+ f;,D 'D30+ fHD20" f 2 . DI+---- f&O+ f % , D +- 'HD20+? -- f D 3 0 + f 7 , D CH2DO+I 'D30+ 3 ~ H ~ D O + f ; , ~ 'D3O' 3 ~ H D ~ O + f ; , ~With the previous assumptions (cf.eqn. (7)),Then, with the rule of the geometric mean (see eqn. (14)), and the appropriatep values,S D =The partition function ratios for lyonium ions have been evaluated by Swain andBader 32 at 25" and by Conway and Salomon 93 27 as a function of temperature fromTABLE TEMPERATURE DEPENDENCE OF THERMODYNAMIC QUANTITIES USED IN THECALCULATIONS"C fD30+k30t Kii * K12 K13 L +;,D- dF,H(mv0 5 4 x 104 3-92. 6-42 8-78 9-8 - 9.925 1 . 9 0 ~ 104 3-96 6.05 8-52 8.2 - 14.850 9 . 3 0 ~ 103 3.99 5.79 8.34 7.2 - 18.080 4 . 5 8 ~ 103 4.00 5-51 8.14 6.2 - 21.8* The K11 values reported here 37 are almost identical with those we have used previously,9~ 38which were deduced from data given in ref.(35) and (36).The terms in OH cancel if (I) is rate-determining and coverage arising by the quasi-equilibriumreaction H2+2 MH is negligible, so that any fractionation of H and D in the surface, consideredpreviously,ss 14 is insignificant228 ELECTROCHEMICAL PROTON DISCHARGEthe data of Heinzinger and Weston 33 (see table 1). The various ratios can be evalu-ated 349 32 using again the rule of the geometric mean, i.e.,The lyonium ion concentration ratios in eqn. (13) can be evaluated for any tem-perature from a knowledge of the equilibrium constants of the following reactions :H20 + D20 = 2HD0 Kl 1 (1 5)H20 + D3O+ = H2DO++ D2O K12 (1 6)H20 + D30f = HD20++ HDO K13 (17)(18)K11 has been determined by Urey 35 at 25" and by Kirshenbaum 36 and more recentlyby Narten 37 for several temperatures ; K12 and K13 are related to L 34 using the ruleof the geometric mean.L has been determined experimentally 33 and, using thesedata, we have evaluated L and hence Kl1 and K13 for 0, 25, 50 and 80°C (table 1).From eqn. (1 5)-( 1 S),2D30++ 3H20 = 2 H p - t 3D20These concentration ratios, evaluated for four temperatures, are given in table 2.From eqn. (13), (14) and (19) (see tables 1 and 2), it follows thatsD,Oo = 54'84f#,H/.f+,D;sD,50° = 29'32.f#,H/.f#,D;sD,25° = 37'75.f+,Hlf,,,D;sD,80° = 22'55f+,H/.f#,D*It is found that SD is independent of the (CD/CH)~ ratio (but see Vielstich et aZ.39).TABLE 2.-LYONIUM ION CONCENTRATION RATIOS FOR (c~/c& = 0.249O C cHD20+/cD30+ CHD~O +/CD~O+ cH30+'cD30+0 17.6 101 19725 17.1 97 18350 16.8 93 17480 16.4 89 1 62The ratio f# ,H/'# ,D is evaluated as discussed previously 9 (cf.ref. (23), (24)). Theresults are shown in fig. 2 for four cases. The first and second cases (a and a)correspond to a linear three-atom model of the activated complex as discussed pre-viously 9910. A third case (A) corresponds to the " dual site " model of the activatedcomplex 9 and represents the case where the proton is discharged between two metalatoms and below the surface tangential to the outermost layer of surface atoms.9~ 11The terms kl and k2 refer to the 0-Hf and M-H stretching force constants,respectively, and k,, ka, kj and kA are bending force constants for the activated com-plexes considered; the origin of these data is discussed in ref.(9). A fourth caseis shown (0) which corresponds to the activated complex model proposed by Bader.40In this model, the contribution to the isotope effect from the symmetric mode in theactivated complex is relatively small in comparison with that from the degenerate bend-ing mode. This case corresponds to that of a simple transfer mechanism in whichthe activated state is charged and, as a result, high bending frequencies arise. ThusBader 40 cites 1 6 5 0 cm-1 (see below) as a typical bending frequency for the H-speciesin a transition state 0-H-O(-), one end of which has negative charge density M. SALOMON AND B . E. CONWAY 229I I I I I I I 1 i2.8 30 3 2 3’4 3.6I/TX 103FIG. 2.Theoretical log SD against 1/T relation.0, kl = 1.16 mD A-1; k2 = 0.1 mD A-1; k4 = 014x 10-11 ergIrad2.k2 = 2-48 mD A-1 ; k4 = 0 .1 7 ~ 10-11 erg/rad2. A, kl = 0; k2 = 0.8 mD A-1 ;ka = 0.25 ki = 0.16 x 1011 erg/radz.U, kl = 058 mD A-1;ka = 0-15,0, v& = 1650 cm-1 [cf. Bader 40 and Bell 47 for F-H-F-1.I I I I I I I28 30 3.2 3 4 36l / T x 103FIG. 3.-Semi-logarithmic plot of relative rate factor R against 1/T.0, , A, and 0 as in fig. 2 ; the straightbe corresponds to the expt. values of Post and Hiskey.4230 ELECTROCHEMICAL PROTON DISCHARGEthe above frequency is similar to the observed value found in hydrogen-bondedsystems,41 and the observed and calculated values for F-H-F-.42 The slopedSD/dT obtained from fig. 2 is 0.016 deg.-1 (cf. the old experimental values of 0.01-0.02 deg.-1).43 This treatment assumes the vibrations in the activated complex to betemperature independent, i.e., if hydrogen bonding effects are neglected.This isprobably not a seriously unsatisfactory assumption but may contribute to the scatterof predicted R values from the observed data (see below).If secondary isotope effects are neglected, it should be possible to calculate Ras a function of temperature from thef+,H/f+,D Values derived for the SD evaluation.Using estimates of+," ,D -4; ,H previously calculated38 from the temperature dependenceof L (table l), R is obtained as a function of 1/T (fig. 3). The straight line is thatcorresponding to the experimental values 44 and the points are those calculated fromeqn. (8) using the data given in table 1 and the caption of fig.2. Eqn. (8) and (13)were derived for a fully charged activated complex and agreement with experiment isevidently acceptable. Hence, an adiabatic electron transfer mechanism, (e.g., seeref. (18)) may not apply to the proton discharge reaction and will be discussed furtherbelow. If such a concept were applicable, lower bending frequencies would tend toarise in the activated complex 10 and R values would be larger.EXPERIMENTAL RELATION BETWEEN R AND SD FOR MERCURYIn this section, R and SD are shown to be related by reference to experimentaldata at 25°C and no a priori assumptions concerning the activated complex will beinvoked. The only assumption which is made is that the rule of the geometric meanapplies to the partition functions for isotopically analogous species in acidified aqueoussolutions (cf.Merlivat et al. 45, who find the rule of the geometric mean to applyto liquid H20 and D20 over a moderate temperature range).The rate of (I) can be written in a simplified form asi = kC,30+ exp [ -pA&F/RT].From eqn. (9) and (21),Dividing through by 3kDcD30+, we obtain (cf. eqn. (13)). cP){ \cH sIn eqn. (23), (CD/CH)~ is an experimentally adjustable quantity and the lyoniumconcentration ratios can be calculated from the experimental data of Heinzinger andWeston.33 The value of k & ~ in eqn. (23) may be obtained (neglecting secondaryisotope effects) from the experimental value of R, since R is now defined byAt 25", R is 1.9 (Post and Hiskey 44) and ~;,,D-$:,H + 14 (0.8) mV 38 so that k ~ / k ~ =26.6Lyonium ion concentration ratios are obtained from the eqn.(19) using experi-mental CH,O/CHDO ratios obtained from the data of Heinzinger and Weston 33 whostudied the separation factors a for the reaction= (kH/kD) exp -[p(+,",D-4:H)F/RT]* (24)H20(~) + HDO(g) = H2O(g) + HDO(s) (IVM . SALOMON AND B . E . CONWAY 23 1The separation factors CCA, ccw, a& for (IV) in the presence of an acid, in pure water,and in the presence of a neutral salt, can be shown to lead to the following expression :In eqn. (25), N is the mole fraction of the indicated species. The ratio CXA/CC; isfound to be 0.992 at 25" for a 0-958 M HC104 solution.39 For varying (CDICH)~,CHzo/CDHo can be calculated from eqn. (25) and the results are shown in table 3.Using kH/k= = 2.66 from the experimental value of R for Hg, SD calculated fromeqn.(23) equals 3.7 and is independent of (CD/Q8 as found above in the theoreticalcalculations. This value of SD = 3.7 is, in fact, very close to the a priori theoreticalvalue calculated above from eqn. (13) and is also close to the experimenta1values.11, 39, 43, 46TABLE 3.-EXPERTMENTAL (CH~O/~HDO) RATIOS AS A FUNCTION OF(CD/CH)~ FOR 1 N ACJD !iOLUTIONS.33(CD/CH) 'HZO'~HDO SD0.0 10 49.29 3.70.050 9.76 3.70.1 11 4-48 3.70-249 2.00 3.7QUANTUM-MECHANICAL EFFECTS I N ELECTROCHEMICAL PROTONDISCHARGEIn the above discussion, the mechanism of proton discharge was treated in aclassical way. It is, however, well known 3 9 479 48 that for light particles such as theproton, quantum-mechanical tunnelling through the barrier is possible.Such effectshave been postulated as occurring at mercury cathodes in the h.e.r.5~ 6979 49 and wehave previously discussed the theoretical consequences 6 ~ 7 but the experimentaltests 6 have been carried out only recently.38 Thus, Conway and Salomon 38 examinedthe h.e.r. and the analogous deuterium reaction (d.e.r.) at mercury in methanol andmethanol-d solutions under high purity conditions 50 down to - 125°C. The h.e.r.at platinum electrodes has also been studied in supercooled ethanol HC1 solutionsdown to - 150°C and in neither case is experimental evidence found to supportsignificant proton tunnelling.* This conclusion is based on a temperature independentactivation energy which follows from the electrochemical Arrhenius plot shown infig.4. Also the Tafel slope b for hydrogen and deuterium evolution at mercuryfrom methanolic solutions is independent of H or D mass down to low temperaturesas shown in fig. 5, whereas if most of the proton transfer proceeds by a non-classicalmechanism, dependence of b on the isotopic mass is expected.6In electrochemical proton transfer, additional experimental criteria for the detectionof appreciable tunnelling arise from (a) the isotopic dependence of the Tafel slopeshown previously 6 ; and (b) the magnitude of b in comparison with the classicalvalue 2.3RT/pH; and (c) high potential dependence of S or R.6 In our previouscalculations,6 the barrier width was chosen as 0-55A, i.e., the dimensions used incalculations of activation energies by Butler,22 Parsons and Bockris,sl and Conwayand Bockris.52 If proton transfer occurred appreciably by the tunnelling pathway,b values larger than the experimental ones are predicted.In order that b be equal to* Further experimental data for low temperature kinetics at Ni electrodes will be presented indiscussion232 ELECTROCHEMICAL PROTON DISCHARGE-2 I-2C- 19-18€ - 1 7c;-16& -150 8 -1422204 3 -13- 12 .yI I4 5 6 71/Tx 103FIG. 4.-Electrochemical Arrhenius plot for the h.e.r. and d.e.r. from methanolic acid solutionsat mercury (HC1 in MeOH, ; DC1 in MeOD, 0).-___013012c c, w0.11W9 ' 0.10v-4 Q v1v-4 00sOO€007006 -/ - I I I50 -100 -50 0 50temp., "CFm.S,-Tafel slopes b for th6 h.e.r. (e) and d.t.r. (0) at the mercury cathode in methanolic HC 1as a function of temperatureM. SALOMON AND B . E. CONWAY 233the experimental value of ca. 2.3 2RT/H for the h.e.r. at mercury, the barrier widthmust be ca. 1.5 A (cf. ref. (5)) which is unreasonably large (for example, such a widthwould correspond to a classical activation energy much higher than that observed).Also the Tafel slope for the d.e.r. under these conditions should still be distinguishablefrom that for the h.e.r. as shown by the theoretical results plotted in fig. 6 (and shown-12 - 1 1 -10 -9 - 8 -7 -6 - 5 -4 -3 -2 - 1log [integral tunnelling probability]FIG.6.-Logarithmic tunnelling probability relations for electrochemical proton and deuterontransfer as a function of the barrier width and the rational potential (based on the Eckart barrierof height 20 kcal mole-1).TABLE 4.-TAFEL SLOPES b FOR DlSCHARGE OF H AND D CALCULATED FOR PROTON TRANSFERBY TUNNELLING(barrier height * 20 kcal mole-1 ; unidimensional Eckart barrier 55)barrier width, A bH temp.,OK bH bD ~ H I ~ D bH or bD(298OK) (barrier width 1.5 classical0.3 0.650-5 0.281.0 0.1721.5 0.103253 0.098 0,078 1.25 0.100298 0.103 0.080 1 -29 0.1 18375 0.109 0.081 1 -35 0.148(1.4) (expt. Hg, 0.1N HCl 0.115-0.125)* Choice of this barrier height is somewhat arbitrary, since the observed heat of activation atr] = 0 will not be identical with the barrier height at A ~ M = 0.in table 4). Here the log of the integral tunnelling probability (to which the currentdensity would be proportional) is plotted as a function of the rational electrodepotential A ~ M which modifies the barrier height in the usual way through the sym-metry factor p taken here as 0.5, and also changes the overall energy of reaction byA#M.F.The calculations have been made in the same way as our earlier ones234 ELECTROCHEMICAL PROTON DISCHARGEwhich were based on a single value of the barrier width (Eckart model 55) * but as afunction of temperature and potential.It may be argued that a large barrier width is not inconsistent with the recent modelof the double-layer proposed by Bockris, Devanathan and Miiller.53 In this treat-ment, the distance of closest approach of cations to a cathode surface is taken asapproximately rh+dHZo, where rh is the primary hydration radius of the cation anddHzo as the thickness of the oriented water layer considered 53 to be adsorbed at theelectrode between the hydrated ions and the metal surface.I I I3 4 5 61/Tx lo3FIG.7.-Corrected Arrhenius type plots for the ratios of rate constants of the h.e.r. and d.e.r.in methanolic (MeOD x DCI) solutions.* 5 IHowever, for the hydrogen ion in solution, the proton can penetrate to the supposedinner layer of water at the electrode by the anomalous conductance mechanism 42and the final electrochemical neutralization to form adsorbed H must presumablytake place from an H30+ ion in this inner layer.? Such a situation is then virtuallythe same as that considered in previous treatments, and the barrier width would thenbe ca.0.5-0-6 t$, so that the tunnelling behaviour will be as calculated above for sucha width.Further support for the classical transfer process arises from consideration of thefrequency factor ratio for the h.e.r. and d.e.r. Thus, if we write eqn. (8) in terms ofthe Arrhenius equation for an electrochemical reaction, thenso that aplot of log ( k H / k ~ ) - B(#$',D -&',H)F/RT against 1/T will give the true frequencyfactor ratio &/AD and the true activation energy difference AED+ - AEg(cf. Temkin 26).* Tunnelling may occur from a variety of molecular configurations at the surface and calculationsfor a multidimensional surface are then required.55~ 38 However, they are difficult to apply to thepresent case (cf.ref. (54)).f Thus, if the solvent layer model applied here, the Helmholtz double-layer capacity at cathodicpotentials should be larger for aqueous acids than for corresponding salts, a situation not observedM. SALOMON AND B . E. CONWAY 23 5The results for the h.e.r. and d.e.r. at mercury in methanol solutions are shown infig. 7, from which &/AD = 1-25 and AEg - AES = 0.7 kcal mole-1. Practicallyidentical results are obtained for these quantities for mercury in aqueous acid solutionusing the data of ref. (44). In fig. 7, the Arrhenius parameters AH/AD and Eg-Egare obtained directly. These parameters cannot be obtained simply by a plot oflog ( k H / k ~ ) against 1/T since then the term &',D -&?,H and its temperature coefficientwould contribute to AH/AD and AEg - AE;, giving only their apparent values.The(apparent) frequency factor ratio obtained in this manner is, in fact, about 0.5 forboth the aqueous and non-aqueous systems and has been taken as indicative ofconsiderable proton tunnelling contributions to the rate? 49 Since the true, kinetic-ally significant, ratio is above unity, this conclusion is unnecessary.54The observed absence of appreciable proton tunnelling may be connected with theapplicability of the present model, i.e., tunnelling would be significant were it not forthe non-adiabatic electron transfer resulting in the crossing of the system to a potentialenergy surface leading to a state of higher stability.In ordinary proton transferreactions in which there is no " net " electron transfer, tunnelling of protons mayindeed be the mode of proton transfer as discussed previously,38, 42 e.g. as in protonconductance in ice. We have discussed other possible reasons for the absence ofproton tunnelling previously.38GENERAL DISCUSSIONPreviously,lp 22-24 it has been implicitly assumed that the activated complex iseither partially or totally neutralized. The recent calculations of the energetics ofproton discharge by Bockris and Srinivasan 23 were based on the quasi-thermodynamictreatment of Moriuti and Polanyi 21 and Butler.22 On the basis of an Eyring-Polanyipotential energy surface and the assumption of an adiabatic electron transfer step,they calculated an activation energy very much lower than the observed apparentvalue (cf.ref. (15)). In addition, a symmetric frequency vs of about 3000 cm-1 forthe H-activated complex was found," and for the bending frequency v$, values lessthan 600cm-1 were taken. While the symmetric mode is of importance, as firstpointed out by these authors,23 (cf. ref. (24), (9)), the relative values of vs and v$ appearto be anomalous. Thus, for hydrogen bonded systems, the bending frequenciesvary between 1250 cm-1 (e.g., for F-H-F- which provides a good model for protontransfer transition states, cf. ref. (47)) to 2000 cm-1 (as discussed by Bader 40). AlsoWilson and Johnston 56 have calculated the force constant for " X-H-X " activatedcomplexes and obtained a value of 0-16 x 10-11 erg/rad2 for the H-X half bondwhich corresponds to a bending frequency of 1200-1300 cm-1. Hence the value ofless than 600 cm-1 for the bending frequency appears to be underestimated by Bockrisand Srinivasan.23 Conversely, the symmetric vibration seems to be seriously over-estimated (cf.ref. (40)) and the combined result leads to small values of SD which,it was suggested, could be increased 23 to the experimental value by modifying thetheoretical relation for SD by a proton tunnelling correction. Our experimental evi-dence presented here and in ref. (38) indicates, however, that proton tunnelling does notappear to contribute appreciably to the overall rate of the discharge reaction, at least inmethanolic solutions ; also, the values of AH/& from Post and Hiskey's data 44 leadto similar conclusions for aqueous media.The assumption that v$ <600 cm-1* In our own theoretical calculations 9 based on empirical assignment 16 of force constants,by reference to the properties of analogous stable molecules, the bending and symmetric stretchingfrequencies corresponding to these force constants were in the range 800-1200cm-1 and can givethe correct SD values without tunnelling corrections236 ELECTROCHEMICAL PROTON DISCHARGEoriginates with Keii and Kodera’s treatment 24 in which the activated complex wasconstructed from the intersections of Morse functions for the Hg-H and Hf-OH2“ diatomic ” molecules and in which the Hg and OH2 groups were treated as havinginfinite mass.Also, the tunnelling corrections made in ref. (23), and necessitatedby the values of S calculated classically from an L.E.P. surface, may be too largesince the L.E.P. surface has been claimed recently 15 to be unreliable. This may be theorigin of the discrepancy between the above 23 and previous theoretical indications(cf. ref. (6), (7)) and the present experimental conclusions.Since proton tunnelling is not indicated experimentally and electron tunnellingin Gurney’s sense 19 leads to well-known inconsistencies,229 389 49 we propose a modelfor rate-controlling (I), similar, in some respects, to that in acid-base reactions.The process of activation is considered as involving motion of a proton over a potentialenergy surface in which the initial state is Hg(-) +H30+ and the (excited) final stateis Hg(-)H++HzO.At the activated state (i.e., the structure corresponding to theactivated complex), a non-adiabatic 20 electron transfer is regarded as occurring(cf. ref. (19) and (22)) and is associated with a crossing of potential energy surfacesto give the stable final state species HgH. The stability of the activated stateis determined, amongst other factors, by overlap of orbitals on Hg(-), Hf andOH2. The OH(-) and OH2 groups furnish a p-orbital or some hydrid of s- andp-orbitals and the result is two molecular a-orbitals. Since Hg(-) is a nucleo-philic centre which can supply a pair of electrons to the electrophilic reactant H+,these electrons must occupy a non-bonding orbital or an anti-bonding orbital.Since a metal surface is involved, delocalization effects will be important.TheHg . . . 0 distance is generally small, so that a repulsion of the two electron cloudsshould lead to weaker, more ionic and more polarizable bonding between Hg,H and OH2.571 58 Because of a-antibonding, the changes in bond length andforce constant can be relatively large and electron supply to either end of the bondwould tend to shorten the overall length * and give rise to higher bending forceconstants (lower S values) due to increasing electron supply. Since the electrondensity is high on cathodic Hg and 0, the distance and force constants wouldtend to be sensitive to “ substituent effects ” (i.e., to the supply or removal ofelectrons) because the anti-bonding effect tends to make enery a weaker functionof distance.57 The decrease in SD as the Hg electrode is made more cath-odic 11, 399 46 may be attributed to precisely this effect.Associated electricaleffects, e.g ., electrostriction in the double-layer, were also suggested earlier by us 99 11to explain whyk&D decreases as the cathodic potential (overpotential q) is increased.?Swain et aZ.59 have found k&~ values which vary from 2.8 to 0.85 for the protontransfer step in the decarboxylation of B-keto acids, depending on the nature ofsubstituent groups having varying electron donating character. Similarly, in theHellmann-Feymann treatment for theoretical force constant calculations applied toacid-base proton transfer by Bader,40 the calculated bending force constants for0-H .. . 0- transition states increase from 1290 to 1440 cm-1 as the partial charge* If a large barrier width of ca. 1.5A considered above with regard to tunnelling were taken,the bending frequencies would then tend to be much lower and S anomalously high.7 Direct field effects on the energy of the OH vibrations in the initial state are negligible as maybe shown from the solution of the Schroedinger equation for an electric oscillator in a field E.61The vibrational energies are thene2E2 U = n + - h v - - ( :> 2kwhere v is the frequency, n the quantum number and k the force constant. At E + 3 x 107 V cm-1,as in the doublelayer at A ~ M = 1 V, the U is modified by only 36 cal taking k = 5 x 10s dyne cm-1M. SALOMON AND B.E. CONWAY 237on 0 increases from 0.8 to 1.0, i.e., the weaker is the base centre, the " looser " is thetransition state complex.These considerations provide a basis for treating the electrochemical protondischarge step in terms of an acid-base proton transfer in which the electrode surfaceis the analogue of the base but has variable base strength depending on electrodepotential or surface excess charge, resulting in potential dependent S.One of us (M. S.) acknowledges the award of a Fellowship by the Sprague ElectricCompany. The authors also thank Dr. K. J. Laidler and M. Eusuf for valuable dis-cussions concerning activated complexes and Dr. M. Wolfsberg and Dr.R. F. W. Baderfor discussions in 1962 and 1963 concerning bending and stretching mode frequenciesfor activated complexes involved in proton and H-atom transfers. We are also in-debted to Mr. Belanger for performing the calculations on tunnelling rates.1 Horiuti, Okamoto and Hirota, Sci. Pap. Inst. Physic. Chem. Res. Tokyo, 1936, 29, 233.2 Conway and Salomon, Electrochim. Acta, 1964, 9, 1599 ; see also ref. (29).3Bell, Proc. Roy. SOC. A , 1933, 139,466; 1935,148,241.4 Bernal and Fowler, J. Chem. Physics, 1933, 1, 515.5 Bawn and Ogden, Trans. Furuday Soc., 1934, 30,432.6 Conway, Can. J. Chem., 1959,37, 178.7 Christov, 2. Elektrochem., 1960, 64, 840 ; 2. physik. Chem., 1960,214,40.8 Conway, Proc. Roy. Soc. A , 1958, 247, 400 ; see also Conway, Theory and Principles of Elec-9 Conway and Salomon, Ber., Bunsenges.1964, 68, 331.10 Conway, Proc. Roy. Soc. A , 1960,256, 128.11 Conway and Salomon, J. Physic. Chem., 1964, 68, 2009.12 Conway and Salomon, J. Chem. Physics, 1964, 41, 3169.13 Conway, Proc. Symp. Electrode Processes (Philadelphia, 1959) (The Electrochemical Society,14 Bockris and Srinivasan, J. Electrochem. SOC., 1964, 111, 844.15 Johnston, Davy, Guerra, Weaver and Young, J. Chem. Physics, 1964, 41, 1517.16 Johnston, Adv. Chem. Physics, 1961, 3, 131.17 Glasstone, Laidler and Eyring, Theory of Rate Processes (McGraw-Hill, 1941).18 Hush, J. Chem. Physics, 1958, 28, 962.19 Gurney, Proc. Roy. Soc. A, 1931,134, 137 ; 1932,186, 378.20 Sacher and Laidler, Modern Aspects of Electrochemistry (ed.Bockris and C-nway, Butter-21 Horiuti and Polanyi, Acta Physiochim., 1935, 2, 505.22 Butler, Proc. Roy. Soc. A , 1936, 157, 423.23 Bockris and Srinivasan, J. Electrochem. Soc., 1964, 111, 852.24 Keii and Kodera, J. Res. Inst. Catalysis, Hokkaido, 1957, 5, 105.25 Conway and Bockris, Electrochim. Acta, 1961, 3, 340.26 Temkin, Zhur. Fiz. Khim., 1948, 22, 1081.27 Salomon, Ph.D. Thesis (Ottawa, 1964).28 Westheimer, Chem. Rev., 1961, 61, 265; see also Miller, J. Physic. Chem., 1962, 66, 978;29 Frumkin, Aduances in Electrochemistry, vol. 1, ed. Delahay and Tobias (John Wiley, New30 Schlag, J. Chern. Physics, 1963, 38, 2480.31 Bishop and Laidler, J. Chem. Physics, in press, 1965.32 Swain and Bader, Tetrahedron, 1960, 10, 182 ; see also Swain, Bader and Thornton, Tetra-33 Heinzinger and Weston, J.Physic. Chem., 1964, 68, 744.34Purlee, J. Amer. Chem. Soc., 1959, 81, 263.35 Urey, J. Chem. Soc., 1947, 569.36 Kirshenbaum, PhysicaZ Properties and Analysis of Heavy Water (McGraw-Hill, New York,37 Narten, J. Chem. Physics, 1964, 41, 1318.38 Conway and Salomon, J. Chem. Physics, 1964, 41, 3 169.trode Processes (Ronald Press, New York, in press (1965)).p. 267, John Wiley and Sons, New York, 1961).worths, 1964), vol. 3, chap. 1.and Johnston and Pitzer, Ass. Inst. Chem. Eng. J., 1959, 5,277.York, 1961).hedron, 1960, 10, 200.1951)238 ELECTROCHEMICAL PROTON DISCHARGE39 Butler, Vielstich and Barth, Ber., 1963, 67, 650.40 Bader, Can. J. Chem., 1964, 42, 1822.41 Pimentel and McClellen, The Hydrogen Bond (Freeman, 1960).42 Conway and Salomon, Proc. Symp. EZectroZyte SoZutions (The Electrochem. SOC., ed. Conwayand Barradas (John Wiley and Sons, New York, in press, 1965). Conway, Modern Aspectsof Electrochemistry (Butterworths, 1964), vol. 3.43 Walton and Wolfenden, Trans. Faraday Soc., 1938,34,436.44 Post and Hiskey, J. Amer. Chem. SOC., 1950, 72,4203 ; 1951,73, 161.45 Merlivat, Botter and Nief, J. Cltim. Physique, 1963, 60, 56.46 Rome and Hiskey, J. Amer. Chem. SOC., 1954,76, 5207.47 Bell, Acid-Base Catalysis (Oxford, 1941) ; see also The Proton in Chemistry (Cornell Univ.48 Bell, Trans. Faruday Sac., 1959,55, 1.49 Christov, Electrochim. Acia, 1961, 4, 306 ; see also other references gken by Christov in this50 Azzam, Bockris, Conway and Rosenberg, Truns. Faruhy SOC., 1950,46, 918.51 Parsons and Bockris, Trans. Faruday SOC., 1951, 47,914.52 Conway and Bockris, Can. J. Chem., 1957,35, 1124.53 Devanathan, Bockris and Miiller, Proc. Roy. SOC. A, 1963, 274, 55.54Hulett, Qnart. Rev., 1964, 18, 227.55 Eckhart, Physic. Rev., 1930,35, 1303. Johnston and Rapp, J. Amer. Chem. Soc., 1961,83, 1.56 Wilson and Johnston, J. Amer. Chem. SOC., 1957,79,29.57 Swain, Wiles and Bader, J. Amer. Chem. SOC., 1961,83, 1945.58 Bartlett and Tate, J. Amer. Chem. SOC., 1953, 75, 91.59 Swain, Bader, Esteve and Griffin, J. Amer. Chem. Soc., 1961, 83, 1951.60 Laidler, ChemicaZ Kinetics of Excited States (Oxford, 1955).61 Moelwyn-Hughes, Physical Chemistry (Pergamon Press, 1961), p. 179.Press, 1959).paper

ISSN:0366-9033    

DOI:10.1039/DF9653900223

出版商:RSC    

年代:1965

数据来源: RSC

摘要:

Proton Transfer Across Double LayersMechanism Evaluation from Isotopic EffectsBY J. O’M. BOCKRIS, S . SRINIVASAN AND D. B. MAITHEWSThe Electrochemistry Laboratory, The University of Pennsylvania,Philadelphia, Pa., 19 104, U.S .A.Received 15th February, 1965The separation factor depends sharply upon the mechanism of the hydrogen evolution reaction.Conway’s previous calculations contain errors of principle. Calculations on the basis of classicaltransition state theory are reported. They consist essentially of the calculation of force constantsat the saddle point of potential energy-distance diagrams for several alternative rate-determiningsteps in the hydrogen evolution reaction. Correspondingly, the relevant partition function ratiosfor corresponding isotopic situations have been calculated.An essential difference in result of thesecalculations from previous ones of the Japanese School is that the present calculations take accountof the stretching frequency of the 0-H bond in the activated state. The separation factor cal-culated is thus reduced by about G times, and allows consistence with a rate-determining protondischarge mechanism upon metals for which the rate constant of the hydrogen evolution reactionis low. Relations are deduced which show that the separation factor is a function of the fast re-action following a rate-determining step.Quantum-mechanical calculations of separation factors must be made as corrections to theclassical transition state calculations because otherwise the zero point energy level of the activatedstate is neglected (as was done by Christov). Experimental data report the unexpected dependenceof the separation factor for metals having low rate constants for the hydrogen-evolution reactionupon potential.Explanations in terms of only classical proton transfer rates are improbable.Correspondingly, the variation of the rate of proton transfer with potential is shown to be highlyindependent of assumptions concerning barrier width, and therefore degree of barrier penetration,within certain ranges of the parameters of barrier height and barrier width. The temperature de-pendence of the separation factor is also not a sensitive criterion for the degree of barrier penetrationin proton transfer, but the dependence of the separation factor on potential is such an indicator.The barrier width and height are calculated with the assumption of an Eckart-type barrier bysolving quantum-mechanical equations which relate the rate to the change of potential, to the ab-solute value of separation factor, and to the variation of the separation factor with potential.Inthis way, the most probable value of the barrier width and height upon mercury for the protondischarge reaction from acid solutions is shown to be 4 8, and 22 kcal mole-1. Utilizing theseparameters, the quantum-mechanical correction factors for the separation factor are calculated.Utilizing these values, it is possible to associate the well-known alternative paths for the hydrogenevolution reaction with certain separation factors. Hence, identification of mechanisms canrapidly be made with a few experimentally simple measurenients of H-T separation factor.The barrier penetration fraction of the proton transfer rate on mercury in acid solution at roomtemperature may amount to about 70 % of the total current at an overpotential of 1 V.An im-portant corollary of these calculations is that the barriers assumed in earlier theoretical work inelectrode processes have been too narrow. Probable Echart barriers would have to be at least4%i. Such conclusions are consistent with recent views on the existence of a water layer on elec-trodes as an essential constituent of the double-layer structure.Most methods used to determine the mechanism of electrolytic hydrogen evolu-tion involve work at the steady state in the low current-density range and thuscannot be applied to metals which enter mixed potential reactions with the solution.1The separation-factor method 2 avoids this difficulty.It depends on a theoretical23240 PROTON TRANSFER ACROSS DOUBLE LAYERSanalysis of the separation factors expected from the various mechanisms. Previouscalculations 3-8 have been discrepant ; tunnelling effects have been neglected.The aim of this paper is to give a theoretical analysis of separation factors associatedwith proton transfer and related mechanisms of the passage of hydrogen across ametal-solution boundary,g-ll and to assess numerically the neglected effects oftunnelling.12CLASSICAL EVALUATION OF SEPARATION FACTORSConway’s approach 8 (corrected for an error in the calculated ratio of activitiesof isotopic oxonium ions) gives large isotope effects due to neglect of zero-point-energy differences of the isotopic activated complexes.Since the calculation pro-cedure by Horiuti et aZ.3-7 minimizes the calculation of partition functions of speciesin solution, the same approach was adopted in the present work.METHOD OF CLASSICAL CALCULATION(i) EXPRESSION FOR SEPARATION FACTORThe hydrogen-tritium separation factor is defined by the equationwhere (C,/C& and (CH/Cr), are the ratios of atomic concentrations of hydrogento tritium in the gas phase and in solution, respectively. The ratio (CHIC& isequal to twice the ratio of the velocities of H2 and HT evolution since CR2% CHT.Using this relation, ST may be expressed byfor all mechanisms, except when the diffusion of molecular hydrogen away from theelectrode is the rate-determining step.For a linked discharge-electrochemicaldesorption mechanism,1 1 1 - = -+-,ST &is SE(3)where SDis and SE~ are given by expressions of the form (2).9 In eqn. (2), n = 1/2for the slow discharge mechanism, n = 1 for all other mechanisms, Z ~ / T T is theratio of tunnelling correction factors, fH+/fTf is the partition function ratio of theisotopic activated complexes for the particular step considered, ~HTO,~/~H,O,~ is thepartition function ratio of the HTO and H20 molecules in the gas phase and KTis the equilibrium constant for the reactionHzOl+HTOg+HTOl+HzO,.(4)In eqn. (3), SDiS refers to an expression of the form of (2) for the discharge stepand S E ~ to the electrochemical desorption step.Thus, the calculations consist of (a) calculation of the force constants at thesaddle point of the reactions constituting assumed ra te-determining steps, and (b)the quantum-mechanical penetration and reflection of the barrier. The ~HTO,~/”H,O,~ratio can be calculated from spectroscopic data of the HTO and H20 moleculesin the gas phase; the KT value is known experimentallyJ . O'M. BOCKRIS, S . SRlNIVASAN AND D . B . MATTHEWS 241(ii) PARTITION FUNCTION RATIO OF ISOTOPIC WATER MOLECULES IN GASPHASE (fHT0,glfH20,g)This ratio is given bySpectroscopic data, necessary for the calculation of fHTolfH,o were obtained fromthe work of Libby.14 This value is 289.54.Together with the experimental valueof KT,KT(fHTO, g/fH20. g ) = 16*46. ( 6 )(iii) PARTITION FUNCTION RATIOS OF ISOTOPIC ACTIVATED COMPLEXESIt is assumed that the activated complex H2O-H-M (or its isotopicanalogue) is similar to a linear triatomic molecule (fig. 1, cf. Parsons and Bockris 19,f & / f ; is given byFOR THE SLOW DISCHARGE MECHANISM ( f i / f g )7T J t , T Jr, T Jvib, Twhere f f , f,? and fZb represent the translational,tributions respectively of the indicated species.(a) TRANSLATIONAL PARTITION FUNCTIONRATIO (f,fHlfzT).-The activated complexmay be regarded as immobile, i.e., the trans-lational partition function ratio is unity. Evenif restricted translational motion occurred,there is only a negligible isotope effect, sincethe heavy metal atoms form a part of theisotopic activated complexes.Translationalmotion in two dimensions by H3Of is notrelevant.(frfH/fzT).-A small isotope effect arises dueto the restricted rotation of the isotopicactivated complexes about the two axes,through the centre of gravity of the activatedcomplex, mutually perpendicular to the axisof the molecule. The partition function ratiodue to this restricted rotation is given by(6) ROTATIONAL PARTITION FUNCTION RATIOSince the observed librational frequenciesare small (e.g., for water, 600 cm-1) and(7)rotational and vibrational con-.-J?e-----* . ----- *- -_-- . M T OH2Activoted complexes forslow dischorge mechanism.--- --• ----- *-- ---*M T H OH2Activated complexes fcr sloweiec troc hemicai de sorptionmechanismM MActivated complexes for slowrecombination mechanismFIG.I .-Activated complexes for variousmechanisms.are inversely proportional to the square roots of the corresponding momentsof inertia, then.frfH/f:T = I$/I,f (9242 PROTON TRANSFER ACROSS DOUBLE LAYERSwhere I 8 and Zt are the moments of inertia of the H and T activated complexesabout axes perpendicular to the axis of the molecule and through their respectivecentres of gravity. The calculated rotational partition function ratio is. f f H / . h z T = 962. (10)(C) VIBRATIONAL PARTITION FUNCTION RATIO (ff,H/ff,T)For a linear triatomic molecule, there are four degrees of vibrational freedom.Since one of these is imaginary for the activated complex, three frequencies are tobe considered in calculating the vibrational partition function ratio of the isotopicactivated complexes, which is given byThe suffirres s and b stand for stretching and bending frequencies respectively.Itmay be shown that for linear triatomic molecules with H (or its isotopes) as thecentral atom and heavy end atoms (in our case the metal atom and H20) thatwhere (mH/mT) is the ratio of the mass of the H atom to that of the T atom. Inaddition, since bending frequencies are generally small, we may assume thatFor the calculation of the stretching vibrational frequencies, it is necessary tosolve the secular equation :2 m, + m2 +m31' - A[ (-!- m1 + L ) k , m2 + (-!- m2 + ' ) k 2 m3 - -kl 'n2 + m1m2m3 (kllk22 - G 2 ) = 0,(14)where kll is the force constant for the stretching of the bond between ml and m2,k22 is the force constant for the stretching of the bond between m2 and m3, and klzis a coupling constant.1 is given by the expressionA = 4n2v2. (15)Eqn. (14) is obtained by setting up the expressions for the potential energy, kineticenergy and then by using Lagrange's equations of motion. In order that the forceconstants for the activated complex may be determined, it is necessary to expressthe potential energy as a function of the two variable distances 1-1 and r2. From thetable of values of V as a function of rl and r2 which is obtained by a computer cal-culation, the reaction path and the co-ordinates, rf and r $ , at the saddle point maybe determined. The force constants are obtained by a calculation of the respectivesecond derivatives [i.e., (8 V/ar: ) r , = 7, (82 V/ar ;),= f and (82 V/ drlar2),, = rT ,r2= f ] ofthe potential energy at the saddle point.This method of calculation is the sameas that used by Eyring et aZ.16 Three such calculations were carried out for theslow discharge mechanism, varying the percentage coulombic-exchange energyratios in the Heitler-London expression for the potential energy of a three-atomsystem.16 The results of such calculations are shown in table 1. It may be seenfrom this table that the variations in percentage coulombic energy have little in-fluence on the real stretching frequencies of the activated complexesJ .O'M. BOCKRIS, S . SRINIVASAN AND D . B . MATTHEWS 243The importance of the effect of the stretching frequency to the isotope effect,is seen from the present calculations. Kodera et ~ 1 . 6 ~ 7 considered only the effectof the bending frequencies of the activated complexes and as a result obtained highseparation factors for this mechanism. By the inclusion of the effect of stretchingfrequencies, the partition function ratios of the activated complexes are consider-ably lower-hence also the separation factors-than that calculated by the Japaneseworkers .TABLE 1 .-FORCE CONSTANT (k), STRETCHING VIBRATIONAL FREQUENCIES (w), PARTITIONFUNCTION RATIOS ( f ~ + / f ~ + AND f~ # {f~ +) OF ISOTOPIC ACTIVATED COMPLEXES FOR THE SLOWDISCHARGE MECHANISMcalculation number1 2 3 parameter20201 -053.402688.6- 3.90290621 10176352 i50 i50 i0-1465551 -052.926635.1- 3 2.702773201 5168690 i88 i89 i0.16053931.053-304654.8- 10.6028202048171484 i83 i81 i0.15520.0633 0.0725 0.06727.2072.0307,8972.3257.6362.155This conclusion has also recently been stated, apparently independently, byConway and Salomon.17 These workers obtained higher values for the ratio ofpartition functions of the isotopic activated complexes (and hence separation factors)in some cases, than those obtained in the present work due to an incorrect choiceof the relevant force constants necessary for the solution of the secular equations.These force constants were not calculated but chosen only by analogy of the activatedcomplex with similar molecules in the ground state.It was assumed that the 0-Hstretching frequency in the activated state is quite small. However, our detailedpotential energy calculations, varying the percentage coulombic energy, showedconsistently high values of force constants for the stretching of the 0-H bond.It is, thus, the opinion of the present authors that the higher partition functionratios obtained by Conway and Salomon are due to the assumptions of a low forceconstant for the 0-H bond in the activated state. Calculations for a dual-siteadsorption model on similar lines made by these workers showed somewhat lowerpartition function ratios than those obtained in the present work, due to the greaternumber of vibrational modes for this model244 PROTON TRANSFER ACROSS DOUBLE LAYERSCLASSICAL SEPARATION FACTORS FOR THE VARIOUS MECHANISMSUsing eqn.(6) and (10) along with the partition function ratios of the activatedcomplexes found in table 1 in eqn. (2), the classical value of the separation factorfor the slow discharge mechanism may be obtained. The classical separationfactors (both H--D and H-T) for all other mechanisms, calculated in a similarmanner, along with that for the slow discharge mechanism are given in table 2.TABLE 2.-THEORETICAL SEPARATION FACTORS FOR THE DIFFERENT MECHANISMS ASCALCULATED JN PRESENT INVESTIGATIONmechanismslow discharge fast-recombinationslow-discharge fast-electrochemical(inequili brium)linked-discharge electrochemical (eitherrate-determining)(i) coulombic energy 100 % for allinteractions(ii) coulombic energy 20 % for M-H andH+-OH2 15 % for H-H interactionsfast-discharge slow-recombination(i) Ni(dNi-Ni = 3-52A)(ii) Pt (dpt-R = 2.77A)fast-discharge slow-electrochemical(i) coulombic energy 100 % for allinteractions(ii) coulombic energy 20 % for Ni-H andH+--OH2 15 % for H-H interactionsslow molecular hydrogen diffusionseparation separation factorsexcluding includingtunnelling tunnellingcorrections correctionsfactorss;: s; SD ST2.4 3.4 3.0 4.63.8 6-2 3.8 6.23.4 5.4 4.1 7.03.6 5.7 4.4 7.55.5 11.3 5.8 13.04.9 9.4 5.5 11.18.3 19.8 9.1 23.09.7 24.7 10.7 28.74.5 8 .2 4.5 8.2For the calculations of the partition function ratios of isotopic activated complexesfor the slow electrochemical and slow recombination mechanisms, the activated com-plexes were treated as linear pseudo-tetra-atomic and symmetrical trapezium-shapedmolecules. Fig. 1 shows the models for these activated complexes. As for theslow discharge mechanism, the saddle point was located from the table of valuesof the potential energy as a function of the variable distances. The potential energysurface generated from one typical calculation is shown in fig. 2. The saddle pointis represented by a dot on the figure.QUANTAL CORRECTION TO CLASSICAL SEPARATION FACTOR CALCULATIONNEED FOR QUANTUM-MECHANICAL CORRECTIONAccording to the classical theory of reaction rates, ZH (or ZT) in eqn.(2), is zerofor the reacting particles with energy less than the barrier height E# and is equalto unity for particles with energy greater than E f . Quantum mechanically, it ispossible for z to have a finite value for particles with energy less than E f and alsoto have a value less than unity for particles with energy greater than E # . The netcontribution of this non-classical penetration and non-classical reflection is expressedby the so-called tunnelling correction factor, ZH (or zr). The magnitude of z de-pends on the dimensions of the energy barrier for the reaction and also on the masJ . O’M. BOCKRIS, S . SRINIVASAN AND D. B . MATTHEWS 245of the particle being transferred.For hydrogen atom or ion transfer (or its isotopes)T may have appreciable values depending on the height and width of the onedimensional barrier along the reaction co-ordinate.It is necessary to see how the tunnel effects introduce only a correction to theclassical rate. The quantum-mechanical rate for the proton discharge is given by(16)coi,. 1 = k1cABO +IE, WE) ~ X P C - ( E - Eo)/kTJdE,where kl is a frequency factor, W(E) is the probability of proton tunnelling at energylevel E, and Eo is the zero point energy for the stretching of the Hf-OHz bond.FIG. 2.Potential energy profile diagram from typical calculation.Since this motion is assumed to lead to reaction, the zero-point energy of theactivated state does not enter into the calculation of & I .For low and wide barriersone attains the classical limit. Under these conditions, W = 0 for E<E” andW = 1 for E> E # . Thus, eqn. (16) becomesThe tunnelling correction z is given byi,, = klcHsO+ kT exp [ -(E* -E,)/kT]. (17)The rate of the reaction is then given by1 = TI,. (19)It is well known that i,,l calculated according to eqn. (17) is not the observedrate when tunnelling effects are negligible, since the zero-point energy of the activatedcomplex has been neglected according to the above one-dimensional model analysis.An a priori calculation using iq alone would have neglected the zero-point energylevels of the activated state-a procedure shown to be invalid.16, 189 19 Thus, ineqn. (19), i, is the classically calculated rate including all modes of vibration (takinginto account the zero-point energy of the activated state)246 PROTON TRANSFER ACROSS DOUBLE LAYERSPREVIOUS WORK O N TUNNEL EFFECTS I N THE SLOW DISCHARGEMECHANISMThe possibility of proton tunnelling effects in the hydrogen evolution reactionwere considered fairly early but detailed calculations on these lines were carriedout only recently by Christov.20 There are, however, several factors which werenot taken into consideration by Christov.Zero-point energy contributions tothe activation energy and to the separation factor were ignored. Thus, to explaina separation factor solely by tunnel effects, would lead to a higher degree oftunnelling than if part of the isotope effect were ascribed as due to zero-pointenergy differences and partly due to tunnelling.In fact, some workers 18 have beenable to explain some observed isotope effects solely on the basis of zero-point energyeffects without considering the tunnel effect. Further, Christov has ignored theimportant dependence of separation factor on potential since his calculations referto the reversible potential. Conway 21 has calculated the effect of proton tunnellingon the kinetics of the hydrogen evolution reaction as well as the H-D separationfactor. Conway, like Christov, used the Eckart barrier in his calculations. How-ever, he used quite narrow barriers (barrier width 0-5A). Though reasonablevariations of the separation factor with potential were observed, it was found thathigh and different Tafel slopes were expected for proton and deuteron discharge.Further, if one were to calculate an activation energy, the value would be too low.Conway proposed the criterion of high and different Tafel slopes for the Hf and Dfdischarge to determine the degree of tunnelling.Due to the contradictory viewsexpressed by these authors and the disagreement with experiment, the role of protontunnelling and its effect on H-T separation factors was examined in the presentwork.CRITERIA FOR SIGNIFICANT TUNNELLING CONTRIBUTIONSIt is difficult to obtain a clear or sensitive quantitative method for assaying thedegree of participation of quantum-mechanical effects of proton transfer from solu-tion. Thus, the Tafel slopes become independent of potential over a wide range ofpotential even though the penetration and reflection currents are very significant.A striking phenomenon has been observed recently 12-the separation factor onhigh overpotential metals is markedly dependent on potential.It can be shownthat this effect is not explainable on classical lines 12 and consequently is an in-dication of non-classical contribution to proton transfer current. The degree ofdependence of separation factor on potential is therefore a sensitive test of tunnelling.METHODOLOGY OF ZH/TT CALCULATIONS(i) EXPRESSION FOR TUNNELLING PROBABILITYIn the calculation of the quantum mechanical rate iq,l and of the tunnellingcorrection, it is essential to know the shape of the barrier along the one-dimensionalnormal mode.The Eckart barrier22 appears to have the closest fit to the realbarrier and was hence used in the present work. The unsymmetrical Eckart barrierhas the formA exp (2744 B exp (27441 + exp (2nxld) (1 + exp ( 2 ~ x l d ) ) ~ V(x) = J . O’M. BOCKRIS, S. SRINIVASAN AND D . B . MATTHEWS 247whereA = Ao+e,q,A0 = V(OO)- V(-OO),B = 2E’ - A+2{E#(Ef -A)}’,E’ = Eg-Peoq. (24)2d is the barrier width and Eg is the barrier height at q = 0. For this barrier,whereandcash 2n(A + p) - C O S ~ 2n(A - p)W(E) = cosh 2x03. + p) + cosh 2na ’Q = + { ( 8 m d 2 ~ ) - 1 } 3 .For barrier widths greater than 3.0 A and Eg >la0 x 10-12 erg, we may use theapproximate formula :z should now be obtained by using eqn. (29) in eqn.(18). But the integral inthe resulting equation for z cannot be solved analytically. Thus, numerical in-tegration was carried out on a digital computer. The results thereby obtained werefound to be in agreement with the graphical method to within 5 %.(ii) CHOICE OF BARRIERSA large number of computations were carried out with various combinationsof barrier parameters at several temperatures and over a wide range of electrodepotential. Comparison of the computed values with the corresponding experi-mental data was then used to determine the most probable barrier parameters.The experimental data available, for comparison, are the Tafel slope, the activationenergy, the separation factor and its variation with potential. Such a comparisonshould therefore yield a unique set of barrier parameters which are of physicalsignificance.(iii) RESULTS OF CALCULATIONS(a) TAFEL sr.oPEs.-The values of J, calculated according to00J = 1 W(E) exp { - (E - Eo)/kTfdEEousing eqn.(29) for W(E) were plotted as a function of potential to obtain the Tafelslopes recorded in table 3. The Tafel slopes were linear over the entire potentialrange except at less than 50 mV. The results show that the Tafel slopes increasewith increase in degree of proton tunnelling. In fig. 3, the classical dependenceof Tafel slope on temperature is compared to the dependence in the presence ofproton tunnelling. For thin barriers, which lead to an independence of b o248 PROTON TRANSFER ACROSS DOUBLE LAYERSTABLE 3.--COMPUTED TAFEL SLOPEST 2d b bV)"K A Protiurn deuterium tritiumA0 E6(10-12 erg) (10-12 erg0.0 1.4 2981.6 3232982732401981.8 3232982732.0 3232982730.4 1.6 2980.6 1.6 2980.8 1.6 2986-05.04.03-06.05.04.03.05.04-03.05.04.03.05.04.03.04.06.04-04.04.04.04.04.04.04.011813113414211812112413411211512710412099-384-391.811613311912311413212311312212112111812913013311812012112311011011497.498.081.481.888.610212911811911013011911011911911911812913013011811911912010910911095.596-898.079-379.383.6129118118108128118108118118118temperature at low temperatures, the Tafel slope is considerably larger than theclassical value at room temperature.The same conclusion was also reached byConway.21 Thus, the present results show that the thin barrier model is not aorrect.Re. 3.-Dependence of computed Tafel slopes on temperatureJ . O'M. BOCKRIS, S. SRINIVASAN AND D . B . MATTHEWS 249(b) DEPENDENCE OF TUNNELLING CORRECTION FACTOR RATIO ON POTENTIAL.-Eqn. (2) may be rewritten aswhere r H , T is equal to the ratio Z&T and & , ~ 1 is the classical separation factorcalculated in the previous sub-section. The variation of separation factor withpotential is hence given byST = rH, TST, CI (31)dST/dq = ST, CddrH, T/dq). (32)TABLE 4.-COMPUTED RESULTS FOR THE MOST PROBABLE BARRIER2d = 4.0A, E;= 1.5 x 10-12erg, A0 = - 0.6 x 10-12erg.TOK3233002789 t r(10-12 erg) H D T H, D H, T0.81-21.41.61.82.00.81.21.41.61.82-00.81-21.41.61.82.03.8513.2572.9572,6652.3752.0795.0894.1073.6343.1902.7682.3517.4175-5694.7524.0153.3542.73 1143441.7301.6651 -5961.5221.4442.0531.9011.8161 -7271.6311.5342.3582.1452.0281 *9071.7811.6551.4881 -43 11 -3971.3591.3201.2761.5881.5161.4741 ~4281.3791,3261 -7281.6341.5791.5221 -4591.3932.0881.8831.7771 -6701-5611 -4402.4832.1 632.0051.8511 a6981.5343.1582.6062.3382.1161.8901.658I I I I I00 09 08 I -2 1.6 1-7 (10-12 erg)FIG.4.-Dependence of r on A+2-59 12.2802.1201.9611.8021-6323.2152.7162.4732.2392-01 21.7774.2923.4093.0092.6412.2991.962111250 PROTON TRANSFER ACROSS DOUBLE LAYERSThe computed figures of t ~ , ZT and rH,T for the most probable barrier para-meters are given in table 4. These parameters were arrived at by a comparisonof the observed and computed variation of the separation factor with potential.A typical plot, showing variations of Ao, used in the calculation of ZH, ZT and hencerH,T, is given in fig. 4. A comparison between the calculated and experimentalvalues of ST as a function of potential at 27 and 50°C is shown in fig. 5.I I I I \ 27OC109 -8 -2 47 -6 -5 --(c) DEPENDENCE OF SEPARATION FACTOR ON TEMPERATURE.-The results at 50 and27°C are in agreement with the theory of proton tunnelling as applied to a dischargefollowed by catalytic mechanism.The results from 5 to -71°C do not agree withthis theory. The results at the lower temperatures may be interpreted on the basisof a change over of the mechanism of the subsequent step to electrochemical de-sorption mechanism. For this mechanism, the separation factor is given by eqn. (3).Such a change over leads to a large reduction in dS/dq, as observed experimentally.Furthermore, the values of S calculated at an overpotential of 1.3 V are also in goodagreement with experiment at temperatures of 5" and below.CONCLUSIONSUSE OF H-T SEPARATION FACTORS I N MECHANISM DETERMINATION OFPROTON TRANSFER PROCESSES AT ELECTRODESThe theoretical separation factors (table 2) indicate that most mechanisms (path andr.d.s.) can be distinguished by means of separation factors except a linked discharge-electrochemical desorption mechanism where the rate-determining step cannot bedetermined.A knowledge of the degree of coverage of hydrogen on the metalis also required to make such a distinction. The theoretically forecast values fora slow molecular hydrogen diffusion mechanism and for a slow recombinationmechanism are also not well separated. However, in this case, the experimentalseparation factors (ST) on the platinum group of metals-which should be inde-pendent of the metal for the slow molecular diffusion mechanism-or the tem-perature coefficient of the separation factors should be helpful in distinguishinJ .O'M. BOCKRIS, S . SRINIVASAN A N D D . B . MATTHEWS 25 1between the two mechanisms. Secondary isotope effects due to HdHDO inter-change reactions play a role only in the slow discharge-fast electrochemical de-sorption mechanism at low overpotentials.The mechanisms on the metals studied in acid and alkaline electrolytes, obtainedby this method, are indicated in table 5.TABLE 5.-EXPERIMENTAL H-T SEPARATION FAmORS AT A c.d. OF 10-2ACm-2 AND ATA TEMPERATURE OF 25°C AND MECHANISMS INDICATED THEREFROMmetalPtPtRhWWNiNic uHgPbPbCdelectrolyte0.5 N HzSO40.5 N NaOH0.5 N H2SO40.5 N H2so40.5 N NaOH0.5 N H2SO40.5 N NaOH0.5 N0.5 N H2so40.5 N HzSO40-5 N NaOH0.5 N H2SO4separation factor9.6 f0.415.3 f0.810.7 f0-46.0 f0-24.4 f0.518.0 f0-94.1 f0-318.1 f2.45.8 f0.36.7 f0.77.2 f0-89.2 f0.5mechanismfast discharge-slow recombinationfast discharge-slow electrochemicalfast discharge-slow recombinationlinked discharge-electrochemicalslow discharge-fast recombinationfast discharge-slow electrochemicalslow discharge-fast recombinationfast discharge-slow electrochemicalslow discharge-fast recombinationlinked discharge-electrochemicallinked discharge-electrochemicallinked discharge-electrochemicaldesorptiondesorptiondesorp t iondesorp tiondesorptiondesorp t iondesorptionUSE OF SEPARATION FACTORS IN ASCERTAINING DEGREE OF PROTONTUNNELLING I N THE SLOW DISCHARGE MECHANISMThe most probable barrier parameters for proton discharge on mercury werefound to be 2d = 4.0 A, E$ = 1.5 x 10-12 erg and A0 = -0.6 x 10-12 erg.Forthese parameters it was found that at q = 1V and at 27"C, ZH = 3.19. From thisvalue of ZH, it follows that the degree of proton tunnelling is 68-7 %. With decreaseof cathodic potential or decrease in temperature, the degree of proton tunnellingdecreases. Christov20 used A0 = 0 in his calculation and arrived at 70 % degreeof tunnelling at q = 0. With the present values of Ao, the degree of tunnellingis 86 % at the reversible potential. The assumption that A0 = 0 made by Christovis invalid. Further, Christov neglected the effect of zero-point energies.Conway and Salomon 17 claim that proton tunnelling effects are not significant.This conclusion was based mainly on the observed independence of activationenergy for proton discharge from methanolic acid solution down to -98°C.Theactivation energy obtained was 1 1.2 kcal mole-1 compared to 20 kcal mole-1 inaqueous solutions. The activation energy of 11 -2 kcal mole-1 is incompatible withoverpotential measurements above 1 V since the barrier height would be less thanzero under such conditions, assuming the symmetry factor to be half. Their resultappears to be connected with the observed variation of the transfer coefficient withpotential.The low-temperature separation factor data indicate that the removal of ad-sorbed hydrogen is by the electrochemical desorption step.The present work showsthat the Tafel slope and its temperature dependence are not good criteria for deter-mining the role of proton tunnelling in the hydrogen evolution reaction252 PROTON TRANSFER ACROSS DOUBLE LAYERSRELATION OF KINETICS OF HYDROGEN EVOLUTION TO DOUBLE LAYERSTRUCTUREImportant conclusions of a confirmatory nature, about the structure of theelectrode-solution double layer may be made on the basis of the present study.The present results of the most probable width (2d = 4 4 is equivalent to a protontransfer distance of 3.7& between the metal surface and the centre of the oxygenbonded to the discharging proton. This distance compares favourably with a dis-tance of 3.8A as calculated from the Bockris, Devanathan and Muller23 theoryof the double layer. Further evidence for this arises from the potential-energycalculation for the slow electrochemical desorption mechanism. Earlier modelsof double-layer structure showed no activation energy for this reaction but theBockris, Devanathan and Muller model showed that there is an activation energyfor this reaction.Financial support from the National Aeronautics and Space Administration underResearch Grant No. NsG-325 and the National Science Foundation under GrantNo. GK-40 and G-15952, carried out at the Electrochemistry Laboratory, is grate-fully acknowledged.1 Srinivasan, Ph. D. Thesis (University of Pennsylvania, Philadelphia, 1963).2 Horiuti and Okamoto, Sci. Inst. Physic. Chem. Res. (Tokyo), 1936, 28, 231.3 Okamoto and Horiuti and Hirota, Sci. Inst. Physic. Chem. Res. (Tokyo), 1936,29, 223.4 Horiuti, Keii and Hirota, J. Res. Inst. Cut., 1951,2, 1.5 Horiuti and Nakamura, J. Res. Inst. Cut., 1951,2, 73.6 Keii and Kodera, J. Res. Inst. Cut., 1957, 5, 105.7 Kodera and Saito, J. Res. Inst. Cut., 1959, 7 , 5.8 Conway, Proc. Roy. SOC. A , 1958,247,400.9 Bockris and Srinivasan, J. Electrochem. SOC., 1964,111, 844.10 Bockris and Srinivasan, J. Electrochem. Sac., 1964, 111, 853.11 Bockris and Srinivasan, J. Electrochem. SOC., 1964, 111, 858.12 Matthews, Ph. D. Thesis (University of Pennsylvania, Philadelphia, 1965).13 Sepall and Mason, Can. J. Chem., 1960,38,2024.14Libby, J. Chem. Physics, 1943, 11, 101.15 Parsons and Bockris, Trans. Furaduy SOC., 1951, 47,914.16 Glasstone, Laidler and Eyring, Theory of Rate Processes (McGraw-Hill, N.Y.).17 Conway and Salomon, Ber., 1964, 68, 331.18 Melander, Isotope Efects on Reaction Rates (Ronald Press, N.Y., 1960).19 Sharp and Johnston, J. Chem. Physics, 1962,37, 1541.20 Christov, Electrochim. Acta, 1961,4, 306.21 Conway, Can. J. Chem., 1959,37,178.22 Eckart, Physic. Rev., 1930, 35, 1303.23 Bockris, Devanathan and Muller, Proc. Roy. SOC. A, 1963, 274, 55

ISSN:0366-9033    

DOI:10.1039/DF9653900239

出版商:RSC    

年代:1965

数据来源: RSC

摘要:

GENERAL DISCUSSIONProf. V. Gold (King's College, London) said: The statement by Salomon andConway that the use of symmetry numbers in rate expressions in general leads toerror would appear to be misleading. It has been shown, for the particular case ofthe H2DO+ and HD2O+ ions considered by Salomon and Conway, that the use ofsymmetry numbers in this context gives the correct statistical factors, provided thedistinct existence of enantiomeric transition states is allowed for.1It is of interest to examine the degree of analogy between isotope effects in electro-chemical proton discharge and " chemical proton discharge ", e.g., by addition toolefm. In both cases there is a rate isotope effect and a product isotope effect2(or separation factor). In all four models for electrochemical proton transferconsidered by Salomon and Conway (fig.l), the rate-limiting step involves protontransfer from the hydronium ion. The same assumption is implied by the formula-tion of the transition state for the " slow-discharge mechanism " as H20-H-Mby Bockris et al. The isotope effects on this kind of electrochemical proton transfercan be examined in terms of the previously developed theory of isotope effects on" chemical " proton (and deuteron) transfer'3 according to which rate and productisotope effects are related by eqn. (2.7) of our paper. Gold and Kessick's k ~ / k ~and r appear to correspond to Salomon and Conway's R and SD respectively.Prof. K. J. Laidler (Univ. of Ottawa) said: Prof. Gold has questioned the state-ment of Salomon and Conway that the use of symmetry numbers in rate theorytends to lead to error, and suggests that error is avoided if one properly allowsfor the existence of enantiomeric activated complexes.This is a step in the rightdirection, but treatments by Schlag 4 and by Bishop and myself 5 show that theexistence of enantiomers is only part of the difficulty. The crux of the problem isthat there may be I* ways by which reactants can reach the activated state, and Y *ways by which the activated complex might hypothetically revert into reactants.The ratio Z*/r* is equal to the ratio of symmetry numbers, c/o*, where CJ is the sym-metry number for the reactants and o* that for the activated complex. Sinceactivated complexes cannot revert to reactants, but must by definition becomeproducts, the correct procedure is to multiply the rate expression by the statisticalfactor l*.Multiplication by o/o*, as in the conventional activated complex formula-tions, leads to error unless r z is equal to unity.It is therefore correct to omit symmetry numbers in the formulation of absoluterates, and to multiply by I * . This procedure automatically takes care of thepossibility of enantiomeric activated complexes, and also deals with other cases inwhich r* is not equal to unity. Salomon and Conway's warning that in rate theorythe use of symmetry numbers leads to error is therefore correct.Prof. B. E. Conway (Ottawa) (communicated) : We believe our remarks regardingthe use of symmetry numbers for obtaining the statistical stoichiornetric factors inrate expressions are essentially correct.The problem has been examined bySchlag 6 and by Bishop and Laidler 7 where use of the number of product reaction1 Gold, Trans. Faraday SOC., 1964, 60, 738.2 Gold and Kessick, Proc. Chern. Soc., 1964, 295.3 Gold, Trans. Faraday Soc., 1960, 56, 255.4 Schlag, J. Chem. Physics, 1963, 38, 2480.Bishop and Laidler, J. Chem. Physics, 1965,42,1688.Schlag, J. Chem. Phys., 1963, 38, 2480.Bishop and Laidler, J. Chern. Pizys., 1965, 42, 1688.25254 GENERAL DISCUSSIONpaths is recommended as preferable. The proper result is only obtained when sym-metry numbers are used by introducing a " correction factor " allowing for thenumber of enantiomeric forms, e.g., in the H2DO+ and HD20f case, as Gold haspointed out.Use of the procedure of Bishop and Laidler gives more generally anddirectly the correct result by a preferable procedure.We agree that Gold's " rate " and " product " isotope effects in chemical reactionsare analogous to our R and S factors, respectively and the R and S values can berelated semi-quantitatively as we have shown in our paper. The analogy betweenthe chemical and electrochemical isotope effects, correctly stressed by Gold, is treatedin our paper where we point out the role of the electrode as a base.Prof. S. G. Christov (Inst. Physic. Chem., Bulgarian Academy of Sciences) said:Electron tunnelling was first assumed by Gurney 1 at the reversible metal/solutionpotential, and proton tunnelling by Polanyi 2 in the electrochemical hydrogen evolu-tion.Bawn and Ogden 3 have calculated the ratio of the integral permeabilitiesof the potential barrier for H and D, which are related to the electrolytic separationfactor. However, the basic problem of the electrochemical kinetics, i.e., the rela-tion between current density i and electric field 4 was first treated by Christov.4It was shown for large tunnelling that this relation has the form 4, 5where A+ is the potential drop across the barrier, E ion charge, and T temperature).The factor A(A4,T) is, in general, a potential function, depending on the barriershape and dimensions and on the ion mass too. This expression leads to Ohm'slaw, but in the general case one cannot derive the Tafel equation.The latter wasobtained by the writer 5 for the Eckhart barrier by superimposing on it a linearor non-linear electric potential; in the first case, a normal Tafel slope b = 0.116and in the second, a higher slope b = 0.125 V was obtained. Conway 6 first demon-strated the expected influence of the mass on the i against A 4 relation, and obtainedhigher Tafel slopes for a very thin Eckart barrier (including a non-linear potential).A general tunnel theory of charge-transfer processes was developed by Christov,7using the asymmetrical parabolic barrier (linear electric potential). In applyingthis theory to electrode processes 8 it was possible to derive a simple relation forthe previously 4 predicted dependence of the Tafel slope b on the width (70 = 2 4and height (Eo at A 4 = 0) of the barrier as well as on the ion mass m and temperatureT.This relation has the formi = A(A4,T)(exp [aeA+/kT] -exp [ -(1 -a)eA4/kT]), (1)bib' = ylS for y > 6;bib' = 1 for y<6, - where y = Eo/kT and 6 = 2x2d,/2rnEo/h (h, Planck constant) are two dimensionlessparameters and bl = 2.3 kT/ae. It was also shown (ref. (8), p. 203), that a relationof the form b/bl =f(6/y) is valid for the Eckart barrier too (in this case the barrierhalf-width is I = nd). As pointed out earlier (ref. (8), p. 212), the single valuesb H = 0.25 V and b~ = 0.17 V obtained by Conway,6 represent two points on thecurve b/bl = j ( S / y ) (ref. (8), p. 203).1 Gurney, Proc. Roy. SOC. A, 1932, 136, 378.3 Bawn and Ogden, Trans.Farday SOC., 1934,30,432.4 Christov, Ann. de I'Univ. de Sofia, Fac. Phys. Math., 1945-46, XLII, 69 ; 1946-47, XLIII, 63 ;6 Conway, Can. J. Chem., 1959,37, 178.7 Christov, 2. Elektrochem., 1960, 64, 840.8 Christov, Electrochim. Acta, 1961, 4, 194, 306.2 Polanyi, Naturwiss., 1933, 21, 316.C.R. Acad. Bulg. Sci., 1948, 1, 43. 5 Christov, 2. Elektrochem., 1958, 62, 567GENERAL DISCUSSION 255The law has not a great practical importance because the proton tunnellingnormally occurs in the region of moderate tunnelling (6 > y), for which b/bl = 1.Nevertheless, the relation b/ba =f(s/r) may be very useful as a criterion for thedetermination of the possible barrier dimensions with regard to the experimentalb-values.All the general conclusions in the papers of Salomon and Conway about Tafelslopes for H and D, based on detailed calculation for various barrier widths, arepredicted by the above general law.However, some lower values for bH and bDin this work (table 4, for TO = 1.5 A) are evidently unreasonable, because it is im-possible to obtain b/bZ< 1 by tunnelling.Of the experimental results in Conway’s paper, only the proton transfers inmethanol solutions at low temperatures do not occur by very large tunnelling,*but moderate tunnelling is not excluded. The latter case is consistent, as shown bythe writers,ll 2 with all experimental facts (Tafel slopes, activation energies, separa-tion factors). The most probable barrier dimensions for Hz and D2 evolution atmercury in H20-solutions are found to be Eo = 1-6 x 10-12 erg (at q = 0) andTO = 1.7-2-1 A.1-3 A barrier width of about 2 A is not impossible 1, 2 ; it iscompatible with a thickness of the double layer 60-2-5 A corresponding to adielectric constant D-5 which agrees well with the results of Mott and Watts-Tobin.4 This conclusion is consistent with a configuration, by which the threeprotons of H30f ion lie in a plane parallel to the metal surface, as assumed byEssin and Kojeurow 5 to be more probable ; in this case with a0-2.5 A one obtainsTO = 1-8-2 A.f It is therefore not necessary to introduce the hypothesis of a non-adiabatic electron transfer to the transition state to explain the absence of largeproton tunnelling, as stated by Salomon and Conway.If we assume a barrier width of ~ogO.5-0.8 A (for an orientation of one H-O-bond normal to the electrode surface), which leads to large proton tunnelling, itis again possible to explain the experimental facts by supposing a significant con-tribution of non-equilibrium solvation of the transition state to the activation energy.It is, indeed, very difficult to detect experimentally moderate tunnel effects.The value of the frequency factor ratio &/KH>2 is only a sufficient, but not anecessary, condition for significant tunnelling.The result of Temkin 8KI/KA =5-50 and the writer’s result 1-3 Kb/.lU;, = 2-1 refer to the apparent potential barrier.There exist, however, theoretical methods for estimating the lower limit of the tunneleffect using experimental data.Prof.B. E. Conway (Ottuwa) and Dr. M. Salomon (Princeton) (communicated):Prof. Christov has remarked on the chronological order of facts and resultson electrochemical proton tunnelling. Although Polanyi and Gurney were, ashe mentions, the first to introduce the possibility of tunnelling in electrode reactions,* There is a cancellation between the effects of temperature decrease and barrier height decreasein comparison with hydrogen evolution at ordinary temperatures and water solutions.?The classical activation energy, determined by the intersection of two Morse curves, will bein this case much higher than that observed, as affirmed by Conway. The application of Morsecurve in polar liquids is, however, not reliable (see below).1 Christov, Electrochim.Acta, 1961,4, 194, 306.3 Christov, Dokl. Akad. Nauk. S.S.S.R., 1959, 125, 141.3 Christov, Proc. 1st Austral. ConJ Electrochemistry, 1963 (Pergamon Press, 1964), p. 723.4 Mott and Watts-Tobin, Electrochim. Acta, 1961, 4, 79.5 Essin and Kojeurow, Zhur. fiz. Khim., 1943, 17, 4.6 Bockris and Srinivasan, J. Electrochem. SOC., 1964, 111, 844.7 Post and Hiskey, J. Anier. Chem. Soc., 1950, 72, 4203 ; 1951, 73, 161.Temkin, Works ofthe Electrochemistry Coiiference (Moscow, 1953), p. 181256 GENERAL: D I s CUSS I o Nthe matter was also referred to in some detail by Topley and Eyring.1 Bernal andFowler 2 also applied similar principles to field-assisted diffusion of the protonalready in 1933. In our 1958 paper 3 we already pointed out that the first cal-culations which were at all complete were those of Bawn and Ogden in 1934 butthis work does not appear to have been mentioned by Christov in his earlier papers.Also, in the paper of Bockris, Srinivasan and Matthews it is stated that protontunnelling effects have previously been neglected and we have remarked criticallyon this point elsewhere.We agree that Christov was the first to show the tunnellingTafel relation but the mass dependence of the slope b was demonstrated by Conway,who also examined the case where a quantized distribution might be involved in theOH vibrations of the proton donor. The mass dependence of b was also suggestedas a critical criterion of extensive tunnelling of the proton.The extent to which the relation of b to bcl may be useful will depend on tem-perature.In the same way that the activation energy may diminish with decreasingtemperature, the value of b may not diminish in the classically required mannerproportional to 7'. We have obtained some preliminary results at Ni, reportedverbally at this Discussion, which indicate such effects with regard to the Tafelslope.We agree with Prof. Christov that under most conditions, e.g., near room tem-perature, the degree of tunnelling may only be small or moderate; the effects arethen relatively trivial. We, however, emphasized elsewhere 4 that the principalinterest will be in the study of the reaction under conditions where extensiuetunnelling* might have been expected and this has been the basis of our experimentalwork and that of other work on homogeneous proton transfer reactions.Our previously calculated slopes 5 were obtained for a particular barrier width.Generalized calculations, following his own paper 6 where Tafel relations were ob-tained, were given by Christov 7 in a very useful way and it is gratifying that oursingle points are consistent with his general relation.Dr.M. Salomon (Princeton) (communicated): There appears to exist a majordifference of opinion concerning the existence of proton tunnelling between Prof.Bockris, and Prof. Conway and myself. This difference arises mainly from themodel of the activated complex used by Prof. Bockris and by the present authors.In our work, we have examined the experimental data, found no evidence to supporttunnelling, and offered some theoretical model to explain the absence of protontunnelling; i.e., we have chosen a model which we think can best explain theexperimental findings.Prof. Bockris, on the other hand, has chosen a model,made the calculations and then compared the results with experiment. It was foundthat the classical model did not predict the observed isotope effects so that a tunnel-ling correction was necessitated. The main objection to this procedure is theclassical model used and a number of errors of principle that require additionalcomment.(i) Any quantum-mechanical caIculation of potential energy surfaces (semi-empirical) is valid only if the adiabatic assumption is not violated, i.e., if the electrons* cf.Weiss, this Discussion.1 Topley and Eyring, J. Amer. Chem. Soc., 1933, 55, 5058.2 Bernal and Fowler, J. Chem. Physics, 1933, 1, 515.3 Symp. Change Transfer Processes (Chem. Inst. Canada, 1958) ; see Can. J. Chem., 1959,37,178.4 Conway and Salomon, J. Chem. Physics, 1964, 41, 3169.5 Conway, Can. J. Chem., 1959,37, 178.6 Z. Elektrochern., 1958, 62, 567. 7 Christov, Electrochim. Actn, 1961, 4, 194GENERAL DISCUSSION 257remain in one state.1 The calculations presented by Bockris et al. in this dis-cussion and elsewhere 2 are based upon thermodynamic cycles originally treatedby Horiuti and Polanyi 3 and Butler.4 The energetics of the discharge mechanismcan, in this treatment, be represented by the following relations :andwhere AHi and AH1 are the enthalpies for initial and final states, respectively, in thedischarge mechanism.Use of these two equations implies a change in electronicstate so that construction of a potential energy surface from these relations violatesthe adiabatic principle. Furthermore, the only constant terms in eqn. (1) and (2)are the dissociation energy DH, of molecular hydrogen and the ionization energy IHof atomic hydrogen. The metallic work function (bm must be considered as a variablesince only the values in vacuo are known while the effects of adsorbed hydrogen andwater molecules are unknown. The repulsive energy function R is an adjustableparameter depending upon the values chosen for the heat AHads of adsorptionand the solvation energy of the proton AH,.(ii) It has been argued that our treatment overestimates the bending frequencywhile it underestimates the stretching frequency in the activated complex.Wehave chosen our bending frequencies empirically as discussed in our paper andthink that no further discussion is required since they are logical bending frequenciesby comparison with those for other structures. Our assignment of a stretchingfrequency may be subject to some criticism since we have not presented a detailedsurface to support it. Such a calculation has been carried out and will be publishedshortly. The fact remains that we have still chosen our values to fit best the experi-mental data and not vice versa.In Bockris’s treatment here and elsewhere,Z the HzO-H+ bond does not sufferany displacement in the activated complex and yet bending frequencies much lessthan 600cm-1 are implied while the observed bending frequencies for H30f are1400-1700 cm-1.5 If the proton to oxygen bond is not stretched in the activationprocess, then the only remaining particle which exhibits motion (Le., transfer) isthe electron.(iii) The interaction between Hg and 0 is taken as being negligible by Bockrisand Srinivasan.2 This is an unreasonable assumption and was attributed to thelarge barrier width which also seems to be unreasonable as discussed in our paper.The percentage coulombic energy for the Hg-H bond, p2, was taken as a variableparameter, but the values taken for p2 are not in accord with theoretical expectation.Rosen and Ikehara 9 have shown that p increases markedly as the effective quantumnumber Zefi increases.Thus, p is 14 % for H2, 18 % for Na2, 24 % for Ni2,1024 % for Ni-H11 and 26 % for Pt-H.11 Hence the values of 5 and 3 % forp2 do not appear reasonable.AHi = +DHz+IH+AHs-+m, (1)AHf = &DH2 + AHads + R, (2)1 Glasstone, Laidler and Eyring, Theory of Rate Processes (McGraw-Hill, 1941).2 Bockris and Srinivasan, J. Electrochem. Soc., 1964, 111, 844.3 Horiuti and Polanyi, Acta physicochem., 1935, 2, 505.4 Butler, Proc. Roy. SOC. A, 1951, 157, 423.5 Walrafen, J. Chem. Physics, 1962, 36, 1935.6 Gomer, Field Emission and Field Ionization (Harvard, 1961), p. 6-9.7 Bockris and Parsons, Trans. Faraday SOC., 1949,45, 916.8 Conway and Salomon, J .Chem. Physics, 1964,41, 3169.9 Rosen and Ikehara, PhyJic. Reu., 1933, 43, 5.10 Horiuti, Okamoto and Hirota, Sci. Pap. Inst. Phys. Chem. Res. (Tokyo), 1936, 29, 233.11 Horiuti and Nakamura, J. Res. Car., 1951, 2, 73.258 GENERAL DISCUSSIONProf. J. O’M. Bockris, Dr. S. Srinivasan (University of Pennsylvania) and Dr.D. B. Matthews (University of Virginia) (communicated): The fact that a reactioninvolves charge transfer does not necessarily mean that the adiabatic principle isviolated. Thus, there can be adiabatic and non-adiabatic homogeneous redoxreactions. The adiabatic principle as first stated by Ehrenfest 1 is as follows :“ A system will always remain in a definite quantum level if its surroundings arechanged sufliciently slowly.” A condition for the validity of the adiabatic principleis the Born-Oppenheimer principle which states that “ nuclear motions in ordinarymolecular vibrations are so slow that they do not affect the electronic state of themolecules ’,.When two potential energy surfaces intersect, resonance splittingoccurs leading to the formation of an upper and a lower surface. If the masspoint representative of the system makes a transition from the lower to the uppersurface in the vicinity of the crossing point, then the change is non-adiabatic and,if it remains on the lower surface, the change is adiabatic. It is the latter type ofreaction with which we are concerned in the proton discharge step of the hydrogenevolution reaction. Thus, a quantum mechanical calculation of potential energysurfaces is valid in this reaction.The mechanism of charge transfer discussed aboveis treated in detail in a forthcoming publication.2In the calculation of the relative enthalpies of the initial and final states, theelectronic work function in uacuo is the relevant quantity. Only when one isinterested in barriers for electron transfer does one have to consider the effectsof adsorbed hydrogen and water molecules on the work function. Further, theeffect of work function changes may be seen in comparing rates of hydrogen evolu-tion on two metals, but this effect should cancel out when a ratio of rates of H2and HD or HT evolution are considered.The reasons for stating that the bending frequencies, in the calculations ofConway and Salomon, are over-estimated are given in our reply to comments ofthese workers.Further, in their calculations, stretching frequencies of the activ-ated complex were chosen to fit the experimental results. In our work, stretchingfrequencies were calculated by the semi-empirical method of Eyring et al. Toexamine the limitations of this method, several calculations were carried out, tosee the effects of varying the assumptions, e.g., the ratio of coulombic to exchangeenergy. The resulting separation factors were then compared with experiment.The calculated stretching frequency varied between 2773 and 2906 cm-1 for theH isotope of the activated complex in the slow discharge mechanism, and was not3400 cm-1 as stated in Salomon’s comments.The activation process in the slow discharge mechanism is the stretching of theH+-OH2 bond.This bond should be stretched by an amount corresponding to anactivation energy of about 20 kcalmole-1. However, as a consequence of thesteepness of the Morse curve for the pseudo-diatomic molecule H+-OH2 the amountof stretching of this bond may be expected to be small compared to the bond lengthitself (1 -05 A).The model used for the activated complex is a pseudo-triatomic molecule. Thus,the activated complex has three real frequencies-two bending and one stretching.The bending frequency for this molecule has no counterparts in the pseudo-diatomicmolecules H+--OH2 or its isotopes. It is assumed that the bending frequencies ofthe latter molecule do not contribute to an isotope effect in the transition state.In the potential energy calculation, it is the interaction between Hg and OH2(latter treated as single atoms) which was considered small and hence neglected.1 Ehrenfest, Ann.Physik., 1927, 51, 327.2 Bockris and Matthews, submitted for publication to Proc. Roy. SOC. A GENERAL DISCUSSION 259The basis of this assumption is the absence of any pseudo-diatomic compound forma-tion between Hg and OHz. There is evidence for chemisorption of water on mercury,but this takes place only when the water molecule is adjacent to the metal.For the percentage of coulombic energy of the Hg-H bond, three (and not two,i.e., 3 and 5 % only) were used, viz., 3, 5 and 20 %. The low value of 3 % wasused from the relationship between percentage ionic character and difference inelectronegativities.Even over the wide variation from 3 to 20 % for the Hg-Hbond and 5 to 39 % for the 0-H bond in percentage coulombic energy, the varia-tion in the classical separation factor is less than 10 %. A wider variation in per-centage coulombic energy from 20 to 100 % was used in the calculations for theslow electrochemical desorption calculation and the separation factor variation isless than 20 %. Further, the calculations revealed that increase of percentagecoulombic energy decreases the separation factor. Thus, the effect of increasingthe percentage coulombic energy any further will only slightly reduce the separationfactor.The experimental variation of H-T separation factor on mercury with potentialindicates that the separation factor reaches a constant value at high over-potentials.At these over-potentials, the tunnelling corrections should be unity due to the lowbarrier height, and hence the experimental values should correspond to the classicalseparation factors.The agreement, obtained between the experimental and theor-etical values, is, in fact, a remarkable one. Further, using the same method ofcalculation for the classical separation factors in the other mechanisms, the agree-ment between the theoretical and experimental values is also quite good. For thesemechanisms, the tunnelling correction factors is again practically unity at the currentdensities at which the separation factors were determined.The consistency of themethod of calculation used is thus evidenced.The approach, used by the present authors, is that normal to most investigations ;viz., to take the facts and attempt to find a model to explain them. The presentmodel, including the tunnelling contributions which it implies, does. This criterionof the degree of probability of the views expressed applies less well to the views ofConway and Salomon. The only way, therefore, in which their concepts shouldbe preferred to ours is that the latter did contain an error in respect to the adiabaticprinciple. This claim of Salomon receives comment above.Prof. B. E. Conway (Ottawa) said: First I would like to defend my positionwith regard to the statement made in the paper of Bockris, Srinivasan and Matthewsthat we have made “ errors of principle” in our previous calculations.1 Thecriticism is that we did not consider the zero-point energies associated with thetransition state.It must be stated first that zero-point energy effects in the transitionstate were, in fact, considered in our paper in 1960 2 which was evidently overlookedby Bockris et al. in their criticism. In our 1958 paper, the purpose was to calculaterelative values of the maximum isotope effect for various mechanisms. We donot accept this as an error of principle since the fuller quantitative significanceof such zero-point energy factors was not generally treated until about that time andlater. Thus, in Wiberg’s review 3 a similar position to that in our 1958 paper wastaken and in the review by Bockris himself4 the same factor was neglected.Inour own calculations in 1958, the zero-point energy factor in the transition statewas not considered owing to some difficulties of principle which are involved and,1 Proc. Roy. SOC. A , 1958,247,400.2 Proc. Roy. SOC. A, 1960, 256, 128.3 Chem. Rev., 1955,55, 713.4 Modern Aspects of Electrochemistry, I, chap. IV (Butterworths, London, 1954)260 GENERAL DISCUSSIONwe believe, are still relevant. Thus, Kassel pointed out in 1935 1 that there mustbe difficulties involved in the statistical-mechanical treatment of vibrations in thetransition state owing to uncertainty in the quantization of the levels since the rateof passage of the reacting particle across the transition state region is such as tocause an uncertainty A? in energy (expressed in terms of wave numbers) of ca.700 cm-1.This is comparable with the frequencies of the vibrational modes in thetransition state. Also, as pointed out by Bell 2 in his treatment of a coulombicmodel for proton transfer, the zero-point energy effect in the transition state is can-celled by the tunnel correction for small curvature at the crossing region, so thatthe relative rate constant ratio for H and D transfer becomes dependent only on thezero-point energy difference in the initial state as considered in ref. (1).Bockris et al. also claim in two places in their paper that proton tunnelling effectsin the hydrogen evolution reaction at electrodes have been previously neglected.This is misleading: the first work was done in 1934 by Bawn and Bgden (ref.( 5 )in our paper); two other papers on the role of tunnelling have been published byourselves (ref. (6) and (12)) and Christov has published at least six major con-tributions on this problem (e.g., see ref. (7) in our paper).Dr . D. B. Matthews (University of Virginia) said: Conway and Salomon referto the theory of Gurney3 as a non-adiabatic theory. The terminology of Sacherand Laidler,4 which has been adopted by Conway and Salomon, has been criticizedrecently by Marcus.5 In particular, an electron tunnelling process is not a non-adiabatic process. Since adiabatic behaviour results from the relatively slow move-ment of nuclei compared to the electron,6 then the rapid tunnelling of an electronis an adiabatic process.Conway and Salomon discuss the theory of Gurney 3 under the heading of case(a), yet under case (b) they have given a description of the theory of Gurney asmodified by Butler.7 The Gurney theory treats the proton discharge process asoccurring by proton transfer followed by electron tunnelling to the proton in theactivated state. The major error in the theory of Gurney was the neglect of theM-H interaction. This correction to Gurney’s theory was made by Butler 7followi ng the work of Horiuti and Polanyi.8They also state that “ the activated state is charged and, as a result, high bendingfrequencies arise ”.This statement requires one to specify the relative positionsof the nuclei in the activated state since the magnitude of the bending frequencydepends strongly on configuration. Their statement is true only for symmetricactivated complexes of the type X .. . H . . . X. Furthermore, the activatedstate is best considered as being comprised of two resonant states 9-11 M . . . H. . . H20 and Me- . . . H+ . . . H20. Thus as far as the energy of the activated stateis considered the charge distribution is immaterial.Conway and Salomon claim to have made measurements on the h.e.r. for Hgin methanol down to temperatures of -125°C yet their data show measurements67134J. Chem. Physics, 1935, 3, 339.Gurney, Proc. Roy. SOC. A , 1931, 134, 137.Sacher, Laidler, Modern Aspects of Electrochemistry, vol. 11, ed. Bockris and Conway (Butter-worths Sci.Publ., 1964).Kauzmann, Quantum Chemistry (Academic Press Inc., New York, 1957).Butler, Proc. Roy. SOC. A, 1936, 157, 423.2 Bell, Trans. Faraday SOC., 1961, 57, 961.5 Marcus, Ann. Reu. Physic. Chem., 1964, 15, 155.8 Horiuti and Polanyi, Actu Physicochim., 1935, 2, 505.9 Bockris and Matthews, Electroanalyt. Chem., in press.10 Bockris and Matthews, Proc. Roy. SOC. A, to be published.11 Matthews, Modern Aspects of Electrochemistry, vol. IV, ed. Bockris and Conway (Butter-worths Sci. Publ.), to be publishedGENERAL DISCUSSION 26 1down to only -90°C. From the point of view of obtaining evidence for protontunnelling, the minimum temperature at which measurements were made on theh.e.r. with Hg is very important.In their discussion of proton tunnelling Conway and Salomon have assumed(2d)~cb:art = (2d)real, which is not correct.As a rough guide,(2d)Eckart : (2d)real: (2d)parab.= 5 3 : 2.In fig. 6 and table 4 of their paper Tafel parameters less than classical are reported.However, proton tunnelling leads to high Tafel slopes and in no case does theorypredict values less than classical. This discrepancy points to serious errors intheir method of calculation.Conway and Salomon quote double-layer capacity measurements as evidenceagainst large proton transfer distances ; in fact these measurements support suchproposals. Thus, if the proton were able to migrate up to the electrode surface,then other cations not capable of the anomalous conductance mechanism shouldproduce different double-layer capacities at cathodic potentials.If the protonstops one layer of water molecules from the electrode surface then all is well.Conway and Salomon refer to the well-known inconsistencies of the Gurneymodel.1 Once allowance is made for the M-H interaction, as was done by Horiutiand Polanyi 2 and by Butler 3 then such inconsistencies no longer exist. Theargument that the dependence of io on the electronic work function of the metalis inconsistent with the Gurney model is not tenable. For the low io metals (e.g.,Hg, Pb, Cd, TI, Sn, Ga) the value of io decreases with increase of work function.4Moreover, when one considers the relation of the measured potential to the metal-solution potential difference 5 then one finds an absence of any direct dependenceof io on work function, and the observed dependence may be shown to be a resultof the interrelationship of work function and heat of adsorption of atomic hydrogenon the metal.4Prof.J . O’M. Bockris (University of Pennsylvania) (communicated): I do notthink that there is escape from the fact that an error of principle was committed byConway in neglecting the zero-point energy contributions to the activated state.6Zero-point energy differences of the transition state in separation factor calculationshad been already a recognized procedure for some years at the time.7-9I reiterate our statement that proton tunnelling has been neglected in the con-sideration of the hydrogen evolution reaction until the present time, except inChristov’s work,lo to which I have paid full recognition in my paper with Srinivasanand Matthews.In particular, tunnelling was rejected by Butler expressly, and protontunnelling specifically by Conway and Salomon in the present Discussion. Bawnand Ogden’s work 11 is thus the only one to which Conway may validly refer ; lackof account, however, is given to this work owing to the fact that it was based ongrossly wrong experimental measurements which were wrong by many hundreds ofpercent for artifactal experimental reason which becomes clear on studying their paper.1 Gurney, Proc. Roy. Soc. A . 1931,134,137.2 Horiuti and Polanyi!ActuPhysicochim., 1935,2,505. 3 Butler, Proc. Roy. Soc. A . 1936,157,423.4 Conway and Bockris, J.Chem. Physics, 1958, 28, 354.5 Bockris and Potter, J. Electrochem. Soc., 1952, 99, 169.6 Conway, Proc. Ray. SOC. A , 1958,247,400.7 Okamoto, Horiuti and Hirota, Sci. Pup. Inst. Phys. Chem. Res. (Tokyo), 1936, 29, 223. * Horiuti, Keii and Hirota, J. Res. Inst. Cut., 1951, 2, 1.9 Keii and Kodera, J. Res. Inst. Cut., 1957, 5, 105.10 Christov, Electrochim. Actu, 1961, 4, 194, 306.l1 Bawn and Ogden, Trans. Furuday Soc., 1934, 30,432262 GENERAL DISCUSSIONProf. B. E. Conway (Ottawa) and Dr. M. Salomon (Princeton) (communicated):A number of criticisms of our paper have been raised by Dr. Matthews. (i) Therehas been much confusion in the past regarding the use of the terms “ non-adiabatic ”and “ adiabatic”. Our usage seems to be satisfactory and consistent with theclarification published recently.1 The term “ non-adiabatic ” used in the sense ofthese authors will apply when the electronic rearrangements are fast compared withnuclear motions, as must arise in an electron tunnelling process referred to incase (b) of our paper.The term is used in a different and wider sense by Marcus 2and his definition is less applicable to our case. In a previous review 3 it has beenrecommended that the terms “ adiabatic ” and “ non-adiabatic ” be abandonedon account of the difficulties and arbitrariness of the definitions and use of thesetwo terms. As pointed out elsewhere,4 “ these terms, unless they are stringently,defined, may lead to unnecessary confusion ”. Dr. Matthews’s difference ofopinion arises from his use of different definitions for the terms referred to in ourpaper which were used in the sense of the quoted references.(ii) Dr.Matthews claims that in our summary of possible types of proton transfermechanisms, that in case (a) is not Gurney’s mechanism, while that in (b) is. Thisis certainly not claimed ; Gurney’s mechanism in case (a) is referred to only in regardto the absence of any conventional “unique” activated complex such as may beconsidered in an adiabatic process (see above) ; the mechanism in (b) is in any casenot that of Gurney but is related rather to that of Butler and Horiuti and Polanyi,since we stated that H atom adsorption will be involved and referred to Butler,and Horiuti and Polanyi in our discussion of Gurney’s mechanism.We alreadyreferred to the difficulties with Gurney’s theory in our paper by quotation of therelevant references.(iii) The statement made by us regarding high bending frequencies v b is basedon (a) the existence of such frequencies in stable molecules, e.g., FHF-, B2H6 analo-gous to activated complexes in proton transfer reactions ; (b) the calculated valuesof these frequencies (ref. (40) of our paper) and (c) the deduced frequencies for transitionstates in homogeneous proton transfer reactions (e.g., ref. (57) of our paper), wherev b is between 1793 and 2440cm-1. Contrary to what Dr. Matthews claims, thecharge distribution is of basic importance as indicated by Bader’s calculations andfrom the experimental indications of the effects of electron-releasing or electron-withdrawing substituents on the isotope effect in acid-base proton transfer.Dr.Matthews also mentions the two resonant states M . . . H . . . H20 andMe- . . . H+ . . . H20. In our discussion, we considered tunnelling to the“activated” H3O+ ion, so we do not see how the two resonant states normallyconsidered will be involved in the classical way he implies.(iv) Dr. Matthews says that we have claimed to have worked down to -125°Cbut our results are given only to -90°C. Inspection of fig. 4 of our paper indicatesthat the lowest temperature points go down to 1/T = 0.0067(6)”K-1, or 148°K.The new results for Ni presented verbally in this Discussion were also made downto this temperature. The temperatures attained were as low or lower than any othersyet studied in proton transfer reactions.51 Sacher and Laidler, Modern Aspects of Electrochemistry, In, chap.I (Butterworths, London,3 Laidler and Shuler, Chem. Rev., 1951, 48, 153.4 Laidler, Chemical Kinetics of Excited States (Oxford, 1955), p. 35.5 cf. Caldin and Kasparian, this Discussion. Bell, Fendley and Hulett, Proc. Roy. SOC. A , 1956,235, 453. Bell and Thomas, J. Chem. Soc., 1939, 1573. Bell and Norris, J. Chem. SOC.,1941, 118, 854. Caldin and Long, Proc. Roy. SOC. A, 1955, 228, 263. Caldin and Trickett,Trans. Faradzy SOC., 1953, 49, 772. Caldin and Harbron, J. Chem. SOC., 1962, 2454.1964). 2 Marcus, Ann. Rev. Physic. Chem., 1964, 15, 155GENERAL DISCUSSION 263(v) We have not assumed that the Eckart barrier width is identical with the“ real ” molecular barrier width of ca.0.6 A but have examined a range of Eckartbarrier widths. We do, however, suggest that the relevant barrier width is likelyto be substantially less than the figure of ca. 4A used by Bockris, Srinivasan andMatthews in this Discussion. We agree that there will be a difference between thereal and equivalent Eckart and parabolic barrier widths.(vi) For small barrier widths, the Tafel slopes are always larger than the classicalvalues.1 For the larger barrier width and over a range of temperatures, thetunnelling calculation, based on the method of Bell, gives Tafel slopes which donot depend to the same extent on temperature as do the classical slope values.Hence discrepancies increase with temperature.(vii) We have already expressed the expectation that the capacity for the H+ion would be different from that for other cations if appreciable equilibrium pene-tration of the inner solvent region occurred.However, kinetic penetration of theproton under steady-state discharge conditions is what is involved in the mechanismof the h.e.r. Most capacity measurements do show an increase of the double-layer capacity with increasing cathodic potentials which offers some support forow view.Prof. S. G. Christov (Inst. Physic. Chern., Bulgarian Academy of Sciences) said:The theoretical method for evaluation of the separation factor S employed in thepaper of Bockris, Srinivasan and Matthews is, in principle, the best one.How-ever, the calculations of the classical values of S on the basis of an Eyring energysurface cannot be very reliable, as follows from the very low value obtained for thebarrier height.2 The application of Morse curves for exact calculations of ion-transfers in water is surely not reasonable, because the potential energy is due notonly to the exchange-coulomb forces, but also to a very significant extent to pureelectrostatic forces between the H+-ion and all the neighbouring H20-dipoles.The tunnel corrections in this paper are calculated, using an Eckart potential,in the same manner as in writer’s papers.39 4 The results confirm all the generalconclusions in the latter papers about the dependence of Tafel slopes b on barrierdimensions, isotope mass and temperature, which follow directly from the generallaw b/bl =f(6/y).The numerical values for b are more correct than those ofSalomon and Conway, as far as b/bl>l. However, the use of the pure Eckartpotential, including a non-linear term, leads to higher Tafel slopes than for a linearelectric potential (ref. (2), p. 579), therefore the b-values in their paper are over-estimated by about 10 mV.The important contribution of Bockris et al. is the attempt to explain the depend-ence of the H/T separation factor ST upon electrode potential in terms of the tunneltheory.The potential dependence of the tunnel correction factor z = i/il is includedin eqn. (l), in which A( A4,T) = z( A4,T)Al(T) 4 ; this leads, by very large tunnelling,to considerable deviations from the normal Tafel line.4 However, a moderatevariation of z with A@ is compatible with the practical validity of Tafel law, asfirst shown by the writer (ref.(2), p. 579) for the Eckart barrier (non-linear electricpotential). This result is confirmed by the Bockris et al. calculations, too. More-over, the barrier dimensions, for which b = bl, and an accessible potential dependenceof b may be expected, were also predicted before on the basis of the general relation1 Can. J. Chem., 1959,37, 178.2 Bockris and Srinivasan, J. Electrochem. Soc., 1964,111, 849.3 Christov, 2. Elektrochem., 1958,62, 567.4 Christov, Electrochim. Acta, 1961,4,194, 306264 GENERAL DISCUSSIONb/bz = f’(6/y) (ref. (3), p. 203) ; for Eo = 1.5 x 10-12 erg it was found TO = 2l= 3.7 A(ref.(8), p. 212), which is very near to Bockris’s result, TO = 4A.However, the significant dependence of z on electrode potential in the region, forwhich b c: bl, is connected essentially with the unsymmetrical non-linear term inthe Eckart function. Applying instead of the latter a linear electric potential, weobtain a much smaller potential dependence of z, as shown previously (ref. (2),table 4) ; in this case for EO = 1.5 x 10-12 erg, it was found that b-bl at a smallerbarrier width z0-2.7A (ref. (2), p. 212). This value is preferable, because itcorresponds to a homogeneous electric field in the double layer, as accepted in notvery dilute solutions.Their affirmation that Christov has ignored the zero-point energy contribution,is incorrect, because it is included in the “ true ” classical activation energy, whichis an unknown in the theoretical equations, as explained before.192 In this way itis possible to find a lower value for the net tunnel correction.The result 192 isEH =ED ( k0.3 kcal) is obtained by calculations, using the experimental data ofPost and Hiskey.3 In this case the potential dependence of z has been ignoredby the writer; the reason is that such a dependence is not observed by Post andHiskey. The writer’s calculations 49 1 9 2 agree well with all data of these authors.The results for H/T separation were unknown at the time, but it is possible now toinclude the new data in similar calculations; in this case it is not excluded thatET#EH “ED, i.e., the zero-point energy difference ET -EH#O may contribute moreto ST than ED-EH to SD.The results for ZH = 3.19 (at q = 1 V) and tunnelling degree = 86 % (at q = 0)are near to those found by Christov: ZH = 3.33 (at q = 0), and 70 % (at y = 0).However, the difference is due mainly to the reduced barrier width (4A instead of4.7 A *), and not to the non-zero reaction heat (A0 = -0.6 x 10-12 erg, instead ofA0 = 0), which cannot greatly influence the tunnel corrections in the present caseof moderate tunnelling.The present investigation of Bockris et al.agrees in many important pointswith the earlier conclusions of the writer. Their numerical values for the barrierdimensions correspond well with the experimental data for ST and its potentialdependence.However, they lead to apparent activation energies E;i and EL (atq = 0) of less than 21.7 kcal, while according to Post and Hiskey,3 Eh = 21.7and Eb = 22.5 kcal/mole (at q = 0). It is impossible that E<E’.The barrier width 20 = 21 = 4~4, found by means of the extended Eckart model,is surely not the real one. One can obtain the same agreement with experimentwith an equivalent parabolic barrier with nearly the same curvature at the top, i.e.,with a width of about 21/71 = 1.2 A. The most probable value of the real barrierwill be an intermediate one, i.e., TO = 1.8-2 A, as affirmed by the writer earlier.:!Prof. J. O’M. Bockris, Dr. S. Srinivasan (Univ. of Pennsylvania) and Dr. D. B.Matthews (Univ. of Virginia) (communicated) : The model used for the transitionstate is that of a pseudo-triatomic molecule 5 in the slow discharge mechanism.As in the theory of Eyring,6 the potential energy of the system was calculatedas a function of the variable distances H20 .. . H and H . . . M by treating* The latter value, found by Christov, was used from Bockris et al. in a previous paper.1 Christov, Electrochim. Acta, 1961, 4, 194, 306.2 Christov, Proc. 1st Austral. Con$ Electrochemistry, 1963 (Pergamon Press, 1964), p. 723.3 Post and Hiskey, J. Amer. Chem. SOC., 1950,72,4203 ; 1951,73, 161.4 Christov, Dokl. Akad. Nauk. S.S.S.R., 1959, 125, 141.5 Parsons and Bockris, Trans. Farahy SOC., 1951,47,914.6 Glasstone, Laidler and Eyring, The Theory of Rate Processes (McGraw-Hill, N.Y., 1941)GENERAL DISCUSSION 265the potential energy of the system as a three-electron problem, from which thesaddle point was located.Contributions to the energy of the system, due toion-neighbouring water dipole interactions, are small ( - 1 kcal mole-1) comparedto the breaking H20 . . . H+ and forming €3 . . . M bonds. Thus, they are onlya second-order effect and should not significantly alter the force constants andhence the vibrational frequencies of the transition state which were calculated.As an example, we may consider the approximately equal frequencies of the &ofion in the gaseous and liquid states.Further, the ion dipole interaction may only lead to a restricted rotation andnot affect the vibrational frequencies of the normal modes.The isotope effectdue to this librational mode was taken into account in the calculations.The comments of Christov regarding the dependence of proton tunnelling cal-culations on the nature of the electric field at the electrode-solution interface (i.e.,linear or non-linear) are based on an interpretation of the symmetry factor p whichis not generally accepted. This matter has been treated by Bockris and Matthews.1, 2Regarding inclusion of zero-point energy differences in the calculations of separa-tion factors, such differences cannot be ignored. The approximation of Christovis equivalent to assuming &lass = 1. Theoretically,3 (SH,D)cla&! = 2.4 for slowdischarge-fast recombination on Hg and theoretically and experimentally 39 4(SH,T)C~~SS = 3.4 for the same mechanism.These results are a consequence ofthe fact that although the differences involved are small (-1 kcal) they occur inexponential form in the expression for Sclass. The calculations of Christov con-cerned the imaginary separation factor,and hence the above results are not directly applicable but the same principles arerelevant. The effect of A0 on the tunnel correction to the separation factor is givenin fig. 4 of the paper presented by Bockris, Srinivasan and Matthews.5The apparent anomaly concerning relative values of barrier height and measuredactivation energy noted by Christov is readily resolvable. The measured activationenergy for Hg in 7-5 N HCl was 20-3 kcal mole-1 compared to 21.3 kcal mole-1in 1 N acid solution.The barrier height of 21.6 kcal (1.5 x 10-12 erg) is thusconsistent with a measured activation energy of 20.3 kcal mole-1.Prof. J . O’M. Bockris (University of Pennsylvania) (communicated): I am sur-prised that Prof. Christov doubts that potential energy surfaces can be used ade-quately in calculation of the vibrational partition functions in the activated state(necessary in the classical calculations of separation factors). A careful examina-tion was made by Srinivasans of the variation of the curvature of the potentialenergy surface in the neighbourhood of the transition state as a function of theratio of coulombic to exchange forces and the results which have been used in ourcalculations take into account a wide choice of this ratio.It is, indeed, true that the Eckart barrier is used in calculating barrier width.This is not, however, the real barrier width to be used in a model.Remarks byConway and Salomon have involved this misunderstanding. Dr. Matthews haspointed out the appropriate relationships elsewhere in the Discussion contributions.1 Bockris and Matthews, Proc. Roy. Sac. A , to be published ; J. Electroanal. Chem., 1965,9, 325.2 Matthews, Modern Aspects of Electrochemistry, vol. 4, ed. Bockris and Conway (Butter-3 Bockris and Srinivasan, J. Electrochem. SOC., 1964, 111, 844.4 Bockris, Matthews and Gileadi, Electrochim. Acta, to be published.5 Bockris, Srinivasan and Matthews, this Discussion.6 Srinivasan, Ph.D. Thesis (University of Pennsylvania, 1963.worths Sci.Publ.), to be published266 GENERAL DISCUSSIONThe barrier width which arises as a result of the Bockris, Srinivasan and Matthewscalculations agrees well with those of other authors.It is good to see that Prof. Christov agrees with our independent investigationof proton tunnelling at electrodes. The necessity for this investigation arose be-cause of the fact that Prof. Christov’s earlier calculations did neglect zero-pointenergies.1 A large fraction of the evidence which he adduced for tunnelling wasbased upon separation factors. However, the value of the separation factor ismade up to a considerable extent of contributions from the zero-point energy andtherefore the evidence which he adduced was in this respect not convincing.Inour calculations, the zero-point energy contribution and the tunnelling contributionsto the separation factor have been separately calculated, and the result is a qualitativeconfirmation of Christov’s prediction that tunnelling protons made a contributionto the velocity of the proton discharge reaction on mercury (in work to be published,it will be shown that this is not so on metals of the transition group).2Prof. S. G. Christov (Sofia) (communicated) : Electrostatical interactions betweenproton and water molecules in the transition state (reversible or non-reversiblesolvation) surely cannot be excluded in exact calculations, as pointed out in thisdiscussion, too. Therefore the result of Bockris et al. (SI.I,D)~~~S. = 2.4 seems to benot very reliable.The calculations of Christov are consistent with the reasonablevalue Sclass. = ,/2, which leads to S = Scl. (rH/rD) = 2.5-2.9.3In calculating the current density by proton tunnelling it is not necessary to intro-duce the symmetry factor (ref. (l), eqn. (12)). The difference in Tafel slopes byapplying a linear or non-linear electric field is due only to the different mode ofbarrier deformation in both cases.4Full experimental data both for H and Devolution on Hg are available onlyfor 0.1 N HCl.5 The barrier height E = 21.6 kcal, assumed by Bockris et al., isinconsistent not only with the experimental activation energy for H(Eh = 21.7 kcal),but also with those for D(Eh = 22.5 kcal), because it is essential that E>EfI andE> EA.Prof.B. E. Conway and Dr. M . Salomon (Ottawa) said: We would like to raisethe following points regarding the calculations of Bockris, Srinivasan and Matthews :(i) Energies of activation are calculated for the proton discharge mechanism by theseauthors using the London-Eyring-Polanyi (L.E.P.) method and the values obtainedare 2, 4 or 6 kcal mole-1, depending on the fraction of coulombic interaction energyassumed. These values seem too low to be realistic in view of the fact that theexperimental apparent heat of activation at the reversible potential is 18-20 kcalmole-1 at mercury, as measured by Bockris and Parsons.6 The authors seem alsoto introduce an inconsistency into their paper by considering a barrier height E:for the tunnelling calculations of 1.5 x 10-12 erg (ca.22 kcal mole-1) yet the L.E.P.surface calculations, mentioned above, from which vibrational frequencies v ’ werecalculated, give much lower values. If the L.E.P. surface calculation is used forestimating the classical isotope effect through v # values, then, it seems, it mustalso be used with respect to the E# value in the calculations of thetunnelling correction. (ii) In relation to the above point and to the question raisedin the text of our own paper, it seems that the L.E.P. calculation gives unrealistic1 Christov, Electrochim. Acta, 1961, 4, 194, 306.2 Bockris, Gileadi and Haynes, to be published.3 Christov, Electrochim. Acta, 1961, 4, 194, 306.4 Christov, 2. Electrochem., 1958, 62, 567.5 Post and Hiskey, J.Amer. Chem. Soc., 1950, 72,4203 ; 1951, 73, 161.6 Bockris and Parsons, Trans. F‘raday SOC., 1949, 45,916GENERAL DISCUSSION 267values to the frequencies v p and v8 for the bending and symmetrical stretching modes,respectively, in the activated complex for proton discharge. Thus in real mole-cules, e.g., FHF-, v p is 12OOcm-1 or higher. In homogeneous proton transfertransition states, v p has been deduced as 1793-2440 cm-1, e.g., for the decarboxyl-ation of substituted aryl P-keto acids 1 and calculated as 770-1980 cm-1 by Bader 3depending on the charge distribution in the transition state. Correspondingly,much lower v, values are indicated in the range 250-600 cm-1 and values as highas 2800-2900 cm-1 obtained by Bockris et al. appear unlikely.2 The latter resultarises because in their calculations it is found that at the “ activated state” theOH+ bond is not significantly stretched from the equilibrium value in H30f.Webelieve this is very unlikely and appears inconsistent with (a) the observed activationenergy of 18-20 kcal mole-1 and (b), the results of previous potential energy profilecalculations 3 and (c) the observed effect of potential on the reaction rate wherelog i is linear in overpotential at mercury over nine decades of rate up to ca. 1.3 Vabove the reversible potential. Also, no bending mode frequencies are involvedin their calculation for the transition state. This seems unlikely and inconsistentwith most other treatments of three-atom XHX systems.The difficulties undoubtedly arise from the unsatisfactory nature of the L.E.P.type of calculation recently criticized by Johnston and co-workers.4 While, inour work, we have made only empirical, but rational, estimates of the force con-stants for vibrations in the transition state, we believe that this method may bepreferable until more satisfactory a priori methods are available.The calculationsof Bader 2 seem to offer the kind of improvements which are required for furtheradvances in this problem and for the related treatment of transition states in homo-geneous proton transfer reactions. The authors claim that the calculations can beused with simple measurements of SD or ST to identify the rate-determining pechan-ism of the h.e.r. at various metals. With the difficulties mentioned above and theuncertainties in a priori calculations of activation energies and isotope effects, evenfor homogeneous reactions, we regard their suggestion as over-optimistic and urgea more cautious approach.(iii) While proton tunnelling at thin barriers can lead to a potential-dependentisotope effect as we have shown,S we do not see how this effect can arise when thebarrier width is as large (ca.4 A) as that used by Bockris, Srinivasan and Matthews.Thus, the calculations of Christov 6 indicate identical Tafel slopes for H and Ddischarge by tunnelling already when the barrier width exceeds ca. 3.4A (withE’ = 1.5 x 10-12 erg) ; hence the relative rate ratio for discharge of H and D speciesshould be independent of overpotential, and hence SD constant.We do not believethat a potential dependence of SD or ST is inconsistent with a classical isotope effectsince with varying electron availability at the base centre (the cathode surface inthe electrochemical proton transfer case) in homogeneom acid-base proton transferreactions, the isotopic ratio of the rate constants k H and k D can either increase ordecrease with changing base strength of the proton acceptor depending on thesymmetry of the proton in the activated complex. Similar effects will, we believe,be operative in the h.e.r. as pointed out in our own paper.1 Swain, Wiles and Bader, J. Amer. Chem. SOC., 1961, 83, 1945.2 Bader, Can. J. Chem., 1964,42, 1822.3 Bockris and Parsons, Trans. Farday SOC., 1951,47,914.Conway and Bockris, Can. J. Chem.,4 Johnston et al., J. Chem. Physics, 1964, 41, 1517 ; cf. Adv. Chem. Physics, 1961,3, 131.5 Can. J. Chem., 1959,37, 178.6 Christov, Electrochim. Acta, 1961, 4, 306 ; Proc. 1st Austral. Con$ Electrochemistry, ed.1957,35, 1124.Gutmann (Pergarnon Press, 1965)268 GENERAL DISCUSSION(iv) The barrier widths to be used in electrochemical proton transfer requirefurther examination. First, we must distinguish between the real distance 2abetween initial and final state equilibrium positions of the proton and the distance2d to be used in an equivalent Eckart barrier. Generally 2d>2a for the Eckartbarrier to reproduce the curvature at the top of the barrier corresponding to theresonance split intersection of two Morse functions.On this basis, the value of4 ~ 4 seems large compared with the barrier widths deduced in this Discussion (e.g.,see the paper by Caldin and Kasparian) for tunnelling effects. There are also otherdifficulties of a more physical nature. If the proton is situated at the equilibriumposition of H30+ (HgOt ?) in the outer layer region of the double-layer model ofBockris, Devanathan and Miiller 1 (see fig. la) it seems that two intermediate protonDIPOLELAYER (B, DaM)IIIII!IIII1IIIIII"H,OZ " ENTITYaFIG. la.-Double successive transfer out of HgOi in hydrated ion layer. Total jump distance ca.0*6+1*38+2.8+0-35 A (= 5.13 A).transfer steps between H30+ and neighbouring water molecules (cf. the conductancemechanism) are required before the proton is in a situation where tunnel transferdirectly to the electrode is likely to be involved.It seems unlikely that the protonwill tunnel across two layers of water molecules to the electrode base when thesewater molecules themselves can be available as base centres before the proton hasreached the electrode. Dr. Matthews has argued (in discussion of our own paper)that the fact that the Helmholtz double-layer capacity for aqueous acid solutions issimilar to that for the corresponding alkali metal salt solutions (as pointed out inour paper) supports their use of a wide barrier. We believe this is not necessarilyso for the following reasons. The double-layer capacity behaviour reflects theequilibrium thermodynamic properties of the adsorbed ions in the double-layerand statistically it is only this behaviour for the proton which is evidently similarto that of other ions.However, here we are more concerned with the detailedkinetic picture for proton transfer, and we suggest that kinetically with regard to1 Bockris, Devanathan and Muller, Proc. Roy. Soc. A , 1963, 274, 55GENERAL DISCUSSION 269the classical or quantum-mechanical rate-determining step, it is a proton which hasbecome transferred to an inner water molecule in the double-layer that shouldbe considered in the rate calculations. In effect, the homogeneous transfer of aproton from the outer region to the inner water layer (fig. lb,lc) is to be regardedWATERDIPOLELAYER LAYER I___yI1I1DISCHP iR‘///A I Ib CFIG.lb, c.-Probable successive events in proton transfer in model of Bockris, Devanathan andMuller (1 963).FIG. Id.-Conventional model 28 + 0-6 A ; E+ =18-20 kcal. Butler (1936), Parsons and Bockris(1951), Conway, Bockris and Lovrecek (1955),Conway and Salomon (1964). %’ - ’ III 4 i: Idas an equilibrium step prior to the rate-determining proton transfer at the electrodeinterface. The capacity behaviour will still be correctly accounted for if thisequilibrium is in favour of hydrated protons in the outer layer. The relevant kineticbarrier width will then be much closer to that considered by Butler 1 and Bockris1 Butler, Proc. Roy. Soc. A, 1936, 157, 423270 GENERAL DISCUSSIONand Parsons 1 and used as a basis for the calculations in our own paper in thisDiscussion. This equilibrium step may account for the negative volume ofactivation for the h.e.r.at mercury observed by Hills and mentioned elsewhere.A final difficulty arises when alkaline solutions are considered. Under such con-ditions, an H20 molecule is the source of protons and it seems intuitively unlikelythat any water molecules, other than those adsorbed close to the electrode, willparticipate in the discharge reaction.(v) In the paper by Bockris, Srinivasan and Matthews, it has been implied thatour apparent activation energy of 11 -2 kcal mole-1 for the h.e.r. at Hg in methanolis impossible, this figure being compared with the value of 20 kcal mole-1 obtainedby Bockris and Parsons for aqueous solutions.This implication is misleadingsince we already pointed out 2 that the same data of Bockris and Parsons 3 3 4 alsogive a heat of activation AH+- of ca. 9 kcal mole-1 (fig. 2) (q = 0) for aqueous- 13-12!3s.EM0 c( - i l- 10BOCKRIS €!I PARSONS (1949)H20 CHS=8*8-II k c a l . \BOCKRIS 8 PARSONS(1949)/‘-TO VERYLOW TEMPI Isolutions when log io is plotted against 1/T. The same result is obtained with Minc’sdata.5 The method we have used is preferable to that previously employed for theaqueous solutions (viz., obtaining dq/dT at constant current density) since thelatter method gives apparent values of AH# which are a function of temperatureand only the mean value (20 kcal) was taken previously by Bockris and Parsons.The method they used was based on Agar’s analysis 11 which is inapplicable whenis a function of temperature, a fact confirmed by our present results at lowtemperatures.The following general approach will clarify the point and we shall include anydependence of j3 on T.Writing the current density for a simple discharge step asi = k exp (-A W f / R T ) exp (- /34J/RT) exp (- #lqF/RT), (1)1 Bockris and Parsons, Trans. Faradzy SOC., 1951,47,914.2 Conway and Salomon, J. Chem. Physics, 1964,41, 3169.3 Bockris and Parsons, Trans. Faraday SOC., 1949,45,916.4 Bockris and Parsons, Trans. Faraday SOC., 1951,47,914. Conway and Bockris, Can. J. Chem.,1957,35,1124. 5 Minc, Bull. Acad. Polon. Sci., 1959, 8, 29GENERAL DISCUSSION 271where W’ is the activation energy at zero metal-solution p.d., 4,.is the metal-solutionp.d. at the reversible potential, and 4,.+q = the actual metal-solution p.d. ; atzero overpotential (y = 0),It is convenient to write the apparent activation energy at the reversible potential,by differentiating In io w.r.t. 1/T, in the form *In i, = kf-AW‘/RT--P4,F/RT. (2)If B # f(T), AW+ +P&P will be the real activation energy or barrier height at q = 0,but AW+ +P&F+ Fd4,./d(l/T) will be the apparent measured value since 4,. isusuallyf(T). If B =f(T), the apparent activation energy at a given T will beTwhich differs from the barrier height at q = 0 byT d&/d (k) + $ dP/d (i).Hence, an apparent activation energy of 1 1.2 kcal mole-1 need not be inconsistent,as claimed, with overpotentials of >1 V, since the apparent value deduced fromd In iold ( 1 / T ) is not identical with the real barrier height at q = 0.In the generalcase, the term in d#?/d(l/T) may be significant.Prof. J. O’M. Bockris, Dr. S. Srinivasan (Univ. of Pennsylvania) and Dr. D. B.Matthews (Univ. of Virginia) (communicated) : The main purpose was not to calculateactivation energies for the reactions but differences in zero-point energies for the iso-topic activated complexes. In the absence of knowledge of the exact potential func-tion, the London-Eyring-Polanyi method was used but the coulombic-exchangeenergy ratios were varied in the different calculations. Differences between calcul-ated and experimental activation energies, as observed in the present work, have alsobeen found in previous calculations, even for simpler reactions.1 However, withconsiderable variation of coulombic to exchange energy ratios, though the calculatedactivation energies were markedly altered, the H/T or H/D isotope effects wereconsistent and independent of the coulombic-exchange energy ratio.This follows 2from the fact that even though the potential functions are approximate, a choiceof the right mechanism gives reasonable values of the separation factor.As regards the use of the experimental activation energy for the calculationof the tunnelling correction factor ratio, the separation factor calculation may bedivided into two parts-calculation of classical separation factor (&I) and of thetunnelling correction factor ratios, as given by the equations = ~ C l ( ~ H l r T ) * (1)* Less informatively, eqn.(3) can be written (cf. Temkin, Zhur. Fiz. Khim., 1948, 22, 1081),+R BAH+ gdp/d(-:>- yd/3/dfF),where AH and A S are the enthalpy and entropy changes for the hydrogen electrode half-cell reactionor the corresponding standard values when 4, is the standard reversible potential.1 Glasstone, Laidler and Eyring, Tle Theory of Rate Prucesses:(McGraw-Hill, N.Y., 1941).2 Eyring, comments on ref. (1 1)272 GENERAL DISCUSSIONScl is relatively independent of the theoretically calculated activation energieswhich are considerably lower than the experimentally observed values. For thetunnelling correction factor calculation the most important parameters are thebarrier height and width.Thus, it is more appropriate to use the experimentalvalues of barrier heights for this calculation, as was done in the present work.The best evidence for the method is that (a) the calculated value of the classicalseparation factor is in good agreement with the experimentally observed constantvalue of separation factor at high overpotentials, where the tunnelling correctionfactor ratio is unity and (6) the separation factors calculated as a function of over-potential at lower overpotentials are consistent with the corresponding experimentalvalues.1The calculations of the vibrational frequencies of the transition state is a difficultproblem; these have been made for several reactions, using mainly the London-Eyring-Polanyi method.2 Recently, a Sat0 potential was used.3 In the largenumber of potential energy calculations for reactions of the typeA+ BC +AB + C,where A, B and C are atoms or treated as pseudo atoms, using the L.E.P.method,it was found that in the transition state one bond was hardly stretched whereas theother is considerably stretched.2949 5 This was observed in the present calculationsas well. For such a model, it necessarily follows that the stretching frequency ishigh. Further, since the activated complex is unsymmetric with one of the bondsbeing fairly strong and the other relatively weak, its bending frequencies are small.Thus, the assumption of low bending frequencies is consistent with the model.The method, used by Salomon and Conway, to calculate the separation factorsis empirical and therefore its validity depends on the analogous molecules chosen.To obtain the bending frequencies vb, comparison was made with the species FHF-.This ion has a high bending frequency since it is symmetrical (there are two resonantstructures FHF- and F-HF) and the interactions between the F and two H atomsare strong.In our case, the transition state is highly unsymmetric and one bondis strong and the other weak. Thus, a low bending frequency should be expected.The transition state should be compared with a molecule like ICN or a hydrogen-bonded species of the type A . . . H . . . B, which have considerably lower(2)/Rbending frequencies (for ICN, v b = 321 cm-16 and for A-H .. . B,/Rv b = 300-900 cm-9.7 Low bending frequencies of the activated complexes havebeen calculated previously for practically all reactions of the type (2).Similar methods, i.e., using L.E.P. potential energy surfaces, were used for thecalculation of the separation factors for the three mechanisms (slow discharge,gslow recombination,lc and slow electrochemical desorption 11). Due to the ap-proximate nature of the potential functions, the coulombic-exchange energy ratios1 Bockris, Matthews and Gileadi, Electrochim. Acta, in press.2 Glasstone, Laidler and Eyring, The Theory of Rate Processes (McGraw-Hill, N.Y., 1941).3 Sharp and Johnston, S. Chem. Physics, 1962, 37, 154.4 Polanyi, J. Chem. Physics, 1955, 23, 1505.5 Bigeleisen, Klein, Weston and Wolfsberg, J.Chem. Physics, 1959, 30, 1340.6 Herzberg, Infa-red and Raman Spectra of Polyatomic Molecules (Van Nostrand, New York,7 Pimentel and McClellan, The Hydrogen Bond (W. H. Freeman and Co., San Francisco, 1959).1949)GENERAL DISCUSSION 273were varied widely. Further, for the slow recombination mechanism, calculations 10were made for the two possible metal-metal distances, and also for two metals(thus varying the M-H bond energy as well as the M-M distance). The highdegree of constancy within each group of mechanism during the considerablevariations chosen for the uncertain parameters, together with the distinct numericaldifferences between the prediction for each model and the good agreement withthe experimental values on several metals yield sufficient proof for the validity ofthe method of calculations.Thus, determinations of H-T separation factor aremost useful in the investigation of mechanism of electrolytic hydrogen evolution.The fact that the observed relative Zug(rate) ratio for H and D is independentof potential does not necessarily mean that the relative rate ratio will be independentof potential.Conway and Salomon correctly point out that for equivalent barriers (2d)Eckmt #(2d)real. It is for this reason that the results of Caldin and Kasparian presentedat this Discussion are not directly comparable to the results of Bockris, Matthewsand Srinivasan. The latter authors obtained (2d)Eckart = 4.0A. Caldin andKasparin presented calculations which gave parabolic barrier widths from 1 1 3 to1.92 A with a mean value, (2d)par.= 1 . 5 2 A . This value is equivalent to (2d)Eckart =3.80A which is of similar magnitude as the value deduced by Bockris, Srinivasanand Matthews.The authors agree with Conway and Salomon regarding capacity measurementsand their relevance to the double layer structure. These opinions, however, negatethe original contention of Conway and Salomon as presented at the Discussion.The authors did not wish to imply that the activation energy obtained by Conwayand Salomon was impossible. His comments are thus non-controversial. Theimportant point is : Why is the transfer coefficient a dependent on temperature?Furthermore, since this dependence of a on temperature is important, as shown byConway and Salomon in eqn.(4) of their comments, how can conclusions regardingproton tunnelling be made without first taking account of this anomalous dependenceof a on temperature?Dr. H . W. Nfimberg (Kernforschungsanlage Jiilich) (communicated) : The modelconcept adopted by Conway and Salomon in their paper and relevant discussionremarks of treating an electrode at which a hydrogen evolution reaction occurs asa " base " of variable strength according to the electrode material and the appliedelectrode potential seems to form an extremely fruitful approach for useful com-parisons between the principles of homogeneous proton transfers in solutions andthe heterogeneous proton transfer in the course of an electrode process and viceversa.In this connection the following arguments are put forward, adopting the modelproposed by Eigen,l for the homogeneous recombination of the H3O+ ion and theanion of a weak acid.Once a H30+ ion has by diffusion approached the electrodeto a distance of, say, 5.5-8A units it can jump along the favourably organizedhydrogen-bridge system provided by the hydration shell of the H3Of and the waterlayer 2 adsorbed at the electrode surface (" hydration shell ") of the electrodesurface).* This jump along the " ice-like " water structure occurs with a very highrate (see proton mobility in ice 3) having no significant activation energy compared* see, e.g., fig. la in the Discussion remark of Conway and Salomon.1 Eigen, 2. physik.Chem., 1954,1, 154. Eigen, Angew. Chem., 1963, 75, 489.2 Bockris, Devanathan and Muller, Proc. Roy. Soc. A , 1963, 274, 55.3 Eigen and De Maeyer, 2. Efektrochem., 1956, 60, 1037. Eigen, De Maeyer and Spatz, Ber.Bunsen. physik. Chem., 1964, 68, 19274 GENERAL DISCUSSIONwith other steps of the electrode process and brings the proton within the distanceof a hydrogen bond (0*4-0.6& from the electrode surface. This location shouldbe the initial state for the actual charge transfer and therefore a barrier width ofthis magnitude as employed by Salomon and Conway seems conceivable. Thelarge value of the barrier width used by Bockris et aZ.1 is difficult to reconcile on theselines, if it is not to be regarded as a purely formalistic equivalent value for an actual,much smaller, barrier width.Admittedly, one might argue that the proton jumpvia the hydrogen-bridge system of 2-3 water molecules (5-5-8A units) belongs al-ready to the charge transfer reaction as a prior step. However, as the jump is muchfaster than the charge transfer it should not affect at all the real barrier width of theactual charge transfer step?Solvent reorientation, i.e., formation of a favourably orientated H-bridge systemfor the proton jump, will become important only if the charge transfer is muchfaster and no other prior step, as the formation of H3Of-o~ H,O,+-ions respec-tively, if a hydrated H,O+-ion is considered, e.g., by dissociation of a weak acidbecomes rate-determining.Concerning the analogy between the H3O+ discharge at the electrode and thehomogeneous recombination of H30+ and an anion of a weak acid in aqueous solu-tion, in the latter case normally the whole process is controlled by the diffusionrate of both reactants up to the critical distance for the proton jump, unless stericeffects or intramolecular hydrogen bridges in the anion interfere with the formationof a favourably organized hydrogen-bridge system29 4-6 However, in the elec-trode case it depends on the electrode material and the potential-adjustable valueof the charge-transfer rate constant if the charge-transfer step or the mass transferof H3O+ up to the jump distance is rate-determining for the overall process.Though there is a certain analogy between the uptake of a proton by an anionA- in homogeneous recombination and the discharge step of a proton at an electrodethere are significant differences. While in homogeneous recombination the ac-ceptance of a proton by A- leads to the formation of an acid molecule HA theproduct of the charge transfer step at an electrode is an H atom being more or lessstrongly adsorbed at the metal surface.Consecutive steps not concerned with thecharge transfer step convert the adsorbed H atoms further via recombination anddesorption (Tafel reaction) or by electrochemical desorption (Heyrovsky-Horiutireaction) finally into H2 molecules ; if not the H atoms formed in the charge-transferstep can migrate into the electrode material (Pd electrode).Prof. J . O’M. Bockris (University of Pennsylvania) (communicated) : Prof.Conway and Dr.Salomon seem to misunderstand the method of calculation ofBockris, Srinivasan and Matthews, the main purpose of which was to test the de-pendence of the ratio of the partition functions of the isotopic activated complexesas a function of the ratio of coulombic to exchange energies. The significance ofthese calculations is to emphasize the relative independence of the calculated separa-tion factors upon that which is most uncertain in potential energy surface calcula-tions (i.e., ratio of coulombic to exchange energy). The heights of the resultingbarriers do not affect the separation factors as seen from the calculations for the1 Bockris, Srinivasan and Matthews, this Discussion.2 see contributions to general part of this Discussion by Dr.Parsons and by Prof. Symons.3 Eigen, 2. physik. Chem., 1954,1,154.4Eigen, Kruse, Maass and De Maeyer, Progress in Reaction Kinetics, ed. Porter (PergamonPress, London, 1964), vol. 2, p. 287.5 Niirnberg and Durbeck, 2. anal. Chem., 1964,205,217.6 Numberg in Polurography 1964, ed. Hills (Proc. 3rd Int. Congr. PoZarogruphy (Southampton,1964) (Macmillan Ltd., London, 1965).Eigen, Angew. Chem., 1963,75,489GENERAL DISCUSSION 275three possible mechanisms of the hydrogen evolution reaction on the various metals.Thus, though there are shortcomings in an absolute calculation of the reactionrates by Eyring’s method, this method is valuable to calculate the relative rates ofisotopic reactions.An important conclusion arises concerning the applicability of the present separa-tion factor calculations to the determination of mechanism in the hydrogen evolutionreaction.It seems likely that the opinion of Conway and Salomon is based largelyupon the earlier experiences with Conway and the neglect of zero-point energy,;!which makes a great difference in a theoretical analysis. A thorough examinationwas made by Bockris and Srinivasan 1 concerning variation of the classical valueof the separation factor with the variables and the results obtained were encouraging.The point is that the principal reaction mechanisms which one seeks to distinguishin the hydrogen evolution reaction are that in which protons are discharged in arate-determining way, followed by desorption by atomic hydrogen combination andthe method by which the desorption reaction takes place in a rate-controlling fashionby proton collision with the hydrogen atom and an electron; and in this case, thecalculated separation factors are different by several times for the two mechanisms,the latter reaction having the high value.It is difficult to conceive errors whichwould confuse the issue sufficiently for one not to be able to recognize the differ-ence between these two reactions by means of isotope separation factor measure-ments, and that has not been previously possible in the long history of the hydrogenevolution reaction. The usefulness of the method is enhanced by the fact that thenecessary experimental work is easy to carry out, particularly with tritium ratherthan with deuterium.3Implication of a lack of cogency in the interpretation by Bockris, Srinivasanand Matthews of the variation of the separation factor with potential in terms ofproton tunnelling may be compared with Christov’s evaluation.4 A large numberof models, including that suggested by Conway and Saloinon, were examined byDr.Matthews,s but it was only the proton tunnelling explanation which was con-sistent-and quantitatively-with the fact, presumably unavailable to Conwayand Salomon, of the potential variation of the separation factor on mercury. Inter-pretation agrees with the earlier calculations of Christov; with the barrier width ofCaldin and Kasparian,6 and of the only model of the double layer which appearsto be able to explain the constancy of the capacity of the negative branch overpotential ranges of about 1 V for mercury.7Prof.G. J. Hills (Southampton University) said: The papers of Salomon andConway, and of Bockris, Srinivasan and Matthews, may well be regarded as furtherevidence that the direct-discharge of hydrated protons is the rate-determining stepof the hydrogen evolution reaction at a mercury electrode in dilute acid solution.However, we wish to report some preliminary studies of the pressure coefficientsof this reaction, the results of which support, if anything, the alternative ion+atomstep. Briefly, at 25°C the Tafel slope is found to be independent of pressure up to2000 atm whereas the exchange current density increases markedly with pressure1 Bockris and Srinivasan, J.EZectrochern. SOC., 1964, 111, 844, 853, 858.2 Conway, Proc. Roy. SUC. A , 1958,247,400.3 Bockris, Srinivasan and Devanathan, J. Electroanal. Chem., 1963, 6, 205.4 Christov, Electrochim. Acta, 1961, 4, 194, 306.5 Matthews, Ph.D. Thesis (University of Pennsylvania, 1965).6 Caldin and Kasparian, this Discussion.7 Bockris, Devanathan and Muller, Proc. Roy. Soc. A, 1963, 274, 55.8 Kinnibrugh, Thesis (Southampton), 1965276 GENERAL DISCUSSIONat constant overpotential. It follows that the volume of activation, defined asAV’ = -(RTB In iolap>,,,is negative and, for 0.1 m HCl, is -3.4 ml per faraday.Although a negative volume might result from the reorganization of structuredwater molecules, when water is expelled from the region of the double layer, thereis a resultant increase in volume.1 Moreover, the hydrogen atom is large and itis therefore not easy to reconcile a negative volume of activation with the stepOn the other hand, the ion + atom step,especially if it proceeded through the small, intermediate ion H: could involve alarge and negative volume of activation.In order that such a reaction should accordwith the other diagnostic criteria, viz., a Tafel slope of 2RT’F and the correct pHdependence, it is necessary to postulate not only that the interphase is saturatedwith hydrogen atoms but also that the electrode coverage is unity. In view of thelow heat of adsorption of hydrogen on mercury, this is unlikely and such a con-sideration could be the stumbling block to the acceptance of mechanism (B) as therate-determining step, although Horiuti 2 has argued otherwise and coverage is arelative term.Charge transfer to water molecules,H2O + e +H(ads) + OH-,or the formation of hydrated electronsnH2O + e +e (hydrated),could also be more readily reconciled with negative volumes of activation but lesseasily with the observed pH dependence.Prof. B. E. Conway (Ottawa) and Dr. M. Salomon (Princeton) (communicated) :In final reply to Prof. Bockris and Dr. Matthews, we regard ICN as an inappropriatemodel molecule, since a heavier mass than that of H is involved in the bendingmotions; hence a lower frequency must be expected. Also, we cannot agree thatfor activated complexes associated with practically all cases of reactions of the typeRA- - -H- - -B, low bending frequencies have been calculated.The opposite has beenreported in the published work,3,4 both experimentally and theoretically.A reasonable explanation of the dependence of p on temperature was given byBockris and Parsons 5 in classical terms which we accepted 6 for the kinetics at Hgsince other criteria did not indicate extensive tunnelling. In other cases, e.g., atNi, an explanation based on increasing tunnelling with decreasing temperaturemay be a contributing factor. However, it does not seem that this can be the generalexplanation, since the anomalous dependence of b on T continues to temperatureswell above room temperature. Other contributing factors may be the increasingorientation of solvent dipoles in the double-layer with decreasing temperaturewhich could lead to a temperature dependence of the local profile of electric field(down which the proton must pass in the discharge step) and hence of the fractionp of the p.d. required to reach the transition state.H+(H20)% + e -tH(ads) + relaxed water molecules. (A)H+H++e-+H2, (B)+1 Hills and Payne, Trans. Faraday SOC., 1965, 61, 316, 326.2 Horiuti, Trans. Symp. EZectrode Processes (Philadelphia, 1959, J. Wiley, IDC., N.Y.), p. 17.3 Swain, Wiles and Bader, J. Arner. Chern. Soc., 1961, 83, 1945.4 Bader, Can. J. Chern., 1964,42,1822.5 Bockris and Parsons, Trans. Faraday SOC., 1949,45,916.6 Conway and Salomon, J. Chern. Physics, 1964,41, 3169 and this DiscussionGENERAL DISCUSSION 277With regard to the question of the double-layer model and proton transferdistances, there is a real remaining difficulty. The double-layer model may beapproximately consistent with the tunnelling distance proposed, but physicallythis would not seem to correspond to a feasible single proton transfer event (seefig. la-c). This inconsistency can be avoided by the distinction we proposed be-tween what is significant thermodynamically with regard to double-layer propertiesand what are the local kinetic steps of proton transfer immediately prior toneutralization.In reply to Prof. Hills, it seems that the volume change accompanying expulsionof water from the double-layer, which would give a positive AV’, may not be relevantsince this would be a process presumably occurring after the transition state hadbeen reached. It is the motion of the proton into the transition state that I envisagedas being associated with a possibly negative value of AV. What is the pressureeffect in alkaline solution where a charged species is formed in the proton transfer,rather than one being removed?Dr. Roger Parsons (University of Bristol) said: It seems to me that in this dis-cussion too little attention has been paid to the frequency factor of the reactionsconsidered. While it is true that many errors in the model will tend to cancel whenthe ratio of rates of reaction of two isotopes is calculated, it seems reasonable torequire that the model should also lead to a plausible frequency factor for eachreaction.I should like to suggest that it is not always correct to assume an immobiletransition state in the discharge mechanism for hydrogen evolution. Temkin showedsome years ago 1 that a reasonable frequency factor for this reaction was obtainedusing a model not unlike the Marcus-Hush model for redox reactions in which thetransition state is assumed to translate freely in two dimensions. Temkin’s cal-culation was later extended to metals on which the adsorbed hydrogen coverageis appreciable.2 It is also worth noticing that the effect of freezing a mercury electrodeon the rate of hydrogen evaluation can be interpreted in terms of a decrease of themobility of the activated complex in the discharge reaction.31 Temkin, Trudy Soveshchuniyu PO Elektrokhimii (Moscow, 1953), p. 181.2 Parsons, Trans. Furuday SOC., 1960, 56, 1340.3 Bockris, Parsons and Rosenberg, Trans. Faraday SOC., 1951,47, 766

ISSN:0366-9033    

DOI:10.1039/DF9653900253

出版商:RSC    

年代:1965

数据来源: RSC

摘要:

Albery, W. J., 159, 162, 163.Ahrens, M.-L., 112.Ausloos, P., 36,65.Baughan, E. C., 219.Beens, H., 183.Bell, R. P., 16,48, 49, 57, 94, 97, 131.Bewick, A., 149, 163.Bockris, J. 0. M., 60, 239, 258, 261, 264, 265,Brouwer, D. M., 121.Caldin, E. F., 25,62.Case, B., 101.Challis, B. C., 67.Christov, S. G., 60, 254, 263, 266.Cocivera, M., 105.271, 274.Conway,-B. E., 47, 60, 130, 134, 182, 216, 219,223,253, 255,259,262,266,276.Covington, A. K., 172,176, 180.Eigen, M., 7,46, 102, 130, 131, 163, 217.Eisenberg, H., 218.Fleiscbmam, M., 52,149,162.Franck, E. U., 200.Gandini, A., 103.Gillespie, R. J., 135, 181, 222.Godfrey, T. S., 194.Gold, V., 84, 94, 97, 100, 103, 253.Grellmann, K. H., 183.Grunwald, E., 105.Gurr, M., 183.Hakka, L.E., 75.Hartmann, D., 200.Henchman, M. J., 63.Hensel, F., 200.Hiddleston, J. N., 149.Hills, G. J., 59, 207, 220, 275.Hulett, J. R., 58, 60.Johnson, K. E., 217.Jones, J. R., 58.Kasparian, M., 25.Kessick, M. A., 84.Kohnstam, G., 217.Kreevoy, M. M., 57, 100, 131, 166, 180.Kresge, A. J., 46, 48, 75, 96, 97, 98, 99.Laidler, K. J., 253.Lias, S. G., 36.Lilley, T. H., 180, 181.Long, F. A., 45, 67, 94, 99, 132.Mackor, E. L., 121.MacLean, C., 121.Mandel, M., 220.Matthews, D. B., 50,239, 258, 260, 264, 271.Mead, C. A., 166.Mylonakis, S., 75.Noyes, R. M., 130, 216.Nhberg, H. W., 52,136,160,162, 273.Ovenden, P. J., 207,220.Parsons, R., 55, 101, 277.Plesch, P. H., 103.Porter, G., 194.Rogers, N. A. J., 50.Ross, R. A,, 65.Salomon, M., 223, 255, 256, 262, 266, 276.Sato, Y., 75.Spiro, M., 98.Srinivasan, S., 239, 258, 264, 271.Strehlow, H., 112,133.suppan, P., 194.Symons, M. C. R., 55, 216.Tait, M. J., 172.Weiss, J. J., 45, 57.Weller, A. H., 183.Wells, C. F., 132, 133, 134.Weston, R. E., Jr., 178.Whitehouse, D. R., 207,220.Wyatt, P. A. H., 221.Wynne-Jones, Lord, 149,172.Zollinger, H. 102.AUTHOR INDEX** The references in heavy type indicate papers submitted for discussion.27

ISSN:0366-9033    

DOI:10.1039/DF9653900278

出版商:RSC    

年代:1965

数据来源: RSC